Related papers: Local persistense and blocking in the two dimensio…
The generalization of dynamical scaling to local scale invariance is reviewed. Starting from a recapitulation of the phenomenology of ageing phenomena, the generalization of dynamical scaling to local scale transformation for any given…
We study the mathematical theory of second order systems with two species, arising in the dynamics of interacting particles subject to linear damping, to nonlocal forces and to external ones, and resulting into a nonlocal version of the…
This paper establishes a link between the non-local behaviour of granular materials and the presence of transient clusters of jammed particles within the flow. These clusters are first evidenced in simulated dense granular flows subjected…
The zero-temperature Glauber dynamic is used to investigate the persistence probability $P(t)$ in the randomic two-dimensional ferromagnetic Ising model on a Voronoi-Delaunay tessellation. We consider the coupling factor $J$ varying with…
We study purely dissipative relaxational dynamics in the three-dimensional Ising universality class. To this end, we simulate the improved Blume-Capel model on the simple cubic lattice by using local algorithms. We perform a finite size…
In this paper, we study the initial-boundary value problem of a repulsion Keller--Segel system with a logarithmic sensitivity modeling the reinforced random walk. By establishing an energy-dissipation identity, we prove the existence of…
In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane $\mathbb{R}^2$ or a bounded strip…
Local conserved charges in principal chiral models in 1+1 dimensions are investigated. There is a classically conserved local charge for each totally symmetric invariant tensor of the underlying group. These local charges are shown to be in…
We study a two-dimensional quaternary inhibitory system. This free energy functional combines an interface energy favoring micro-domain growth with a Coulomb-type long range interaction energy which prevents micro-domains from unlimited…
We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either…
For an anisotropic euclidean $\phi^4$-theory with two interactions $[u (\sum_{i=1^M {\phi}_i^2)^2+v \sum_{i=1}^M \phi_i^4]$ the $\beta$-functions are calculated from five-loop perturbation expansions in $d=4-\varepsilon$ dimensions, using…
We consider a nonlocal parabolic equation describing the dynamics of a population structured by a spatial position and a phenotypic trait, submitted to dispersion , mutations and growth. The growth term may be of the Fisher-KPP type but may…
We consider concentric circular defects in the two-dimensional Ising model, which are distributed according to a generalized Fredholm sequence, i. e. at exponentially increasing radii. This type of aperiodicity does not change the bulk…
We consider a model of cell motion with boundary signal production which describes some aspects of eukaryotic cell migration. Generic polarity markers located in the cell are transported by actin which they help to polymerize. This leads to…
We investigate the life time distribution in one and two dimensional coarsening processes modelled by Ising - Glauber dynamics at zero temperature. We find that the life time distribution obeys a scaling ansatz, asymptotically. An…
We introduce a new class of nonlocal nonlinear conservation laws in one space dimension that allow for nonlocal interactions over a finite horizon. The proposed model, which we refer to as the nonlocal pair interaction model, inherits at…
In this article, we present a method to find a solution to a one-dimensional nonlocal conservation law that respects a space-dependent mapping, referred to as the obstacle. This is achieved by generalizing existing results for the local…
We analyze the situation of a local quantum field theory with constraints, both indexed by the same set of space-time regions. In particular we find ``weak'' Haag-Kastler axioms which will ensure that the final constrained theory satisfies…
First, we systemize ealier results the uniform persistence for discrete model $A_{n+1}=A_nF(A_{n-m})$ of population growth, where $F:(0,\infty)\to(0,\infty)$ is continuous and strictly decreasing. Second, we investigation the effect of…
We introduce a rigorous approach to the study of the symmetry breaking and pattern formation phenomenon for isotropic functionals with local/nonlocal interactions in competition. We consider a general class of nonlocal variational problems…