Stochastic model for the dynamics of interacting Brownian particles

Mayorga, M.; Romero-Salazar, L.; Rubı́, J. M.

doi:10.1016/s0378-4371(01)00617-3

Cited by 20 publications

(59 citation statements)

References 41 publications

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“…Factorizing the two-particle distribution function in the form [29]: ρ (2) ( r − r ′ , t) ≃ ρ( r)g( r − r ′ , t), with g( r − r ′ , t) the two-particle correlation function, we define the effective quantities…”

Section: A Effective Medium Approximationmentioning

confidence: 99%

Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

2009

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We study the shear-induced diffusion effect and the transition to irreversibility in suspensions under oscillatory shear flow by performing an analysis of the entropy production associated to the motion of the particles. We show that the Onsager coupling between different contributions to the entropy production is responsible for the scaling of the mean square displacement on particle diameter and applied strain. We also show that the shear-induced effective diffusion coefficient depends on the volume fraction and use Lattice-Boltzmann simulations to characterize the effect through the power spectrum of particle positions for different Reynolds numbers and volume fractions. Our study gives a thermodynamic explanation of the the transition to irreversibility through a pertinent analysis of the second law of thermodynamics.

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Section: A Effective Medium Approximationmentioning

confidence: 99%

Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

2009

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“…Each sequence S would be dynamically modeled with a neighborhood sized number of RNA-RNA interactions. Instead, we pursue a thermodynamic approach based on the Fokker-Planck equation to quantify stochastic processes in liquid medium [20]. RNA interactions are assumed to function over sequence lengths encompassing small single-stranded and solvent-accessible regions.…”

Section: Spatial Transcriptome Information Cloud (Stic) Model Construmentioning

confidence: 99%

“…Brownian effects are ubiquitous in numerous examples of soft condensed matter physics [20] in which the system can be modeled as a set of interacting degrees of freedom in contact with a heat reservoir. Brownian motion plays an important role when one infers macroscopic behaviors from mesoscopic levels of description, frequently a desire in the study of complex systems.…”

Section: Rna Diffusionmentioning

confidence: 99%

“…Dynamics at the mesoscopic level is governed by a set of Langevin processes or equivalently by the corresponding N-particle Fokker-Planck equation. This scheme applies nonequilibrium thermodynamics to derive the kinetic equations describing the evolution of an N-particle probability distribution function [20]. One then considers a system of N Brownian particles diluted in a solvent, which acts as a thermal reservoir.…”

Section: Rna Diffusionmentioning

confidence: 99%

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Models of RNA Interaction from Experimental Datasets: Framework of Resilience

Seffens¹

2017

Applications of RNA-Seq and Omics Strategies - From Microorganisms to Human Health

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Resilience is a network property of systems responding under stress, which for biomedicine correlates to chronic or acute insults. Current need exists for models and algorithms to study whole transcriptome differences between tissues and disease states to understand resilience. Goal of this effort is to interpret cellular transcription in a dynamic system biology framework of RNA molecules forming an information structure with regulatory properties acting on individual transcripts. We develop and evaluate a bioinformatics framework based on information theory that utilizes RNA expression data to create a whole transcriptome model of interaction that could lead to the discovery of new biological control mechanisms. This addresses a fundamental question as to why transcription yields such a small fraction of protein products. We focus on a transformative concept that individual transcripts collectively form an "information cloud" of sequence words, which for some genes may have significant regulatory impact. Extending the concept of cis-and trans-regulation, we propose to search for RNAs that are modulated by interactions with the transcriptome cloud and calling such examples nebula regulation. This framework has implications as a paradigm change for RNA regulation and provides a deeper understanding of nucleotide sequence structure and -omic language meaning.

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“…Apart from a fundamental scientific interest in developing and extending systematic methods of kinetic theory, our studies are motivated by the following physical reasons: Firstly, a wide variety of complex systems, such as colloidal suspensions, polymers, micelles etc., can be viewed as interacting Brownian particles that are in contact with a heat bath [7,8,9]. There are several approaches to the statistical description of Brownian dynamics where interaction between particles is taken into account, see, e.g., [10,11,12,13,14], and references therein. In the case of a Gaussian external field, the system investigated in our paper can be considered as a "prototype" of that of interacting Brownian particles.…”

Section: Introductionmentioning

confidence: 99%

The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

Sliusarenko

Chechkin

Slyusarenko

2015

Journal of Mathematical Physics

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By generalizing Bogolyubov's reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton's equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As the result, a generalization of the classical BogolyubovBorn-Green-Kirkwood-Yvon (BBGKY) hierarchy is derived. In order to get a kinetic equation for the one-particle distribution function, we use a regular cut off procedure of the BBGKY hierarchy by assuming weak interaction between the particles and weak intensity of the field.Within this approximation we get the corresponding Fokker-Planck equation for the system in a non-Gaussian stochastic field. Two particular cases by assuming either Gaussian statistics of external perturbation or homogeneity of the system are discussed.

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Stochastic model for the dynamics of interacting Brownian particles

Cited by 20 publications

References 41 publications

Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

Transition to irreversibility in sheared suspensions: An analysis based on a mesoscopic entropy production

Models of RNA Interaction from Experimental Datasets: Framework of Resilience

The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

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