Macroscopic phenomenological relations for nonlinear processes in kinetic theory

Nonlinear irreversible processes between states which are not local equilibrium states are investigated by methods of the kinetic theory. The phenomenological equations for the second-order fluxes in a multicomponent mixture are derived, and relations between some of the second-order phenomenological coefficients are established. It is shown that new independent forces appear in the second-order equation, namely the gradients of the chemical potentials. Expressions for the entropy, entropy flux, and entropy source are evaluated. These expressions are related to the phenomenological equations and coefficients, e.g., all the second-order contributions of the forces in the equations for the fluxes can be obtained by differentiation of the expression for the second-order entropy source with respect to the coupled forces.     

Transient modeling for kinetic swelling/deswelling of the ionic-strength-sensitive hydrogel

The multi-effect-coupling ionic-strength-stimulus (MECis) model is presented for transient simulation of the kinetic deformation behavior of the ionic-strength-sensitive hydrogel, based on the laws of conservation of mass and momentum, where the chemical, electrical and mechanical effects are considered on the kinetics of the hydrogel. The simulated kinetic swelling/shrinking characteristics by the MECis model are compared with the experiments. It is concluded that the model is able to predict well the responsive variation of the ionic-strength-sensitive hydrogel with time.     

Ternary versus binary fragmentation processes

Using a statistical multifragmentation model, the ratio of ternary to binary fragmentation processes is calculated for the reaction ¹⁰⁰Mo + ¹⁰⁰Mo as a function of the excitation energy and compared to experimental data. The results suggest that for excitation energies above 2 MeV/A ternary multifragmentation of the compound nucleus is not the dominant channel. It is shown that the data can be explained by considering the binary fragmentation of one of the colliding Mo nuclei.     

Simulation of kinetic processes by the Monte-Carlo method

Statistical simulation of kinetic processes involving the interaction between different particle species is carried out by a Monte-Carlo method which differs from the classical application of this method by omitting calculations of the trajectories and mean free paths. Data on the latter quantities are included in the experimentally determined cross sections and rate constants used in the simulation. This qualitatively changes the computational procedure, simplifying and accelerating it. Data are provided on the simulation of a second-order sequential process and on the synthesis and dissociation of carbon dioxide, and they are compared to the known experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 55–60, October, 1973.     

Spartan random processes in time series modeling

A Spartan random process (SRP) is used to estimate the correlation structure of time series and to predict (interpolate and extrapolate) the data values. SRPs are motivated from statistical physics, and they can be viewed as Ginzburg-Landau models. The temporal correlations of the SRP are modeled in terms of ‘interactions’ between the field values. Model parameter inference employs the computationally fast modified method of moments, which is based on matching sample energy moments with the respective stochastic constraints. The parameters thus inferred are then compared with those obtained by means of the maximum likelihood method. The performance of the Spartan predictor (SP) is investigated using real time series of the quarterly S&P 500 index. SP prediction errors are compared with those of the Kolmogorov-Wiener predictor. Two predictors, one of which is explicit, are derived and used for extrapolation. The performance of the predictors is similarly evaluated.     

Defect charge states for classical modeling of diffusion processes in insulators

Some point defect properties can be accurately modeled by describing the ions classically, in terms of the shell model. This is particularly the case for point-defect diffusion in strongly ionic crystals. First, we discuss the issue of what ionic charge should be attributed to shell-model ions, including the possibility of partly covalent materials. We then discuss the issue of what defect charge states are likely to be of experimental interest and at the same time amenable to classical modeling. Finally, we discuss the rather common case where the defect charge is not well localized at a single ionic site, and where the electronic charge distribution of the defect and its neighbors will not remain fixed throughout a diffusion step.     

Advanced control and modeling of deposition processes

During the last decade, striking improvements could be achieved for the precise control of deposition processes in optical coating technology. For example, as a consequence of enormous progresses in measure- ment and computer technology, direct optical monitoring in a broad spectral range can be considered as a common tool in many production environments nowadays. Besides the development of the corresponding hardware and measurement channels, advanced approaches for the evaluation of the acquired data and new multiple sensor monitoring strategies moved into the focus of modern research on the way towards de- terministic deposition techniques. In this context, also innovative concepts for the simulation of deposition processes to forecast the result for a specified coating design and automatic online correction algorithms gained of importance to reduce the risk of failure in coating production. The present contribution will be dedicated to selected aspects in this field, especially addressing broad band optical monitoring systems. A short review on examples for existing hardware configurations and software tools will be presented illus- trating the advantages of modern process control techniques. Novel approaches based on the modeling of thin film growth are discussed as an additional strategy to improve the predictability of coating processes.     

Experimental and kinetic modeling study of oxidation of acetonitrile

Oxidation of acetonitrile has been studied in a flow reactor in the absence and presence of nitric oxide. The experiments were conducted at atmospheric pressure in the temperature range 1150–1450 K, varying the excess air ratio from slightly fuel-lean to very lean. Oxidation of CH₃CN was slow below 1300 K. Nitric oxide, hydrogen cyanide and nitrous oxide were detected as important products. A detailed chemical kinetic model for oxidation of acetonitrile was developed, based on a critical evaluation of data from literature. The rate coefficients for the reactions of CH₃CN and CH₂CN with O₂ were calculated from ab initio theory. Modeling predictions were in satisfactory agreement with experiments. Calculations were sensitive to thermal dissociation of CH₃CN and to the branching fraction for CH₃CN + OH to CH₂CN + H₂O and HOCN + CH₃, respectively. More work is desirable for these steps, as well as for reactions of CH₂CN and HCCN.     

Linear relaxation processes governed by fractional symmetric kinetic equations

The fractional symmetric Fokker-Planck and Einstein-Smoluchowski kinetic equations that describe the evolution of systems influenced by stochastic forces distributed with stable probability laws are derived. These equations generalize the known kinetic equations of the Brownian motion theory and involve symmetric fractional derivatives with respect to velocity and space variables. With the help of these equations, the linear relaxation processes in the force-free case and for the linear oscillator is analytically studied. For a weakly damped oscillator, a kinetic equation for the distribution in slow variables is obtained. Linear relaxation processes are also studied numerically by solving the corresponding Langevin equations with the source given by a discrete-time approximation to white Levy noise. Numerical and analytical results agree quantitatively.     

Two-scale modeling of adsorption processes at structured surfaces

We present an algorithm for the simulation of vicinal surface growth. It combines a lattice gas anisotropic Ising model with a phase-field model. The molecular behavior of individual adatoms is described by the lattice gas model. The microstructure dynamics on the vicinal surface are calculated using the phase-field method. In this way, adsorption processes on two different length scales can be described: nucleation processes on the terraces (lattice gas model) and step-flow growth (phase field model). The hybrid algorithm that is proposed here, is therefore able to describe an epitaxial layer-by-layer growth controlled by temperature and by deposition rate. This method is faster than kinetic Monte Carlo simulations and can take into account the stochastic processes in a comparable way.     

Transport processes in α-quartz through computer modeling

The charging and discharging processes in a-quartz sandwiched between two blocking contacts are studied by solving numerically the transport equations. Results for the transient current are in good agreement with experiment. The rotation of crystallographic planes upon the application of an electric field is also quantitatively justified through results of the spatial distribution of the electric field.     

Experimental and kinetic modeling study of sooting atmospheric-pressure cyclohexane flame

Experimental data and modelling results of the main products and intermediates from a fuel-rich sooting premixed cyclohexane flame were presented in this work. Model predictions well agree with experimental data both in sooting and non-sooting flames. Major and minor species are properly predicted, together with the soot yield. The initial benzene peak was demonstrated to be due to the fast dehydrogenation reactions of the cycloalkane, which gives rise to cyclohexene and cyclohexadiene both via molecular and radical pathways. Once formed cyclohexadiene quickly forms benzene whereas in the postflame zone, benzene comes from the recombination and addition reactions of small radicals, with C₃H₃ + C₃H₃ playing the most important role in these conditions. An earlier soot inception was detected in the cyclohexane flame with respect to a n-hexane flame and this feature is not reproduced by the model that foresees soot formation significant only in the second part of the flame. The model insensitivity of soot to the reactant hydrocarbon was also observed comparing the predictions of three flames of cyclohexane, 1-hexene and n-hexane with the same temperature profile. A sensitivity analysis revealed that soot primarily comes from the HACA mechanism for the three flames, acetylene being the key species in the nucleation. Experimental data on soot inception seem to indicate the importance of the early formation of benzene, that depends on the fuel structure. It is thus important to further investigate the role of benzene and aromatics in order to explain this discrepancy.     

Fission neutron multiplicity versus fragment mass and kinetic energy

High spin states of ¹²⁷ Ba have been investigated by means of the OSIRIS anti-compton γ -spectrometer. Five new bands, 48levels and 77transitions were found. Spin suggestions for four bandheads could be given. On ground of these suggestions routhians and alignments were compiled for the observed bands, giving a first insight into the high spin structure of this nucleus.     

Interactions between kinetic and radiative processes inside moving absorbing fluids

The aim of this paper is to present several features of the couplings occurring between radiative transfer and the kinetics of a moving dielectric. After determining how the velocity field affects the apparent thermo-optical properties of matter, the energy transport problem is investigated in instationary regime and the general form of transient radiative transfer equation inside a moving medium is built. Then, the model is applied to the particular case of turbulent flows: a system of two equations for mean and fluctuating radiative energies is presented, and the resolution of this system is finally carried out.     

Absence of kinetic effects in reaction-diffusion processes in scale-free networks

We show that the chemical reactions of the model systems of A+A-->0 and A+B-->0 when performed on scale-free networks exhibit drastically different behavior as compared to the same reactions in normal spaces. The exponents characterizing the density evolution as a function of time are considerably higher than 1, implying that both reactions occur at a much faster rate. This is due to the fact that the discerning effects of the generation of a depletion zone (A+A) and the segregation of the reactants (A+B) do not occur at all as in normal spaces. Instead we observe the formation of clusters of A (A+A reaction) and of mixed A and B (A+B reaction) around the hubs of the network. Only at the limit of very sparse networks is the usual behavior recovered.