Related papers: General Expression for the Chemical System Respons…
This paper is a computational bifurcation analysis of a non-linear partial differential equation (PDE) characterizing equilibrium configurations in Micro electromechanical Systems (MEMS). MEMS are engineering systems that utilize…
The article presents new model of equilibrium in open chemical systems suggesting a linear dependence of the reaction shift from equilibrium in presence of the external thermodynamic force. Basic equation of this model contains traditional…
A consistent description of simultaneous heat and particle transport, including cross effects, and the associated entropy balance is given in the framework of a deterministic dynamical system. This is achieved by a multibaker map where,…
Chemical reactions can be understood as transformations of multigraphs (molecules) that preserve vertex labels (atoms) and degrees (sums of bonding and non-bonding electrons), thereby implying the atom-atom map of a reaction. The…
The article sets forth comprehensive basics of thermodynamics of chemical equilibrium as balance of the thermodynamic forces. Based on the linear equations of irreversible thermodynamics, De Donder definition of the thermodynamic force, and…
Generalized multibaker maps are introduced to model dissipative systems which are spatially extended only in certain directions and escape of particles is allowed in other ones. Effects of nonlinearity are investigated by varying a control…
The article investigates a possible influence of the open chemical system reaction to the external impact on the system transition to a new equilibrium. Potential system response is taken as a combination of various powers of the reaction…
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a…
The transition states and dividing surfaces used to find rate constants for bimolecular reactions are shown to undergo qualitative changes, known as Morse bifurcations, and to exist for a large range of energies, not just immediately above…
We develop a general classification of the nature of the instabilities yielding spatial organization in open nonideal reaction-diffusion systems, based on linear stability analysis. This encompasses dynamics where chemical species diffuse,…
Known graphical conditions for the generic or global convergence to equilibria of the dynamical system arising from a reaction network are shown to be invariant under the so-called successive removal of intermediates, a systematic procedure…
We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from…
We propose a new and general formalism for elementary chemical reactions where quantum electronic variables are used as reaction coordinates. This formalism is in principle applicable to all kinds of chemical reactions ionic or covalent.…
Polynomial dynamical systems (DSs) can model a wide range of physical processes. A special subset of these DSs that can model chemical reactions under mass-action kinetics is called chemical dynamical systems (CDSs). A fundamental problem,…
Chemical reactions involve the movement of charges, and this work presents a mathematical model for describing chemical reactions in electrolytes. The model is developed using an energy variational method that aligns with classical…
We study the long-time behavior of the solutions of a two-component reaction-diffusion system on the real line, which describes the basic chemical reaction $A <=> 2 B$. Assuming that the initial densities of the species $A, B$ are bounded…
The bulk macroscopic response of a system of particles or inclusions with field-induced forces is studied. The susceptibilities and transport coefficients in such a system are expressed as averages of a multiple scattering expansion. A…
The theory of chemical kinetics form the basis to describe the dynamics of chemical systems. Owing to physical and thermodynamic constraints, chemical reaction systems possess various structures, which can be utilized to characterize…
Diverse physical systems are characterized by their response to small perturbations. Near thermodynamic equilibrium, the fluctuation-dissipation theorem provides a powerful theoretical and experimental tool to determine the nature of…
We distinguish a mechanical representation of the world in terms of point masses with positions and momenta and the chemical representation of the world in terms of populations of different individuals, each with intrinsic stochasticity,…