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Uchida G, Washizu H, Miyoshi H. Diffusion with a broad class of stochastic diffusion coefficients. Phys Rev E 2024; 109:064117. [PMID: 39020921 DOI: 10.1103/physreve.109.064117] [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: 05/10/2024] [Indexed: 07/20/2024]
Abstract
In many physical or biological systems, diffusion can be described by Brownian motions with stochastic diffusion coefficients (DCs). In the present study, we investigate properties of the diffusion with a broad class of stochastic DCs with an approach that is different from subordination. We show that for a finite time, the propagator is non-Gaussian and heavy tailed. This means that when the mean square displacements are the same, for a finite time, some of the diffusing particles with stochastic DCs diffuse farther than the particles with deterministic DCs or exhibiting a fractional Brownian motion. We also show that when a stochastic DC is ergodic, the propagator converges to a Gaussian distribution in the long time limit. The speed of convergence is determined by the autocovariance function of the DC.
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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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Hu M, Chen H, Wang H, Burov S, Barkai E, Wang D. Triggering Gaussian-to-Exponential Transition of Displacement Distribution in Polymer Nanocomposites via Adsorption-Induced Trapping. ACS NANO 2023; 17:21708-21718. [PMID: 37879044 DOI: 10.1021/acsnano.3c06897] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/27/2023]
Abstract
In many disordered systems, the diffusion of classical particles is described by a displacement distribution P(x, t) that displays exponential tails instead of Gaussian statistics expected for Brownian motion. However, the experimental demonstration of control of this behavior by increasing the disorder strength has remained challenging. In this work, we explore the Gaussian-to-exponential transition by using diffusion of poly(ethylene glycol) (PEG) in attractive nanoparticle-polymer mixtures and controlling the volume fraction of the nanoparticles. In this work, we find "knobs", namely nanoparticle concentration and interaction, which enable the change in the shape of P(x,t) in a well-defined way. The Gaussian-to-exponential transition is consistent with a modified large deviation approach for a continuous time random walk and also with Monte Carlo simulations involving a microscopic model of polymer trapping via reversible adsorption to the nanoparticle surface. Our work bears significance in unraveling the fundamental physics behind the exponential decay of the displacement distribution at the tails, which is commonly observed in soft materials and nanomaterials.
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Affiliation(s)
- Ming Hu
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Hongbo Chen
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
| | - Hongru Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
| | - Stanislav Burov
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Eli Barkai
- Department of Physics, Institute of Nanotechnology and Advanced Materials, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Dapeng Wang
- State Key Laboratory of Polymer Physics and Chemistry, Changchun Institute of Applied Chemistry, Chinese Academy of Sciences, Changchun, Jilin 130022, People's Republic of China
- University of Science and Technology of China, Hefei, Anhui 230026, People's Republic of China
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Jhwueng DC, Wu CY. A Novel Phylogenetic Negative Binomial Regression Model for Count-Dependent Variables. BIOLOGY 2023; 12:1148. [PMID: 37627032 PMCID: PMC10452298 DOI: 10.3390/biology12081148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/09/2023] [Revised: 08/16/2023] [Accepted: 08/18/2023] [Indexed: 08/27/2023]
Abstract
Regression models are extensively used to explore the relationship between a dependent variable and its covariates. These models work well when the dependent variable is categorical and the data are supposedly independent, as is the case with generalized linear models (GLMs). However, trait data from related species do not operate under these conditions due to their shared common ancestry, leading to dependence that can be illustrated through a phylogenetic tree. In response to the analytical challenges of count-dependent variables in phylogenetically related species, we have developed a novel phylogenetic negative binomial regression model that allows for overdispersion, a limitation present in the phylogenetic Poisson regression model in the literature. This model overcomes limitations of conventional GLMs, which overlook the inherent dependence arising from shared lineage. Instead, our proposed model acknowledges this factor and uses the generalized estimating equation (GEE) framework for precise parameter estimation. The effectiveness of the proposed model was corroborated by a rigorous simulation study, which, despite the need for careful convergence monitoring, demonstrated its reasonable efficacy. The empirical application of the model to lizard egg-laying count and mammalian litter size data further highlighted its practical relevance. In particular, our results identified negative correlations between increases in egg mass, litter size, ovulation rate, and gestation length with respective yearly counts, while a positive correlation was observed with species lifespan. This study underscores the importance of our proposed model in providing nuanced and accurate analyses of count-dependent variables in related species, highlighting the often overlooked impact of shared ancestry. The model represents a critical advance in research methodologies, opening new avenues for interpretation of related species data in the field.
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Wang X, Chen Y. Langevin picture of anomalous diffusion processes in expanding medium. Phys Rev E 2023; 107:024105. [PMID: 36932587 DOI: 10.1103/physreve.107.024105] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/03/2022] [Accepted: 01/11/2023] [Indexed: 06/18/2023]
Abstract
The expanding medium is very common in many different fields, such as biology and cosmology. It brings a nonnegligible influence on particle's diffusion, which is quite different from the effect of an external force field. The dynamic mechanism of a particle's motion in an expanding medium has only been investigated in the framework of a continuous-time random walk. To focus on more diffusion processes and physical observables, we build the Langevin picture of anomalous diffusion in an expanding medium, and conduct detailed analyses in the framework of the Langevin equation. With the help of a subordinator, both subdiffusion process and superdiffusion process in the expanding medium are discussed. We find that the expanding medium with different changing rate (exponential form and power-law form) leads to quite different diffusion phenomena. The particle's intrinsic diffusion behavior also plays an important role. Our detailed theoretical analyses and simulations present a panoramic view of investigating anomalous diffusion in an expanding medium under the framework of the Langevin equation.
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Affiliation(s)
- Xudong Wang
- School of Mathematics and Statistics, Nanjing University of Science and Technology, Nanjing 210094, People's Republic of China
| | - Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing 210095, People's Republic of China
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Doerries TJ, Chechkin AV, Metzler R. Apparent anomalous diffusion and non-Gaussian distributions in a simple mobile-immobile transport model with Poissonian switching. J R Soc Interface 2022; 19:20220233. [PMID: 35857918 PMCID: PMC9257594 DOI: 10.1098/rsif.2022.0233] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2022] [Accepted: 06/15/2022] [Indexed: 09/01/2023] Open
Abstract
We analyse mobile-immobile transport of particles that switch between the mobile and immobile phases with finite rates. Despite this seemingly simple assumption of Poissonian switching, we unveil a rich transport dynamics including significant transient anomalous diffusion and non-Gaussian displacement distributions. Our discussion is based on experimental parameters for tau proteins in neuronal cells, but the results obtained here are expected to be of relevance for a broad class of processes in complex systems. Specifically, we obtain that, when the mean binding time is significantly longer than the mean mobile time, transient anomalous diffusion is observed at short and intermediate time scales, with a strong dependence on the fraction of initially mobile and immobile particles. We unveil a Laplace distribution of particle displacements at relevant intermediate time scales. For any initial fraction of mobile particles, the respective mean squared displacement (MSD) displays a plateau. Moreover, we demonstrate a short-time cubic time dependence of the MSD for immobile tracers when initially all particles are immobile.
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Affiliation(s)
- Timo J. Doerries
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
| | - Aleksei V. Chechkin
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
- Faculty of Pure and Applied Mathematics, Hugo Steinhaus Center, Wrocław University of Science and Technology, Wyspianskiego 27, 50-370 Wrocław, Poland
- Akhiezer Institute for Theoretical Physics, National Science Center ‘Kharkiv Institute of Physics and Technology’, 61108 Kharkiv, Ukraine
| | - Ralf Metzler
- Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany
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Wang W, Metzler R, Cherstvy AG. Anomalous diffusion, aging, and nonergodicity of scaled Brownian motion with fractional Gaussian noise: overview of related experimental observations and models. Phys Chem Chem Phys 2022; 24:18482-18504. [DOI: 10.1039/d2cp01741e] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
How does a systematic time-dependence of the diffusion coefficient $D (t)$ affect the ergodic and statistical characteristics of fractional Brownian motion (FBM)? Here, we examine how the behavior of the...
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Wang X, Chen Y. Ergodic property of random diffusivity system with trapping events. Phys Rev E 2022; 105:014106. [PMID: 35193240 DOI: 10.1103/physreve.105.014106] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/14/2021] [Accepted: 12/10/2021] [Indexed: 12/25/2022]
Abstract
A Brownian yet non-Gaussian phenomenon has recently been observed in many biological and active matter systems. The main idea of explaining this phenomenon is to introduce a random diffusivity for particles moving in inhomogeneous environment. This paper considers a Langevin system containing a random diffusivity and an α-stable subordinator with α<1. This model describes the particle's motion in complex media where both the long trapping events and random diffusivity exist. We derive the general expressions of ensemble- and time-averaged mean-squared displacements which only contain the values of the inverse subordinator and diffusivity. Further taking specific time-dependent diffusivity, we obtain the analytic expressions of ergodicity breaking parameter and probability density function of the time-averaged mean-squared displacement. The results imply the nonergodicity of the random diffusivity model with any kind of diffusivity, including the critical case where the model presents normal diffusion.
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Affiliation(s)
- Xudong Wang
- School of Science, Nanjing University of Science and Technology, Nanjing, 210094, P.R. China
| | - Yao Chen
- College of Sciences, Nanjing Agricultural University, Nanjing, 210094, P.R. China
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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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