Paul C. Bressloff
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View article: Stochastic 1D search-and-capture as a <i>G/M/c</i> queueing model
Stochastic 1D search-and-capture as a <i>G/M/c</i> queueing model Open
We study the accumulation of resources within a target due to the interplay between continual delivery, driven by 1D stochastic search processes, and sequential consumption. The assumption of sequential consumption is key because it change…
View article: Stochastic calculus of run-and-tumble motion: an applied perspective
Stochastic calculus of run-and-tumble motion: an applied perspective Open
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case, this means switching between rightward and leftward velo…
View article: Diffusion-mediated adsorption versus absorption at partially reactive targets: a renewal approach
Diffusion-mediated adsorption versus absorption at partially reactive targets: a renewal approach Open
Renewal theory is finding increasing applications in non-equilibrium statistical physics. One example relates the probability density and survival probability of a Brownian particle or an active run-and-tumble particle with stochastic rese…
View article: Random search with stochastic resetting: When finding the target is not enough
Random search with stochastic resetting: When finding the target is not enough Open
In this paper, we consider a random search process with stochastic resetting and a partially accessible target U. In contrast to standard search processes, we assume that when the searcher first finds the target by contacting the surface ∂…
View article: Encounter-based model of a run-and-tumble particle with stochastic resetting
Encounter-based model of a run-and-tumble particle with stochastic resetting Open
In this paper we analyze the effects of stochastic resetting on an encounter-based model of an unbiased run-and-tumble particle (RTP) confined to the half-line with a partially absorbing wall at x = 0. The RTP tumbles at a constant …
View article: Random search with stochastic resetting: when finding the target is not enough
Random search with stochastic resetting: when finding the target is not enough Open
In this paper we consider a random search process with stochastic resetting and a partially accessible target $\calU$. That is, when the searcher finds the target by attaching to its surface $\partial \calU$ it does not have immediate acce…
View article: Encounter-based model of a run-and-tumble particle with stochastic resetting
Encounter-based model of a run-and-tumble particle with stochastic resetting Open
In this paper we analyze the effects of stochastic resetting on an encounter-based model of an unbiased run-and-tumble particle (RTP) confined to the half-line $[0,\infty)$ with a partially absorbing wall at $x=0$. The RTP tumbles at a con…
View article: Kuramoto model with stochastic resetting and coupling through an external medium
Kuramoto model with stochastic resetting and coupling through an external medium Open
Most studies of collective phenomena in oscillator networks focus on directly coupled systems, as exemplified by the classical Kuramoto model. However, there are a growing number of examples in which oscillators interact indirectly via a c…
View article: Stochastic calculus of run-and-tumble motion: an applied perspective
Stochastic calculus of run-and-tumble motion: an applied perspective Open
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case this means switching between rightward and leftward veloc…
View article: Cellular diffusion processes in singularly perturbed domains
Cellular diffusion processes in singularly perturbed domains Open
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $$\varOmega \subset {\mathbb {R}}^d$$ containing a set of small subdoma…
View article: Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting
Generalized Itô’s lemma and the stochastic thermodynamics of diffusion with resetting Open
Methods from the theory of stochastic processes are increasingly being used to extend classical thermodynamics to mesoscopic non-equilibrium systems. One characteristic feature of these systems is that averaging the stochastic entropy with…
View article: Cellular diffusion processes in singularly perturbed domains
Cellular diffusion processes in singularly perturbed domains Open
There are many processes in cell biology that can be modeled in terms of particles diffusing in a two-dimensional (2D) or three-dimensional (3D) bounded domain $Ω\subset \R^d$ containing a set of small subdomains or interior compartments $…
View article: Entropy production for diffusion processes across a semipermeable interface
Entropy production for diffusion processes across a semipermeable interface Open
The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat, and work to nonequilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate averag…
View article: Global density equations for interacting particle systems with stochastic resetting: From overdamped Brownian motion to phase synchronization
Global density equations for interacting particle systems with stochastic resetting: From overdamped Brownian motion to phase synchronization Open
A wide range of phenomena in the natural and social sciences involve large systems of interacting particles, including plasmas, collections of galaxies, coupled oscillators, cell aggregations, and economic “agents.” Kinetic methods for red…
View article: Transition path theory for diffusive search with stochastic resetting
Transition path theory for diffusive search with stochastic resetting Open
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states w…
View article: Entropy production for diffusion processes across a semipermeable interface
Entropy production for diffusion processes across a semipermeable interface Open
The emerging field of stochastic thermodynamics extends classical ideas of entropy, heat and work to non-equilibrium systems. One notable finding is that the second law of thermodynamics typically only holds after taking appropriate averag…
View article: Truncated stochastically switching processes
Truncated stochastically switching processes Open
There are a large variety of hybrid stochastic systems that couple a continuous process with some form of stochastic switching mechanism. In many cases the system switches between different discrete internal states according to a finite-st…
View article: Asymptotic analysis of conversion-limited phase separation
Asymptotic analysis of conversion-limited phase separation Open
Liquid–liquid phase separation plays a major role in the formation and maintenance of various membrane-less subcellular structures in the cytoplasm and nucleus of cells. Biological condensates contain enhanced concentrations of proteins an…
View article: Global density equations for a population of actively switching particles
Global density equations for a population of actively switching particles Open
There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom of the particle evolve according to a hybrid stochastic differential equation whose drift term depe…
View article: Global density equations for interacting particle systems with stochastic resetting: from overdamped Brownian motion to phase synchronization
Global density equations for interacting particle systems with stochastic resetting: from overdamped Brownian motion to phase synchronization Open
A wide range of phenomena in the natural and social sciences involve large systems of interacting particles, including plasmas, collections of galaxies, coupled oscillators, cell aggregations, and economic ``agents'. Kinetic methods for re…
View article: A generalized Dean-Kawasaki equation for an interacting Brownian gas in a partially absorbing medium
A generalized Dean-Kawasaki equation for an interacting Brownian gas in a partially absorbing medium Open
The Dean-Kawasaki (DK) equation is a stochastic partial differential equation (SPDE) for the global density $ρ$ of a gas of $N$ over-damped Brownian particles. In the thermodynamic limit $N\rightarrow \infty$ with weak pairwise interaction…
View article: Asymptotic analysis of particle cluster formation in the presence of anchoring sites
Asymptotic analysis of particle cluster formation in the presence of anchoring sites Open
The aggregation or clustering of proteins and other macromolecules plays an important role in the formation of large-scale molecular assemblies within cell membranes. Examples include lipid rafts and postsynaptic domains (PSDs). PSDs are r…
View article: Truncated stochastically switching processes
Truncated stochastically switching processes Open
There are a large variety of hybrid stochastic systems that couple a continuous process with some form of stochastic switching mechanism. In many cases the system switches between different discrete internal states according to a finite-st…
View article: Semipermeable interfaces and the target problem
Semipermeable interfaces and the target problem Open
In this chapter, we review our recent work on first passage time (FPT) problems for absorption by a target whose interface is semipermeable. For pedagogical reasons, we focus on a single Brownian particle searching for a single target in a…
View article: Global density equations for a population of actively switching particles
Global density equations for a population of actively switching particles Open
There are many processes in cell biology that can be modelled in terms of an actively switching particle. The continuous degrees of freedom evolve according to a hybrid stochastic differential equation (hSDE) whose drift term depends on a …
View article: Transition path theory for diffusive search with stochastic resetting
Transition path theory for diffusive search with stochastic resetting Open
Many chemical reactions can be formulated in terms of particle diffusion in a complex energy landscape. Transition path theory (TPT) is a theoretical framework for describing the direct (reaction) pathways from reactant to product states w…
View article: Asymptotic analysis of conversion-limited phase separation
Asymptotic analysis of conversion-limited phase separation Open
Liquid-liquid phase separation plays a major role in the formation and maintenance of various membrane-less subcellular structures in the cytoplasm and nucleus of cells. Biological condensates contain enhanced concentrations of proteins an…
View article: Encounter-based reaction-subdiffusion model I: surface adsorption and the local time propagator
Encounter-based reaction-subdiffusion model I: surface adsorption and the local time propagator Open
In this paper, we develop an encounter-based model of partial surface adsorption for fractional diffusion in a bounded domain. We take the probability of adsorption to depend on the amount of particle-surface contact time, as specified by …
View article: Encounter-based reaction-subdiffusion model II: partially absorbing traps and the occupation time propagator
Encounter-based reaction-subdiffusion model II: partially absorbing traps and the occupation time propagator Open
In this paper we develop an encounter-based model of reaction-subdiffusion in a domain Ω with a partially absorbing interior trap . We assume that the particle can freely enter and exit , but is only absorbed within . We take the probabili…