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Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this chapter, we review the Brownian motion of a particle moving in the vicinity of a…
The power-law TST reaction rate coefficient for an elementary bimolecular reaction is studied when the reaction takes place in a nonequilibrium system with power-law distributions. We derive a generalized TST rate coefficient, which not…
Unlike macroscopic engines, the molecular machinery of living cells is strongly affected by fluctuations. Stochastic Thermodynamics uses Markovian jump processes to model the random transitions between the chemical and configurational…
We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…
The issue of retarded long-range resonant interactions between two molecules with oscillating dipole moments is reinvestigated within the framework of classical electrodynamics. By taking advantage of a theorem in complex analysis, we…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of…
Small separation between reactants, not exceeding $10^{-8}-10^{-7}cm$, is the necessary condition for various chemical reactions. It is shown that random advection and stretching by turbulence leads to formation of scalar-enriched sheets of…
The work described is concerned with the way micron-size particles attached to a surface are resuspended when exposed to a turbulent flow. An improved version of the Rock'n'Roll model (Reeks and Hall, 2001) is developed where this model…
The classical mass action law in chemical kinetics is put into the context of multiscale thermodynamics.Despite the purely dissipative character of the classical mass action law, inertial effects also play a role in chemical kinetics.…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
This work demonstrates the application of a birth-death Markov process, inspired by radioactive decay, to capture the dynamics of innovation processes. Leveraging the Bass diffusion model, we derive a Gompertz-like function explaining the…
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,…
Using analytical calculations and computer simulations we consider both the lateral diffusion of a membrane protein and the fluctuation spectrum of the membrane in which the protein is embedded. The membrane protein interacts with the…
The propulsion of active particles by self-diffusiophoresis is driven by asymmetric catalytic reactions on the particle surface that generate a mechanochemical coupling between the fluid velocity and the concentration fields of fuel and…
A class of Brownian dynamics algorithms for stochastic reaction-diffusion models which include reversible bimolecular reactions is presented and analyzed. The method is a generalization of the $\lambda$--$\newrho$ model for irreversible…
We suggest a better mathematical method, fractional calculus, for studying the behavior of the atom-field interaction in photonic crystals. By studying the spontaneous emission of an atom in a photonic crystal with one-band isotropic model,…
The resonant activation effect (RA) has been well studied in different ways during the last two decades. It consists in the presence of a minimum in the mean time spent by a Brownian particle to exit from a potential well in the presence of…
Many processes in chemistry, physics, and biology depend on thermally activated events in which the system changes its state by surmounting an activation barrier. Examples range from chemical reactions, protein folding, and nucleation…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…