Related papers: A Becker-D\"oring type model for cell polarization
Ionic crystals, such as solid electrolytes and complex oxides, are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum-scale…
Bessel processes $(X_{t,k})_{t\ge0}$ in $N$ dimensions are classified via associated root systems and multiplicity constants $k\ge0$. They describe interacting Calogero-Moser-Suther\-land particle systems with $N$ particles and are related…
We study hydrodynamic limits of the cluster coagulation model; a coagulation model introduced by Norris [$\textit{Comm. Math. Phys.}$, 209(2):407-435 (2000)]. In this process, pairs of particles $x,y$ in a measure space $E$, merge to form a…
We demonstrate algorithm for numerical modelling of Bose-Einstein correlations (BEC) formulated on quantum statistical level for a single event and exploring the property that identical particles subjected to Bose statistics do bunch…
An interesting problem in statistical physics is the condensation of classical particles in droplets or clusters when the pair-interaction is given by a stable Lennard-Jones-type potential. We study two aspects of this problem. We start by…
We present a model for sticky particles in which cluster sizes after a reaction have $\ell$ fewer total particles than the sum of their reactants. The finite particle system is modeled as a Markov process under a mean-field assumption for…
I present some simple exactly solvable models of spin diffusion caused by synchrotron radiation noise in storage rings. I am able to use standard stochastic differential equation and Fokker-Planck methods and I thereby introduce, and…
The lepton polarization asymmetry in the B\to\ell^{+}\ell^{-} decay, when one of the leptons is polarized, is investigated using the most general form of the effective Hamiltonian. The sensitivity of the asymmetry to the new Wilson…
A novel mechanism for cell differentiation is proposed, based on the dynamic clustering in a globally coupled chaotic system. A simple model with metabolic reaction, active transport of chemicals from media, and cell division is found to…
We prove that any subcritical solution to the Becker-D\"{o}ring equations converges exponentially fast to the unique steady state with same mass. Our convergence result is quantitative and we show that the rate of exponential decay is…
We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on…
We consider the problem of gelation in the cluster coagulation model introduced by Norris [\textit{Comm. Math. Phys.}, 209(2):407-435 (2000)], where pairs of clusters of types $(x,y)$ taking values in a measure space $E$, merge to form a…
Driving the analogy between the coherent excitation of a two-state quantum system and the torque equation of motion, we present exact analytic solutions to different models for manipulation of polarization in birefringent medium. These…
Coagulation-fragmentation processes describe the stochastic association and dissociation of particles in clusters. Cluster dynamics with cluster-cluster interactions for a finite number of particles has recently attracted attention…
This paper aims to develop numerical approximations of the Keller--Segel equations that mimic at the discrete level the lower bounds and the energy law of the continuous problem. We solve these equations for two unknowns: the organism (or…
We develop a simple computational model for cell boundary evolution in plastic deformation. We study the cell boundary size distribution and cell boundary misorientation distribution that experimentally have been found to have scaling forms…
We demonstrate that collective vibrational strong coupling of molecules in thermal equilibrium can give rise to significant local electronic polarizations in the thermodynamic limit. We do so by first showing that the full non-relativistic…
A Balancing Domain Decomposition by Constraints (BDDC) preconditioner is constructed and analyzed for the solution of composite Discontinuous Galerkin discretizations of reaction-diffusion systems of ordinary and partial differential…
We consider a parabolic non-local free boundary problem that has been derived as a limit of a bulk-surface reaction-diffusion system which models cell polarization. In previous papers, we have established well-posedness of this problem and…
We consider the quasi-classical limit of Nelson-type regularized polaron models describing a particle interacting with a quantized bosonic field. We break translation-invariance by adding an attractive external potential decaying at…