相关论文: Landscape dynamics, interbasin kinetics and ultram…
In principle, all of the dynamical complexities of many-body systems are encapsulated in the potential energy landscapes on which the atoms move - an observation that suggests that the essentials of the dynamics ought to be determined by…
We revisit the diffusion properties and the mean drift induced by an external field of a random walk process in a class of branched structures, as the comb lattice and the linear chains of plaquettes. A simple treatment based on scaling…
In this thesis, we study the diffusive and ballistic behaviors of random walk in random environment (RWRE) in an integer lattice with dimension at least 2. Our contributions are in three directions: a conditional law of large numbers and…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
Random walk has wide applications in many fields, such as machine learning, biology, physics, and chemistry. Random walk can be discrete or continuous in time and space. Asymmetric random walk could be described by drift-diffusion equation.…
We consider a generalised diffusion equation in two dimensions for modeling diffusion on a comb-like structures. We analyse the probability distribution functions and we derive the mean squared displacement in $x$ and $y$ directions.…
We conjecture that the random walk and the corresponding diffusion in the relativistic velocity space is an adequate method for describing the acceleration process in relativistic jets. Considering a simple toy model, the main features of…
We consider the group of permutations of the vertices of a lattice. A random walk is generated by unit steps that each interchange two nearest neighbor vertices of the lattice. We study the heat equation on the permutation group, using the…
The ground motion prediction equation is commonly used to predict the seismic intensity distribution. However, it is not easy to apply this method to seismic distributions affected by underground plate structures, which are commonly known…
Here we present the entropic dynamics formalism for networks. That is, a framework for the dynamics of graphs meant to represent a network derived from the principle of maximum entropy and the rate of transition is obtained taking into…
The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some…
We analyze differences in dynamics and in properties of the sampled potential energy landscape between different equilibrium trajectories, for a system of rigid water molecules interacting with a two body potential. On entering in the…
Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant…
We study small perturbations of diffusion processes in $\mathbb{R}^d$ that leave invariant a finite collection of hypersurfaces. Each surface is assumed to be repelling for the unperturbed process, and the unperturbed motion on each of the…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
This article analyzes the formulation of space-time continuous hyperbolic hydrodynamic models for systems of interacting particles moving on a lattice, by connecting their local stochastic lattice dynamics to the formulation of an…
L\'evy walk process is one of the most effective models to describe superdiffusion, which underlies some important movement patterns and has been widely observed in the micro and macro dynamics. From the perspective of random walk theory,…
We consider systems of mean-field interacting diffusions, where the pairwise interaction structure is described by a sparse (and potentially inhomogeneous) random graph. Examples include the stochastic Kuramoto model with pairwise…
The concept of fragility provides a possibility to rank different supercooled liquids on the basis of the temperature dependence of dynamic and/or thermodynamic quantities. We recall here the definitions of kinetic and thermodynamic…
We construct a N-dimensional Gaussian landscape with multiscale, translation invariant, logarithmic correlations and investigate the statistical mechanics of a single particle in this environment. In the limit of high dimension N>>1 the…