Related papers: On pattern formation in the thermodynamically-cons…
One of the classical models in mathematical biology is the Lotka-Volterra competition model, describing the dynamics of two populations competing for resources. Two possible regimes in this system are given by their coexistence or…
We analyze a one-dimensional two-scalar fields reaction advection diffusion model for the globally subcritical transition to turbulence. In this model, the homogeneous turbulent state is disconnected from the laminar one and disappears in a…
Pattern formation is ubiquitous in nature and the mechanism widely-accepted to underlay them is based on the Turing instability, predicted by Alan Turing decades ago. This is a non-trivial mechanism that involves nonlinear interaction terms…
The study of pattern-forming instabilities in reaction-diffusion systems on growing or otherwise time-dependent domains arises in a variety of settings, including applications in developmental biology, spatial ecology, and experimental…
From infiltration of water into the soil during rainstorms to seasonal plant growth and death, the ecohydrological processes that are thought to be relevant to the formation of banded vegetation patterns in drylands occur across multiple…
Spontaneous pattern formation is a phenomenon ubiquitous in nature, examples ranging from Rayleigh-Benard convection to the emergence of complex organisms from a single cell. In physical systems, pattern formation is generally associated…
Reaction-diffusion processes on networked systems have received mounting attention in the past two decades, and the corresponding theory of network dynamics has been continuously enriched with the advancement of network science. Recently,…
We typically observe large-scale outcomes that arise from the interactions of many hidden, small-scale processes. Examples include age of disease onset, rates of amino acid substitutions, and composition of ecological communities. The…
On the basis of new, concise foundations, this paper establishes the four laws of thermodynamics, the Maxwell relations, and the stability requirements for response functions, in a form applicable to global (homogeneous), local…
We introduce a nonstationary spatio-temporal statistical model for gridded data on the sphere. The model specifies a computationally convenient covariance structure that depends on heterogeneous geography. Widely used statistical models on…
We establish stability criterion for a two-class retrial system with Poisson inputs, general class-dependent service times and class-dependent constant retrial rates. We also characterise an interesting phenomenon of partial stability when…
Patterns in reaction-diffusion systems often contain two spatial scales; a long scale determined by a typical wavelength or domain size, and a short scale pertaining to front structures separating different domains. Such patterns naturally…
We discovered a new type of spiral wave solutions in reaction-diffusion systems --- spike spiral wave, which significantly differs from spiral waves observed in FitzHugh-Nagumo-type models. We present an asymptotic theory of these waves in…
In a differential approach elaborated, we study the evolution of the parameters of Gaussian, mixed, continuous variable density matrices, whose dynamics are given by Hermitian Hamiltonians expressed as quadratic forms of the position and…
Localized patterns in singularly perturbed reaction-diffusion equations typically consist of slow parts -- in which the associated solution follows an orbit on a slow manifold in a reduced spatial dynamical system -- alternated by fast…
Recently implemented quantum devices such as quantum processors and quantum simulators combine highly complicated quantum dynamics with high-resolution measurements. We present a passivity deformation methodology that sets thermodynamic…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
We consider a class of stochastic dynamical systems, called piecewise deterministic Markov processes, with states $(x, \s)\in \O\times \G$, $\O$ being a region in $\bbR^d$ or the $d$--dimensional torus, $\G$ being a finite set. The…
Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…
Motivated by the modeling of three-dimensional fluid turbulence, we define and study a class of stochastic partial differential equations (SPDEs) that are randomly stirred by a spatially smooth and uncorrelated in time forcing term. To…