Related papers: A d dimensional nucleation and growth model
In this work, we consider a diffusive two-species d-dimensional model and study it in great details. Two types of particles, with hard-core, diffuse symmetrically and cross each other. For arbitrary dimensions, we obtain the exact density,…
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…
A modeling of the soil structure and surface roughness by means of the concepts of the fractal growth is presented. Two parameters are used to control the model: the fragmentation dimension, $D_f$, and the maximum mass of the deposited…
The results of the computer simulation of the aggregates growth of the similarly charged particles in the framework of deterministic Laplacian growth model on a square lattice are presented. Cluster growth is controlled by three parameters…
We characterize equilibrium properties and relaxation dynamics of a two-dimensional lattice containing, at each site, two particles connected by a double-well potential (dumbbell). Dumbbells are oriented in the orthogonal direction with…
In this article, several aspects of the dynamics of a toy model for longrange Hamiltonian systems are tackled focusing on linearly unstable unmagnetized (i.e. force-free) cold equilibria states of the Hamiltonian Mean Field (HMF). For…
Symmetry-breaking order at low temperatures is often accompanied by slow relaxation dynamics, due to diverging free-energy barriers arising from interfaces between different ordered states. Here, we extend this correspondence to classical…
Nucleation is a key step in the synthesis of new material from solution. Well-established lattice-gas models can be used to gain insight into the basic physics of nucleation pathways involving a single nucleus type. In many situations a…
The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond…
Motivated by recent interests in fracton topological phases, we explore the interplay between gapped 2D $\mathbb{Z}_N$ topological phases which admit fractional excitations with restricted mobility and geometry of the lattice on which such…
Decay of a high-energy double occupancy state, doublon, in a narrow-band lattice requires creation of a coherent many-particle excitation. This leads to an exponentially long relaxation time of such a state. We show that, if the average…
Two discrete N-level alternatives to the popular imaginary cubic oscillator are proposed and studied. In a certain domain ${\cal D}$ of parameters $a$ and $z$ of the model, the spectrum of energies is shown real (i.e., potentially,…
The model of competition between densities of two different species, called predator and prey, is studied on a one dimensional periodic lattice, where each site can be in one of the four states say, empty, or occupied by a single predator,…
The dual of an arbitrary $D$-dimensional nonabelian lattice gauge theory, obtained after character expansion and integration over the gauge group, is shown to be a {\em local} lattice theory in the eigenspace of the Casimir operators. For…
A method to reconstruct the energy landscape of small peptides is presented with reference to a 2d off--lattice model. The starting point is a statistical analysis of the configurational distances between generic minima and directly…
We show that the critical density of the Activated Random Walk model on $\mathbb{Z}^d$ is strictly less than one when the sleep rate $\lambda$ is small enough, and tends to $0$ when $\lambda\to 0$, in any dimension $d\geqslant 1$. As far as…
Exploiting the framework of peridynamics, a dimensionally-reduced plate formulation is developed that allows for the through-thickness nucleation and growth of fracture surfaces, enabling the treatment of delamination in a lower-dimensional…
We study numerically the thermalisation and temporal evolution of the reduced density matrix for a two-site subsystem of a fermionic Hubbard model prepared far from equilibrium at a definite energy. Even for very small systems near quantum…
We consider a vertex model in d dimensions characterized by lines which run in a preferred direction. We show that this vertex model is soluble if the weights of vertices with intersecting lines are given by a free-fermion condition, and…
Inspired by recent experiments on DNA replication, we apply a one-dimensional nucleation-and-growth model to DNA-replication kinetics, focusing on how to extract the time-dependent nucleation rate I(t) and growth speed v from data. We…