Related papers: On pattern formation in the thermodynamically-cons…
We analyse a dynamic control problem for scalar reaction-diffusion equations, focusing on the emulation of pattern formation through the selection of appropriate active controls. While boundary controls alone prove inadequate for…
In this paper we prove the nonlinear orbital stability of a large class of steady states solutions to the Hamiltonian Mean Field (HMF) system with a Poisson interaction potential. These steady states are obtained as minimizers of an energy…
Small systems in a thermodynamic medium --- like colloids in a suspension or the molecular machinery in living cells --- are strongly affected by the thermal fluctuations of their environment. Physicists model such systems by means of…
Understanding how patterns and travelling waves form in chemical and biological reaction-diffusion models is an area which has been widely researched, yet is still experiencing fast development. Surprisingly enough, we still do not have a…
A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade…
Motivated by recent physics papers describing rules for natural network formation, we study an elliptic-parabolic system of partial differential equations proposed by Hu and Cai. The model describes the pressure field thanks to Darcy's type…
In this paper we study pattern formation arising in a system of a single reaction-diffusion equation coupled with subsystem of ordinary differential equations, describing spatially-distributed growth of clonal populations of precancerous…
The implementation of a combination of continuous weak measurement and classical feedback provides a powerful tool for controlling the evolution of quantum systems. In this work, we investigate the potential of this approach from three…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
In this paper, we study properties and patterns on permutations of multisets whose multivariate generating functions are symmetric. We interpret this phenomenon through the lens of group actions and define such a property or pattern as…
We compare spot patterns generated by Turing mechanisms with those generated by replication cascades, in a model one-dimensional reaction-diffusion system. We determine the stability region of spot solutions in parameter space as a function…
We analyze the onset of classical field configurations after a phase transition. Firstly, we motivate the problem by means of a toy model in quantum mechanics. Subsequently, we consider a scalar field theory in which the system-field…
We present a combined numerical and analytical study of pattern formation in an active system where particles align, possess a density-dependent motility, and are subject to a logistic reaction. This is a model for suspensions of…
Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that…
Pattern formation in biological, chemical and physical problems has received considerable attention, with much attention paid to dissipative systems. For example, the Ginzburg--Landau equation is a normal form that describes pattern…
We present exact solutions for the non-equilibrium steady states of a class of dissipative spinless fermionic systems with arbitrary Hamiltonian pairing terms, global charging energy interactions, and uniform single particle loss on every…
A quasi-static process is realized in a purely quantum-mechanical model which is described by oscillator (or particle) systems having relative-phase interactions. Time development of a mixture of two oscillator (or particle) systems which…
We present results from comprehensive event-driven (ED) simulations of nonlinear pattern formation in freely-evolving granular gases. In particular, we focus on the the morphologies of density and velocity fields in the inhomogeneous…
We discuss parameter dependent polynomial ordinary differential equations that model chemical reaction networks. By classical quasi-steady state (QSS) reduction we understand the following familiar heuristic: Set the rate of change for…
This paper investigates pattern formation in reaction--diffusion systems with both diffusive and nondiffusive components, providing necessary and sufficient conditions for diffusion-driven instability (DDI) and establishing the existence of…