Related papers: General Expression for the Chemical System Respons…
Spatio-temporal bifurcations and complex dynamics in globally coupled intrinsically bistable electrochemical systems with an S-shaped current-voltage characteristic under galvanostatic control are studied theoretically on a one-dimensional…
We build a rigorous nonequilibrium thermodynamic description for open chemical reaction networks of elementary reactions. Their dynamics is described by deterministic rate equations satisfying mass action law. Our most general framework…
The GENERIC theory provides a framework for the description of non-equilibrium phenomena in isolated systems beyond local thermal equilibrium and beyond linear non-equilibrium (i.e., linear relations between thermodynamic forces and…
The response of many materials to applied forces and boundary constraints depends upon internal geometric changes at multiple submacroscopic levels. Hierarchical structured deformations provide a mathematical setting for the description of…
As an important set of thermodynamic quantities, knowledge of the equation of state over a broad range of temperatures and chemical potentials in the QCD phase diagram is crucial for our understanding of strongly-interacting matter. There…
This paper is devoted to the analysis of global stability of the chemostat system with a perturbation term representing any type of exchange between species. This conversion term depends on species and substrate concentrations but also on a…
We present a systematic mathematical analysis of the qualitative steady-state response to rate perturbations in large classes of reaction networks. This includes multimolecular reactions and allows for catalysis, enzymatic reactions,…
Experiments observing the liquid surface in a vertically oscillating container have indicated that modeling the dynamics of such systems require maps that admit states at infinity. In this paper we investigate the bifurcations in such a…
We investigate classes of interacting systems that allow for a mapping to disordered noninteracting systems. As we show, such a mapping is possible for interacting systems with a suppressed density of states at the chemical potential,…
The paper explores a possible application of the discrete thermodynamics to a 2-level laser. The model accounts for the laser openness to incoming pumping power and coming out energy with the emitted light. As an open system, a laser should…
We analyze a system of globally coupled logistic maps with asynchronous updating. We show that its dynamics differs considerably from that of the synchronous case. For growing values of the coupling intensity, an inverse bifurcation cascade…
In living cells, chemical reactions form a complex network. Complicated dynamics arising from such networks are the origins of biological functions. We propose a novel mathematical method to analyze bifurcation behaviors of a reaction…
A new variational method for studying the equilibrium states of an interacting particles system has been proposed. The statistical description of the system is realized by means of a density matrix. This method is used for description of…
In equilibrium systems with short-ranged interactions, the relative stability of different thermodynamic states generally does not depend on system size (as long as this size is larger than the interaction range). Here, we use a large…
Originating from the pioneering study of Alan Turing, the bifurcation analysis predicting spatial pattern formation from a spatially uniform state for diffusing morphogens or chemical species that interact through nonlinear reactions is a…
We discuss how the thermalization of an elementary quantum system is modified when the system is placed in an environment out of thermal equilibrium. To this aim we provide a detailed investigation of the dynamics of an atomic system placed…
We present two approaches for describing chemical reactions taking place in fluid phase. The first method mirrors the usual derivation of the hydrodynamic equations of motion by relating conserved---or to account for chemical reactions,…
The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium, that have yet to relax to a steady state. A relation between information, escape rate, and the…
We obtain exact analytic expressions for a class of functions expressed as integrals over the Haar measure of the unitary group in d dimensions. Based on these general mathematical results, we investigate generic dynamical properties of…
Feedback circuits in biochemical networks which underly cellular signaling pathways are important elements in creating complex behavior. A specific aspect thereof is how stability of equilibrium points depends on model parameters. For…