Related papers: A Becker-D\"oring type model for cell polarization
We study Frenkel exciton-polariton Bose-Einstein condensation in a two-dimensional defect-free triangular photonic crystal with an organic semiconductor active medium containing bound excitons with dipole moments oriented perpendicular to…
This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…
In this paper we deal with diffusive relaxation limits of nonlinear systems of Euler type modeling chemotactic movement of cells toward Keller--Segel type systems. The approximating systems are either hyperbolic--parabolic or…
We study in detail the application of renormalisation theory to models of cluster aggregation and fragmentation of relevance to nucleation and growth processes. In particular, we investigate the Becker-Doring (BD) equations, originally…
We develop a nonperturbative approach to the bulk polarization of crystalline electric insulators in $d\geq1$ dimensions. Formally, we define polarization via the response to background fluxes of both charge and lattice translation…
A reaction-diffusion system with mass conservation modelling cell polarity is considered. A range of the parameters is found where the solution converges exponentially to the constant equilibrium and the $\omega$-limit set of the solution…
We prove an explicit formula for the Bergman kernel of polarized abelian varieties. As applications, we show that if two positive line bundles represent the same first Chern class and have identical Bergman kernel functions for some tensor…
We develop a model in the framework of nuclear fragmentation at thermodynamic equilibrium which can be mapped onto an Ising model with constant magnetization. We work out the thermodynamic properties of the model as well as the properties…
Reaction-diffusion systems have been widely used to study spatio-temporal phenomena in cell biology, such as cell polarization. Coupled bulk-surface models naturally include compartmentalization of cytosolic and membrane-bound polarity…
We compute the polarization power spectra for global strings, monopoles, textures and nontopological textures, and compare them to inflationary models. We find that topological defect models predict a significant (1 microK) contribution to…
We consider the thermal behavior of a large number of matrix degrees of freedom in the planar limit. We work in $0+1$ dimensions, with $D$ matrices, and use $1/D$ as an expansion parameter. This can be thought of as a non-commutative…
Condensation of microcavity polaritons and the substantial influence of pair-breaking disorder and decoherence leading to a laser regime has been recently considered using two different models: a model for direct two band excitons in a…
In this note, we study an infinite reaction network called the stochastic Becker-D\"oring process, a sub-class of the general coagulation-fragmentation models. We prove pathwise convergence of the process towards the deterministic…
Concentration gradients of signaling molecules are essential for patterning during development and they have been observed in both unicellular and multicellular systems. In subcellular systems, clustering of the signaling molecule has been…
Cell polarity and movement are fundamental to many biological functions. Experimental and theoretically studies have indicated that interactions of certain proteins lead to the cell polarization which plays a key role in controlling the…
For a coagulation equation with Becker-Doring type interactions and time-independent monomer input we study the detailed long-time behaviour of nonnegative solutions and prove the convergence to a self-similar function.
We prove the following asymptotic behavior for solutions to the generalized Becker-D\"oring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical…
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. This representation is based upon a triangular matrix of transition rates. We expand the state vector of mass multiplicities, which…
We examine the validity of the hypothesis of self-similarity in systems coarsening under the driving force of interface energy reduction in which three dimensional particles are intersected by a one or two dimensional diffusion matrix. In…
We develop the first theoretical model for the analytical description of ion concentration polarization (ICP)-based electrokinetic molecular concentration, which had not been possible due to the extraordinary complexity of the system. We…