Related papers: Excluded volume effects in on- and off-lattice rea…
This paper considers particle propagation in a cylindrical molecular communication channel, e.g. a simplified model of a blood vessel. Emitted particles are influenced by diffusion, flow, and a vertical force induced e.g. by gravity or…
Thermal boundary conditions has played an increasingly important role in revealing the nature of short-range spin glasses and is likely to be relevant also for other disordered systems. Diffusion method initializing each replica with a…
In particle-in-cell simulations and some other statistical computations, the representation of modelled distributions with tracked macro-particles can become locally excessive. Merging or resampling dense clusters or highly-populated phase…
This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
Cell proliferation and cell movement are fundamentally stochastic processes which lead to variability in the growth and spatial structure of cell populations in many biological settings, such as cell invasion, wound healing, and tumour…
While the impact of crowding on the diffusive transport of molecules within a cell is widely studied in biology, it has thus far been neglected in traffic systems where bulk behavior is the main concern. Here, we study the effects of…
Crowd management is a complex, challenging and crucial task. Lack of appropriate management of crowd has, in past, led to many unfortunate stampedes with significant loss of life. To increase the crowd management efficiency, we deploy…
Rate-equation models are a widely-used and inexpensive tool for the simulation of interstellar chemistry under a range of physical conditions. However, their application to grain-surface chemical systems necessitates a number of simplifying…
Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale kinetics in such systems are effective,…
A statistical mechanical theory is presented to predict the effects of macromolecular crowding on protein association equilibria, accounting for both excluded volume and attractive interactions between proteins and crowding molecules.…
We study a strongly interacting crowded system of self-propelled stiff filaments by event-driven Brownian dynamics simulations and an analytical theory to elucidate the intricate interplay of crowding and self-propulsion. We find a…
Diffusion-based tabular data synthesis models have yielded promising results. However, when the data dimensionality increases, existing models tend to degenerate and may perform even worse than simpler, non-diffusion-based models. This is…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…
In active matter, such as the Vicsek Model of flocking, particles possesses an internal degree of freedom, such as their director, which is subject to interaction with other particles, provided they are within a certain range. In an effort…
We study driven particle systems with excluded volume interactions on a two-lane ladder with periodic boundaries, using Monte Carlo simulation, cluster mean-field theory, and numerical solution of the master equation. Particles in one lane…
In this study, the impact of turbulent diffusion on mixing of biochemical reaction models is explored by implementing and validating different models. An original codebase called CHAD (Coupled Hydrodynamics and Anaerobic Digestion) is…
We consider strong convergence of the finite differences approximation in space for stochastic reaction diffusion equations with multiplicative noise under a one-sided Lipschitz condition only. We derive convergence with an implicit rate…
A new upscaling procedure that provides 1D representations of 2D mixing-limited reactive transport systems is developed and applied. A key complication with upscaled models in this setting is that the procedure must differentiate between…