Related papers: Hamiltonian Perspective on Compartmental Reaction-…
We present an adaptive algorithm that guarantees synchronization in diffusively coupled systems. We first consider compartmental systems of ODEs, where each compartment represents a spatial domain of components interconnected through…
Nakao and Mikhailov proposed using continuous models (mean-field models) to study reaction-diffusion systems on networks and the corresponding Turing patterns. This work aims to show that p-adic analysis is the natural tool to carry out…
Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing…
Reaction-diffusion systems where transition rates exhibit quenched disorder are common in physical and chemical systems. We study pair reactions on a periodic two-dimensional lattice, including continuous deposition and spontaneous…
Reaction networks are widely used models to describe biochemical processes. Stochastic fluctuations in the counts of biological macromolecules have amplified consequences due to their small population sizes. This makes it necessary to favor…
In this paper, we are concerned with the state feedback stabilization of ODE-PDE cascade systems governed by a linear ordinary differential equation and the 1-d reaction-diffusion equation posed on a bounded interval. In contrast to the…
We introduce the geometric structure underlying the port-Hamiltonian models for distributed parameter systems exhibiting moving material domains.
This is a pedagogical account on reaction-diffusion systems and their relationship with integrable quantum spin chains. Reaction-diffusion systems are paradigmatic examples of non-equilibrium systems. Their long-time behaviour is strongly…
We study the diffusion phenomena on the negatively curved surface made up of congruent heptagons. Unlike the usual two-dimensional plane, this structure makes the boundary increase exponentially with the distance from the center, and hence…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
Diffusion within porous media, such as biological tissues, exhibits departures from conventional Fick's laws, which could result in space-fractional diffusion. The paper considers a reaction-diffusion system with two spatial compartments --…
A crisp survey is given of chemical reaction networks from the perspective of general nonlinear network dynamics, in particular of consensus dynamics. It is shown how by starting from the complex-balanced assumption the reaction dynamics…
We survey recent results on reaction-diffusion equations with discontinuous hysteretic nonlinearities. We connect these equations with free boundary problems and introduce a related notion of spatial transversality for initial data and…
The stationary state of stochastic processes such as reaction-diffusion systems can be related to the ground state of a suitably defined quantum Hamiltonian. Using this analogy, we investigate the applicability of a real space…
Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
This paper establishes existence, uniqueness, and an L^1-comparison principle for weak solutions of a PDE system modeling phase transition reaction-diffusion in congested crowd motion. We consider a general reaction term and mixed…
One-dimensional reaction-diffusion systems are mapped through a similarity transformation onto integrable (and a priori non-stochastic) quantum chains. Time-dependent properties of these chemical models can then be found exactly. The…
This paper addresses the derivation of generic and tractable sufficient conditions ensuring the stability of a coupled system composed of a reaction-diffusion partial differential equation (PDE) and a finite-dimensional linear time…
This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…