1
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Zhang Y. Examples of atoms absorbing photon via Schrödinger equation and vacuum fluctuations. Sci Rep 2024; 14:983. [PMID: 38200170 PMCID: PMC10781713 DOI: 10.1038/s41598-024-51411-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2023] [Accepted: 01/04/2024] [Indexed: 01/12/2024] Open
Abstract
The absorption of photons by atoms encompasses fundamental quantum mechanical aspects, particularly the emergence of randomness to account for the inherent unpredictability in absorption outcomes. We demonstrate that vacuum fluctuations can be the origin of this randomness. An illustrative example of this is the absorption of a single photon by two symmetrically arranged atoms. In the absence of a mechanism to introduce randomness, the Schrödinger equation alone can govern the time evolution of the process initially. Then, it becomes stuck, and an entangled state of the two atoms emerges. This entangled state consists of two components: in one, the first atom is excited by the photon while the second is in the ground state, and in the other, the second atom is excited while the first remains in the ground state. These components form a superposition state characterized by an unbreakable symmetry in the absence of external influences. Consequently, the absorption process remains incomplete. When vacuum fluctuations come into play, they can induce fluctuations in the weights of these components, akin to Brownian motion. Over time, one component diminishes, thereby breaking the entanglement between the two atoms and allowing the photon absorption process to conclude. The remaining component shows which atom completes the photon absorption. Vacuum fluctuations not only introduce randomness but also have the potential to give rise to the Born rule in this context. Furthermore, the Casimir effect, which is closely tied to vacuum fluctuations, presents a promising experimental avenue for validating this mechanism. Similar studies can also be conducted with varying numbers of atoms.
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Affiliation(s)
- Yongjun Zhang
- Science College, Liaoning Technical University, Fuxin, 123000, China.
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2
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Li Y, Suleiman K, Xu Y. Anomalous diffusion, non-Gaussianity, nonergodicity, and confinement in stochastic-scaled Brownian motion with diffusing diffusivity dynamics. Phys Rev E 2024; 109:014139. [PMID: 38366530 DOI: 10.1103/physreve.109.014139] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/14/2023] [Accepted: 12/07/2023] [Indexed: 02/18/2024]
Abstract
Scaled Brownian motions (SBMs) with power-law time-dependent diffusivity have been used to describe various types of anomalous diffusion yet Gaussian observed in granular gases kinetics, turbulent diffusion, and molecules mobility in cells, to name a few. However, some of these systems may exhibit non-Gaussian behavior which can be described by SBM with diffusing diffusivity (DD-SBM). Here, we numerically investigate both free and confined DD-SBM models characterized by fixed or stochastic scaling exponent of time-dependent diffusivity. The effects of distributed scaling exponent, random diffusivity, and confinement are considered. Different regimes of ultraslow diffusion, subdiffusion, normal diffusion, and superdiffusion are observed. In addition, weak ergodic and non-Gaussian behaviors are also detected. These results provide insights into diffusion in time-fluctuating diffusivity landscapes with potential applications to time-dependent temperature systems spreading in heterogeneous environments.
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Affiliation(s)
- Yongge Li
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Kheder Suleiman
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
| | - Yong Xu
- School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China
- MOE Key Laboratory for Complexity Science in Aerospace, Northwestern Polytechnical University, Xi'an 710072, China
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3
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Rusch R, Franosch T, Jung G. Noise-cancellation algorithm for simulations of Brownian particles. Phys Rev E 2024; 109:015303. [PMID: 38366417 DOI: 10.1103/physreve.109.015303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2023] [Accepted: 12/12/2023] [Indexed: 02/18/2024]
Abstract
We investigate the usage of a recently introduced noise-cancellation algorithm for Brownian simulations to enhance the precision of measuring transport properties such as the mean-square displacement or the velocity-autocorrelation function. The algorithm is based on explicitly storing the pseudorandom numbers used to create the randomized displacements in computer simulations and subtracting them from the simulated trajectories. The resulting correlation function of the reduced motion is connected to the target correlation function up to a cross-correlation term. Using analytical theory and computer simulations, we demonstrate that the cross-correlation term can be neglected in all three systems studied in this paper. We further expand the algorithm to Monte Carlo simulations and analyze the performance of the algorithm and rationalize that it works particularly well for unbounded, weakly interacting systems in which the precision of the mean-square displacement can be improved by orders of magnitude.
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Affiliation(s)
- Regina Rusch
- Institut für Theoretische Physik, Technikerstraße 21-A, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Thomas Franosch
- Institut für Theoretische Physik, Technikerstraße 21-A, Universität Innsbruck, A-6020 Innsbruck, Austria
| | - Gerhard Jung
- Laboratoire Charles Coulomb (L2C), Université de Montpellier, Centre National de la Recherche Scientifique, 34095 Montpellier, France
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4
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Dupont N, Gabardos L, Arrouas F, Ombredane N, Billy J, Peaudecerf B, Guéry-Odelin D. Hamiltonian Ratchet for Matter-Wave Transport. PHYSICAL REVIEW LETTERS 2023; 131:133401. [PMID: 37832021 DOI: 10.1103/physrevlett.131.133401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2023] [Revised: 07/26/2023] [Accepted: 08/15/2023] [Indexed: 10/15/2023]
Abstract
We report on the design of a Hamiltonian ratchet exploiting periodically at rest integrable trajectories in the phase space of a modulated periodic potential, leading to the linear nondiffusive transport of particles. Using Bose-Einstein condensates in a modulated one-dimensional optical lattice, we make the first observations of this spatial ratchet, which provides way to coherently transport matter waves with possible applications in quantum technologies. In the semiclassical regime, the quantum transport strongly depends on the effective Planck constant due to Floquet state mixing. We also demonstrate the interest of quantum optimal control for efficient initial state preparation into the transporting Floquet states to enhance the transport periodicity.
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Affiliation(s)
- N Dupont
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
- Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium
| | - L Gabardos
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - F Arrouas
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - N Ombredane
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - J Billy
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - B Peaudecerf
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
| | - D Guéry-Odelin
- Laboratoire Collisions Agrégats Réactivité, UMR 5589, FERMI, UT3, Université de Toulouse, CNRS, 118 Route de Narbonne, 31062 Toulouse CEDEX 09, France
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5
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Liang Y, Wang W, Metzler R. Anomalous diffusion, non-Gaussianity, and nonergodicity for subordinated fractional Brownian motion with a drift. Phys Rev E 2023; 108:024143. [PMID: 37723819 DOI: 10.1103/physreve.108.024143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Accepted: 08/11/2023] [Indexed: 09/20/2023]
Abstract
The stochastic motion of a particle with long-range correlated increments (the moving phase) which is intermittently interrupted by immobilizations (the trapping phase) in a disordered medium is considered in the presence of an external drift. In particular, we consider trapping events whose times follow a scale-free distribution with diverging mean trapping time. We construct this process in terms of fractional Brownian motion with constant forcing in which the trapping effect is introduced by the subordination technique, connecting "operational time" with observable "real time." We derive the statistical properties of this process such as non-Gaussianity and nonergodicity, for both ensemble and single-trajectory (time) averages. We demonstrate nice agreement with extensive simulations for the probability density function, skewness, kurtosis, as well as ensemble and time-averaged mean-squared displacements. We place a specific emphasis on the comparisons between the cases with and without drift.
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Affiliation(s)
- Yingjie Liang
- College of Mechanics and Materials, Hohai University, 211100 Nanjing, China
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Wei Wang
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
| | - Ralf Metzler
- University of Potsdam, Institute of Physics and Astronomy, 14476 Potsdam-Golm, Germany
- Asia Pacific Centre for Theoretical Physics, Pohang 37673, Republic of Korea
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6
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Ulbrich JA, Fernández-Rico C, Rost B, Vialetto J, Isa L, Urbach JS, Dullens RPA. Effect of curvature on the diffusion of colloidal bananas. Phys Rev E 2023; 107:L042602. [PMID: 37198802 DOI: 10.1103/physreve.107.l042602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Accepted: 02/22/2023] [Indexed: 05/19/2023]
Abstract
Anisotropic colloidal particles exhibit complex dynamics which play a crucial role in their functionality, transport, and phase behavior. In this Letter, we investigate the two-dimensional diffusion of smoothly curved colloidal rods-also known as colloidal bananas-as a function of their opening angle α. We measure the translational and rotational diffusion coefficients of the particles with opening angles ranging from 0^{∘} (straight rods) to nearly 360^{∘}(closed rings). In particular, we find that the anisotropic diffusion of the particles varies nonmonotonically with their opening angle and that the axis of fastest diffusion switches from the long to the short axis of the particles when α>180^{∘}. We also find that the rotational diffusion coefficient of nearly closed rings is approximately an order of magnitude higher than that of straight rods of the same length. Finally, we show that the experimental results are consistent with slender body theory, indicating that the dynamical behavior of the particles arises primarily from their local drag anisotropy. These results highlight the impact of curvature on the Brownian motion of elongated colloidal particles, which must be taken into account when seeking to understand the behavior of curved colloidal particles.
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Affiliation(s)
- Justin-Aurel Ulbrich
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Carla Fernández-Rico
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Brian Rost
- Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA
| | - Jacopo Vialetto
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Lucio Isa
- Department of Materials, ETH Zürich, 8093 Zurich, Switzerland
| | - Jeffrey S Urbach
- Department of Physics and Institute for Soft Matter Synthesis and Metrology, Georgetown University, Washington, DC 20057, USA
| | - Roel P A Dullens
- Department of Chemistry, Physical and Theoretical Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
- Institute for Molecules and Materials, Radboud University, Heyendaalseweg 135, 6525 AJ Nijmegen, The Netherlands
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7
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Spiechowicz J, Marchenko IG, Hänggi P, Łuczka J. Diffusion Coefficient of a Brownian Particle in Equilibrium and Nonequilibrium: Einstein Model and Beyond. ENTROPY (BASEL, SWITZERLAND) 2022; 25:42. [PMID: 36673183 PMCID: PMC9857877 DOI: 10.3390/e25010042] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/24/2022] [Revised: 12/21/2022] [Accepted: 12/21/2022] [Indexed: 06/17/2023]
Abstract
The diffusion of small particles is omnipresent in many processes occurring in nature. As such, it is widely studied and exerted in almost all branches of sciences. It constitutes such a broad and often rather complex subject of exploration that we opt here to narrow our survey to the case of the diffusion coefficient for a Brownian particle that can be modeled in the framework of Langevin dynamics. Our main focus centers on the temperature dependence of the diffusion coefficient for several fundamental models of diverse physical systems. Starting out with diffusion in equilibrium for which the Einstein theory holds, we consider a number of physical situations outside of free Brownian motion and end by surveying nonequilibrium diffusion for a time-periodically driven Brownian particle dwelling randomly in a periodic potential. For this latter situation the diffusion coefficient exhibits an intriguingly non-monotonic dependence on temperature.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
| | - Ivan G. Marchenko
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
- Kharkiv Institute of Physics and Technology, 61108 Kharkiv, Ukraine
- Education and Research Institute of Computer Physics and Energy, Karazin Kharkiv National University, 61022 Kharkiv, Ukraine
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Max-Planck Institute for Physics of Complex Systems, 01187 Dresden, Germany
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia in Katowice, 41-500 Chorzów, Poland
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8
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Pedergnana T, Noiray N. Exact potentials in multivariate Langevin equations. CHAOS (WOODBURY, N.Y.) 2022; 32:123146. [PMID: 36587313 DOI: 10.1063/5.0124031] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/02/2022] [Accepted: 12/01/2022] [Indexed: 06/17/2023]
Abstract
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the Jacobian matrix of the mapping. In this work, a detailed analysis of the transformation rules for Langevin equations under general nonlinear mappings is presented. We show how to identify systems with exact potentials by understanding their differential-geometric properties. To demonstrate the power of our method, we use it to derive exact potentials for broadly studied models of nonlinear deterministic and stochastic oscillations. In selected examples, we visualize the identified potentials. Our results imply a broad class of exactly solvable stochastic models, which can be self-consistently defined from given deterministic gradient systems.
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Affiliation(s)
- Tiemo Pedergnana
- CAPS Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, Sonneggstrasse 3, 8092 Zürich, Switzerland
| | - Nicolas Noiray
- CAPS Laboratory, Department of Mechanical and Process Engineering, ETH Zürich, Sonneggstrasse 3, 8092 Zürich, Switzerland
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9
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Granek O, Kafri Y, Tailleur J. Anomalous Transport of Tracers in Active Baths. PHYSICAL REVIEW LETTERS 2022; 129:038001. [PMID: 35905354 DOI: 10.1103/physrevlett.129.038001] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Revised: 12/23/2021] [Accepted: 06/21/2022] [Indexed: 06/15/2023]
Abstract
We derive the long-time dynamics of a tracer immersed in a one-dimensional active bath. In contrast to previous studies, we find that the damping and noise correlations possess long-time tails with exponents that depend on the tracer symmetry. For generic tracers, shape asymmetry induces ratchet effects that alter fluctuations and lead to superdiffusion and friction that grows with time when the tracer is dragged at a constant speed. In the singular limit of a completely symmetric tracer, we recover normal diffusion and finite friction. Furthermore, for small symmetric tracers, the active contribution to the friction becomes negative: active particles enhance motion rather than oppose it. These results show that, in low-dimensional systems, the motion of a passive tracer in an active bath cannot be modeled as a persistent random walker with a finite correlation time.
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Affiliation(s)
- Omer Granek
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Yariv Kafri
- Department of Physics, Technion-Israel Institute of Technology, Haifa 3200003, Israel
| | - Julien Tailleur
- Université de Paris, Laboratoire Matière et Systèmes Complexes (MSC), UMR 7057 CNRS, F-75205 Paris, France
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10
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Joo R, Picardi S, Boone ME, Clay TA, Patrick SC, Romero-Romero VS, Basille M. Recent trends in movement ecology of animals and human mobility. MOVEMENT ECOLOGY 2022; 10:26. [PMID: 35614458 PMCID: PMC9134608 DOI: 10.1186/s40462-022-00322-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/29/2021] [Accepted: 04/07/2022] [Indexed: 06/15/2023]
Abstract
Movement is fundamental to life, shaping population dynamics, biodiversity patterns, and ecosystem structure. In 2008, the movement ecology framework (MEF Nathan et al. in PNAS 105(49):19052-19059, 2008) introduced an integrative theory of organismal movement-linking internal state, motion capacity, and navigation capacity to external factors-which has been recognized as a milestone in the field. Since then, the study of movement experienced a technological boom, which provided massive quantities of tracking data of both animal and human movement globally and at ever finer spatio-temporal resolutions. In this work, we provide a quantitative assessment of the state of research within the MEF, focusing on animal movement, including humans and invertebrates, and excluding movement of plants and microorganisms. Using a text mining approach, we digitally scanned the contents of [Formula: see text] papers from 2009 to 2018 available online, identified tools and methods used, and assessed linkages between all components of the MEF. Over the past decade, the publication rate has increased considerably, along with major technological changes, such as an increased use of GPS devices and accelerometers and a majority of studies now using the R software environment for statistical computing. However, animal movement research still largely focuses on the effect of environmental factors on movement, with motion and navigation continuing to receive little attention. A search of topics based on words featured in abstracts revealed a clustering of papers among marine and terrestrial realms, as well as applications and methods across taxa. We discuss the potential for technological and methodological advances in the field to lead to more integrated and interdisciplinary research and an increased exploration of key movement processes such as navigation, as well as the evolutionary, physiological, and life-history consequences of movement.
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Affiliation(s)
- Rocío Joo
- Department of Wildlife Ecology and Conservation, Fort Lauderdale Research and Education Center, University of Florida, Fort Lauderdale, FL USA
- Global Fishing Watch, Washington DC, USA
| | - Simona Picardi
- Department of Wildlife Ecology and Conservation, Fort Lauderdale Research and Education Center, University of Florida, Fort Lauderdale, FL USA
- Jack H. Berryman Institute and Department of Wildland Resources, S.J. & Jessie E. Quinney College of Natural Resources, Utah State University, Logan, UT USA
| | - Matthew E. Boone
- Department of Wildlife Ecology and Conservation, Fort Lauderdale Research and Education Center, University of Florida, Fort Lauderdale, FL USA
| | - Thomas A. Clay
- School of Environmental Sciences, University of Liverpool, Liverpool, UK
- Institute of Marine Sciences, University of California Santa Cruz, Santa Cruz, CA USA
| | | | - Vilma S. Romero-Romero
- Systems Engineering, Faculty of Engineering and Architecture, University of Lima, Lima, Peru
| | - Mathieu Basille
- Department of Wildlife Ecology and Conservation, Fort Lauderdale Research and Education Center, University of Florida, Fort Lauderdale, FL USA
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11
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Fick diffusion coefficients via molecular dynamics: An alternative approach in the Fourier domain. J Mol Liq 2021. [DOI: 10.1016/j.molliq.2021.115460] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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12
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Bao JD, Wang XR, Liu WM. Ergodic time scale and transitive dynamics in single-particle tracking. Phys Rev E 2021; 103:032136. [PMID: 33862786 DOI: 10.1103/physreve.103.032136] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2020] [Accepted: 02/26/2021] [Indexed: 11/07/2022]
Abstract
We investigate ergodic time scales in single-particle tracking by introducing a covariance measure Ω(Δ;t) for the time-averaged relative square displacement recorded in lag-time Δ at elapsed time t. The present model is established in the generalized Langevin equation with a power-law memory function. The ratio Ω(Δ;Δ)/Ω(Δ;t) is shown to obey a universal scaling law for long but finite times and is used to extract the effective ergodic time. We derive a finite-time-averaged Green-Kubo relation and find that, to control the deviations in measurement results from ensemble averages, the ratio Δ/t must be neither too small nor close to unity. Our paper connects the experimental self-averaging property of a tracer with the theoretic velocity autocorrelation function and sheds light on the transition to ergodicity.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, China
| | - Xiang-Rong Wang
- Department of Physics, The Hong Kong University of Science and Technology, Kowloon, Hong Kong, China
| | - Wu-Ming Liu
- Institute of Physics, Chinese Academy of Science, Beijing 100190, China
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13
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Wittmann R, Löwen H, Brader JM. Order-preserving dynamics in one dimension – single-file diffusion and caging from the perspective of dynamical density functional theory. Mol Phys 2021. [DOI: 10.1080/00268976.2020.1867250] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
Affiliation(s)
- René Wittmann
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Hartmut Löwen
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Düsseldorf, Germany
| | - Joseph M. Brader
- Department of Physics, University of Fribourg, Fribourg, Switzerland
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14
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Abstract
Superstatistical approaches have played a crucial role in the investigations of mixtures of Gaussian processes. Such approaches look to describe non-Gaussian diffusion emergence in single-particle tracking experiments realized in soft and biological matter. Currently, relevant progress in superstatistics of Gaussian diffusion processes has been investigated by applying χ2-gamma and χ2-gamma inverse superstatistics to systems of particles in a heterogeneous environment whose diffusivities are randomly distributed; such situations imply Brownian yet non-Gaussian diffusion. In this paper, we present how the log-normal superstatistics of diffusivities modify the density distribution function for two types of mixture of Brownian processes. Firstly, we investigate the time evolution of the ensemble of Brownian particles with random diffusivity through the analytical and simulated points of view. Furthermore, we analyzed approximations of the overall probability distribution for log-normal superstatistics of Brownian motion. Secondly, we propose two models for a mixture of scaled Brownian motion and to analyze the log-normal superstatistics associated with them, which admits an anomalous diffusion process. The results found in this work contribute to advances of non-Gaussian diffusion processes and superstatistical theory.
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15
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Mazaheri M, Ehrig J, Shkarin A, Zaburdaev V, Sandoghdar V. Ultrahigh-Speed Imaging of Rotational Diffusion on a Lipid Bilayer. NANO LETTERS 2020; 20:7213-7219. [PMID: 32786953 PMCID: PMC7564080 DOI: 10.1021/acs.nanolett.0c02516] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We studied the rotational and translational diffusion of a single gold nanorod linked to a supported lipid bilayer with ultrahigh temporal resolution of two microseconds. By using a home-built polarization-sensitive dark-field microscope, we recorded particle trajectories with lateral precision of 3 nm and rotational precision of 4°. The large number of trajectory points in our measurements allows us to characterize the statistics of rotational diffusion with unprecedented detail. Our data show apparent signatures of anomalous diffusion such as sublinear scaling of the mean-squared angular displacement and negative values of angular correlation function at small lag times. However, a careful analysis reveals that these effects stem from the residual noise contributions and confirms normal diffusion. Our experimental approach and observations can be extended to investigate diffusive processes of anisotropic nanoparticles in other fundamental systems such as cellular membranes or other two-dimensional fluids.
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Affiliation(s)
- Mahdi Mazaheri
- Max
Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Jens Ehrig
- Max
Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Alexey Shkarin
- Max
Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
| | - Vasily Zaburdaev
- Department
of Biology, Friedrich Alexander University
Erlangen-Nürnberg, Staudtstraße 5, 91058 Erlangen, Germany
- Max-Planck-Zentrum
für Physik und Medizin, 91058 Erlangen, Germany
| | - Vahid Sandoghdar
- Max
Planck Institute for the Science of Light, Staudtstraße 2, 91058 Erlangen, Germany
- Max-Planck-Zentrum
für Physik und Medizin, 91058 Erlangen, Germany
- Department
of Physics, Friedrich Alexander University
Erlangen-Nürnberg, Staudtstraße 5, 91058 Erlangen, Germany
- E-mail:
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16
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Bao JD. Generalization of the Kubo relation for confined motion and ergodicity breakdown. Phys Rev E 2020; 101:062131. [PMID: 32688488 DOI: 10.1103/physreve.101.062131] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2019] [Accepted: 05/07/2020] [Indexed: 06/11/2023]
Abstract
A time-dependent generalized Kubo relation is derived by introducing the notion of a diffusion function for a particle confined in a harmonic potential. The relation reduces to the standard Kubo relation as a special case but holds for anomalous diffusion, nonergodic processes, and bounded motion. We analyze in detail the behaviors of the diffusion and memory functions and report a generalized Stokes-Einstein relation concerning anomalous diffusion. Furthermore, we demonstrate that when a high finite-frequency cutoff is imposed on the noise spectral density, a breakdown in ergodicity accompanied by the appearance of nonstationarity in the velocity autocorrelation function occurs in forced systems. This breakdown is taken as explicit evidence for either decay-spring-memory or recovering-force effects leading to nonexponential relaxation kinematics.
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Affiliation(s)
- Jing-Dong Bao
- Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China
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17
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Funo K, Lambert N, Nori F, Flindt C. Shortcuts to Adiabatic Pumping in Classical Stochastic Systems. PHYSICAL REVIEW LETTERS 2020; 124:150603. [PMID: 32357046 DOI: 10.1103/physrevlett.124.150603] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
Adiabatic pumping is characterized by a geometric contribution to the pumped charge, which can be nonzero even in the absence of a bias. However, as the driving speed is increased, nonadiabatic excitations gradually reduce the pumped charge, thereby limiting the maximal applicable driving frequencies. To circumvent this problem, we here extend the concept of shortcuts to adiabaticity to construct a control protocol which enables geometric pumping well beyond the adiabatic regime. Our protocol allows for an increase, by more than an order of magnitude, in the driving frequencies, and the method is also robust against moderate fluctuations of the control field. We provide a geometric interpretation of the control protocol and analyze the thermodynamic cost of implementing it. Our findings can be realized using current technology and potentially enable fast pumping of charge or heat in quantum dots, as well as in other stochastic systems from physics, chemistry, and biology.
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Affiliation(s)
- Ken Funo
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Neill Lambert
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
| | - Franco Nori
- Theoretical Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
- Physics Department, The University of Michigan, Ann Arbor, Michigan 48109-1040, USA
| | - Christian Flindt
- Department of Applied Physics, Aalto University, 00076 Aalto, Finland
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18
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dos Santos TJ, Abreu CR, Horta BA, Tavares FW. Self-diffusion coefficients of methane/n-hexane mixtures at high pressures: An evaluation of the finite-size effect and a comparison of force fields. J Supercrit Fluids 2020. [DOI: 10.1016/j.supflu.2019.104639] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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19
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Han L, Chernyak V, Yan YA, Zheng X, Yan Y. Stochastic Representation of Non-Markovian Fermionic Quantum Dissipation. PHYSICAL REVIEW LETTERS 2019; 123:050601. [PMID: 31491295 DOI: 10.1103/physrevlett.123.050601] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/26/2018] [Indexed: 06/10/2023]
Abstract
Quantum Brownian motion plays a fundamental role in many areas of modern physics. In the path-integral formulation, environmental fluctuations can be characterized by auxiliary stochastic fields. Intriguingly, for fermionic environments the stochastic fields must be Grassmann valued so as to memorize the order of the random forces exerted on the system. Such nonclassical fields cannot be represented by conventional means. We propose a strategy to map the Grassmann-number fields to conventional c-number noises and a set of quantized pseudolevels. The resulting stochastic equation of motion (SEOM) enables direct stochastic simulation of the fermionic dissipative dynamics. The SEOM gives exact physical observables of noninteracting systems, and yields accurate approximate results for interacting systems. The practicality and accuracy of the proposed strategy and the SEOM are exemplified by numerical studies conducted on a single-impurity Anderson model.
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Affiliation(s)
- Lu Han
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Vladimir Chernyak
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, China
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
| | - Yun-An Yan
- School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics & CAS Center for Excellence in Nanoscience, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei, Anhui 230026, China
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20
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Diniz RMB, Cressoni JC, da Silva MAA, Mariz AM, de Araújo JM. Narrow log-periodic modulations in non-Markovian random walks. Phys Rev E 2017; 96:062143. [PMID: 29347279 DOI: 10.1103/physreve.96.062143] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/10/2017] [Indexed: 11/07/2022]
Abstract
What are the necessary ingredients for log-periodicity to appear in the dynamics of a random walk model? Can they be subtle enough to be overlooked? Previous studies suggest that long-range damaged memory and negative feedback together are necessary conditions for the emergence of log-periodic oscillations. The role of negative feedback would then be crucial, forcing the system to change direction. In this paper we show that small-amplitude log-periodic oscillations can emerge when the system is driven by positive feedback. Due to their very small amplitude, these oscillations can easily be mistaken for numerical finite-size effects. The models we use consist of discrete-time random walks with strong memory correlations where the decision process is taken from memory profiles based either on a binomial distribution or on a delta distribution. Anomalous superdiffusive behavior and log-periodic modulations are shown to arise in the large time limit for convenient choices of the models parameters.
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Affiliation(s)
- R M B Diniz
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil
| | - J C Cressoni
- Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, SP, Brazil.,Instituto de Física, Universidade Federal de Alagoas, Maceió, AL, 57072-970, Brazil
| | - M A A da Silva
- Departamento de Física e Química, FCFRP, Universidade de São Paulo, 14040-903 Ribeirão Preto, SP, Brazil
| | - A M Mariz
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil
| | - J M de Araújo
- Departamento de Física Teórica e Experimental, Universidade Federal do Rio Grande do Norte, Natal, RN, 59078-900, Brazil
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21
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Subdiffusion via dynamical localization induced by thermal equilibrium fluctuations. Sci Rep 2017; 7:16451. [PMID: 29184075 PMCID: PMC5705761 DOI: 10.1038/s41598-017-16601-0] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/09/2017] [Accepted: 11/15/2017] [Indexed: 12/03/2022] Open
Abstract
We reveal the mechanism of subdiffusion which emerges in a straightforward, one dimensional classical nonequilibrium dynamics of a Brownian ratchet driven by both a time-periodic force and Gaussian white noise. In a tailored parameter set for which the deterministic counterpart is in a non-chaotic regime, subdiffusion is a long-living transient whose lifetime can be many, many orders of magnitude larger than characteristic time scales of the setup thus being amenable to experimental observations. As a reason for this subdiffusive behaviour in the coordinate space we identify thermal noise induced dynamical localization in the velocity (momentum) space. This novel idea is distinct from existing knowledge and has never been reported for any classical or quantum system. It suggests reconsideration of generally accepted opinion that subdiffusion is due to broad distributions or strong correlations which reflect disorder, trapping, viscoelasticity of the medium or geometrical constraints.
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22
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Fang X, Vitrac O. Predicting diffusion coefficients of chemicals in and through packaging materials. Crit Rev Food Sci Nutr 2017; 57:275-312. [PMID: 25831407 DOI: 10.1080/10408398.2013.849654] [Citation(s) in RCA: 47] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Most of the physicochemical properties in polymers such as activity and partition coefficients, diffusion coefficients, and their activation with temperature are accessible to direct calculations from first principles. Such predictions are particularly relevant for food packaging as they can be used (1) to demonstrate the compliance or safety of numerous polymer materials and of their constitutive substances (e.g. additives, residues…), when they are used: as containers, coatings, sealants, gaskets, printing inks, etc. (2) or to predict the indirect contamination of food by pollutants (e.g. from recycled polymers, storage ambiance…) (3) or to assess the plasticization of materials in contact by food constituents (e.g. fat matter, aroma…). This review article summarizes the classical and last mechanistic descriptions of diffusion in polymers and discusses the reliability of semi-empirical approaches used for compliance testing both in EU and US. It is concluded that simulation of diffusion in or through polymers is not limited to worst-case assumptions but could also be applied to real cases for risk assessment, designing packaging with low leaching risk or to synthesize plastic additives with low diffusion rates.
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Affiliation(s)
- Xiaoyi Fang
- a AgroParisTech, UMR 1145 Ingénierie Procédés Aliments , Massy , France.,b INRA, UMR 1145 Ingénierie Procédés Aliments , Massy , France
| | - Olivier Vitrac
- a AgroParisTech, UMR 1145 Ingénierie Procédés Aliments , Massy , France.,b INRA, UMR 1145 Ingénierie Procédés Aliments , Massy , France
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23
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Abstract
We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.
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Affiliation(s)
- Xin Bian
- Division of Applied Mathematics, Brown University, Providence, RI 02912, USA.
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24
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Spiechowicz J, Łuczka J, Hänggi P. Transient anomalous diffusion in periodic systems: ergodicity, symmetry breaking and velocity relaxation. Sci Rep 2016; 6:30948. [PMID: 27492219 PMCID: PMC4974640 DOI: 10.1038/srep30948] [Citation(s) in RCA: 40] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2016] [Accepted: 07/11/2016] [Indexed: 11/18/2022] Open
Abstract
We study far from equilibrium transport of a periodically driven inertial Brownian particle moving in a periodic potential. As detected for a SQUID ratchet dynamics, the mean square deviation of the particle position from its average may involve three distinct intermediate, although extended diffusive regimes: initially as superdiffusion, followed by subdiffusion and finally, normal diffusion in the asymptotic long time limit. Even though these anomalies are transient effects, their lifetime can be many, many orders of magnitude longer than the characteristic time scale of the setup and turns out to be extraordinarily sensitive to the system parameters like temperature or the potential asymmetry. In the paper we reveal mechanisms of diffusion anomalies related to ergodicity of the system, symmetry breaking of the periodic potential and ultraslow relaxation of the particle velocity towards its steady state. Similar sequences of the diffusive behaviours could be detected in various systems including, among others, colloidal particles in random potentials, glass forming liquids and granular gases.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
| | - Peter Hänggi
- Institute of Physics, University of Augsburg, 86135 Augsburg, Germany
- Nanosystems Initiative Munich, Schellingstr, 4, D-80799 Műnchen, Germany
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25
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Chakrabarty A, Wang F, Sun K, Wei QH. Effects of translation-rotation coupling on the displacement probability distribution functions of boomerang colloidal particles. SOFT MATTER 2016; 12:4318-4323. [PMID: 27079870 DOI: 10.1039/c6sm00568c] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
Prior studies have shown that low symmetry particles such as micro-boomerangs exhibit behaviour of Brownian motion rather different from that of high symmetry particles because convenient tracking points (TPs) are usually inconsistent with their center of hydrodynamic stress (CoH) where the translational and rotational motions are decoupled. In this paper we study the effects of the translation-rotation coupling on the displacement probability distribution functions (PDFs) of the boomerang colloid particles with symmetric arm length. By tracking the motions of different points on the particle symmetry axis, we show that as the distance between the TP and the CoH is increased, the effects of translation-rotation coupling becomes pronounced, making the short-time 2D PDF for fixed initial orientation to change from elliptical, to bean and then to crescent shape, and the angle averaged PDFs change from ellipsoidal-particle-like PDF to a shape with a Gaussian top and long displacement tails. We also observed that at long times the PDFs revert to Gaussian. These 2D PDF shapes provide a clear physical picture of the non-zero mean displacements observed in boomerangs particles.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Feng Wang
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
| | - Kai Sun
- Department of Material Science and Engineering, University of Michigan, Ann Harbor, MI 48109, USA
| | - Qi-Huo Wei
- Liquid Crystal Institute, Kent State University, Kent, OH 44242, USA.
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26
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Morgado WAM, Queirós SMD. Thermostatistics of small nonlinear systems: Poissonian athermal bath. Phys Rev E 2016; 93:012121. [PMID: 26871038 DOI: 10.1103/physreve.93.012121] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2015] [Indexed: 06/05/2023]
Abstract
We extend an earlier study [W. A. M. Morgado and S. M. Duarte Queirós, Phys. Rev. E 90, 022110 (2014)PLEEE81539-375510.1103/PhysRevE.90.022110] to the case of a small system subject to nonlinear interaction and in contact with an athermal shot-noise reservoir. We first focus on steady state properties, namely, on the impact of the singular measure of the reservoir in the steady state energy. We introduce the concept of temperatures of higher order, which aim to represent the effect produced by the cumulants of the noise of order larger than 2 in the form of sources of energy of higher order and new response functions such as high-order specific heats that zero out when the system is thermal or linear. Afterwards, we study the effect of the nature of the noise in the heat and energy fluxes and determine asymptotic expressions for its large deviation functions. Finally, by analyzing the probabilistics of the injected power, we verify that the exponential form of its fluctuation relation is only asymptotically valid, whereas in the thermal case it is valid for the injected power at all times.
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Affiliation(s)
- Welles A M Morgado
- Department of Physics, PUC-Rio and National Institute of Science and Technology for Complex Systems, Rua Marquês de São Vicente 225, 22453-900 Rio de Janeiro-RJ, Brazil
| | - Sílvio M Duarte Queirós
- Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Dr Xavier Sigaud, 150, 22290-180 Rio de Janeiro-RJ, Brazil
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27
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Self-powered macroscopic Brownian motion of spontaneously running liquid metal motors. Sci Bull (Beijing) 2015. [DOI: 10.1007/s11434-015-0836-6] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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28
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Roh S, Yi J, Kim YW. Analysis of diffusion trajectories of anisotropic objects. J Chem Phys 2015; 142:214302. [DOI: 10.1063/1.4921958] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Sunghan Roh
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Deajeon 305-338, Republic of Korea
| | - Juyeon Yi
- Department of Physics, Pusan National University, Busan 609-735, South Korea
| | - Yong Woon Kim
- Graduate School of Nanoscience and Technology, Korea Advanced Institute of Science and Technology, Deajeon 305-338, Republic of Korea
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29
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Spiechowicz J, Łuczka J. Diffusion anomalies in ac-driven Brownian ratchets. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062104. [PMID: 26172658 DOI: 10.1103/physreve.91.062104] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/31/2015] [Indexed: 06/04/2023]
Abstract
We study diffusion in ratchet systems. As a particular experimental realization we consider an asymmetric SQUID subjected to an external ac current and a constant magnetic flux. We analyze mean-square displacement of the Josephson phase and find that within selected parameter regimes it evolves in three distinct stages: initially as superdiffusion, next as subdiffusion, and finally as normal diffusion in the asymptotic long-time limit. We show how crossover times that separates these stages can be controlled by temperature and an external magnetic flux. The first two stages can last many orders longer than characteristic time scales of the system, thus being comfortably detectable experimentally. The origin of abnormal behavior is noticeable related to the ratchet form of the potential revealing an entirely new mechanism of emergence of anomalous diffusion. Moreover, a normal diffusion coefficient exhibits nonmonotonic dependence on temperature leading to an intriguing phenomenon of thermal noise suppressed diffusion. The proposed setup for experimental verification of our findings provides a new and promising testing ground for investigating anomalies in diffusion phenomena.
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Affiliation(s)
- Jakub Spiechowicz
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
| | - Jerzy Łuczka
- Institute of Physics, University of Silesia, 40-007 Katowice, Poland
- Silesian Center for Education and Interdisciplinary Research, University of Silesia, 41-500 Chorzów, Poland
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30
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Shin HK, Choi B, Talkner P, Lee EK. Normal versus anomalous self-diffusion in two-dimensional fluids: Memory function approach and generalized asymptotic Einstein relation. J Chem Phys 2014; 141:214112. [DOI: 10.1063/1.4902409] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Affiliation(s)
- Hyun Kyung Shin
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
| | - Bongsik Choi
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
| | - Peter Talkner
- Universität Augsburg, Institut für Physik, D-86135 Augsburg, Germany
- Asia Pacific Center for Theoretical Physics (APCTP), San 31, Hyoja-dong, Nam-gu, Pohang, Gyeongbuk 790-784, South Korea
| | - Eok Kyun Lee
- Department of Chemistry, Korea Advanced Institute of Science and Technology, Daejeon 305-701, Republic of Korea
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31
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Chakrabarty A, Konya A, Wang F, Selinger JV, Sun K, Wei QH. Brownian motion of arbitrarily shaped particles in two dimensions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2014; 30:13844-13853. [PMID: 25357180 DOI: 10.1021/la5037053] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We implement microfabricated boomerang particles with unequal arm lengths as a model for nonsymmetric particles and study their Brownian motion in a quasi-two-dimensional geometry by using high-precision single-particle motion tracking. We show that because of the coupling between translation and rotation, the mean squared displacements of a single asymmetric boomerang particle exhibit a nonlinear crossover from short-time faster to long-time slower diffusion, and the mean displacements for fixed initial orientation are nonzero and saturate out at long times. The measured anisotropic diffusion coefficients versus the tracking point position indicate that there exists one unique point, i.e., the center of hydrodynamic stress (CoH), at which all coupled diffusion coefficients vanish. This implies that in contrast to motion in three dimensions where the CoH exists only for high-symmetry particles, the CoH always exists for Brownian motion in two dimensions. We develop an analytical model based on Langevin theory to explain the experimental results and show that among the six anisotropic diffusion coefficients only five are independent because the translation-translation coupling originates from the translation-rotation coupling. Finally, we classify the behavior of two-dimensional Brownian motion of arbitrarily shaped particles into four groups based on the particle shape symmetry group and discussed potential applications of the CoH in simplifying understanding of the circular motions of microswimmers.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute and Department of Chemical Physics, Kent State University , Kent, Ohio 44242, United States
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Thomas P, Sekhar AC. Live cell imaging reveals extensive intracellular cytoplasmic colonization of banana by normally non-cultivable endophytic bacteria. AOB PLANTS 2014; 6:plu002. [PMID: 24790123 PMCID: PMC4038436 DOI: 10.1093/aobpla/plu002] [Citation(s) in RCA: 27] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/25/2013] [Accepted: 12/09/2013] [Indexed: 05/04/2023]
Abstract
It is generally believed that endophytic microorganisms are intercellular inhabitants present in either cultivable or non-cultivable form primarily as root colonizers. The objective of this study was to determine whether the actively mobile micro-particles observed in the intracellular matrix of fresh tissue sections of banana included endophytic bacteria. Tissue sections (50-100 µm) from apical leaf sheaths of surface-disinfected suckers (cv. Grand Naine) displayed 'Brownian motion'-reminiscent abundant motile micro-particles under bright-field and phase-contrast (×1000), which appeared similar in size and motility to the pure cultures of endophytes previously isolated from banana. Observations on callus, embryonic cells and protoplasts with intact cell wall/plasma membrane confirmed their cytoplasmic nature. The motility of these entities reduced or ceased upon tissue fixation or staining with safranin/crystal violet (0.5 % w/v), but continued uninterrupted following treatment with actin-disrupting drugs, ruling out the possibility of micro-organelles like peroxisomes. Staining with 2,3,5-triphenyl tetrazolium chloride (TTC) confirmed them to be live bacteria with similar observations after dilute safranin (0.005 %) treatment. Tissue staining with SYTO-9 coupled with epi-fluorescence or confocal laser scanning microscopy showed bacterial colonization along the peri-space between cell wall and plasma membrane initially. SYTO-9 counterstaining on TTC- or safranin-treated tissue and those subjected to enzymatic permeabilization revealed the cytoplasmic bacteria. These included organisms moving freely in the cytoplasm and those adhering to the nuclear envelope or vacuoles and the intravacuolar colonizers. The observations appeared ubiquitous to different genomes and genotypes of banana. Plating the tissue homogenate on nutrient media seldom yielded colony growth. This study, supported largely by live cell video-imaging, demonstrates enormous intracellular colonization in bananas by normally non-cultivable endophytic bacteria in two niches, namely cytoplasmic and periplasmic, designated as 'Cytobacts' and 'Peribacts', respectively. The integral intracellular association with their clonal perpetuation suggests a mutualistic relationship between endophytes and the host.
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Affiliation(s)
- Pious Thomas
- Division of Biotechnology, Indian Institute of Horticultural Research, Hessarghatta Lake, Bangalore 560 089, India
| | - Aparna Chandra Sekhar
- Division of Biotechnology, Indian Institute of Horticultural Research, Hessarghatta Lake, Bangalore 560 089, India
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33
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Chakrabarty A, Wang F, Fan CZ, Sun K, Wei QH. High-precision tracking of brownian boomerang colloidal particles confined in quasi two dimensions. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2013; 29:14396-14402. [PMID: 24171648 DOI: 10.1021/la403427y] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
In this article, we present a high-precision image-processing algorithm for tracking the translational and rotational Brownian motion of boomerang-shaped colloidal particles confined in quasi-two-dimensional geometry. By measuring mean square displacements of an immobilized particle, we demonstrate that the positional and angular precision of our imaging and image-processing system can achieve 13 nm and 0.004 rad, respectively. By analyzing computer-simulated images, we demonstrate that the positional and angular accuracies of our image-processing algorithm can achieve 32 nm and 0.006 rad. Because of zero correlations between the displacements in neighboring time intervals, trajectories of different videos of the same particle can be merged into a very long time trajectory, allowing for long-time averaging of different physical variables. We apply this image-processing algorithm to measure the diffusion coefficients of boomerang particles of three different apex angles and discuss the angle dependence of these diffusion coefficients.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute and Department of Chemical Physics, Kent State University , Kent, Ohio 44242, United States
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34
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Chakrabarty A, Konya A, Wang F, Selinger JV, Sun K, Wei QH. Brownian motion of boomerang colloidal particles. PHYSICAL REVIEW LETTERS 2013; 111:160603. [PMID: 24182246 DOI: 10.1103/physrevlett.111.160603] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/05/2013] [Revised: 08/02/2013] [Indexed: 05/16/2023]
Abstract
We investigate the Brownian motion of boomerang colloidal particles confined between two glass plates. Our experimental observations show that the mean displacements are biased towards the center of hydrodynamic stress (CoH), and that the mean-square displacements exhibit a crossover from short-time faster to long-time slower diffusion with the short-time diffusion coefficients dependent on the points used for tracking. A model based on Langevin theory elucidates that these behaviors are ascribed to the superposition of two diffusive modes: the ellipsoidal motion of the CoH and the rotational motion of the tracking point with respect to the CoH.
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Affiliation(s)
- Ayan Chakrabarty
- Liquid Crystal Institute, Kent State University, Kent, Ohio 44242, USA
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Evers F, Zunke C, Hanes RDL, Bewerunge J, Ladadwa I, Heuer A, Egelhaaf SU. Particle dynamics in two-dimensional random-energy landscapes: experiments and simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:022125. [PMID: 24032793 DOI: 10.1103/physreve.88.022125] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/13/2013] [Indexed: 06/02/2023]
Abstract
The dynamics of individual colloidal particles in random potential energy landscapes was investigated experimentally and by Monte Carlo simulations. The value of the potential at each point in the two-dimensional energy landscape follows a Gaussian distribution. The width of the distribution, and hence the degree of roughness of the energy landscape, was varied and its effect on the particle dynamics studied. This situation represents an example of Brownian dynamics in the presence of disorder. In the experiments, the energy landscapes were generated optically using a holographic setup with a spatial light modulator, and the particle trajectories were followed by video microscopy. The dynamics is characterized using, e.g., the time-dependent diffusion coefficient, the mean squared displacement, the van Hove function, and the non-Gaussian parameter. In both experiments and simulations the dynamics is initially diffusive, showing an extended subdiffusive regime at intermediate times before diffusive motion is recovered at very long times. The dependence of the long-time diffusion coefficient on the width of the Gaussian distribution agrees with theoretical predictions. Compared to the dynamics in a one-dimensional potential energy landscape, the localization at intermediate times is weaker and the diffusive regime at long times reached earlier, which is due to the possibility to avoid local maxima in two-dimensional energy landscapes.
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Affiliation(s)
- Florian Evers
- Condensed Matter Physics Laboratory, Heinrich-Heine-University, Universitätsstraße 1, 40225 Düsseldorf, Germany
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Höfling F, Franosch T. Anomalous transport in the crowded world of biological cells. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2013; 76:046602. [PMID: 23481518 DOI: 10.1088/0034-4885/76/4/046602] [Citation(s) in RCA: 589] [Impact Index Per Article: 53.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/04/2023]
Abstract
A ubiquitous observation in cell biology is that the diffusive motion of macromolecules and organelles is anomalous, and a description simply based on the conventional diffusion equation with diffusion constants measured in dilute solution fails. This is commonly attributed to macromolecular crowding in the interior of cells and in cellular membranes, summarizing their densely packed and heterogeneous structures. The most familiar phenomenon is a sublinear, power-law increase of the mean-square displacement (MSD) as a function of the lag time, but there are other manifestations like strongly reduced and time-dependent diffusion coefficients, persistent correlations in time, non-Gaussian distributions of spatial displacements, heterogeneous diffusion and a fraction of immobile particles. After a general introduction to the statistical description of slow, anomalous transport, we summarize some widely used theoretical models: Gaussian models like fractional Brownian motion and Langevin equations for visco-elastic media, the continuous-time random walk model, and the Lorentz model describing obstructed transport in a heterogeneous environment. Particular emphasis is put on the spatio-temporal properties of the transport in terms of two-point correlation functions, dynamic scaling behaviour, and how the models are distinguished by their propagators even if the MSDs are identical. Then, we review the theory underlying commonly applied experimental techniques in the presence of anomalous transport like single-particle tracking, fluorescence correlation spectroscopy (FCS) and fluorescence recovery after photobleaching (FRAP). We report on the large body of recent experimental evidence for anomalous transport in crowded biological media: in cyto- and nucleoplasm as well as in cellular membranes, complemented by in vitro experiments where a variety of model systems mimic physiological crowding conditions. Finally, computer simulations are discussed which play an important role in testing the theoretical models and corroborating the experimental findings. The review is completed by a synthesis of the theoretical and experimental progress identifying open questions for future investigation.
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Affiliation(s)
- Felix Höfling
- Max-Planck-Institut für Intelligente Systeme, Heisenbergstraße 3, 70569 Stuttgart, and Institut für Theoretische Physik IV, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany
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38
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Prüstel T, Meier-Schellersheim M. Exact Green's function of the reversible diffusion-influenced reaction for an isolated pair in two dimensions. J Chem Phys 2012; 137:054104. [PMID: 22894329 DOI: 10.1063/1.4737662] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology.
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Affiliation(s)
- Thorsten Prüstel
- Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.
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Ghosh PK, Hänggi P, Marchesoni F, Nori F, Schmid G. Brownian transport in corrugated channels with inertia. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 86:021112. [PMID: 23005727 DOI: 10.1103/physreve.86.021112] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2011] [Revised: 06/11/2012] [Indexed: 06/01/2023]
Abstract
Transport of suspended Brownian particles dc driven along corrugated narrow channels is numerically investigated in the regime of finite damping. We show that inertial corrections cannot be neglected as long as the width of the channel bottlenecks is smaller than an appropriate particle diffusion length, which depends on the the channel corrugation and the drive intensity. With such a diffusion length being inversely proportional to the damping constant, transport through sufficiently narrow obstructions turns out to be always sensitive to the viscosity of the suspension fluid. The inertia corrections to the transport quantifiers, mobility, and diffusivity markedly differ for smoothly and sharply corrugated channels.
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Affiliation(s)
- P K Ghosh
- Advanced Science Institute, RIKEN, Wako-shi, Saitama 351-0198, Japan
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Wang Y, Zhao N, Yan Y. Langevin dynamics of correlated subdiffusion and normal diffusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041142. [PMID: 22680452 DOI: 10.1103/physreve.85.041142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/15/2011] [Revised: 11/29/2011] [Indexed: 06/01/2023]
Abstract
We analyze the dissipative dynamics of a particle governed by a two-dimensional generalized Langevin equation with coupled fractional Gaussian noise and white noise in its respective coordinates, assuming the lowest-order coupling form. Two situations are studied: In the first the particle is free from external force and in the second the particle is subject to a two-dimensional harmonic potential. We derive the general expressions for the mean values, variances, and velocity autocorrelation function and evaluate their temporal evolutions via the numerical Laplace inversion technique. Through the analytical results of the short-time and long-time behaviors, we also explicitly elucidate the effects of fluctuation correlation coupling and interoscillator coupling on the dynamic behaviors of the particle. It is shown that in both situations the couplings do not affect the short-time behavior of self-diffusions in each coordinate, and the subdiffusive and normal diffusive features of these processes resemble those in a one-dimensional system with fractional Gaussian noise and white noise, respectively. However, over a long time period, the fluctuation correlation extends the characteristic time scales for the self-diffusions of a free particle; while only the interoscillator coupling induces a retardation of the relaxation processes of a bounded particle toward equilibrium. Moreover, both couplings generate a cross diffusion, whose long-time approximation has two possible forms, the selection of which depends on the relevant time scales of self-diffusions in each coordinate.
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Affiliation(s)
- Yingxi Wang
- College of Chemistry, Sichuan University, Chengdu 610064, China
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41
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Denisov S, Zaburdaev V, Hänggi P. Lévy walks with velocity fluctuations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:031148. [PMID: 22587079 DOI: 10.1103/physreve.85.031148] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/01/2012] [Indexed: 05/31/2023]
Abstract
The standard Lévy walk is performed by a particle that moves ballistically between randomly occurring collisions when the intercollision time is a random variable governed by a power-law distribution. During instantaneous collision events, the particle randomly changes the direction of motion but maintains the same constant speed. We generalize the standard model to incorporate velocity fluctuations into the process. Two types of models are considered, namely (i) with a walker changing the direction and absolute value of its velocity during collisions only, and (ii) with a walker whose velocity continuously fluctuates. We present a full analytic evaluation of both models and emphasize the importance of initial conditions. We show that, in the limit of weak velocity fluctuations, the integral diffusion characteristics and the bulk of diffusion profiles are identical to those for the standard Lévy walk. However, the type of underlying velocity fluctuations can be identified by looking at the ballistic regions of the diffusion profiles. Our analytical results are corroborated by numerical simulations.
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Affiliation(s)
- S Denisov
- Institute of Physics, University of Augsburg, Augsburg, Germany
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42
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Martens S, Schmid G, Schimansky-Geier L, Hänggi P. Biased Brownian motion in extremely corrugated tubes. CHAOS (WOODBURY, N.Y.) 2011; 21:047518. [PMID: 22225392 DOI: 10.1063/1.3658621] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Biased Brownian motion of point-size particles in a three-dimensional tube with varying cross-section is investigated. In the fashion of our recent work, Martens et al. [Phys. Rev. E 83, 051135 (2011)] we employ an asymptotic analysis to the stationary probability density in a geometric parameter of the tube geometry. We demonstrate that the leading order term is equivalent to the Fick-Jacobs approximation. Expression for the higher order corrections to the probability density is derived. Using this expansion orders, we obtain that in the diffusion dominated regime the average particle current equals the zeroth order Fick-Jacobs result corrected by a factor including the corrugation of the tube geometry. In particular, we demonstrate that this estimate is more accurate for extremely corrugated geometries compared with the common applied method using a spatially-dependent diffusion coefficient D(x, f) which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the finite element calculation of a sinusoidal-shaped tube.
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Affiliation(s)
- S Martens
- Department of Physics, Humboldt-Universität zu Berlin, Newtonstr. 15, 12489 Berlin, Germany.
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Vazquez MV, Valdes-Parada FJ, Dagdug L, Alvarez-Ramirez J. Enhanced diffusion in conic channels by means of geometric stochastic resonance. J Chem Phys 2011; 135:174102. [DOI: 10.1063/1.3657405] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Franosch T, Grimm M, Belushkin M, Mor FM, Foffi G, Forró L, Jeney S. Resonances arising from hydrodynamic memory in Brownian motion. Nature 2011; 478:85-8. [PMID: 21979048 DOI: 10.1038/nature10498] [Citation(s) in RCA: 169] [Impact Index Per Article: 13.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2011] [Accepted: 08/18/2011] [Indexed: 01/28/2023]
Abstract
Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations. This hydrodynamic 'memory' translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin's pioneering experiments on Brownian motion, direct experimental observation of this colour is still elusive. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere's positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors, our results reveal that the particle-fluid-trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications.
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Affiliation(s)
- Thomas Franosch
- Institut für Theoretische Physik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Staudtstraße 7, 91058 Erlangen, Germany
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Belushkin M, Winkler RG, Foffi G. Backtracking of Colloids: A Multiparticle Collision Dynamics Simulation Study. J Phys Chem B 2011; 115:14263-8. [DOI: 10.1021/jp205084u] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- M. Belushkin
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne
| | - R. G. Winkler
- Theoretical Soft-Matter and Biophysics, Institute for Advanced Simulation, Forschungszentrum Jülich, D-52425 Jülich
| | - G. Foffi
- Institute of Theoretical Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne
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Martens S, Schmid G, Schimansky-Geier L, Hänggi P. Entropic particle transport: higher-order corrections to the Fick-Jacobs diffusion equation. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:051135. [PMID: 21728518 DOI: 10.1103/physreve.83.051135] [Citation(s) in RCA: 46] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2011] [Indexed: 05/31/2023]
Abstract
Transport of point-size Brownian particles under the influence of a constant and uniform force field through a planar three-dimensional channel with smoothly varying, axis-symmetric periodic side walls is investigated. Here we employ an asymptotic analysis in the ratio between the difference of the widest and the most narrow constriction divided through the period length of the channel geometry. We demonstrate that the leading-order term is equivalent to the Fick-Jacobs approximation. By use of the higher-order corrections to the probability density we show that in the diffusion-dominated regime the average transport velocity is obtained as the product of the zeroth-order Fick-Jacobs result and the expectation value of the spatially dependent diffusion coefficient D(x), which substitutes the constant diffusion coefficient in the common Fick-Jacobs equation. The analytic findings are corroborated with the precise numerical results of a finite element calculation of the Smoluchowski diffusive particle dynamics occurring in a reflection symmetric sinusoidal-shaped channel.
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Affiliation(s)
- S Martens
- Department of Physics, Humboldt-Universität zu Berlin, Berlin, Germany.
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Shit A, Ghosh P, Chattopadhyay S, Chaudhuri JR. Development of a semiclassical method to compute mobility and diffusion coefficient of a Brownian particle in a nonequilibrium environment. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:031125. [PMID: 21517472 DOI: 10.1103/physreve.83.031125] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/19/2010] [Revised: 11/22/2010] [Indexed: 05/30/2023]
Abstract
We explore the issue of a quantum-noise-induced directed transport of an overdamped Brownian particle that is allowed to move in a spatially periodic potential. The established system-reservoir model has been employed here to study the quantum-noise-induced transport of a Brownian particle in a periodic potential, where the reservoir is being modulated externally by a Gaussian-colored noise. The mobility of the Brownian particle in the linear response regime has been calculated. Then, using Einstein's relation, the analytical expression for the diffusion rate is evaluated for any arbitrary periodic potential for the high-temperature quantum regime.
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Affiliation(s)
- Anindita Shit
- Department of Chemistry, Bengal Engineering and Science University, Shibpur, Howrah 711103, India
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48
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Zaid IM, Dunkel J, Yeomans JM. Lévy fluctuations and mixing in dilute suspensions of algae and bacteria. J R Soc Interface 2011; 8:1314-31. [PMID: 21345857 DOI: 10.1098/rsif.2010.0545] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.
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Affiliation(s)
- Irwin M Zaid
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, 1 Keble Road, Oxford OX1 3NP, UK.
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49
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Urdapilleta E. Survival probability and first-passage-time statistics of a Wiener process driven by an exponential time-dependent drift. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2011; 83:021102. [PMID: 21405813 DOI: 10.1103/physreve.83.021102] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2010] [Indexed: 05/30/2023]
Abstract
The survival probability and the first-passage-time statistics are important quantities in different fields. The Wiener process is the simplest stochastic process with continuous variables, and important results can be explicitly found from it. The presence of a constant drift does not modify its simplicity; however, when the process has a time-dependent component the analysis becomes difficult. In this work we analyze the statistical properties of the Wiener process with an absorbing boundary, under the effect of an exponential time-dependent drift. Based on the backward Fokker-Planck formalism we set the time-inhomogeneous equation and conditions that rule the diffusion of the corresponding survival probability. We propose as the solution an expansion series in terms of the intensity of the exponential drift, resulting in a set of recurrence equations. We explicitly solve the expansion up to second order and comment on higher-order solutions. The first-passage-time density function arises naturally from the survival probability and preserves the proposed expansion. Explicit results, related properties, and limit behaviors are analyzed and extensively compared to numerical simulations.
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Affiliation(s)
- Eugenio Urdapilleta
- División de Física Estadística e Interdisciplinaria & Instituto Balseiro, Centro Atómico Bariloche, Avenida E. Bustillo Km 9.500, S.C. de Bariloche 8400, Río Negro, Argentina.
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