Non-equilibrium phase diagram of stationary states for low-pressure diamond growth

Now, it is well known that stable diamond growth and etching of graphite can berealized simultaneously under low pressures, but it is difficult to explain by classicalthermodynamics.Based on the non-equilibrium thermodynamic coupling theorem. low-pressure diamondgrowth can be explained clearly as follows:The change of Gibbs free energy (G) is the criterion of reaction direction at constant tem-perature and pressure. Therefore,

NON-EQUILIBRIUM STATIONARY STATE IN CHEMICAL REACTION OF SiO_2/Fe AT INTERFACE OF SLAG/METAL AND ITS STABILITY DURING ARC WELDING

For characteristics of open and far from thermodynamic equilibrium in welding chemical reaction, a new kind of quantitative method, which is used to analyze direction and extent for chemical reaction of SiO2/Fe during quasi-steady state period, is introduced with the concept of non-equilibrium stationary state. The main idea is based on thermodynamic driving forces, which result in non-zero thermodynamic fluxes and lead to chemical reaction far away from thermodynamic equilibrium. There exists certain dynamic equilibrium relationship between rates of diffusion fluxes in liquid phase of reactants or products and the rate equation of chemical reaction when welding is in quasi-steady state. As result of this, a group of non-linear equations containing concentrations of all substances at interface of slag/liquid-metal may be established. Moreover the stability of this non-equilibrium stationary state is discussed using dissipative structure theory and it is concluded theoretically that this non-equilibrium stationary state for welding chemical reaction is of stability.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional pe-riodic optical lattice potentials.The stationary state perturbation solutions of the coupled two-component nonlinearSchr?dinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method.Theoretical analysisrevels that the perturbation solution is the chaotic one,which indicates the existence of chaos and chaotic region inparameter space.The corresponding numerical calculation results agree well with the analytical results.By applying thechaotic perturbation solution,we demonstrate the atomic spatial population and the energy distribution of the systemare chaotic generally.

STABILITY OF STATIONARY STATE SOLUTION FOR A REACTION DENSITY-DEPENDENT DIFFUSION EQUATION

In this paper we are interested in the large time behavior of the nonlinear diffusion equationWe consider functions which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u= 0 or u=1 is unstable under some assumptions, etc.

Numerical Path Integral Approach to Quantum Dynamics and Stationary Quantum States

Applicability of Feynman path integral approach to numerical simulations of quantum dynamics of an electron in real time domain is examined.Coherent quantum dynamics is demonstrated with one dimensional test cases(quantum dot models)and performance of the Trotter kernel as compared with the exact kernels is tested.Also,a novel approach for finding the ground state and other stationary sates is presented.This is based on the incoherent propagation in real time.For both approaches the Monte Carlo grid and sampling are tested and compared with regular grids and sampling.We asses the numerical prerequisites for all of the above.

Entropy Production Rate Changes in Lysogeny/Lysis Switch Regulation of Bacteriophage Lambda

According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli （E. coil） infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.

A projective ternary phase diagram of stationary non-equilibrium states for low-pressure diamond growth

SINCE 1980,activated low-pressure diamond growth by chemical vapor deposition(CVD)pro-cess has been one of the worldwide interesting projects.However,in the last decades severalthermodynamic explanations were unsatisfactory.Bachmann et al.summarized a lot ofpublished experimental data into an empirical ternary carbon-hydrogen-oxygen(C-H-O)

Perturbative Treatment for Stationary State of Local Master Equation

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.

H^2-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach

The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H2- exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C norm are derived.