Related papers: Scaling limit of a discrete prion dynamics model
We prove convergence of renormalized correlations of primary fields, i. e., spins, disorders, fermions and energy densities, in the scaling limit of the critical Ising model in arbitrary finitely connected domains, with fixed (plus or…
Inhomogeneities in deposition may lead to formation of rough surfaces, whose height fluctuations can be probed directly by scanning microscopy, or indirectly by scattering. Analytical or numerical treatments of simple growth models suggest…
We present the results of a mixed action approach, employing dynamical twisted mass fermions in the sea sector and overlap valence fermions, with the aim of testing the continuum limit scaling behaviour of physical quantities, taking the…
Motivated by the recent contribution \cite{BB17} we study the scaling limit behavior of a class of one-dimensional stochastic differential equations which has a unique attracting point subject to a small additional repulsive perturbation.…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
Mathematical modelling of biological population dynamics often involves proposing high fidelity discrete agent-based models that capture stochasticity and individual-level processes. These models are often considered in conjunction with an…
By analogy with Carleson's observation on Cardy's formula describing crossing probabilities for the scaling limit of critical percolation, we exhibit ``privileged geometries'' for Stochastic Loewner Evolutions with various parameters, for…
In this paper, we study the dynamics of the ratio-dependent type prey-predator model with different free boundaries. The two free boundaries, determined by prey and predator respectively, implying that they may intersect each other as time…
For large $n$, take a random $n \times n$ permutation matrix and its associated discrete copula $X_n$. For $a, b = 0, 1, \ldots, n$, let $y_n(\frac{a}{n},\frac{b}{n}) = \frac{1}{n} ( X_{a,b} - \frac{ab}{n} )$; define $y_n: [0,1]^2 \to R$ by…
We present a numerical study on the dynamics of imbibition fronts in porous media using a pipe network model. This model quantitatively reproduces the anomalous scaling behavior found in imbibition experiments [Phys. Rev. E {\bf 52}, 5166…
In two papers we proposed a continuum model for the dynamics of systems of self propelling particles with kinematic constraints on the velocities and discussed some of its properties. The model aims to be analogous to a discrete algorithm…
A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the…
We present a model for stable crack growth in a constrained geometry. The morphology of such cracks show scaling properties consistent with self affinity. Recent experiments show that there are two distinct self-affine regimes, one on small…
Infection spread among individuals is modelled with a continuous time Markov chain, in which subject interactions depend on their distance in space. The well known SIR model and non local variants of the latter are then obtained as large…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
The double scaling limit of a new class of the multi-matrix models proposed in \cite{MMM91}, which possess the $W$-symmetry at the discrete level, is investigated in details. These models are demonstrated to fall into the same universality…
Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete…
Scaling relationships have been proposed to describe shear-driven size segregation based on intruder experiments and simulations. While these models have shown agreement with experimental and numerical results under uniform shear rate,…
We introduce a new phenomenological one-scale model for the evolution of domain wall networks, and test it against high-resolution field theory numerical simulations. We argue that previous numerical estimates of wall velocities are…
We discuss the asymptotic behaviour of models of lattice polygons, mainly on the square lattice. In particular, we focus on limiting area laws in the uniform perimeter ensemble where, for fixed perimeter, each polygon of a given area occurs…