1
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Sposini V, Nampoothiri S, Chechkin A, Orlandini E, Seno F, Baldovin F. Being Heterogeneous Is Advantageous: Extreme Brownian Non-Gaussian Searches. PHYSICAL REVIEW LETTERS 2024; 132:117101. [PMID: 38563912 DOI: 10.1103/physrevlett.132.117101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Revised: 11/15/2023] [Accepted: 02/01/2024] [Indexed: 04/04/2024]
Abstract
Redundancy in biology may be explained by the need to optimize extreme searching processes, where one or few among many particles are requested to reach the target like in human fertilization. We show that non-Gaussian rare fluctuations in Brownian diffusion dominates such searches, introducing drastic corrections to the known Gaussian behavior. Our demonstration entails different physical systems and pinpoints the relevance of diversity within redundancy to boost fast targeting. We sketch an experimental context to test our results: polydisperse systems.
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Affiliation(s)
- Vittoria Sposini
- Faculty of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
| | - Sankaran Nampoothiri
- Department of Physics, Gandhi Institute of Technology and Management (GITAM) University, Bengaluru 561203, India
| | - Aleksei Chechkin
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego Str. 27, 50-370 Wroclaw, Poland
- Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Akhiezer Institute for Theoretical Physics, 61108 Kharkov, Ukraine
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Flavio Seno
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Fulvio Baldovin
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
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2
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Sposini V, Nampoothiri S, Chechkin A, Orlandini E, Seno F, Baldovin F. Being heterogeneous is disadvantageous: Brownian non-Gaussian searches. Phys Rev E 2024; 109:034120. [PMID: 38632764 DOI: 10.1103/physreve.109.034120] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2023] [Accepted: 02/01/2024] [Indexed: 04/19/2024]
Abstract
Diffusing diffusivity models, polymers in the grand canonical ensemble and polydisperse, and continuous-time random walks all exhibit stages of non-Gaussian diffusion. Is non-Gaussian targeting more efficient than Gaussian? We address this question, central to, e.g., diffusion-limited reactions and some biological processes, through a general approach that makes use of Jensen's inequality and that encompasses all these systems. In terms of customary mean first-passage time, we show that Gaussian searches are more effective than non-Gaussian ones. A companion paper argues that non-Gaussianity becomes instead highly more efficient in applications where only a small fraction of tracers is required to reach the target.
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Affiliation(s)
- Vittoria Sposini
- Faculty of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
| | - Sankaran Nampoothiri
- Department of Physics, Gandhi Institute of Technology and Management (GITAM) University, Bengaluru 561203, India
| | - Aleksei Chechkin
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wroclaw University of Science and Technology, Wyspianskiego Street 27, 50-370 Wroclaw, Poland
- Institute for Physics and Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany
- Akhiezer Institute for Theoretical Physics, 61108 Kharkov, Ukraine
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Flavio Seno
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Fulvio Baldovin
- Dipartimento di Fisica e Astronomia 'G. Galilei' - DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
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3
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Srinivasan H, Sharma VK, García Sakai V, Mitra S. Nature of Subdiffusion Crossover in Molecular and Polymeric Glassformers. PHYSICAL REVIEW LETTERS 2024; 132:058202. [PMID: 38364148 DOI: 10.1103/physrevlett.132.058202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2023] [Revised: 11/21/2023] [Accepted: 01/03/2024] [Indexed: 02/18/2024]
Abstract
A crossover from a non-Gaussian to Gaussian subdiffusion has been observed ubiquitously in various polymeric and molecular glassformers. We have developed a framework that generalizes the fractional Brownian motion model to incorporate non-Gaussian features by introducing a jump kernel. We illustrate that the non-Gaussian fractional Brownian motion model accurately characterizes the subdiffusion crossover. From the solutions of the non-Gaussian fractional Brownian motion model, we gain insights into the nature of van Hove self-correlation in non-Gaussian subdiffusive regime, which is found to exhibit exponential tails, providing first such experimental evidence in molecular glassformers. The validity of the model is supported by comparison with incoherent quasielastic neutron scattering data obtained from several molecular and polymeric glassformers.
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Affiliation(s)
- H Srinivasan
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
| | - V K Sharma
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
| | - V García Sakai
- ISIS Neutron and Muon Centre, Rutherford Appleton Laboratory, Didcot, United Kingdom
| | - S Mitra
- Solid State Physics Division, Bhabha Atomic Research Centre, Mumbai 400085, India
- Homi Bhabha National Institute, Anushaktinagar, Mumbai 400094, India
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4
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Gong J, Li Q, Zeng S, Wang J. Non-Gaussian anomalous diffusion of optical vortices. Phys Rev E 2024; 109:024111. [PMID: 38491579 DOI: 10.1103/physreve.109.024111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/11/2023] [Accepted: 12/15/2023] [Indexed: 03/18/2024]
Abstract
Anomalous diffusion of different particlelike entities, the deviation from typical Brownian motion, is ubiquitous in complex physical and biological systems. While optical vortices move randomly in evolving speckle fields, optical vortices have only been observed to exhibit pure Brownian motion in random speckle fields. Here we present direct experimental evidence of the anomalous diffusion of optical vortices in temporally varying speckle patterns from multiple-scattering viscoelastic media. Moreover, we observe two characteristic features, i.e., the self-similarity and the antipersistent correlation of the optical vortex motion, indicating that the mechanism of the observed subdiffusion of optical vortices can only be attributed to fractional Brownian motion (FBM). We further demonstrate that the vortex displacements exhibit a non-Gaussian heavy-tailed distribution. Additionally, we modulate the extent of subdiffusion, such as diffusive scaling exponents, and the non-Gaussianity of optical vortices by altering the viscoelasticity of samples. The discovery of the complex FBM but non-Gaussian subdiffusion of optical vortices may not only offer insight into certain fundamental physics, including the anomalous diffusion of vortices in fluids and the decoupling between Brownianity and Gaussianity, but also suggest a strong potential for utilizing optical vortices as tracers in microrheology instead of the introduced exogenous probe particles in particle tracking microrheology.
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Affiliation(s)
- Jiaxing Gong
- Department of Biomedical Engineering, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Qi Li
- Department of Biomedical Engineering, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Shaoqun Zeng
- Britton Chance Center for Biomedical Photonics, Wuhan National Laboratory for Optoelectronics, MoE Key Laboratory for Biomedical Photonics, School of Engineering Sciences, Huazhong University of Science and Technology, Wuhan 430074, China
| | - Jing Wang
- Department of Biomedical Engineering, College of Life Science and Technology, Huazhong University of Science and Technology, Wuhan 430074, China
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5
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Voulgarakis NK. Multilayered noise model for transport in complex environments. Phys Rev E 2023; 108:064105. [PMID: 38243501 DOI: 10.1103/physreve.108.064105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 11/09/2023] [Indexed: 01/21/2024]
Abstract
Transport in complex fluidic environments often exhibits transient subdiffusive dynamics accompanied by non-Gaussian probability density profiles featuring a nonmonotonic non-Gaussian parameter. Such properties cannot be adequately explained by the original theory of Brownian motion. Based on an extension of kinetic theory, this study introduces a chain of hierarchically coupled random walks approach that effectively captures all these intriguing characteristics. If the environment consists of a series of independent white noise sources, then the problem can be expressed as a system of hierarchically coupled Ornstein-Uhlenbech equations. Due to the linearity of the system, the most essential transport properties have a closed analytical form.
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Affiliation(s)
- Nikolaos K Voulgarakis
- Department of Mathematics and Statistics, Washington State University, Pullman, Washington 99164, USA
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6
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Kumar A, Daschakraborty S. Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane. Phys Chem Chem Phys 2023; 25:31431-31443. [PMID: 37962400 DOI: 10.1039/d3cp04081j] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2023]
Abstract
A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.
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Affiliation(s)
- Abhay Kumar
- Department of Chemistry, Indian Institute of Technology Patna, Bihar 801106, India.
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7
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Singh RK, Burov S. Universal to nonuniversal transition of the statistics of rare events during the spread of random walks. Phys Rev E 2023; 108:L052102. [PMID: 38115504 DOI: 10.1103/physreve.108.l052102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/08/2023] [Accepted: 09/11/2023] [Indexed: 12/21/2023]
Abstract
Through numerous experiments that analyzed rare event statistics in heterogeneous media, it was discovered that in many cases the probability density function for particle position, P(X,t), exhibits a slower decay rate than the Gaussian function. Typically, the decay behavior is exponential, referred to as Laplace tails. However, many systems exhibit an even slower decay rate, such as power-law, log-normal, or stretched exponential. In this study, we utilize the continuous-time random walk method to investigate the rare events in particle hopping dynamics and find that the properties of the hop size distribution induce a critical transition between the Laplace universality of rare events and a more specific, slower decay of P(X,t). Specifically, when the hop size distribution decays slower than exponential, such as e^{-|x|^{β}} (β>1), the Laplace universality no longer applies, and the decay is specific, influenced by a few large events, rather than by the accumulation of many smaller events that give rise to Laplace tails.
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Affiliation(s)
- R K Singh
- Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
| | - Stanislav Burov
- Department of Physics, Bar-Ilan University, Ramat-Gan 5290002, Israel
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8
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Rusciano F, Pastore R, Greco F. Rusciano et al. Reply. PHYSICAL REVIEW LETTERS 2023; 131:119802. [PMID: 37774259 DOI: 10.1103/physrevlett.131.119802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2023] [Accepted: 08/08/2023] [Indexed: 10/01/2023]
Affiliation(s)
- Francesco Rusciano
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
| | - Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
| | - Francesco Greco
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
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9
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Rey M, Volpe G, Volpe G. Light, Matter, Action: Shining Light on Active Matter. ACS PHOTONICS 2023; 10:1188-1201. [PMID: 37215318 PMCID: PMC10197137 DOI: 10.1021/acsphotonics.3c00140] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/31/2023] [Revised: 04/04/2023] [Accepted: 04/04/2023] [Indexed: 05/24/2023]
Abstract
Light carries energy and momentum. It can therefore alter the motion of objects on the atomic to astronomical scales. Being widely available, readily controllable, and broadly biocompatible, light is also an ideal tool to propel microscopic particles, drive them out of thermodynamic equilibrium, and make them active. Thus, light-driven particles have become a recent focus of research in the field of soft active matter. In this Perspective, we discuss recent advances in the control of soft active matter with light, which has mainly been achieved using light intensity. We also highlight some first attempts to utilize light's additional properties, such as its wavelength, polarization, and momentum. We then argue that fully exploiting light with all of its properties will play a critical role in increasing the level of control over the actuation of active matter as well as the flow of light itself through it. This enabling step will advance the design of soft active matter systems, their functionalities, and their transfer toward technological applications.
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Affiliation(s)
- Marcel Rey
- Physics
Department, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Giovanni Volpe
- Physics
Department, University of Gothenburg, 41296 Gothenburg, Sweden
| | - Giorgio Volpe
- Department
of Chemistry, University College London, 20 Gordon Street, WC1H 0AJ London, United Kingdom
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10
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Ciarlo A, Pastore R, Greco F, Sasso A, Pesce G. Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations. Sci Rep 2023; 13:7408. [PMID: 37149715 PMCID: PMC10164168 DOI: 10.1038/s41598-023-34433-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2023] [Accepted: 04/29/2023] [Indexed: 05/08/2023] Open
Abstract
We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.
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Affiliation(s)
- Antonio Ciarlo
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant'Angelo, Via Cintia, 80126, Naples, Italy.
| | - Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125, Naples, Italy
| | - Francesco Greco
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125, Naples, Italy
| | - Antonio Sasso
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant'Angelo, Via Cintia, 80126, Naples, Italy
| | - Giuseppe Pesce
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte Sant'Angelo, Via Cintia, 80126, Naples, Italy
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11
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Rusciano F, Pastore R, Greco F. Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids. Int J Mol Sci 2023; 24:ijms24097871. [PMID: 37175578 PMCID: PMC10177888 DOI: 10.3390/ijms24097871] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/28/2023] [Revised: 04/09/2023] [Accepted: 04/10/2023] [Indexed: 05/15/2023] Open
Abstract
Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.
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Affiliation(s)
- Francesco Rusciano
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, Italy
| | - Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, Italy
| | - Francesco Greco
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, Italy
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12
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Alexandre A, Lavaud M, Fares N, Millan E, Louyer Y, Salez T, Amarouchene Y, Guérin T, Dean DS. Non-Gaussian Diffusion Near Surfaces. PHYSICAL REVIEW LETTERS 2023; 130:077101. [PMID: 36867824 DOI: 10.1103/physrevlett.130.077101] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2022] [Accepted: 12/22/2022] [Indexed: 06/18/2023]
Abstract
We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a nonzero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance, gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.
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Affiliation(s)
- Arthur Alexandre
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Maxime Lavaud
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Nicolas Fares
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Department of Physics, Ecole Normale Supérieure de Lyon, 69364 Lyon, France
| | - Elodie Millan
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Yann Louyer
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - Thomas Salez
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | | | - Thomas Guérin
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
| | - David S Dean
- Université de Bordeaux, CNRS, LOMA, UMR 5798, F-33400 Talence, France
- Team MONC, INRIA Bordeaux Sud Ouest, CNRS UMR 5251, Bordeaux INP, Université de Bordeaux, F-33400 Talence, France
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13
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Shi H, Du L, Huang F, Guo W. Weak ergodicity breaking and anomalous diffusion in collective motion of active particles under spatiotemporal disorder. Phys Rev E 2023; 107:024114. [PMID: 36932613 DOI: 10.1103/physreve.107.024114] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2021] [Accepted: 01/12/2023] [Indexed: 06/18/2023]
Abstract
The effects of spatiotemporal disorder, i.e., both the noise and quenched disorder, on the dynamics of active particles in two dimensions are investigated. We demonstrate that within the tailored parameter regime, nonergodic superdiffusion and nonergodic subdiffusion occur in the system, identified by the observable quantities (the mean squared displacement and ergodicity-breaking parameter) averaged over both the noise and realizations of quenched disorder. Their origins are attributed to the competition effects between the neighbor alignment and spatiotemporal disorder on the collective motion of active particles. These results may be helpful for further understanding the nonequilibrium transport process of active particles, as well as for detection of the transport of self-propelled particles in complex and crowded environments.
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Affiliation(s)
- Hongda Shi
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Luchun Du
- Department of Physics, Yunnan University, Kunming 650091, China
| | - Feijie Huang
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
| | - Wei Guo
- Key Laboratory of Artificial Microstructures in Yunnan Higher Education Institutions, School of Physical Science and Technology, Kunming University, Kunming 650214, China
- Yunnan Key Laboratory of Metal-Organic Molecular Materials and Devices, Kunming University, Kunming 650214, China
- National Laboratory of Solid State Microstructures, Department of Physics, Nanjing University, Nanjing 210093, China
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14
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Nakai F, Masubuchi Y, Doi Y, Ishida T, Uneyama T. Fluctuating diffusivity emerges even in binary gas mixtures. Phys Rev E 2023; 107:014605. [PMID: 36797902 DOI: 10.1103/physreve.107.014605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2022] [Accepted: 12/22/2022] [Indexed: 01/19/2023]
Abstract
Diffusivity in some soft matter and biological systems changes with time, called the fluctuating diffusivity. In this work, we propose a novel origin for fluctuating diffusivity based on stochastic simulations of binary gas mixtures. In this system, the fraction of one component is significantly small, and the mass of the minor component molecule is different from that of the major component. The minor component exhibits fluctuating diffusivity when its mass is sufficiently smaller than that of the major component. We elucidate that this fluctuating diffusivity is caused by the time scale separation between the relaxation of the velocity direction and the speed of the minor component molecule.
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Affiliation(s)
- Fumiaki Nakai
- Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Yuichi Masubuchi
- Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Yuya Doi
- Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Takato Ishida
- Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
| | - Takashi Uneyama
- Department of Materials Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa, Nagoya 464-8603, Japan
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15
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Transport in the Brain Extracellular Space: Diffusion, but Which Kind? Int J Mol Sci 2022; 23:ijms232012401. [PMID: 36293258 PMCID: PMC9604357 DOI: 10.3390/ijms232012401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/26/2022] [Revised: 10/10/2022] [Accepted: 10/12/2022] [Indexed: 11/17/2022] Open
Abstract
The mechanisms of transport of substances in the brain parenchyma have been a hot topic in scientific discussion in the past decade. This discussion was triggered by the proposed glymphatic hypothesis, which assumes a directed flow of cerebral fluid within the parenchyma, in contrast to the previous notion that diffusion is the main mechanism. However, when discussing the issue of “diffusion or non-diffusion”, much less attention was given to the question that diffusion itself can have a different character. In our opinion, some of the recently published results do not fit into the traditional understanding of diffusion. In this regard, we outline the relevant new theoretical approaches on transport processes in complex random media such as concepts of diffusive diffusivity and time-dependent homogenization, which expands the understanding of the forms of transport of substances based on diffusion.
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16
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Xiong D, Wang J. Subdiffusive energy transport and antipersistent correlations due to the scattering of phonons and discrete breathers. Phys Rev E 2022; 106:L032201. [PMID: 36266887 DOI: 10.1103/physreve.106.l032201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/23/2021] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
While there are many physical processes showing subdiffusion and some useful particle models for understanding the underlying mechanisms have been established, a systematic study of subdiffusive energy transport is still lacking. Here we present convincing evidence that, in the range of system size investigated, the energy subdiffusion can take place in a Hamiltonian lattice system with both harmonic nearest-neighbor and anharmonic long-range interactions. In particular, we show that the interaction range dependence of antipersistent energy-current correlations are relevant to this special type of energy subdiffusion. The underlying mechanisms are related to the various scattering processes of phonons and discrete breathers. Our results shed light on understanding the extremely slow energy transport.
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Affiliation(s)
- Daxing Xiong
- MinJiang Collaborative Center for Theoretical Physics, College of Physics and Electronic Information Engineering, Minjiang University, Fuzhou 350108, China
| | - Jianjin Wang
- Department of Physics, Jiangxi Science and Technology Normal University, Nanchang 330013, Jiangxi, China
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17
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Joung H, Kim C, Yu J, Lee S, Paeng K, Yang J. Impact of Chain Conformation on Structural Heterogeneity in Polymer Network. NANO LETTERS 2022; 22:5487-5494. [PMID: 35748615 DOI: 10.1021/acs.nanolett.2c01574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Polymer networks generally consist of an ensemble of single chains. However, understanding how chain conformation affects the structure and properties of polymer networks remains a challenge for optimizing their functionality. Here, we present the fabrication and comparative study of a polymer network composed of collapsed self-entangled chains (intrachain entangled network) and a standard polymer network in which random-coil chains are entangled with each other (interchain entangled network). For poly(methyl methacrylate) thin films composed of these networks, we coupled solvent vapor swelling and single-molecule tracking techniques to examine the anomalies in the dynamics of a small-molecular probe included in the system. We demonstrate that when compared to the interchain entangled network the intrachain one exhibits a more substantial structural heterogeneity, particularly under highly crowded conditions. This network also exhibits physical compactness, which keeps the heterogeneous network structure frozen over time and impedes network plasticization through solvent uptake by the film.
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Affiliation(s)
- Hyeyoung Joung
- Department of Chemistry, Yonsei University, Wonju, Gangwon 26493, Korea
| | - Chanwoo Kim
- Department of Chemistry, Yonsei University, Wonju, Gangwon 26493, Korea
| | - Jaesang Yu
- Department of Chemistry, Yonsei University, Wonju, Gangwon 26493, Korea
| | - Soohyun Lee
- Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea
| | - Keewook Paeng
- Department of Chemistry, Sungkyunkwan University, Suwon 16419, Korea
| | - Jaesung Yang
- Department of Chemistry, Yonsei University, Wonju, Gangwon 26493, Korea
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18
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Šlepavičius J, Avendaño C, Conchúir BÓ, Patti A. Structural relaxation dynamics of colloidal nanotrimers. Phys Rev E 2022; 106:014604. [PMID: 35974591 DOI: 10.1103/physreve.106.014604] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2022] [Accepted: 06/29/2022] [Indexed: 06/15/2023]
Abstract
By Molecular Dynamics simulation, we investigate the dynamics of isotropic fluids of colloidal nanotrimers whose interactions are described by varying the strength of attractive and repulsive terms of the Mie potential. To provide a consistent comparison between the systems described by different force fields, we determine the phase diagram and critical points of each system, characterize the morphology of high-density liquid phases at the same reduced temperature and density, and finally investigate their long-time relaxation dynamics. In particular, we detect an especially complex dynamics that reveals the existence of slow and fast nanotrimers and the resulting occurrence of non-Gaussianity, which develops at intermediate timescales. Deviations from Gaussianity are temporary and vanish within the timescales of the system's density fluctuations decay, when a Fickian-like diffusion regime is eventually observed.
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Affiliation(s)
- Justinas Šlepavičius
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Carlos Avendaño
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Breanndán Ó Conchúir
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
- IBM Research Europe, The Hartree Centre STFC Laboratory Sci-Tech Daresbury Warrington, Warrington WA4 4AD, United Kingdom
| | - Alessandro Patti
- Department of Chemical Engineering, The University of Manchester, Manchester M13 9PL, United Kingdom
- Department of Applied Physics, University of Granada, Fuente Nueva s/n, 18071 Granada, Spain
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19
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Lu Y, Liu XY, Hu GH. Double-Spring Model for Nanoparticle Diffusion in a Polymer Network. Macromolecules 2022. [DOI: 10.1021/acs.macromol.2c00257] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Yu Lu
- School of Mechanics and Engineering Science, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, P. R. China
| | - Xin-Yue Liu
- School of Mechanics and Engineering Science, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, P. R. China
| | - Guo-Hui Hu
- School of Mechanics and Engineering Science, Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200444, P. R. China
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20
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Rusciano F, Pastore R, Greco F. Fickian Non-Gaussian Diffusion in Glass-Forming Liquids. PHYSICAL REVIEW LETTERS 2022; 128:168001. [PMID: 35522520 DOI: 10.1103/physrevlett.128.168001] [Citation(s) in RCA: 24] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/15/2021] [Accepted: 03/09/2022] [Indexed: 05/23/2023]
Abstract
Fickian yet non-Gaussian diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated with some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct timescales for Fickianity, τ_{F}, and for restoring of Gaussianity, τ_{G}>τ_{F}, as well as their associated length scales, ξ_{F} and ξ_{G}. We find τ_{G}∝τ_{F}^{γ} with γ≃1.8 for both systems. In the deep FnGD regime, the displacement distributions display exponential tails. We show that, in simulations, the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master curve [l(t)/(ξ_{G})]∝(t/τ_{G})^{α}, with α=0.33. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent α. We further discuss the connections of the timescales and length scales characterizing FnGD with structural relaxation and dynamic heterogeneity.
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Affiliation(s)
- Francesco Rusciano
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
| | - Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
| | - Francesco Greco
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, Piazzale Tecchio 80, Napoli 80125, Italy
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21
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Nampoothiri S, Orlandini E, Seno F, Baldovin F. Polymers critical point originates Brownian non-Gaussian diffusion. Phys Rev E 2022; 104:L062501. [PMID: 35030826 DOI: 10.1103/physreve.104.l062501] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/08/2021] [Accepted: 12/11/2021] [Indexed: 01/04/2023]
Abstract
We demonstrate that size fluctuations close to polymers critical point originate the non-Gaussian diffusion of their center of mass. Static universal exponents γ and ν-depending on the polymer topology, on the dimension of the embedding space, and on equilibrium phase-concur to determine the potential divergency of a dynamic response, epitomized by the center-of-mass kurtosis. Prospects in experiments and stochastic modeling brought about by this result are briefly outlined.
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Affiliation(s)
- Sankaran Nampoothiri
- Dipartimento di Fisica e Astronomia "G. Galilei"-DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Enzo Orlandini
- Dipartimento di Fisica e Astronomia "G. Galilei"-DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Flavio Seno
- Dipartimento di Fisica e Astronomia "G. Galilei"-DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
| | - Fulvio Baldovin
- Dipartimento di Fisica e Astronomia "G. Galilei"-DFA, Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova (PD), Italy
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22
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Pastore R, Ciarlo A, Pesce G, Sasso A, Greco F. A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter. SOFT MATTER 2022; 18:351-364. [PMID: 34888591 DOI: 10.1039/d1sm01133b] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξf and tf. We find that ξf stays constant, whereas tf grows as the inverse of the long-time diffusion coefficient tf ∝ D-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.
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Affiliation(s)
- Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, Italy.
| | - Antonio Ciarlo
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Giuseppe Pesce
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Antonio Sasso
- Department of Physics E. Pancini, University of Naples Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, 80126 Napoli, Italy
| | - Francesco Greco
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, 80125 Napoli, Italy.
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23
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Bley M, Hurtado PI, Dzubiella J, Moncho-Jordá A. Active interaction switching controls the dynamic heterogeneity of soft colloidal dispersions. SOFT MATTER 2022; 18:397-411. [PMID: 34904609 DOI: 10.1039/d1sm01507a] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
We employ Reactive Dynamical Density Functional Theory (R-DDFT) and Reactive Brownian Dynamics (R-BD) simulations to investigate the dynamics of a suspension of active soft Gaussian colloids with binary interaction switching, i.e., a one-component colloidal system in which every particle stochastically switches at predefined rates between two interaction states with different mobility. Using R-DDFT we extend a theory previously developed to access the dynamics of inhomogeneous liquids [Archer et al., Phys. Rev. E: Stat., Nonlinear, Soft Matter Phys., 2007, 75, 040501] to study the influence of the switching activity on the self and distinct part of the Van Hove function in bulk solution, and determine the corresponding mean squared displacement of the switching particles. Our results demonstrate that, even though the average diffusion coefficient is not affected by the switching activity, it significantly modifies the non-equilibrium dynamics and diffusion coefficients of the individual particles, leading to a crossover from short to long times, with a regime for intermediate times showing anomalous diffusion. In addition, the self-part of the van Hove function has a Gaussian form at short and long times, but becomes non-Gaussian at intermediates ones, having a crossover between short and large displacements. The corresponding self-intermediate scattering function shows the two-step relaxation patters typically observed in soft materials with heterogeneous dynamics such as glasses and gels. We also introduce a phenomenological Continuous Time Random Walk (CTRW) theory to understand the heterogeneous diffusion of this system. R-DDFT results are in excellent agreement with R-BD simulations and the analytical predictions of CTRW theory, thus confirming that R-DDFT constitutes a powerful method to investigate not only the structure and phase behavior, but also the dynamical properties of non-equilibrium active switching colloidal suspensions.
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Affiliation(s)
- Michael Bley
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Straße 3, D-79104 Freiburg, Germany.
| | - Pablo I Hurtado
- Departamento de Electromagnetismo y Física de la Materia, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
- Institute Carlos I for Theoretical and Computational Physics, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain.
| | - Joachim Dzubiella
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder Straße 3, D-79104 Freiburg, Germany.
- Research Group for Simulations of Energy Materials, Helmholtz-Zentrum Berlin für Materialien und Energie, D-14109 Berlin, Germany
| | - Arturo Moncho-Jordá
- Institute Carlos I for Theoretical and Computational Physics, Facultad de Ciencias, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain.
- Departamento de Física Aplicada, Universidad de Granada, Campus Fuentenueva S/N, 18071 Granada, Spain
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24
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Pacheco-Pozo A, Sokolov IM. Convergence to a Gaussian by Narrowing of Central Peak in Brownian yet Non-Gaussian Diffusion in Disordered Environments. PHYSICAL REVIEW LETTERS 2021; 127:120601. [PMID: 34597078 DOI: 10.1103/physrevlett.127.120601] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/19/2021] [Revised: 07/28/2021] [Accepted: 08/10/2021] [Indexed: 06/13/2023]
Abstract
In usual diffusion, the concentration profile, starting from an initial distribution showing sharp features, first gets smooth and then converges to a Gaussian. By considering several examples, we show that the art of convergence to a Gaussian in diffusion in disordered media with infinite contrast may be strikingly different: sharp features of initial distribution do not smooth out at long times. This peculiarity of the strong disorder may be of importance for diagnostics of disorder in complex, e.g., biological, systems.
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Affiliation(s)
- Adrian Pacheco-Pozo
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
| | - Igor M Sokolov
- Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin, Germany
- IRIS Adlershof, Zum Großen Windkanal 2, D-12489 Berlin, Germany
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25
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Uttieri M, Hinow P, Pastore R, Bianco G, Ribera d'Alcalá M, Mazzocchi MG. Homeostatic swimming of zooplankton upon crowding: the case of the copepod Centropages typicus. J R Soc Interface 2021; 18:20210270. [PMID: 34157893 DOI: 10.1098/rsif.2021.0270] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Abstract
Crowding has a major impact on the dynamics of many material and biological systems, inducing effects as diverse as glassy dynamics and swarming. While this issue has been deeply investigated for a variety of living organisms, more research remains to be done on the effect of crowding on the behaviour of copepods, the most abundant metazoans on Earth. To this aim, we experimentally investigate the swimming behaviour, used as a dynamic proxy of animal adaptations, of males and females of the calanoid copepod Centropages typicus at different densities of individuals (10, 50 and 100 ind. l-1) by performing three-dimensional single-organism tracking. We find that the C. typicus motion is surprisingly unaffected by crowding over the investigated density range. Indeed, the mean square displacements as a function of time always show a crossover from ballistic to Fickian regime, with poor variations of the diffusion constant on increasing the density. Close to the crossover, the displacement distributions display exponential tails with a nearly density-independent decay length. The trajectory fractal dimension, D3D ≅ 1.5, and the recently proposed 'ecological temperature' also remain stable on increasing the individual density. This suggests that, at least over the range of animal densities used, crowding does not impact on the characteristics of C. typicus swimming motion, and that a homeostatic mechanism preserves the stability of its swimming performance.
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Affiliation(s)
- Marco Uttieri
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, Naples 80121, Italy.,CoNISMa, ULR Partehnope, Piazzale Flaminio 9, Rome 00196, Italy
| | - Peter Hinow
- Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, WI 53201, USA
| | - Raffaele Pastore
- Department of Chemical, Materials and Production Engineering, University of Naples Federico II, P.le Tecchio 80, Napoli 80125, Italy
| | - Giuseppe Bianco
- Department of Biology, Lund University, Sölvegatan 37, Lund 22362, Sweden
| | - Maurizio Ribera d'Alcalá
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, Naples 80121, Italy
| | - Maria Grazia Mazzocchi
- Department of Integrative Marine Ecology, Stazione Zoologica Anton Dohrn, Villa Comunale, Naples 80121, Italy
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