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The responsivity of perturbation sensing can be effectively enhanced by using higher-order exceptional points (HOEPs) due to their nonlinear response to frequency perturbations. However, experimental realization can be difficult due to the…
Large time dynamics of reaction-diffusion systems modeling some irreversible reaction networks are investigated. Depending on initial masses, these networks possibly possess boundary equilibria, where some of the chemical concentrations are…
In this paper, we present the construction of tensor network states (TNS) for some of the degenerate ground states of 3D stabilizer codes. We then use the TNS formalism to obtain the entanglement spectrum and entropy of these ground-states…
Recent studies of nonequilibrium phase transitions have shown that in many systems which have transitions involving an arrested phase, the arrested states show suppressed density fluctuations and a cusp in the configurational entropy at the…
We introduce a new measure of instability of area-preserving twist diffeomorphisms, which generalizes the notions of angle of splitting of separatrices, and flux through a gap of a Cantori. As an example of application, we establish a sharp…
We demonstrate that the shallow water moment equations satisfy an auxiliary entropy conservation law, where the entropy function corresponds to the total energy. Additionally, we show that the classical Newtonian slip friction and Manning…
Filyokov and Karpov [Inzhenerno-Fizicheskii Zhurnal 13, 624 (1967)] have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states : the principle is to maximize the Shannon entropy…
Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…
A basic model of a dynamical distribution network is considered, modeled as a directed graph with storage variables corresponding to every vertex and flow inputs corresponding to every edge, subject to unknown but constant inflows and…
This work is devoted to the construction of feedback laws which guarantee the robust global exponential stability of the uncongested equilibrium point for general discrete-time freeway models. The feedback construction is based on a control…
The algebraic flux correction (AFC) schemes presented in this work constrain a standard continuous finite element discretization of a nonlinear hyperbolic problem to satisfy relevant maximum principles and entropy stability conditions. The…
We examine the thermalisation/localization trade off in an interacting and disordered Kitaev model, specifically addressing whether signatures of many-body localization can coexist with the systems topological phase. Using methods…
Linear-threshold networks (LTNs) capture the mesoscale behavior of interacting populations of neurons and are of particular interest to control theorists due to their dynamical richness and relative ease of analysis. The aim of this paper…
We study necessary and sufficient conditions for contraction and incremental stability of dynamical systems with respect to non-Euclidean norms. First, we introduce weak pairings as a framework to study contractivity with respect to…
This chapter concerns "control volume analysis", the standard engineering tool for the analysis of flow systems, and its application to entropy balance calculations. Firstly, the principles of control volume analysis are enunciated and…
We study the existence and long-time asymptotics of weak solutions to a system of two nonlinear drift-diffusion equations that has a gradient flow structure in the Wasserstein distance. The two equations are coupled through a…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
In this work we analyze the entropic properties of the Euler equations when the system is closed with the assumption of a polytropic gas. In this case, the pressure solely depends upon the density of the fluid and the energy equation is not…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
Recent development of contraction theory based analysis of singularly perturbed system has opened the door for inspecting differential behavior of multi time-scale systems. In this paper a contraction theory based framework is proposed for…