Related papers: Coagulation, diffusion and the continuous Smolucho…
We develop a theory of fluctuations for Brownian systems with weak long-range interactions. For these systems, there exists a critical point separating a homogeneous phase from an inhomogeneous phase. Starting from the stochastic…
We prove well-posedness of global solutions for a class of coagulation equations which exhibit the gelation phase transition. To this end, we solve an associated partial differential equation involving the generating functions before and…
The features of turbulence modulation produced by a heavy loaded suspension of small solid particles or liquid droplets are discussed by using a physically-based regularisation of particle-fluid interactions. The approach allows a robust…
Spatial reaction-diffusion models have been employed to describe many emergent phenomena in biological systems. The modelling technique most commonly adopted in the literature implements systems of partial differential equations (PDEs),…
Incorporating boundary conditions into stochastic models of passive or active particle motion is usually implemented at the level of the associated forward or backward Kolmogorov equation, whose solution determines the probability…
We study the validity of a Smoluchowski-Kramers approximation for a class of wave equations in a bounded domain of $\mathbb{R}^n$ subject to a state-dependent damping and perturbed by a multiplicative noise. We prove that in the small mass…
For a specific choice of the diffusion, the parabolic-elliptic Patlak-Keller-Segel system with non-linear diffusion (also referred to as the quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold phenomenon: there is…
The dynamical density functional theory of Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)], a theory for the non-equilibrium dynamics of the one-body density profile of a colloidal fluid, is applied to a binary fluid mixture of…
Stochastic reaction-diffusion models have become an important tool in studying how both noise in the chemical reaction process and the spatial movement of molecules influences the behavior of biological systems. There are two primary…
Porosity evolution of dust aggregates is crucial in understanding dust evolution in protoplanetary disks. In this study, we present useful tools to study the coagulation and porosity evolution of dust aggregates. First, we present a new…
In this paper, two new stochastic algorithms for calculating parametric derivatives of the solution to the Smoluchowski coagulation equation are presented. It is assumed that the coagulation kernel is dependent on these parameters. The new…
It is known that classical solutions to the one-dimensional quasilinear Smoluchowski-Poisson system with nonlinear diffusion $a(u)=(1+u)^{-p}$ may blow up in finite time if $p>1$ and exist globally if $p<1$. The case $p=1$ thus appears to…
We suggest an approach to detect the conformation of single molecule by using the photon counting statistics. The generalized Smoluchoswki equation is employed to describe the dynamical process of conformational change of single molecule.…
A new approach to thermo-quantum diffusion is proposed and a nonlinear quantum Smoluchowski equation is derived, which describes classical diffusion in the field of the Bohm quantum potential. A nonlinear thermo-quantum expression for the…
Motivated by a phenomenon of phase transition in a model of alignment of self-propelled particles, we obtain a kinetic mean-field equation which is nothing else than the Doi equation (also called Smoluchowski equation) with dipolar…
The Smoluchowsky equation for a system of interacting Brownian particles in a temperature gradient is derived from the Kramers equation by means of a multiple time-scale method. The interparticle interactions are assumed to be represented…
In this paper, we consider a continuous fragmentation--coagulation model in which the reacting particles can be transported in physical space through either advection or diffusion. We prove new results on the generation of $C_0$-semigroups…
In this paper we study the discrete coagulation--fragmentation models with growth, decay and sedimentation. We demonstrate the existence and uniqueness of classical global solutions provided the linear processes are sufficiently strong.…
We consider self-similar solutions to Smoluchowski's coagulation equation for kernels $K=K(x,y)$ that are homogeneous of degree zero and close to constant in the sense that \[ -\eps \leq K(x,y)-2 \leq \eps…
We compute the evolution of the space-dependent mass distribution of galaxies in clusters due to binary aggregations by solving a space-dependent Smoluchowski equation. We derive the distribution of intergalactic distance for different…