We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely ...

Gliomas, the most aggressive form of brain cancer, are known for their widespread invasion into the tissue near the tumor lesion. Exponential models, which have been widely used in other types of cancers, cannot be used for the simulation of tumor growth, due to the diffusive behavior of glioma. Diffusive models that have been proposed in the last two decades seem to better approximate the expa...

The Inhomogeneous Stochastic Simulation Algorithm (ISSA) is a variant of the stochastic simulation algorithm in which the spatially inhomogeneous volume of the system is divided into homogeneous subvolumes, and the chemical reactions in those subvolumes are augmented by diffusive transfers of molecules between adjacent subvolumes. The ISSA can be prohibitively slow when the system is such that ...

The interactions between planktonic organisms and their aquatic environment are mediated by diffusive processes on the scale of millimeters and smaller. The uptake of nutrients and food and the release of metabolic products creates localized patchiness that diffusive processes homogenize. Organism size determines, to a large extent, the character of these interactions. This paper builds a frame...

We propose a model for the formation of chromatin loops based on the diffusive sliding of molecular slip links. These mimic the behavior of molecules like cohesin, which, along with the CTCF protein, stabilize loops which contribute to organizing the genome. By combining 3D Brownian dynamics simulations and 1D exactly solvable nonequilibrium models, we show that diffusive sliding is sufficient ...

We consider the linear dissipative Boltzmann equation describing inelastic interactions of particles with a fixed background. For the simplified model of Maxwell molecules first, we give a complete spectral analysis, and deduce from it the optimal rate of exponential convergence to equilibrium. Moreover we show the convergence to the heat equation in the diffusive limit and compute explicitely ...

In this dissertation, we address the issue of collaborative information processing for diffusive source parameter estimation using wireless sensor networks (WSNs) capable of sensing in dispersive medium/environment, from signal processing perspective. We begin the dissertation by focusing on the mathematical formulation of a special diffusion phenomenon, i.e., an underwater oil spill, along wit...

The ignition of a gaseous reactive mixture subject to a localized energy source is analysed using large activation energy asymptotics. The energy released by the source results in a thermal non-uniformity in a small region of the gas. We distinguish two different regimes, non-diffusive and diffusive, depending on the dominant cooling mechanism during the ignition stage: expansion effects or hea...

We exploit a recently developed formalism to study the temporal behavior of the energy and heat transport in metals. This formalism shows the transition between ballistic and diffusive regimes and it highlights some interesting effects such as oscillations in the energy transport at very short-time scales. The energy relaxation of the conduction-band electrons in metals is considered to be gove...

Q -conditional symmetries of the classical diffusive Lotka–Volterra system in the case of one space variable are completely described and a set of such symmetries in explicit form is constructed. The relevant non-Lie ansatz to reduce the diffusive Lotka–Volterra systems with correctly specified coefficients to ODE systems and examples of new exact solutions are found. A possible biological inte...