Related papers: Analyzing Turing's Systems via Dynamic Bifurcation…
We develop a rigorous, field-theoretical approach to the study of spontaneous emission in inertial and dissipative nematic liquid crystals, disclosing an alternative application of the massive Stueckelberg gauge theory to describe critical…
Different perturbation theory treatments of the Ginzburg-Landau phase transition model are discussed. This includes a criticism of the perturbative renormalization group (RG) approach and a proposal of a novel method providing critical…
Although the roll/streak structure is ubiquitous in pre-transitional wall-bounded shear flow, this structure is linearly stable if the idealization of laminar flow is made. Lacking an instability, the large transient growth of the…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
The low-temperature properties and crossover phenomena of $d$-dimensional transverse Ising-like systems within the influence domain of the quantum critical point are investigated solving the appropriate one-loop renormalization group…
Nonlocal interactions are ubiquitous in nature and play a central role in many biological systems. In this paper, we perform a bifurcation analysis of a widely-applicable advection-diffusion model with nonlocal advection terms describing…
We face the problem of detecting and featuring footprints of quantum criticality in the finite-temperature behavior of quantum many-body systems. Our strategy is that of comparing the phase diagram of a system displaying a T=0 quantum phase…
We report new measurements of single particle dispersion in turbulent two-dimensional (2D) flows. Laboratory experiments in electromagnetically driven and Faraday wave driven turbulence reveal a transition from weakly dispersing…
Two classes of time-periodic systems of ordinary differential equations with a small nonnegative parameter, those with fast and slow time, are studied. Right-hand sides of these systems are three times continuously differentiable with…
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both…
Alan Turing's work in Morphogenesis has received wide attention during the past 60 years. The central idea behind his theory is that two chemically interacting diffusible substances are able to generate stable spatial patterns, provided…
The population model of Busenberg and Travis is a paradigmatic model in ecology and tumour modelling due to its ability to capture interesting phenomena like the segregation of populations. Its singular mathematical structure enforces the…
This is the first of two articles on the study of a particle system model that exhibits a Turing instability type effect. The model is based on two discrete lines (or toruses) with Ising spins, that evolve according to a continuous time…
This paper analyzes the stability of a reactiondiffusion equation coupled with a finite-dimensional controller through Dirichlet boundary input and Neumann boundary output. Going against the flow, we intend to propose numerical certificates…
Systems switching between different dynamical phases is an ubiquitous phenomenon. The general understanding of such a process is limited. To this end, we present a general expression that captures fluctuations of a system exhibiting a…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
Current early warning signs for tipping points often fail to distinguish between catastrophic shifts and less dramatic state changes, such as spatial pattern formation. This paper introduces a novel method that addresses this limitation by…
Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…
This study explores transitions between states with different winding number in two-band superconducting rings. From the time-dependent Ginzburg-Landau (TDGL) equations for two-component superconductors, we apply linear instability theory…
In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude…