Related papers: Pattern formations and optimal packing
We consider solving multi-objective optimization problems in a distributed manner by a network of cooperating and learning agents. The problem is equivalent to optimizing a global cost that is the sum of individual components. The…
This paper is to investigate the control problem of maximizing the net benefit of a single species while the cost of the resource allocation is minimized in a population model which can be described by a reaction diffusion advection…
When exposed to a thermal gradient, reaction networks can convert thermal energy into the chemical selection of states that would be unfavourable at equilibrium. The kinetics of reaction paths, and thus how fast they dissipate available…
The stochastic motion in a nonhomogeneous medium with traps is studied and diffusion properties of that system are discussed. The particle is subjected to a stochastic stimulation obeying a general L\'evy stable statistics and experiences…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
A simple reaction-diffusion-advection equation is proposed in a dichotomous tree network to discuss an optimal network. An optimal size ratio r is evaluated by the principle of maximization of total reaction rate. In the case of…
Graph is a prevalent discrete data structure, whose generation has wide applications such as drug discovery and circuit design. Diffusion generative models, as an emerging research focus, have been applied to graph generation tasks.…
Optimal control of diffusion processes is intimately connected to the problem of solving certain Hamilton-Jacobi-Bellman equations. Building on recent machine learning inspired approaches towards high-dimensional PDEs, we investigate the…
The fundamental solutions of diffusion equation for the local-equilibrium and nonlocal models are considered as the limiting cases of the solution of a problem related to consideration of the Brownian particles random walks. The differences…
We consider a singularly perturbed reaction diffusion problem as a first order two-by-two system. Using piecewise discontinuous polynomials for the first component and $H_{div}$-conforming elements for the second component we provide a…
A central problem in data analysis is the low dimensional representation of high dimensional data, and the concise description of its underlying geometry and density. In the analysis of large scale simulations of complex dynamical systems,…
This paper provides a new numerical strategy to solve fractional in space reaction-diffusion equations on bounded domains under homogeneous Dirichlet boundary conditions. Using the matrix transform method the fractional Laplacian operator…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
We study diffusion-driven pattern-formation in networks of networks, a class of multilayer systems, where different layers have the same topology, but different internal dynamics. Agents are assumed to disperse within a layer by undergoing…
Reaction-diffusion processes across layered media arise in several scientific domains such as pattern-forming E. coli on agar substrates, epidermal-mesenchymal coupling in development, and symmetry-breaking in cell polarisation. We develop…
We consider a reaction-diffusion system with discontinuous reaction terms modeled by non-ideal relays. The system is motivated by an epigenetic population model of evolution of two-phenotype bacteria which switch phenotype in response to…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
We consider the following geometric optics problem: Construct a system of two reflectors which transforms a spherical wavefront generated by a point source into a beam of parallel rays. This beam has a prescribed intensity distribution. We…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
We develop a description of diffusion limited growth in solid-solid transformations, which are strongly influenced by elastic effects. Density differences and structural transformations provoke stresses at interfaces, which affect the phase…