Related papers: Turing instabilities on Cartesian product networks
Diffusion and flow-driven instability, or transport-driven instability, is one of the central mechanisms to generate inhomogeneous gradient of concentrations in spatially distributed chemical systems. However, verifying the transport-driven…
Spatial patterns arising spontaneously due to internal processes are ubiquitous in nature, varying from regular patterns of dryland vegetation to complex structures of bacterial colonies. Many of these patterns can be explained in the…
In a finite system driven out of equilibrium by a constant external force the thermodynamic uncertainty relation (TUR) bounds the variance of the conjugate current variable by the thermodynamic cost of maintaining the non-equilibrium…
Spreading phenomena essentially underlie the dynamics of various natural and technological networked systems, yet how spatiotemporal propagation patterns emerge from such networks remains largely unknown. Here we propose a novel approach…
The problem of remotely stabilizing a noisy linear time invariant plant over a Gaussian relay network is addressed. The network is comprised of a sensor node, a group of relay nodes and a remote controller. The sensor and the relay nodes…
The modeling of turbulence, whether it be numerical or analytical, is a difficult challenge. Turbulence is amenable to analysis with linear theory if it is subject to rapid distortions, i.e., motions occurring on a time scale that is short…
Liquids spreading over a solid substrate under the action of various forces are known to exhibit a long wavelength contact line instability. We use an example of thermally driven spreading on a horizontal surface to study how the stability…
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that…
We show how to treat supply networks as physical transport problems governed by balance equations and equations for the adaptation of production speeds. Although the non-linear behaviour is different, the linearized set of coupled…
We consider a reaction-diffusion equation on a network subjected to dynamic boundary conditions, with time delayed behaviour, also allowing for multiplicative Gaussian noise perturbations. Exploiting semigroup theory, we rewrite the…
Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the…
Neural networks have become increasingly popular in controller design due to their versatility and efficiency. However, their integration into feedback systems can pose stability challenges, particularly in the presence of uncertainties.…
We explore the problem of inferring the graph Laplacian of a weighted, undirected network from snapshots of a single or multiple discrete-time consensus dynamics, subject to parameter uncertainty, taking place on the network. Specifically,…
A central issue in the study of large complex network systems, such as power grids, financial networks, and ecological systems, is to understand their response to dynamical perturbations. Recent studies recognize that many real networks…
Rayleigh-Taylor (RT) instability commonly arises in compressible systems with time-dependent acceleration in practical applications. To capture the complex dynamics of such systems, a two-component discrete Boltzmann method is developed to…
The multiplicity of routes from deterministic chaos to turbulence caused by the spontaneous breaking of the local reflectional symmetry in the flows induced by Rayleigh-Taylor instability has been studied using the notion of distributed…
Differential diffusion is a source of instability in population dynamics systems when species diffuse with different rates. Predator-prey systems show this instability only under certain specific conditions, usually requiring Holling-type…
Our recent development of a novel research burner has made it possible to experimentally investigate truly unstretched and planar diffusion flames. Hence it has become feasible to directly validate theoretical models for thermal-diffusive…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
We investigate the linear instability of flows that are stable according to Rayleigh's criterion for rotating fluids. Using Taylor-Couette flow as a primary test case, we develop large Reynolds number matched asymptotic expansion theories.…