1
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Waigh TA, Korabel N. Heterogeneous anomalous transport in cellular and molecular biology. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2023; 86:126601. [PMID: 37863075 DOI: 10.1088/1361-6633/ad058f] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2022] [Accepted: 10/20/2023] [Indexed: 10/22/2023]
Abstract
It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.
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Affiliation(s)
- Thomas Andrew Waigh
- Biological Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Nickolay Korabel
- Department of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
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2
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Höll M, Nissan A, Berkowitz B, Barkai E. Controls that expedite first-passage times in disordered systems. Phys Rev E 2023; 108:034124. [PMID: 37849182 DOI: 10.1103/physreve.108.034124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 08/28/2023] [Indexed: 10/19/2023]
Abstract
First-passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We study the statistical properties of the first-passage time of biased processes in different models, and we employ the big-jump principle that shows the dominance of the maximum trapping time on the first-passage time. We demonstrate that the removal of this maximum significantly expedites transport. As the disorder increases, the system enters a phase where the removal shows a dramatic effect. Our results show how we may speed up transport in strongly disordered systems exploiting scale invariance. In contrast to the disordered systems studied here, the removal principle has essentially no effect in homogeneous systems; this indicates that improving the conductance of a poorly conducting system is, theoretically, relatively easy as compared to a homogeneous system.
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Affiliation(s)
- Marc Höll
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel
| | - Alon Nissan
- Institute of Environmental Engineering, ETH Zurich, Zurich, Switzerland
| | - Brian Berkowitz
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 7610001, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat Gan 52900, Israel
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3
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Nishizawa K, Honda N, Inokuchi S, Ebata H, Ariga T, Mizuno D. Measuring fluctuating dynamics of sparsely crosslinked actin gels with dual-feedback nonlinear microrheology. Phys Rev E 2023; 108:034601. [PMID: 37849150 DOI: 10.1103/physreve.108.034601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2022] [Accepted: 08/06/2023] [Indexed: 10/19/2023]
Abstract
We investigate the fluctuating dynamics of colloidal particles in weakly crosslinked F-actin networks with optical-trap-based microrheology. Using the dual-feedback technology, embedded colloidal particles were stably forced beyond the linear regime in a manner that does not suppress spontaneous fluctuations of particles. Upon forcing, a particle that was stably confined in a cage made of the network's crosslinks started to intermittently jump to the next caging microenvironments. By investigating the statistics of the jump dynamics, we discuss how heterogeneous relaxations observed in equilibrium systems became homogeneous when similar jumps were activated under constant forcing beyond the linear regime.
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Affiliation(s)
- Kenji Nishizawa
- Department of Physics, The University of Tokyo, Tokyo 113-8654, Japan
| | - Natsuki Honda
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
| | - Shono Inokuchi
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
| | - Hiroyuki Ebata
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
| | - Takayuki Ariga
- Graduate School of Frontier Biosciences, Osaka University, Suita 565-0871, Japan
| | - Daisuke Mizuno
- Department of Physics, Kyushu University, Fukuoka 819-0395, Japan
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4
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Ozawa M, Biroli G. Elasticity, Facilitation, and Dynamic Heterogeneity in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2023; 130:138201. [PMID: 37067329 DOI: 10.1103/physrevlett.130.138201] [Citation(s) in RCA: 6] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 03/02/2023] [Indexed: 06/19/2023]
Abstract
We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by a coarse-grained two-dimensional model in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically mediated interactions. By simulations and an analytical theory, we show that the model reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition. We also discuss how it can be generalized and combined with current theories.
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Affiliation(s)
- Misaki Ozawa
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Giulio Biroli
- Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
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5
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Sarkar S, Goswami D. Lifetime of actin-dependent protein nanoclusters. Biophys J 2023; 122:290-300. [PMID: 36518075 PMCID: PMC9892618 DOI: 10.1016/j.bpj.2022.12.015] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2022] [Revised: 09/23/2022] [Accepted: 12/09/2022] [Indexed: 12/23/2022] Open
Abstract
Protein nanoclusters (PNCs) are dynamic collections of a few proteins that spatially organize in nanometer-length clusters. PNCs are one of the principal forms of spatial organization of membrane proteins, and they have been shown or hypothesized to be important in various cellular processes, including cell signaling. PNCs show remarkable diversity in size, shape, and lifetime. In particular, the lifetime of PNCs can vary over a wide range of timescales. The diversity in size and shape can be explained by the interaction of the clustering proteins with the actin cytoskeleton or the lipid membrane, but very little is known about the processes that determine the lifetime of the nanoclusters. In this paper, using mathematical modeling of the cluster dynamics, we model the biophysical processes that determine the lifetime of actin-dependent PNCs. In particular, we investigated the role of actin aster fragmentation, which had been suggested to be a key determinant of the PNC lifetime, and we found that it is important only for a small class of PNCs. A simple extension of our model allowed us to investigate the kinetics of protein-ligand interaction near PNCs. We found an anomalous increase in the lifetime of ligands near PNCs, which agrees remarkably well with experimental data on RAS-RAF kinetics. In particular, analysis of the RAS-RAF data through our model provides falsifiable predictions and novel hypotheses that will not only shed light on the role of RAS-RAF kinetics in various cancers, but also will be useful in studying membrane protein clustering in general.
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Affiliation(s)
- Sumantra Sarkar
- The Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico; Theoretical Biophysics (T-6) Group, Los Alamos National Laboratory, Los Alamos, New Mexico; Department of Physics, Indian Institute of Science, Bengaluru, Karnataka 560012, India.
| | - Debanjan Goswami
- NCI RAS Initiative, The Cancer Research Technology Program, Frederick National Laboratory, Frederick, Maryland.
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6
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Chen Y, Wang X. Different effects of external force fields on aging Lévy walk. CHAOS (WOODBURY, N.Y.) 2023; 33:013102. [PMID: 36725624 DOI: 10.1063/5.0124654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/07/2022] [Accepted: 12/06/2022] [Indexed: 06/18/2023]
Abstract
Aging phenomena have been observed in numerous physical systems. Many statistical quantities depend on the aging time ta for aging anomalous diffusion processes. This paper pays more attention to how an external force field affects the aging Lévy walk. Based on the Langevin picture of the Lévy walk and the generalized Green-Kubo formula, we investigate the quantities that include the ensemble- and time-averaged mean-squared displacements in both weak aging ta≪t and strong aging ta≫t cases and compare them to the ones in the absence of any force field. Two typical force fields, constant force F and time-dependent periodic force F(t)=f0sin(ωt), are considered for comparison. The generalized Einstein relation is also discussed in the case with the constant force. We find that the constant force is the key to causing the aging phenomena and enhancing the diffusion behavior of the aging Lévy walk, while the time-dependent periodic force is not. The different effects of the two kinds of forces on the aging Lévy walk are verified by both theoretical analyses and numerical simulations.
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Affiliation(s)
- Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
| | - Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
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7
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Doerries TJ, Chechkin AV, Schumer R, Metzler R. Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions. Phys Rev E 2022; 105:014105. [PMID: 35193292 DOI: 10.1103/physreve.105.014105] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/01/2021] [Accepted: 12/17/2021] [Indexed: 06/14/2023]
Abstract
We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random-walk models for multirate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover, we find the associated breakthrough curves, the tracer density at a fixed point in space as a function of time, and the mobile and immobile concentration profiles and the respective moments of the transport. Specifically, we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities, transient anomalous transport is observed. Our results have direct applications in geophysical contexts, but also in biological, soft matter, and solid state systems.
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Affiliation(s)
- Timo J Doerries
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Aleksei V Chechkin
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
- Faculty of Pure and Applied Mathematica, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyspianskiego 27, 50-370 Wrocław, Poland
- Akhiezer Institute for Theoretical Physics, 61108 Kharkov, Ukraine
| | - Rina Schumer
- Desert Research Institute, Reno, Nevada 89512, USA
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
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8
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Scalliet C, Guiselin B, Berthier L. Excess wings and asymmetric relaxation spectra in a facilitated trap model. J Chem Phys 2021; 155:064505. [PMID: 34391365 DOI: 10.1063/5.0060408] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Abstract
In a recent computer study, we have shown that the combination of spatially heterogeneous dynamics and kinetic facilitation provides a microscopic explanation for the emergence of excess wings in deeply supercooled liquids. Motivated by these findings, we construct a minimal empirical model to describe this physics and introduce dynamic facilitation in the trap model, which was initially developed to capture the thermally activated dynamics of glassy systems. We fully characterize the relaxation dynamics of this facilitated trap model varying the functional form of energy distributions and the strength of dynamic facilitation, combining numerical results and analytic arguments. Dynamic facilitation generically accelerates the relaxation of the deepest traps, thus making relaxation spectra strongly asymmetric, with an apparent "excess" signal at high frequencies. For well-chosen values of the parameters, the obtained spectra mimic experimental results for organic liquids displaying an excess wing. Overall, our results identify the minimal physical ingredients needed to describe excess processes in the relaxation spectra of supercooled liquids.
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Affiliation(s)
- Camille Scalliet
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
| | - Benjamin Guiselin
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
| | - Ludovic Berthier
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, CNRS, 34095 Montpellier, France
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9
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Vogiatzis GG, van Breemen LCA, Hütter M. Structural Transitions in Glassy Atactic Polystyrene Using Transition-State Theory. J Phys Chem B 2021; 125:7273-7289. [PMID: 34161106 PMCID: PMC8279558 DOI: 10.1021/acs.jpcb.1c02618] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/04/2022]
Abstract
![]()
Transition pathways
on the energy landscape of atactic polystyrene
(aPS) glassy specimens are probed below its glass-transition temperature.
Each of these transitions is considered an elementary structural relaxation
event, whose corresponding rate constant is calculated by applying
multidimensional transition-state theory. Initially, a wide spectrum
of first-order saddle points surrounding local minima on the energy
landscape is discovered by a stabilized hybrid eigenmode-following
method. Then, (minimal-energy) “reaction paths” to the
adjacent minima are constructed by a quadratic descent method. The
heights of the free energy, the potential energy, and the entropy
barriers are estimated for every connected triplet of transition state
and minima. The resulting distribution of free energy barriers is
asymmetric and extremely broad, extending to very high barrier heights
(over 50 kBT); the corresponding
distribution of rate constants extends over 30 orders of magnitude,
with well-defined peaks at the time scales corresponding to the subglass
relaxations of polystyrene. Analysis of the curvature along the reaction
paths reveals a multitude of different rearrangement mechanisms; some
of them bearing multiple distinct phases. Finally, connections to
theoretical models of the glass phenomenology allows for the prediction,
based on first-principles, of the “ideal” glass-transition
temperature entering the Vogel–Fulcher–Tammann (VFT)
equation describing the super-Arrhenius temperature dependence of
glassy dynamics. Our predictions of the time scales of the subglass
relaxations and the VFT temperature are in favorable agreement with
available experimental literature data for systems of similar molecular
weight under the same conditions.
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Affiliation(s)
- Georgios G Vogiatzis
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.,Dutch Polymer Institute, PO Box 902, 5600 AX Eindhoven, The Netherlands
| | - Lambèrt C A van Breemen
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
| | - Markus Hütter
- Polymer Technology, Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands
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10
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Baity-Jesi M, Biroli G, Reichman DR. Revisiting the concept of activation in supercooled liquids. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:77. [PMID: 34125327 PMCID: PMC8203548 DOI: 10.1140/epje/s10189-021-00077-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 05/07/2021] [Indexed: 06/12/2023]
Abstract
In this work, we revisit the description of dynamics based on the concepts of metabasins and activation in mildly supercooled liquids via the analysis of the dynamics of a paradigmatic glass former between its onset temperature [Formula: see text] and mode-coupling temperature [Formula: see text]. First, we provide measures that demonstrate that the onset of glassiness is indeed connected to the landscape, and that metabasin waiting time distributions are so broad that the system can remain stuck in a metabasin for times that exceed [Formula: see text] by orders of magnitude. We then reanalyze the transitions between metabasins, providing several indications that the standard picture of activated dynamics in terms of traps does not hold in this regime. Instead, we propose that here activation is principally driven by entropic instead of energetic barriers. In particular, we illustrate that activation is not controlled by the hopping of high energetic barriers and should more properly be interpreted as the entropic selection of nearly barrierless but rare pathways connecting metabasins on the landscape.
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Affiliation(s)
| | - Giulio Biroli
- Departement de Physique Statistique, École Normale Supérieure, 75005, Paris, France
| | - David R Reichman
- Department of Chemistry, Columbia University, New York, NY, 10027, USA
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11
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Individual variations lead to universal and cross-species patterns of social behavior. Proc Natl Acad Sci U S A 2020; 117:31754-31759. [PMID: 33257554 DOI: 10.1073/pnas.2002013117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The duration of interaction events in a society is a fundamental measure of its collective nature and potentially reflects variability in individual behavior. Here we performed a high-throughput measurement of trophallaxis and face-to-face event durations experienced by a colony of honeybees over their entire lifetimes. The interaction time distribution is heavy-tailed, as previously reported for human face-to-face interactions. We developed a theory of pair interactions that takes into account individual variability and predicts the scaling behavior for both bee and extant human datasets. The individual variability of worker honeybees was nonzero but less than that of humans, possibly reflecting their greater genetic relatedness. Our work shows how individual differences can lead to universal patterns of behavior that transcend species and specific mechanisms for social interactions.
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12
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Jawerth L, Fischer-Friedrich E, Saha S, Wang J, Franzmann T, Zhang X, Sachweh J, Ruer M, Ijavi M, Saha S, Mahamid J, Hyman AA, Jülicher F. Protein condensates as aging Maxwell fluids. Science 2020; 370:1317-1323. [DOI: 10.1126/science.aaw4951] [Citation(s) in RCA: 115] [Impact Index Per Article: 28.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/05/2019] [Revised: 06/18/2019] [Accepted: 10/16/2020] [Indexed: 12/17/2022]
Affiliation(s)
- Louise Jawerth
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
| | - Elisabeth Fischer-Friedrich
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany
- Biotec, TU Dresden, Tatzberg 47-49, 01307 Dresden, Germany
| | - Suropriya Saha
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
| | - Jie Wang
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
| | - Titus Franzmann
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
- Biotec, TU Dresden, Tatzberg 47-49, 01307 Dresden, Germany
| | - Xiaojie Zhang
- EMBL Heidelberg, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - Jenny Sachweh
- EMBL Heidelberg, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - Martine Ruer
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
| | - Mahdiye Ijavi
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
| | - Shambaditya Saha
- Institute of Molecular Biotechnology of the Austrian Academy of Sciences (IMBA), Vienna BioCenter (VBC), Dr. Bohrgasse 3, 1030 Vienna, Austria
| | - Julia Mahamid
- EMBL Heidelberg, Meyerhofstraße 1, 69117 Heidelberg, Germany
| | - Anthony A. Hyman
- Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstraße 108, 01307 Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstr. 108, 01307 Dresden, Germany
| | - Frank Jülicher
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, 01187 Dresden, Germany
- Cluster of Excellence Physics of Life, Technische Universität Dresden, Dresden, Germany
- Center for Systems Biology Dresden, Pfotenhauerstr. 108, 01307 Dresden, Germany
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13
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Xia C, He X, Wang J, Wang W. Origin of subdiffusions in proteins: Insight from peptide systems. Phys Rev E 2020; 102:062424. [PMID: 33466075 DOI: 10.1103/physreve.102.062424] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Accepted: 11/30/2020] [Indexed: 11/07/2022]
Abstract
Subdiffusive kinetics are popular in proteins and peptides as observed in experiments and simulations. For protein systems with diverse interactions, are there multiple mechanisms to produce the common subdiffusion behavior? To approach this problem, long trajectories of two model peptides are simulated to study the mechanism of subdiffusion and the relations with their interactions. The free-energy profiles and the subdiffusive kinetics are observed for these two peptides. A hierarchical plateau analysis is employed to extract the features of the landscape from the mean square of displacement. The mechanism of subdiffusions can be postulated by comparing the exponents by simulations with those based on various models. The results indicate that the mechanisms of these two peptides are different and are related to the characteristics of their energy landscapes. The subdiffusion of the flexible peptide is mainly caused by depth distribution of traps on the energy landscape, while the subdiffusion of the helical peptide is attributed to the fractal topology of local minima on the landscape. The emergence of these different mechanisms reflects different kinetic scenarios in peptide systems though the peptides behave in a similar way of diffusion. To confirm these ideas, the transition networks between various conformations of these peptides are generated. Based on the network description, the controlled kinetics based only on the topology of the networks are calculated and compared with the results based on simulations. For the flexible peptide, the feature of controlled diffusion is distinct from that of simulation, and for the helical peptide, two kinds of kinetics have a similar exponent of subdiffusion. These results further exemplify the importance of the landscape topology in the kinetics of structural proteins and the effect of depth distribution of traps for the subdiffusion of disordered peptides.
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Affiliation(s)
- Chenliang Xia
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China and National Laboratory of Solid State Microstructure, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Xuefeng He
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China and National Laboratory of Solid State Microstructure, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Jun Wang
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China and National Laboratory of Solid State Microstructure, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
| | - Wei Wang
- School of Physics, Nanjing University, Nanjing 210093, People's Republic of China and National Laboratory of Solid State Microstructure, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, People's Republic of China
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14
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Stariolo DA, Cugliandolo LF. Barriers, trapping times, and overlaps between local minima in the dynamics of the disordered Ising p-spin model. Phys Rev E 2020; 102:022126. [PMID: 32942488 DOI: 10.1103/physreve.102.022126] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/20/2020] [Accepted: 07/28/2020] [Indexed: 11/07/2022]
Abstract
We study the low-temperature out-of-equilibrium Monte Carlo dynamics of the disordered Ising p-spin Model with p=3 and a small number of spin variables. We focus on sequences of configurations that are stable against single spin flips obtained by instantaneous gradient descent from persistent ones. We analyze the statistics of energy gaps, energy barriers, and trapping times on subsequences such that the overlap between consecutive configurations does not overcome a threshold. We compare our results to the predictions of various trap models finding the best agreement with the step model when the p-spin configurations are constrained to be uncorrelated.
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Affiliation(s)
- Daniel A Stariolo
- Universidade Federal Fluminense, Departamento de Física and National Institute of Science and Technology for Complex Systems, Av. Gal. Milton Tavares de Souza s/n, Campus da Praia Vermelha, 24210-346 Niterói, RJ, Brazil
| | - Leticia F Cugliandolo
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, UMR 7589 CNRS, Tour 13, 5ème Etage, 4 Place Jussieu, 75252 Paris 05, France.,Institut Universitaire de France, 1 rue Descartes, 75231 Paris Cedex 05, France
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15
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Gray TH, Yong EH. Effective diffusion in one-dimensional rough potential-energy landscapes. Phys Rev E 2020; 102:022138. [PMID: 32942433 DOI: 10.1103/physreve.102.022138] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Accepted: 08/11/2020] [Indexed: 06/11/2023]
Abstract
Diffusion in spatially rough, confining, one-dimensional continuous energy landscapes is treated using Zwanzig's proposal, which is based on the Smoluchowski equation. We show that Zwanzig's conjecture agrees with Brownian dynamics simulations only in the regime of small roughness. Our correction of Zwanzig's framework corroborates well with numerical results. A numerical simulation scheme based on our coarse-grained Langevin dynamics offers significant reductions in computational time. The mean first-passage time problem in the case of random roughness is treated. Finally, we address the validity of the separation of length scales assumption for the case of polynomial backgrounds and cosine-based roughness. Our results are applicable to hierarchical energy landscapes such as that of a protein's folding and transport processes in disordered media, where there is clear separation of length scale between smooth underlying potential and its rough perturbation.
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Affiliation(s)
- Thomas H Gray
- Department of Chemical Engineering and Biotechnology, West Cambridge Site, Philippa Fawcett Drive, University of Cambridge, CB3 0AS, Cambridge, United Kingdom
- T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge, CB3 0HE, United Kingdom
| | - Ee Hou Yong
- Division of Physics and Applied Physics, School of Physical and Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, Singapore 637371
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16
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Xie SJ, Schweizer KS. Microscopic Theory of Dynamically Heterogeneous Activated Relaxation as the Origin of Decoupling of Segmental and Chain Relaxation in Supercooled Polymer Melts. Macromolecules 2020. [DOI: 10.1021/acs.macromol.0c00849] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Shi-Jie Xie
- Departments of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
- Center for Membrane Separation and Water Science & Technology, Ocean College, Zhejiang University of Technology, Hangzhou 310014, PR China
| | - Kenneth S. Schweizer
- Departments of Materials Science, University of Illinois, Urbana, Illinois 61801, United States
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, United States
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, United States
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17
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Gray TH, Yong EH. Overdamped Brownian dynamics in piecewise-defined energy landscapes. Phys Rev E 2020; 101:052123. [PMID: 32575297 DOI: 10.1103/physreve.101.052123] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2018] [Accepted: 04/17/2020] [Indexed: 11/07/2022]
Abstract
We study the overdamped Brownian dynamics of particles moving in piecewise-defined potential energy landscapes U(x), where the height Q of each section is obtained from the exponential distribution p(Q)=aβexp(-aβQ), where β is the reciprocal thermal energy, and a>0. The averaged effective diffusion coefficient 〈D_{eff}〉 is introduced to characterize the diffusive motion: 〈x^{2}〉=2〈D_{eff}〉t. A general expression for 〈D_{eff}〉 in terms of U(x) and p(Q) is derived and then applied to three types of energy landscape: flat sections, smooth maxima, and sharp maxima. All three cases display a transition between subdiffusive and diffusive behavior at a=1, and a reduction to free diffusion as a→∞. The behavior of 〈D_{eff}〉 around the transition is investigated and found to depend heavily upon the shape of the maxima: Energy landscapes made up of flat sections or smooth maxima display power-law behavior, while for landscapes with sharp maxima, strongly divergent behavior is observed. Two aspects of the subdiffusive regime are studied: the growth of the mean squared displacement with time and the distribution of mean first-passage times. For the former, agreement between Brownian dynamics simulations and a coarse-grained equivalent was observed, but the results deviated from the random barrier model's predictions. The discrepancy could be a finite-time effect. For the latter, agreement between the characteristic exponent calculated numerically and that predicted by the random barrier model is observed in the large-amplitude limit.
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Affiliation(s)
- Thomas H Gray
- Statistical Physics Group, Department of Chemical Engineering and Biotechnology, West Cambridge Site, Philippa Fawcett Drive, University of Cambridge, CB3 0AS, Cambridge, United Kingdom.,T.C.M. Group, Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - Ee Hou Yong
- School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
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18
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Zaccone A, Terentjev EM. Rheology of hard glassy materials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2020; 32:395402. [PMID: 32579542 DOI: 10.1088/1361-648x/ab9914] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/22/2020] [Accepted: 06/03/2020] [Indexed: 06/11/2023]
Abstract
Glassy solids may undergo a fluidization (yielding) transition upon deformation whereby the material starts to flow plastically. It has been a matter of debate whether this process is controlled by a specific time scale, from among different competing relaxation/kinetic processes. Here, two constitutive models of cage relaxation are examined within the microscopic model of nonaffine elasto-plasticity. One (widely used) constitutive model implies that the overall relaxation rate is dominated by the fastest between the structural (α) relaxation rate and the shear-induced relaxation rate. A different model is formulated here which, instead, assumes that the slowest (global) relaxation process controls the overall relaxation. We show that the first model is not compatible with the existence of finite elastic shear modulus for quasistatic (low-frequency) deformation, while the second model is able to describe all key features of deformation of 'hard' glassy solids, including the yielding transition, the nonaffine-to-affine plateau crossover, and the rate-stiffening of the modulus. The proposed framework provides an operational way to distinguish between 'soft' glasses and 'hard' glasses based on the shear-rate dependence of the structural relaxation time.
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Affiliation(s)
- A Zaccone
- Department of Physics 'A Pontremoli', University of Milan, via Celoria 16, 20133 Milano, Italy
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
| | - E M Terentjev
- Cavendish Laboratory, University of Cambridge, JJ Thomson Avenue, CB30HE Cambridge, United Kingdom
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19
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Chetrit E, Meroz Y, Klausner Z, Berkovich R. Correlations within polyprotein forced unfolding dwell-times introduce sequential dependency. J Struct Biol 2020; 210:107495. [PMID: 32173465 DOI: 10.1016/j.jsb.2020.107495] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2019] [Revised: 02/15/2020] [Accepted: 03/11/2020] [Indexed: 02/06/2023]
Abstract
Polyproteins, comprised from proteins arrayed in tandem, respond to mechanical loads through partial unfolding and extension. This response to tension that enables their physiological function is related to the ability to dynamically regulate their elasticity. The unique arrangement of their individual mechanical components (proteins and polymeric linkers), and the interactions between them eventually determines their performance. The sequential unfolding-times within a polyprotein are inherently assumed to be independent and identically distributed (iid), thus expected to follow an exponential distribution. Nevertheless, a large body of literature using single molecule force spectroscopy (SMFS) provides evidence that forced unfolding-times of N proteins within a polyprotein do not follow the exponential distribution. Here we use SMFS with Atomic Force Microscopy to measure the unfolding kinetics of Poly-(I91)8 at 180 pN. The unfolding time-intervals were statistically analysed using three common approaches, all exhibiting an N-effect: hierarchical behavior with non-identical unfolding time distributions. Using continuous time random walk approach indicates that the unfolding times display subdiffusive features. Put together with free-energy reconstruction of the whole unfolding polyprotein, we provide physical explanation for this nontrivial behavior, according to which the elongating polypeptide chain with each unfolding event intervenes with the sequential unfolding probabilities and correlates them.
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Affiliation(s)
- Einat Chetrit
- Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel
| | - Yasmine Meroz
- School of Plant Science and Food Security, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Ziv Klausner
- Department of Applied Mathematics, Israel Institute for Biological Research, P.O. Box 19, Ness-Ziona 7410001, Israel
| | - Ronen Berkovich
- Department of Chemical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel; The Ilze Katz Institute for Nanoscience and Technology, Ben-Gurion University of the Negev, Beer-Sheva 8410501, Israel.
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20
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Moran J, Fosset A, Luzzati D, Bouchaud JP, Benzaquen M. By force of habit: Self-trapping in a dynamical utility landscape. CHAOS (WOODBURY, N.Y.) 2020; 30:053123. [PMID: 32491895 DOI: 10.1063/5.0009518] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2020] [Accepted: 04/25/2020] [Indexed: 06/11/2023]
Abstract
Historically, rational choice theory has focused on the utility maximization principle to describe how individuals make choices. In reality, there is a computational cost related to exploring the universe of available choices and it is often not clear whether we are truly maximizing an underlying utility function. In particular, memory effects and habit formation may dominate over utility maximization. We propose a stylized model with a history-dependent utility function, where the utility associated to each choice is increased when that choice has been made in the past, with a certain decaying memory kernel. We show that self-reinforcing effects can cause the agent to get stuck with a choice by sheer force of habit. We discuss the special nature of the transition between free exploration of the space of choice and self-trapping. We find, in particular, that the trapping time distribution is precisely a Zipf law at the transition, and that the self-trapped phase exhibits super-aging behavior.
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Affiliation(s)
- José Moran
- Centre d'Analyse et de Mathématique Sociales, EHESS, 54 Boulevard Raspail, 75006 Paris, France
| | - Antoine Fosset
- Chair of Econophysics and Complex Systems, Ecole polytechnique, 91128 Palaiseau Cedex, France
| | - Davide Luzzati
- Chair of Econophysics and Complex Systems, Ecole polytechnique, 91128 Palaiseau Cedex, France
| | - Jean-Philippe Bouchaud
- Chair of Econophysics and Complex Systems, Ecole polytechnique, 91128 Palaiseau Cedex, France
| | - Michael Benzaquen
- Chair of Econophysics and Complex Systems, Ecole polytechnique, 91128 Palaiseau Cedex, France
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21
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Xie SJ, Schweizer KS. A collective elastic fluctuation mechanism for decoupling and stretched relaxation in glassy colloidal and molecular liquids. J Chem Phys 2020; 152:034502. [DOI: 10.1063/1.5129550] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shi-Jie Xie
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Center for Membrane Separation and Water Science and Technology, Ocean College, Zhejiang University of Technology, Hangzhou 310014, People’s Republic of China
| | - Kenneth S. Schweizer
- Department of Materials Science, University of Illinois, Urbana, Illinois 61801, USA
- Material Research Laboratory, University of Illinois, Urbana, Illinois 61801, USA
- Department of Chemistry, University of Illinois, Urbana, Illinois 61801, USA
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22
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Sun H, Wang Z, He Y. Direct Observation of Spatiotemporal Heterogeneous Gelation by Rotational Tracking of a Single Anisotropic Nanoprobe. ACS NANO 2019; 13:11334-11342. [PMID: 31589398 DOI: 10.1021/acsnano.9b04491] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Polymer network gels usually exhibit spatial heterogeneity of local defects and cross-link density, which can affect their elasticity on the microscopic scale differently. The ability to evaluate the formation and distribution of these heterogeneities is important for guiding the application of gels in biology, medicine, and separation science. Previously, it has been reported that single-particle tracking based microrheology could provide local properties of gel networks with high resolution; however, the particle probes have been limited to spherical micro/nanotracers undergoing translational motions. In this work, we used single gold nanorods (AuNRs) as rotational microrheology probes to study the polyacrylamide gelation process by dual-channel polarization dark-field microscopy. The AuNRs were in Brownian motion during the initial stages of the gelation. As the reaction continues, individual AuNRs are confined locally and almost lost translational motion, but still maintained rotational motion. As the reaction proceeded further, the rotation state of the AuNRs gradually changed from free rotation in 3D to restricted rotation in 2D and eventually stopped completely. The appearance of the intermediate 2D plane indicated the existence of localized anisotropic compression of the gel during the heterogeneous gelation process. Our method can be further applied to investigate the formation of different polymer gels and a wide variety of heterogeneous biophysical and soft material systems.
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Affiliation(s)
- Hua Sun
- College of Chemistry and Chemical Engineering, Shandong Sino-Japanese Center for Collaborative Research of Carbon Nanomaterials , Qingdao University , Qingdao , 266071 , China
- Department of Chemistry, Key Laboratory of Bioorganic Phosphorus Chemistry & Chemical Biology (Ministry of Education) , Tsinghua University , Beijing , 100084 , China
| | - Zonghua Wang
- College of Chemistry and Chemical Engineering, Shandong Sino-Japanese Center for Collaborative Research of Carbon Nanomaterials , Qingdao University , Qingdao , 266071 , China
| | - Yan He
- Department of Chemistry, Key Laboratory of Bioorganic Phosphorus Chemistry & Chemical Biology (Ministry of Education) , Tsinghua University , Beijing , 100084 , China
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23
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Zheng Q, Zhang Y, Montazerian M, Gulbiten O, Mauro JC, Zanotto ED, Yue Y. Understanding Glass through Differential Scanning Calorimetry. Chem Rev 2019; 119:7848-7939. [DOI: 10.1021/acs.chemrev.8b00510] [Citation(s) in RCA: 154] [Impact Index Per Article: 30.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Qiuju Zheng
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
| | - Yanfei Zhang
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
| | - Maziar Montazerian
- Vitreous Materials Laboratory (LaMaV), Department of Materials Engineering (DEMa), Federal University of São Carlos (UFSCar), 13.565-905 São Carlos, SP, Brazil
| | - Ozgur Gulbiten
- Science and Technology Division, Corning Incorporated, Corning, New York 14831, United States
| | - John C. Mauro
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
- Department of Materials Science and Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States
| | - Edgar D. Zanotto
- Vitreous Materials Laboratory (LaMaV), Department of Materials Engineering (DEMa), Federal University of São Carlos (UFSCar), 13.565-905 São Carlos, SP, Brazil
| | - Yuanzheng Yue
- School of Materials Science and Engineering, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
- State Key Laboratory of Silicate Materials for Architectures, Wuhan University of Technology, Wuhan 430070, China
- Department of Chemistry and Bioscience, Aalborg University, DK-9220 Aalborg, Denmark
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24
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Hoy RS. Thermalization of plastic flow versus stationarity of thermomechanical equilibrium in SGR theory. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2019; 42:2. [PMID: 30617641 DOI: 10.1140/epje/i2019-11763-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/05/2018] [Accepted: 12/03/2018] [Indexed: 06/09/2023]
Abstract
We discuss issues related to thermalization of plastic flow in the context of soft glassy rheology (SGR) theory. An apparent problem with the theory in its current form is that the stationarity of thermomechanical equilibrium obtained by requiring that its flow rule satisfy detailed balance in the absence of applied deformation requires plastic flow to be athermal. This prevents proper application of SGR to small-molecule and polymer glasses where plastic flow is often well thermalized. Clearly, one would like to have a SGR-like theory of thermalized plastic flow that satisfies stationarity. We discuss reasons why such a theory could prove very useful and clarify obstacles that must be overcome in order to develop it.
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Affiliation(s)
- Robert S Hoy
- Department of Physics, University of South Florida, 33620, Tampa, FL, USA.
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25
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Zheng J, Sun A, Wang Y, Zhang J. Energy Fluctuations in Slowly Sheared Granular Materials. PHYSICAL REVIEW LETTERS 2018; 121:248001. [PMID: 30608758 DOI: 10.1103/physrevlett.121.248001] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/19/2018] [Indexed: 06/09/2023]
Abstract
Here we show the first experimental measurement of the particle-scale energy fluctuations ΔE in a slowly sheared layer of photoelastic disks. Starting from an isotropically jammed state, applying shear causes the shear-induced stochastic strengthening and weakening of particle-scale energies, whose statistics and dynamics govern the evolution of the macroscopic stress-strain curve. We find that the ΔE behave as a temperaturelike noise field, showing a novel, Boltzmann-type, double-exponential distribution at any given shear strain γ. Following the framework of the soft glassy rheology theory, we extract an effective temperature χ from the statistics of the energy fluctuations to interpret the slow startup shear (shear starts from an isotropically jammed state) of granular materials as an "aging" process: Starting below one, χ gradually approaches one as γ increases, similar to those of spin glasses, thermal glasses, and bulk metallic glasses.
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Affiliation(s)
- Jie Zheng
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Aile Sun
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Yujie Wang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
| | - Jie Zhang
- School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
- Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China
- Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China
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26
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Hou R, Cherstvy AG, Metzler R, Akimoto T. Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing. Phys Chem Chem Phys 2018; 20:20827-20848. [PMID: 30066003 DOI: 10.1039/c8cp01863d] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/02/2023]
Abstract
We examine renewal processes with power-law waiting time distributions (WTDs) and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics. All possible values of the scaling exponent α are considered for the WTD ψ(t) ∼ 1/t1+α. We treat continuous-time random walks (CTRWs) with 0 < α < 1 for which the mean waiting time diverges, and investigate the behaviour of the process for both ordinary and equilibrium CTRWs for 1 < α < 2 and α > 2. We demonstrate that in the presence of a drift CTRWs with α < 1 are ageing and non-ergodic in the sense of the non-equivalence of their ensemble and time averaged displacement characteristics in the limit of lag times much shorter than the trajectory length. In the sense of the equivalence of ensemble and time averages, CTRW processes with 1 < α < 2 are ergodic for the equilibrium and non-ergodic for the ordinary situation. Lastly, CTRW renewal processes with α > 2-both for the equilibrium and ordinary situation-are always ergodic. For the situations 1 < α < 2 and α > 2 the variance of the diffusion process, however, depends on the initial ensemble. For biased CTRWs with α > 1 we also investigate the behaviour of the ergodicity breaking parameter. In addition, we demonstrate that for biased CTRWs the Einstein relation is valid on the level of the ensemble and time averaged displacements, in the entire range of the WTD exponent α.
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Affiliation(s)
- Ru Hou
- School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
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27
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Mardoukhi Y, Jeon JH, Chechkin AV, Metzler R. Fluctuations of random walks in critical random environments. Phys Chem Chem Phys 2018; 20:20427-20438. [PMID: 30043029 DOI: 10.1039/c8cp03212b] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Percolation networks have been widely used in the description of porous media but are now found to be relevant to understand the motion of particles in cellular membranes or the nucleus of biological cells. Random walks on the infinite cluster at criticality of a percolation network are asymptotically ergodic. On any finite size cluster of the network stationarity is reached at finite times, depending on the cluster's size. Despite of this we here demonstrate by combination of analytical calculations and simulations that at criticality the disorder and cluster size average of the ensemble of clusters leads to a non-vanishing variance of the time averaged mean squared displacement, regardless of the measurement time. Fluctuations of this relevant experimental quantity due to the disorder average of such ensembles are thus persistent and non-negligible. The relevance of our results for single particle tracking analysis in complex and biological systems is discussed.
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Affiliation(s)
- Yousof Mardoukhi
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
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28
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Merrigan C, Birwa SK, Tewari S, Chakraborty B. Ergodicity breaking dynamics of arch collapse. Phys Rev E 2018; 97:040901. [PMID: 29758696 DOI: 10.1103/physreve.97.040901] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2017] [Indexed: 11/07/2022]
Abstract
Flows in hoppers and silos are susceptible to clogging due to the formation of arches at the exit. The failure of these arches is the key to reinitiation of flow, yet the physical mechanism of failure is not well understood. Experiments on vibrated hoppers exhibit a broad distribution of the duration of clogs. Using numerical simulations of a hopper in two dimensions, we show that arches become trapped in locally stable shapes that are explored dynamically under vibrations. The shape dynamics, preceding failure, break ergodicity and can be modeled as a continuous-time random walk with a broad distribution of waiting, or trapping, times. We argue that arch failure occurs as a result of this random walk crossing a stability boundary, which is a first-passage process that naturally gives rise to a broad distribution of unclogging times.
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Affiliation(s)
- Carl Merrigan
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - Sumit Kumar Birwa
- TIFR International Center for Theoretical Sciences, Shivakote, Bengaluru 560089, India
| | - Shubha Tewari
- Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
| | - Bulbul Chakraborty
- Martin Fisher School of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
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29
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Akimoto T, Barkai E, Saito K. Non-self-averaging behaviors and ergodicity in quenched trap models with finite system sizes. Phys Rev E 2018; 97:052143. [PMID: 29906876 DOI: 10.1103/physreve.97.052143] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2018] [Indexed: 06/08/2023]
Abstract
Tracking tracer particles in heterogeneous environments plays an important role in unraveling material properties. These heterogeneous structures are often static and depend on the sample realizations. Sample-to-sample fluctuations of such disorder realizations sometimes become considerably large. When we investigate the sample-to-sample fluctuations, fundamental averaging procedures are a thermal average for a single disorder realization and the disorder average for different disorder realizations. Here we report on non-self-averaging phenomena in quenched trap models with finite system sizes, where we consider the periodic and the reflecting boundary conditions. Sample-to-sample fluctuations of diffusivity greatly exceed trajectory-to-trajectory fluctuations of diffusivity in the corresponding annealed model. For a single disorder realization, the time-averaged mean square displacement and position-dependent observables converge to constants because of the existence of the equilibrium distribution. This is a manifestation of ergodicity. As a result, the time-averaged quantities depend neither on the initial condition nor on the thermal histories but depend crucially on the disorder realization.
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Affiliation(s)
- Takuma Akimoto
- Department of Physics, Tokyo University of Science, Noda, Chiba 278-8510, Japan
| | - Eli Barkai
- Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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30
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Abstract
We present a version of soft glassy rheology that includes thermalized strain degrees of freedom. It fully specifies systems' strain-history-dependent positions on their energy landscapes and therefore allows for quantitative analysis of their heterogeneous yielding dynamics and nonequilibrium deformation thermodynamics. As a demonstration of the method, we illustrate the very different characteristics of fully thermal and nearly athermal plasticity by comparing results for thermalized and nonthermalized plastic flow.
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Affiliation(s)
- Robert S Hoy
- Department of Physics, University of South Florida, Tampa, Florida 33620, USA
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31
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Lou Y, Xia J, Tang W, Chen Y. Linking biological and physical aging: Dynamical scaling of multicellular regeneration. Phys Rev E 2017; 96:062418. [PMID: 29347394 DOI: 10.1103/physreve.96.062418] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2016] [Indexed: 05/27/2023]
Abstract
The fight against biological aging (bio-aging) is long-standing, with the focus of intense research aimed at maintaining high rates of tissue regeneration to promote health and longevity. Nevertheless, there are overwhelming complexities associated with the quantitative analysis of aging. In this study, we sought to quantify bio-aging based on physical aging, by mapping instances of multicellular regeneration to the relaxation of physical systems. An experiment of delayed wound healing assays was devised to obtain delay-dependent healing data. The experiment confirmed the slowdown of healing events, which fitted dynamical scaling just as relaxation events do in physical aging. The scaling exponent, which describes the aging rate in physics, is here similarly proposed as an indicator of the deterioration rate of tissue-regenerative power. Parallel equation-based and cell-based simulations also revealed that asymmetric cell cycle-regulatory mechanisms under strong growth-inhibitory conditions predominantly control the critical slowdown of healing analogous to physical criticality. By establishing a direct link between physical aging and biological aging, we are able to estimate the aging rate of tissues and to achieve an integrated understanding of bio-aging mechanism which may improve the modulation of regeneration for clinical use.
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Affiliation(s)
- Yuting Lou
- SCS Lab, Department of Human and Environmental Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan
| | - Jufeng Xia
- Hepato-Biliary-Pancreas Lab, Division of Surgery, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
| | - Wei Tang
- Hepato-Biliary-Pancreas Lab, Division of Surgery, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
| | - Yu Chen
- SCS Lab, Department of Human and Environmental Engineering, Graduate School of Frontier Sciences, The University of Tokyo, Chiba, Japan
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32
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Oswald L, Grosser S, Smith DM, Käs JA. Jamming transitions in cancer. JOURNAL OF PHYSICS D: APPLIED PHYSICS 2017; 50:483001. [PMID: 29628530 PMCID: PMC5884432 DOI: 10.1088/1361-6463/aa8e83] [Citation(s) in RCA: 81] [Impact Index Per Article: 11.6] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
The traditional picture of tissues, where they are treated as liquids defined by properties such as surface tension or viscosity has been redefined during the last few decades by the more fundamental question: under which conditions do tissues display liquid-like or solid-like behaviour? As a result, basic concepts arising from the treatment of tissues as solid matter, such as cellular jamming and glassy tissues, have shifted into the current focus of biophysical research. Here, we review recent works examining the phase states of tissue with an emphasis on jamming transitions in cancer. When metastasis occurs, cells gain the ability to leave the primary tumour and infiltrate other parts of the body. Recent studies have shown that a linkage between an unjamming transition and tumour progression indeed exists, which could be of importance when designing surgery and treatment approaches for cancer patients.
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Affiliation(s)
- Linda Oswald
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
| | - Steffen Grosser
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
| | - David M Smith
- Fraunhofer Institute for Cell Therapy and Immunology, Perlickstr. 1,
04103 Leipzig, Germany
| | - Josef A Käs
- University of Leipzig, Faculty of Physics and Earth Sciences, Debye
Institute, Linnéstr. 5, 04103 Leipzig, Germany
- Author to whom any correspondence should be addressed.
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33
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Diezemann G. Nonlinear response theory for Markov processes. II. Fifth-order response functions. Phys Rev E 2017; 96:022150. [PMID: 28950644 DOI: 10.1103/physreve.96.022150] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2017] [Indexed: 06/07/2023]
Abstract
The nonlinear response of stochastic models obeying a master equation is calculated up to fifth order in the external field, thus extending the third-order results obtained earlier [G. Diezemann, Phys. Rev. E 85, 051502 (2012)PLEEE81539-375510.1103/PhysRevE.85.051502]. For sinusoidal fields the 5ω component of the susceptibility is computed for the model of dipole reorientations in an asymmetric double well potential and for a trap model with a Gaussian density of states. For most realizations of the models a hump is found in the higher-order susceptibilities. In particular, for the asymmetric double well potential model there are two characteristic temperature regimes showing the occurrence of such a hump as compared to a single characteristic regime in the case of the third-order response. In the case of the trap model the results strongly depend on the variable coupled to the field. As for the third-order response, the low-frequency limit of the susceptibility plays a crucial role with respect to the occurrence of a hump. The findings are discussed in light of recent experimental results obtained for supercooled liquids. The differences found for the third-order and the fifth-order response indicate that nonlinear response functions might serve as a powerful tool to discriminate among the large number of existing models for glassy relaxation.
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Affiliation(s)
- Gregor Diezemann
- Institut für Physikalische Chemie, Universität Mainz, Duesbergweg 10-14, 55128 Mainz, Germany
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34
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Abstract
Anomalous diffusion is being discovered in a fast growing number of systems. The exact nature of this anomalous diffusion provides important information on the physical laws governing the studied system. One of the central properties analysed for finite particle motion time series is the intrinsic variability of the apparent diffusivity, typically quantified by the ergodicity breaking parameter EB. Here we demonstrate that frequently EB is insufficient to provide a meaningful measure for the observed variability of the data. Instead, important additional information is provided by the higher order moments entering by the skewness and kurtosis. We analyse these quantities for three popular anomalous diffusion models. In particular, we find that even for the Gaussian fractional Brownian motion a significant skewness in the results of physical measurements occurs and needs to be taken into account. Interestingly, the kurtosis and skewness may also provide sensitive estimates of the anomalous diffusion exponent underlying the data. We also derive a new result for the EB parameter of fractional Brownian motion valid for the whole range of the anomalous diffusion parameter. Our results are important for the analysis of anomalous diffusion but also provide new insights into the theory of anomalous stochastic processes.
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35
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Meroz Y, Ovchinnikov V, Karplus M. Coexisting origins of subdiffusion in internal dynamics of proteins. Phys Rev E 2017; 95:062403. [PMID: 28709262 DOI: 10.1103/physreve.95.062403] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/17/2016] [Indexed: 11/07/2022]
Abstract
Subdiffusion in conformational dynamics of proteins is observed both experimentally and in simulations. Although its origin has been attributed to multiple mechanisms, including trapping on a rugged energy landscape, fractional Brownian noise, or a fractal topology of the energy landscape, it is unclear which of these, if any, is most relevant. To obtain insights into the actual mechanism, we introduce an analytically tractable hierarchical trapping model and apply it to molecular dynamics simulation trajectories of three proteins in solution. The analysis of the simulations introduces a subdiffusive exponent that varies with time and associates plateaus in the mean-squared displacement with traps on the energy landscape. This analysis permits us to separate the component of subdiffusion due to a trapping mechanism from that due to an underlying fluctuating process, such as fractional Brownian motion. The present results thus provide insights concerning the physical origin of subdiffusion in the dynamics of proteins.
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Affiliation(s)
- Yasmine Meroz
- Harvard University, School of Engineering and Applied Sciences, Cambridge, Massachusetts 02138, USA
| | - Victor Ovchinnikov
- Harvard University, Department of Chemistry and Chemical Biology, Cambridge, Massachusetts 02138, USA
| | - Martin Karplus
- Harvard University, Department of Chemistry and Chemical Biology, Cambridge, Massachusetts 02138, USA.,Laboratoire de Chimie Biophysique, ISIS, Université de Strasbourg, 67000 Strasbourg, France
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36
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Abstract
Aging can be observed for numerous physical systems. In such systems statistical properties [like probability distribution, mean square displacement (MSD), first-passage time] depend on a time span t_{a} between the initialization and the beginning of observations. In this paper we study aging properties of ballistic Lévy walks and two closely related jump models: wait-first and jump-first. We calculate explicitly their probability distributions and MSDs. It turns out that despite similarities these models react very differently to the delay t_{a}. Aging weakly affects the shape of probability density function and MSD of standard Lévy walks. For the jump models the shape of the probability density function is changed drastically. Moreover for the wait-first jump model we observe a different behavior of MSD when t_{a}≪t and t_{a}≫t.
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Affiliation(s)
- Marcin Magdziarz
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
| | - Tomasz Zorawik
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego 27, 50-370 Wroclaw, Poland
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37
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Safdari H, Cherstvy AG, Chechkin AV, Bodrova A, Metzler R. Aging underdamped scaled Brownian motion: Ensemble- and time-averaged particle displacements, nonergodicity, and the failure of the overdamping approximation. Phys Rev E 2017; 95:012120. [PMID: 28208482 DOI: 10.1103/physreve.95.012120] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2016] [Indexed: 06/06/2023]
Abstract
We investigate both analytically and by computer simulations the ensemble- and time-averaged, nonergodic, and aging properties of massive particles diffusing in a medium with a time dependent diffusivity. We call this stochastic diffusion process the (aging) underdamped scaled Brownian motion (UDSBM). We demonstrate how the mean squared displacement (MSD) and the time-averaged MSD of UDSBM are affected by the inertial term in the Langevin equation, both at short, intermediate, and even long diffusion times. In particular, we quantify the ballistic regime for the MSD and the time-averaged MSD as well as the spread of individual time-averaged MSD trajectories. One of the main effects we observe is that, both for the MSD and the time-averaged MSD, for superdiffusive UDSBM the ballistic regime is much shorter than for ordinary Brownian motion. In contrast, for subdiffusive UDSBM, the ballistic region extends to much longer diffusion times. Therefore, particular care needs to be taken under what conditions the overdamped limit indeed provides a correct description, even in the long time limit. We also analyze to what extent ergodicity in the Boltzmann-Khinchin sense in this nonstationary system is broken, both for subdiffusive and superdiffusive UDSBM. Finally, the limiting case of ultraslow UDSBM is considered, with a mixed logarithmic and power-law dependence of the ensemble- and time-averaged MSDs of the particles. In the limit of strong aging, remarkably, the ordinary UDSBM and the ultraslow UDSBM behave similarly in the short time ballistic limit. The approaches developed here open ways for considering other stochastic processes under physically important conditions when a finite particle mass and aging in the system cannot be neglected.
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Affiliation(s)
- Hadiseh Safdari
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Department of Physics, Shahid Beheshti University, 19839 Tehran, Iran
| | - Andrey G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Aleksei V Chechkin
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, 61108 Kharkov, Ukraine
- Department of Physics & Astronomy, University of Padova, "Galileo Galilei" - DFA, 35131 Padova, Italy
| | - Anna Bodrova
- Institute of Physics, Humboldt University Berlin, 12489 Berlin, Germany
- Faculty of Physics, M. V. Lomonosov Moscow State University, 119991 Moscow, Russia
| | - Ralf Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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38
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Puosi F, Chulkin O, Bernini S, Capaccioli S, Leporini D. Thermodynamic scaling of vibrational dynamics and relaxation. J Chem Phys 2016; 145:234904. [DOI: 10.1063/1.4971297] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- F. Puosi
- Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - O. Chulkin
- Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - S. Bernini
- Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
| | - S. Capaccioli
- Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
- IPCF-CNR, UOS, Pisa, Italy
| | - D. Leporini
- Dipartimento di Fisica “Enrico Fermi,” Università di Pisa, Largo B. Pontecorvo 3, I-56127 Pisa, Italy
- IPCF-CNR, UOS, Pisa, Italy
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39
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Leibovich N, Dechant A, Lutz E, Barkai E. Aging Wiener-Khinchin theorem and critical exponents of 1/f^{β} noise. Phys Rev E 2016; 94:052130. [PMID: 27967149 DOI: 10.1103/physreve.94.052130] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/20/2016] [Indexed: 06/06/2023]
Abstract
The power spectrum of a stationary process may be calculated in terms of the autocorrelation function using the Wiener-Khinchin theorem. We here generalize the Wiener-Khinchin theorem for nonstationary processes and introduce a time-dependent power spectrum 〈S_{t_{m}}(ω)〉 where t_{m} is the measurement time. For processes with an aging autocorrelation function of the form 〈I(t)I(t+τ)〉=t^{Υ}ϕ_{EA}(τ/t), where ϕ_{EA}(x) is a nonanalytic function when x is small, we find aging 1/f^{β} noise. Aging 1/f^{β} noise is characterized by five critical exponents. We derive the relations between the scaled autocorrelation function and these exponents. We show that our definition of the time-dependent spectrum retains its interpretation as a density of Fourier modes and discuss the relation to the apparent infrared divergence of 1/f^{β} noise. We illustrate our results for blinking-quantum-dot models, single-file diffusion, and Brownian motion in a logarithmic potential.
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Affiliation(s)
- N Leibovich
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
| | - A Dechant
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Lutz
- Department of Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058 Erlangen, Germany
| | - E Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat-Gan 52900, Israel
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40
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Akimoto T, Barkai E, Saito K. Universal Fluctuations of Single-Particle Diffusivity in a Quenched Environment. PHYSICAL REVIEW LETTERS 2016; 117:180602. [PMID: 27835019 DOI: 10.1103/physrevlett.117.180602] [Citation(s) in RCA: 21] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/23/2016] [Indexed: 06/06/2023]
Abstract
Local diffusion coefficients in disordered materials such as living cells are highly heterogeneous. We consider finite systems with quenched disorder in order to investigate the effects of sample disorder fluctuations and confinement on single-particle diffusivity. While the system is ergodic in a single disorder realization, the time-averaged mean square displacement depends crucially on the disorder; i.e., the system is ergodic but non-self-averaging. Moreover, we show that the disorder average of the time-averaged mean square displacement decreases with the system size. We find a universal distribution for diffusivity in the sense that the shape of the distribution does not depend on the dimension. Quantifying the degree of the non-self-averaging effect, we show that fluctuations of single-particle diffusivity far exceed the corresponding annealed theory and also find confinement effects. The relevance for experimental situations is also discussed.
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Affiliation(s)
- Takuma Akimoto
- Graduate School of Science and Technology, Keio University, Yokohama 223-8522, Japan
| | - Eli Barkai
- Department of Physics, Bar Ilan University, Ramat-Gan 52900, Israel
| | - Keiji Saito
- Department of Physics, Keio University, Yokohama 223-8522, Japan
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41
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Bodrova AS, Chechkin AV, Cherstvy AG, Safdari H, Sokolov IM, Metzler R. Underdamped scaled Brownian motion: (non-)existence of the overdamped limit in anomalous diffusion. Sci Rep 2016; 6:30520. [PMID: 27462008 PMCID: PMC4962320 DOI: 10.1038/srep30520] [Citation(s) in RCA: 64] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/10/2016] [Accepted: 07/04/2016] [Indexed: 01/23/2023] Open
Abstract
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion process governed by an underdamped Langevin equation with an explicit time dependence of the system temperature and thus the diffusion and damping coefficients. We show that for this underdamped scaled Brownian motion (UDSBM) the overdamped limit fails to describe the long time behaviour of the system and may practically even not exist at all for a certain range of the parameter values. Thus persistent inertial effects play a non-negligible role even at significantly long times. From this study a general questions on the applicability of the overdamped limit to describe the long time motion of an anomalously diffusing particle arises, with profound consequences for the relevance of overdamped anomalous diffusion models. We elucidate our results in view of analytical and simulations results for the anomalous diffusion of particles in free cooling granular gases.
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Affiliation(s)
- Anna S Bodrova
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.,Faculty of Physics, M.V.Lomonosov Moscow State University, Moscow, 119991, Russia
| | - Aleksei V Chechkin
- Akhiezer Institute for Theoretical Physics, Kharkov Institute of Physics and Technology, Kharkov 61108, Ukraine.,Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.,Department of Physics &Astronomy, University of Padova, 35122 Padova, Italy
| | - Andrey G Cherstvy
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Hadiseh Safdari
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany.,Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran 19839, Iran
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
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42
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Micoulaut M. Relaxation and physical aging in network glasses: a review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:066504. [PMID: 27213928 DOI: 10.1088/0034-4885/79/6/066504] [Citation(s) in RCA: 32] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Recent progress in the description of glassy relaxation and aging are reviewed for the wide class of network-forming materials such as GeO2, Ge x Se1-x , silicates (SiO2-Na2O) or borates (B2O3-Li2O), all of which have an important usefulness in domestic, geological or optoelectronic applications. A brief introduction of the glass transition phenomenology is given, together with the salient features that are revealed both from theory and experiments. Standard experimental methods used for the characterization of the slowing down of the dynamics are reviewed. We then discuss the important role played by aspects of network topology and rigidity for the understanding of the relaxation of the glass transition, while also permitting analytical predictions of glass properties from simple and insightful models based on the network structure. We also emphasize the great utility of computer simulations which probe the dynamics at the molecular level, and permit the calculation of various structure-related functions in connection with glassy relaxation and the physics of aging which reveal the non-equilibrium nature of glasses. We discuss the notion of spatial variations of structure which leads to the concept of 'dynamic heterogeneities', and recent results in relation to this important topic for network glasses are also reviewed.
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Affiliation(s)
- Matthieu Micoulaut
- Paris Sorbonne Universités, LPTMC-UPMC, 4 place Jussieu, 75252 Paris cedex 05, France
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43
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44
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Bi D, Yang X, Marchetti MC, Manning ML. Motility-driven glass and jamming transitions in biological tissues. PHYSICAL REVIEW. X 2016; 6:021011. [PMID: 28966874 PMCID: PMC5619672 DOI: 10.1103/physrevx.6.021011] [Citation(s) in RCA: 252] [Impact Index Per Article: 31.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/20/2023]
Abstract
Cell motion inside dense tissues governs many biological processes, including embryonic development and cancer metastasis, and recent experiments suggest that these tissues exhibit collective glassy behavior. To make quantitative predictions about glass transitions in tissues, we study a self-propelled Voronoi (SPV) model that simultaneously captures polarized cell motility and multi-body cell-cell interactions in a confluent tissue, where there are no gaps between cells. We demonstrate that the model exhibits a jamming transition from a solid-like state to a fluid-like state that is controlled by three parameters: the single-cell motile speed, the persistence time of single-cell tracks, and a target shape index that characterizes the competition between cell-cell adhesion and cortical tension. In contrast to traditional particulate glasses, we are able to identify an experimentally accessible structural order parameter that specifies the entire jamming surface as a function of model parameters. We demonstrate that a continuum Soft Glassy Rheology model precisely captures this transition in the limit of small persistence times, and explain how it fails in the limit of large persistence times. These results provide a framework for understanding the collective solid-to-liquid transitions that have been observed in embryonic development and cancer progression, which may be associated with Epithelial-to-Mesenchymal transition in these tissues.
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Affiliation(s)
- Dapeng Bi
- Department of Physics, Syracuse University, Syracuse, NY, USA
| | - Xingbo Yang
- Department of Physics, Syracuse University, Syracuse, NY, USA
| | - M Cristina Marchetti
- Department of Physics, Syracuse University, Syracuse, NY, USA
- Syracuse Biomaterials Institute, Syracuse, NY, USA
| | - M Lisa Manning
- Department of Physics, Syracuse University, Syracuse, NY, USA
- Syracuse Biomaterials Institute, Syracuse, NY, USA
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45
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Cherstvy AG, Metzler R. Ergodicity breaking and particle spreading in noisy heterogeneous diffusion processes. J Chem Phys 2016; 142:144105. [PMID: 25877560 DOI: 10.1063/1.4917077] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We study noisy heterogeneous diffusion processes with a position dependent diffusivity of the form D(x) ∼ D0|x|(α0) in the presence of annealed and quenched disorder of the environment, corresponding to an effective variation of the exponent α in time and space. In the case of annealed disorder, for which effectively α0 = α0(t), we show how the long time scaling of the ensemble mean squared displacement (MSD) and the amplitude variation of individual realizations of the time averaged MSD are affected by the disorder strength. For the case of quenched disorder, the long time behavior becomes effectively Brownian after a number of jumps between the domains of a stratified medium. In the latter situation, the averages are taken over both an ensemble of particles and different realizations of the disorder. As physical observables, we analyze in detail the ensemble and time averaged MSDs, the ergodicity breaking parameter, and higher order moments of the time averages.
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Affiliation(s)
- Andrey G Cherstvy
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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46
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Metzler R, Jeon JH, Cherstvy AG. Non-Brownian diffusion in lipid membranes: Experiments and simulations. BIOCHIMICA ET BIOPHYSICA ACTA-BIOMEMBRANES 2016; 1858:2451-2467. [PMID: 26826272 DOI: 10.1016/j.bbamem.2016.01.022] [Citation(s) in RCA: 126] [Impact Index Per Article: 15.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/24/2015] [Revised: 01/21/2016] [Accepted: 01/23/2016] [Indexed: 12/14/2022]
Abstract
The dynamics of constituents and the surface response of cellular membranes-also in connection to the binding of various particles and macromolecules to the membrane-are still a matter of controversy in the membrane biophysics community, particularly with respect to crowded membranes of living biological cells. We here put into perspective recent single particle tracking experiments in the plasma membranes of living cells and supercomputing studies of lipid bilayer model membranes with and without protein crowding. Special emphasis is put on the observation of anomalous, non-Brownian diffusion of both lipid molecules and proteins embedded in the lipid bilayer. While single component, pure lipid bilayers in simulations exhibit only transient anomalous diffusion of lipid molecules on nanosecond time scales, the persistence of anomalous diffusion becomes significantly longer ranged on the addition of disorder-through the addition of cholesterol or proteins-and on passing of the membrane lipids to the gel phase. Concurrently, experiments demonstrate the anomalous diffusion of membrane embedded proteins up to macroscopic time scales in the minute time range. Particular emphasis will be put on the physical character of the anomalous diffusion, in particular, the occurrence of ageing observed in the experiments-the effective diffusivity of the measured particles is a decreasing function of time. Moreover, we present results for the time dependent local scaling exponent of the mean squared displacement of the monitored particles. Recent results finding deviations from the commonly assumed Gaussian diffusion patterns in protein crowded membranes are reported. The properties of the displacement autocorrelation function of the lipid molecules are discussed in the light of their appropriate physical anomalous diffusion models, both for non-crowded and crowded membranes. In the last part of this review we address the upcoming field of membrane distortion by elongated membrane-binding particles. We discuss how membrane compartmentalisation and the particle-membrane binding energy may impact the dynamics and response of lipid membranes. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.
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Affiliation(s)
- R Metzler
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany; Department of Physics, Tampere University of Technology, 33101 Tampere, Finland.
| | - J-H Jeon
- Korea Institute for Advanced Study (KIAS), Seoul, Republic of Korea
| | - A G Cherstvy
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
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47
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Cherstvy AG, Metzler R. Anomalous diffusion in time-fluctuating non-stationary diffusivity landscapes. Phys Chem Chem Phys 2016; 18:23840-52. [DOI: 10.1039/c6cp03101c] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023]
Abstract
We investigate the diffusive and ergodic properties of massive and confined particles in a model disordered medium, in which the local diffusivity fluctuates in time while its mean has a power law dependence on the diffusion time.
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Affiliation(s)
- Andrey G. Cherstvy
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
| | - Ralf Metzler
- Institute for Physics & Astronomy
- University of Potsdam
- 14476 Potsdam-Golm
- Germany
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48
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49
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Schroer CFE, Heuer A. Understanding the nonlinear dynamics of driven particles in supercooled liquids in terms of an effective temperature. J Chem Phys 2015; 143:224501. [PMID: 26671384 DOI: 10.1063/1.4937154] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
In active microrheology, the mechanical properties of a material are tested by adding probe particles which are pulled by an external force. In case of supercooled liquids, strong forcing leads to a thinning of the host material which becomes more pronounced as the system approaches the glass transition. In this work, we provide a quantitative theoretical description of this thinning behavior based on the properties of the Potential Energy Landscape (PEL) of a model glass-former. A key role plays the trap-like nature of the PEL. We find that the mechanical properties in the strongly driven system behave the same as in a quiescent system at an enhanced temperature, giving rise to a well-characterized effective temperature. Furthermore, this effective temperature turns out to be independent of the chosen observable and individually shows up in the thermodynamic and dynamic properties of the system. Based on this underlying theoretical understanding, we can estimate its dependence on temperature and force by the PEL-properties of the quiescent system. We furthermore critically discuss the relevance of effective temperatures obtained by scaling relations for the description of out-of-equilibrium situations.
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Affiliation(s)
- Carsten F E Schroer
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, 48149 Münster, Germany
| | - Andreas Heuer
- Institut für Physikalische Chemie, Westfälische Wilhelms-Universität Münster, Corrensstraße 28/30, 48149 Münster, Germany
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50
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Mardoukhi Y, Jeon JH, Metzler R. Geometry controlled anomalous diffusion in random fractal geometries: looking beyond the infinite cluster. Phys Chem Chem Phys 2015; 17:30134-47. [PMID: 26503611 DOI: 10.1039/c5cp03548a] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We investigate the ergodic properties of a random walker performing (anomalous) diffusion on a random fractal geometry. Extensive Monte Carlo simulations of the motion of tracer particles on an ensemble of realisations of percolation clusters are performed for a wide range of percolation densities. Single trajectories of the tracer motion are analysed to quantify the time averaged mean squared displacement (MSD) and to compare this with the ensemble averaged MSD of the particle motion. Other complementary physical observables associated with ergodicity are studied, as well. It turns out that the time averaged MSD of individual realisations exhibits non-vanishing fluctuations even in the limit of very long observation times as the percolation density approaches the critical value. This apparent non-ergodic behaviour concurs with the ergodic behaviour on the ensemble averaged level. We demonstrate how the non-vanishing fluctuations in single particle trajectories are analytically expressed in terms of the fractal dimension and the cluster size distribution of the random geometry, thus being of purely geometrical origin. Moreover, we reveal that the convergence scaling law to ergodicity, which is known to be inversely proportional to the observation time T for ergodic diffusion processes, follows a power-law ∼T(-h) with h < 1 due to the fractal structure of the accessible space. These results provide useful measures for differentiating the subdiffusion on random fractals from an otherwise closely related process, namely, fractional Brownian motion. Implications of our results on the analysis of single particle tracking experiments are provided.
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Affiliation(s)
- Yousof Mardoukhi
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany.
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