Related papers: Grow-up rate and refined asymptotics for a two-dim…
This work deals with a chemotaxis model where an external source involving a sub and superquadratic growth effect contrasted by nonlocal dampening reaction influences the motion of a cell density attracted by a chemical signal. We study the…
We consider the polynuclear growth (PNG) model in 1+1 dimension with flat initial condition and no extra constraints. The joint distributions of surface height at finitely many points at a fixed time moment are given as marginals of a…
Saturated random sequential adsorption packings built of two-dimensional ellipses, spherocylinders, rectangles, and dimers placed on a one-dimensional line are studied to check analytical prediction concerning packing growth kinetics [A.…
We study the scaling properties of the non-equilibrium stationary states (NESS) of a reaction-diffusion model. Under a suitable smallness condition, we show that the density of particles satisfies a law of large numbers with respect to the…
In this paper we consider the parabolic-parabolic Patlak-Keller-Segel models in $\mathbb{T}\times\mathbb{R}$ with advection by a large strictly monotone shear flow. Without the shear flow, the model is $L^1$ critical in two dimensions with…
We present a unifying, consistent, finite-size-scaling picture for percolation theory bringing it into the framework of a general, renormalization-group-based, scaling scheme for systems above their upper critical dimensions $d_c$.…
We study the global strong solutions to a 3-dimensional parabolic-hyperbolic Keller-Segel model with initial data close to a stable equilibrium with perturbations belonging to $L^2(\mathbb R^3)\times H^1(\mathbb{R}^3)$. We obtain global…
We consider the Keller-Segel model for chemotaxis with a nonlinear diffusion coefficent and a singular sensitivity function. We show the existence of travelling waves for wave speeds above a critical value, and establish local…
The Keller-Segel equations are widely used for describing chemotaxis in biology. Recently, a new fully discrete scheme for this model was proposed in [46], mass conservation, positivity and energy decay were proved for the proposed scheme,…
The problem of finding the asymptotic behavior of the maximal density of sphere packings in high Euclidean dimensions is one of the most fascinating and challenging problems in discrete geometry. One century ago, Minkowski obtained a…
In this paper, we study the two dimensional Peskin problem with general elasticity law. Specifically, we prove global regularity for small perturbations, in suitable critical spaces, of the circle solution, possibly containing corners. For…
We consider growing spheres seeded by random injection in time and space. Growth stops when two spheres meet leading eventually to a jammed state. We study the statistics of growth limited by packing theoretically in d dimensions and via…
We study statistical properties of the Kolmogorov-Avrami-Johnson-Mehl nucleation-and-growth model in one dimension. We obtain exact results for the gap density as well as the island distribution. When all nucleation events occur…
We evaluate the average expansion rate of a universe which contains a realistic evolving ensemble of non-linear structures. We use the peak model of structure formation to obtain the number density of structures, and take the individual…
We consider the two dimensional parabolic-elliptic Patlak-Keller-Segel model of chemotactic aggregation for radially symmetric initial data. We show the existence of a stable mechanism of singularity formation and obtain a complete…
The conditions in the protoplanetary disc are determinant for the various planet formation mechanisms. We present a framework which combines self-consistent disc structures with the calculations of the growth rates of planetary embryos via…
In this paper, we extend two classes of functions involved in asymptotic stability analyses. The goal of this extension is to study a maximization problem on the reachable values of a discrete-time dynamical system. This specific…
The massive Schwinger model is studied, using a density matrix renormalization group approach to the staggered lattice Hamiltonian version of the model. Lattice sizes up to 256 sites are calculated, and the estimates in the continuum limit…
The stellar mass dependence of the unbiased giant planet occurrence rate may be the best statistical tool to constrain the formation of such planets. This rate rises and falls as a function of stellar mass, peaking around stars of $\sim…
We analyze nonlinear degenerate coupled PDE-PDE and PDE-ODE systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular…