QUESTIONS AND PROBLEMS OF MATHEMATICAL MODELING QUA NONEQUILIBRIUM OF COMBUSTION PROCESSES

2020 ◽  
Vol 8 (4) ◽  
pp. 31-38
Author(s):  
E.V. Radkevich ◽  
◽  
N.N. Yakovlev ◽  
O.A. Vasil’eva ◽  
◽  
...  
Keyword(s):  
Phase Space ◽  
Chemical Potential ◽  
Blow Up ◽  
Local Equilibrium ◽  
Combustion Process ◽  
Passive Component ◽  
Component Mixture ◽  
Total Differential ◽  
Standard Chemical Potential ◽  
Component Velocity

On the basis of thermodynamic analysis, new mathematical models of the combus- tion process (thermal theory) and vibrational combustion are constructed. A global inhomo- geneity of the system can be described as an inhomogeneous distribution of the enthalpy over a two-component mixture. In this case, for the combustion process in the phase space of the variables (%, P, T, n, S, E), an increase in the enthalpy is not a total differential. An increase in the enthalpy is a total differential on the local equilibrium manifold (a laminar combustion process). These two assertions, which allow one to single out in the phase space the corre- sponding adiabatic of the combustion process (the Hugoniot adiabatic) and the equation for the entropy, close the classical mathematical model of the combustion process. The above numerical experiments show that two regimes of the combustion process (deflagration and detonation) depend on the structure of the standard chemical potential Moreover, a control of the passive component velocity at the inlet results in (depending on the structure of the standard chemical potential) high-frequency oscillations, which are responsible for a blow-up.

scholarly journals Simulation of Vibration Combustion

2021 ◽  
Vol 263 ◽  
pp. 02024
Author(s):  
Evgeny Radkevich ◽  
Olga Vasil’eva
Keyword(s):  
Mathematical Model ◽  
Chemical Potential ◽  
Numerical Results ◽  
Component Mixture ◽  
One Dimensional ◽  
Two Component ◽  
Standard Chemical Potential ◽  
Dimensionless Variables

We consider a mathematical model of the laminar process of vibration combustion proposed recently. It allows us to simulate detonation and deflagration modes, the occurrence of which occurs depending on the structure of the standard chemical potential. For simplicity of presentation and analysis, we consider a one-dimensional mathematical model formulated for the reduced dimensionless variables for the case of a two-component mixture. The obtained numerical results are presented and discussed.

PATH INTEGRAL QUANTIZATION OF SUPERSTRING

2010 ◽  
Vol 25 (02) ◽  
pp. 135-141
Author(s):  
H. A. ELEGLA ◽  
N. I. FARAHAT
Keyword(s):  
Phase Space ◽  
Differential Equations ◽  
Path Integral ◽  
Equations Of Motion ◽  
Singular System ◽  
Constrained Systems ◽  
Classical Structure ◽  
Path Integral Quantization ◽  
Total Differential

Motivated by the Hamilton–Jacobi approach of constrained systems, we analyze the classical structure of a four-dimensional superstring. The equations of motion for a singular system are obtained as total differential equations in many variables. The path integral quantization based on Hamilton–Jacobi approach is applied to quantize the system, and the integration is taken over the canonical phase space coordinates.

scholarly journals On hydrodynamics in the presense of strong external potential field

2021 ◽  
Vol 29 (1) ◽  
pp. 21-28
Author(s):  
A. I. Sokolovsky ◽  
S. A. Sokolovsky
Keyword(s):  
Distribution Function ◽  
Kinetic Equation ◽  
Potential Field ◽  
Chemical Potential ◽  
Local Equilibrium ◽  
Practical Importance ◽  
External Potential ◽  
Equilibrium Distribution Function ◽  
Kinetic Coefficients ◽  
Functional Hypothesis

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.

scholarly journals Kovats retention index-boiling point relationship of 2-phenyl-2-alkyl-acetonitriles on stationary phases of different polarity

2005 ◽  
Vol 11 (2) ◽  
pp. 55-58 ◽  
Author(s):  
Dusan Mijin ◽  
Dusan Antonovic
Keyword(s):  
Stationary Phase ◽  
Retention Index ◽  
Boiling Point ◽  
Chemical Potential ◽  
Stationary Phases ◽  
Kovats Retention Index ◽  
Standard Chemical Potential ◽  
Relationship Of ◽  
Kováts Retention Index ◽  
Methylene Group

Linear and reciprocial Kovats retention index-boiling point relationships known from the literature were used to study the Kovats retention index-boiling point dependence of 2-phenyl-2-alkylacetonitriles on stationary phases of different polarity (OV-17, OV-210 and OV-225). The standard chemical potential of the partitioning of one methylene group of an n-alkane for the stationary phase was calculated and compared with available literature data.

Chemico-Physical Causes of Radiation-Induced “Long Cell” Action Corrosion in Water Cooled Reactors

2010 ◽  
Author(s):  
Genn Saji
Keyword(s):  
Chemical Potential ◽  
Cooling System ◽  
Radiation Chemistry ◽  
Potential Difference ◽  
Equilibrium Potential ◽  
Corrosion Mechanism ◽  
Hydrated Electrons ◽  
Standard Chemical Potential ◽  
Radiation Induced ◽  
Reactor Types

In the previous overview papers [1, 2], the author has identified that ‘long cell action’ corrosion plays a pivotal role in practically all unresolved corrosion issues, irrespective of reactor types and operation. In trying to confirm the existence of radiation-induced ‘long-cell’ action (macro) corrosion cell in the primary cooling system of LWRs, the author attempted to theoretically reproduce the electrochemical potential difference demonstrated during experiments at the INCA Loop in Sweden and the NRI-Rez Loop in the Czech Republic [3, 4]. By performing a radiation chemistry kinetics study combined with electrochemistry calculations, the hydrated electrons, e−aq, reacting mainly with stable molecules, are found to be responsible for inducing a large portion of the potential difference both in the PWR and BWR water chemistry environment. Considering large uncertainties, the author used the standard equilibrium potential as a fitting parameter in the previous studies [3, 4]. The standard chemical potential of the hydrated electron estimated from the fitting parameter is far less than the generally accepted value of 2.86 V. In order to resolve the large discrepancy between the generally accepted values and the estimation from the fitting parameter, the author has developed a ‘mixed’ radiation-electrochemistry formalism, which enables theoretical reconstruction of the observed potential differences more clearly. The previous verifications are updated by using this approach. Through these studies, the author has confirmed the existence of the ‘long cell’ action corrosion mechanism existing in the water-cooled reactors.

scholarly journals Efficient numerical integration of thermal interaction rates

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
G. Jackson ◽  
M. Laine
Keyword(s):  
Phase Space ◽  
Numerical Integration ◽  
Chemical Potential ◽  
Substantial Contribution ◽  
Thermal Interaction ◽  
The Real ◽  
Chemical Potentials

Abstract In many problems in particle cosmology, interaction rates are dominated by 2 ↔ 2 scatterings, or get a substantial contribution from them, given that 1 ↔ 2 and 1 ↔ 3 reactions are phase-space suppressed. We describe an algorithm to represent, regularize, and evaluate a class of thermal 2 ↔ 2 and 1 ↔ 3 interaction rates for general momenta, masses, chemical potentials, and helicity projections. A key ingredient is an automated inclusion of virtual corrections to 1 ↔ 2 scatterings, which eliminate logarithmic and double-logarithmic IR divergences from the real 2 ↔ 2 and 1 ↔ 3 processes. We also review thermal and chemical potential induced contributions that require resummation if plasma particles are ultrarelativistic.

scholarly journals Generalised partition functions: inferences on phase space distributions

2016 ◽  
Vol 34 (6) ◽  
pp. 557-564 ◽  
Author(s):  
Rudolf A. Treumann ◽  
Wolfgang Baumjohann
Keyword(s):  
Phase Space ◽  
Partition Function ◽  
Bessel Functions ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Large Temperature ◽  
Partition Functions ◽  
Functional Dependencies ◽  
Boltzmann Factor ◽  
Nonextensive Statistical Mechanics

Abstract. It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R) both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the corresponding nonextensive statistical mechanics.

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