Related papers: Diffusion in networks with time-dependent transmis…
The study of diffusion in Hamiltonian systems has been a problem of interest for a number of years. In this paper we explore the influence of self-consistency on the diffusion properties of systems described by coupled symplectic maps.…
We study the dynamics of flow-networks in porous media using a pore-network model. First, we consider a class of erosion dynamics assuming a constitutive law depending on flow rate, local velocities, or shear stress at the walls. We show…
One of the first steps in applications of statistical network analysis is frequently to produce summary charts of important features of the network. Many of these features take the form of sequences of graph statistics counting the number…
Quantum graphs model processes in complex systems represented as spatial networks in various fields of natural science and technology. An example is the oscillations of elastic string networks, the nodes of which, besides the continuity…
We consider a class of infinite dimensional (distributed) pH systems which is invariant under Kirchhoff-type interconnections and prove exponential stability and a power balance equation for classical solutions. The results are illustrated…
The uniform shear flow for the rarefied gas is governed by the time-dependent spatially homogeneous Boltzmann equation with a linear shear force. The main feature of such flow is that the temperature may increase in time due to the shearing…
Abstract. The present work considers a change in the momentum under the transfer of a solution through the interface. It is shown that pressure related to the partial volumes of components arises in a solution under diffusion. As a result,…
Starting from Namah and Roquejoffre (Commun. Partial Differ. Equations, 1999) and Fathi (C. R. Acad. Sci., Paris, S\'er. I, Math., 1998), the large time asymptotic behavior of solutions to Hamilton-Jacobi equations has been extensively…
The fast diffusion equation is analyzed on a bounded domain with Dirichlet boundary conditions, for which solutions are known to extinct in finite time. We construct invariant manifolds that provide a finite-dimensional approximation near…
We consider a reaction-diffusion system for two densities lying in adjacent domains of $\mathbb{R}^N$. We treat two configurations: either a cylinder and its complement, or two half-spaces. Diffusion and reaction heterogeneities for the two…
Adaptive networks are well-suited to perform decentralized information processing and optimization tasks and to model various types of self-organized and complex behavior encountered in nature. Adaptive networks consist of a collection of…
A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…
This paper is devoted to the inverse problem of determining the spatially dependent source in a time fractional diffusion-wave equation, with the aid of extra measurement data at subboundary. Uniqueness result is obtained by using the…
We investigate the phenomenon of diffusion in a countably infinite society of individuals interacting with their neighbors in a network. At a given time, each individual is either active or inactive. The diffusion is driven by two…
Soliton transport in tube-like networks is studied by solving the nonlinear Schroedinger equation (NLSE) on finite thickness ("fat") graphs. The dependence of the solution and of the reflection at vertices on the graph thickness and on the…
Regime switching processes have proved to be indispensable in the modeling of various phenomena, allowing model parameters that traditionally were considered to be constant to fluctuate in a Markovian manner in line with empirical findings.…
Proximity networks are time-varying graphs representing the closeness among humans moving in a physical space. Their properties have been extensively studied in the past decade as they critically affect the behavior of spreading phenomena…
We derive a simple sufficient condition for the local asymptotic stability of spatially discrete, continuous-time reaction-diffusion systems of networked dynamical systems at a homogeneous equilibrium point. The framework explicitly…
Reaction-diffusion equations with a nonlinear source have been widely used to model various systems, with particular application to biology. Here, we provide a solution technique for these types of equations in $N$-dimensions. The…
The adsorption phenomenon of neutral particles from the limiting surfaces of the sample in the Langmuir approximation is investigated. The diffusion equation regulating the redistribution of particles in the bulk is assumed to be of…