Fractal dimension of steady nonequilibrium flows

The Kaplan-Yorke information dimension of phase-space attractors for two kinds of steady nonequilibrium many-body flows is evaluated. In both cases a set of Newtonian particles is considered which interacts with boundary particles. Time-averaged boundary temperatures are imposed by Nose-Hoover thermostat forces. For both kinds of nonequilibrium systems, it is demonstrated numerically that external isothermal boundaries can drive the otherwise purely Newtonian flow onto a multifractal attractor with a phase-space information dimension significantly less than that of the corresponding equilibrium flow. Thus the Gibbs' entropy of such nonequilibrium flows can diverge.     

Transient adaptivity applied to two-phase incompressible flows

An anisotropic adaptation process is applied to a three-dimensional incompressible two-phase flow solver. The solver uses a level set/finite element method on unstructured tetrahedral meshes. We show how the level set function can be used to build an anisotropic mesh with good properties. Some computations with a strong transient character and large densities ratios (1/1000) are presented. We show that the efficiency of the computations can be deeply enhanced by mesh adaptations.     

Material point method applied to multiphase flows

The particle-in-cell method (PIC), especially the latest version of it, the material point method (MPM), has shown significant advantage over the pure Lagrangian method or the pure Eulerian method in numerical simulations of problems involving large deformations. It avoids the mesh distortion and tangling issues associated with Lagrangian methods and the advection errors associated with Eulerian methods. Its application to multiphase flows or multi-material deformations, however, encounters a numerical difficulty of satisfying continuity requirement due to the inconsistence of the interpolation schemes used for different phases. It is shown in Section 3 that current methods of enforcing this requirement either leads to erroneous results or can cause significant accumulation of errors. In the present paper, a different numerical method is introduced to ensure that the continuity requirement is satisfied with an error consistent with the discretization error and will not grow beyond that during the time advancement in the calculation. This method is independent of physical models. Its numerical implementation is quite similar to the common method used in Eulerian calculations of multiphase flows. Examples calculated using this method are presented.     

Sound amplification in inhomogeneous flows of nonequilibrium gas

The conditions of the acoustic instability of flows of thermodynamically nonequilibrium gas are determined. It is shown that the growth increments of the velocity, temperature, pressure, and density disturbances are different. When the Mach numbers are small, only the velocity and temperature disturbances grow along the flow.     

Thermal and reactive nonequilibrium of magnetoactive plasma flows

Based on multifluid equations derived from the Boltzman equation under inclusion of ionization and recombination reactions, the following convective processes in magnetoactive plasma flows transverse to homogeneous magnetic fields are investigated:The build-up of the nonuniform plasma state, the intercomponent thermal nonequilibrium and the reactive nonequilibrium in dependence of the flow coordinate. Due to the complexity of the problem, a numerical approach is used, parallel to which an approximate analytical theory is developed.     

Two-dimensional nonequilibrium fluid models for streamers

The self-consistent, two-dimensional fluid simulation for describing nitrogen gas prebreakdown phenomena under atmospheric pressure is presented in cylindrically symmetric geometry. The models of the electron dynamics are characterized either by an equilibrium single-moment equation or by a nonequilibrium three-moment equation. A more accurate flux-corrected transport (MAFCT) technique, which provides a solution with steep and varying gradients in large dynamic ranges, is used to solve the electron fluid equations. Included in the step-by-step presentation are the electron density, the space-charge electric field, the electron average velocity, the electron mean energy, and the electron power deposition from the initial stage to the later stage when the ionizing channel bridges the gap. The differences between equilibrium and nonequilibrium fluid models are discussed in terms of the formation of ionizing channels and the propagation of streamers     

q-deformed boson-realization model applied to vibrational spectrum of sulfur dioxide

Aq-deformed boson-realization model is presented to study both stretching and bending vibrations of sulfur dioxide, where Fermi resonances are taken into account. Our results are compared with those of other models.     

On the stability of certain collisional configurations of hydromagnetic flows

We study the flow of a hydromagnetic fluid toward an obstacle in two different cases: when this is a rigid wall or when two plasma masses collide with each other. The magnetic field far from the obstacle is assumed to be aligned with the flow. The diffusivity is taken as low, and a boundary layer approach for the stationary MHD system is considered. The relevant equations turn out to be a generalization of the Falkner-Skan ones, and while analytical solutions are impossible to obtain, a qualitative analysis shows that whenever the size of the Alfvén speed far from the interface exceeds the size of the fluid velocity, the system has no nontrivial solutions. The interpretation of this is that in this case disturbances occurring in the boundary layer travel upstream and disturb the boundary conditions at the outer layers.     

Influence of short-and long-range interaction forces on the efficiency of collisional vibrational energy transfer in the vibrational quasi-continuum

Based on measurements of the time-resolved delayed fluorescence, the influence of universal interactions on the collisional vibrational energy transfer is studied in mixtures of vibrationally excited polyatomic molecules (acetophenone, benzophenone, and anthraquinone) with inert bath gases (Ar, C₂H₄, SF₆, CCl₄, and C₅H₁₂). From the dependences of the decay rates of delayed fluorescence on bath gas pressure, the efficiencies of the establishment of vibrational (V-V relaxation) and thermal (V-T relaxation) equilibrium after excitation of molecules into the vibrational quasi-continuum of a triplet state are estimated. The main emphasis is on studying the dependences of the efficiency of collisional vibrational energy transfer on temperature and the molecular characteristics of collision partners. It is found that the efficiency increases with the complication of the structure of bath gases for the V-V process and decreases upon the increasing of their mass for the V-T process. For the temperature range 273–553 K, the negative temperature dependence of the V-V transfer probability and the positive (Landau-Teller) dependence of the V-T transfer probability were obtained. It is concluded that the above regularities reflect the dominant role of long-range attractive forces in initiating the quasi-resonant V-V transfer and of short-range repulsive forces in the V-T transfer of vibrational energy.     

Time-dependent perturbation theory for nonequilibrium lattice models

We develop a time-dependent perturbation theory for nonequilibrium interacting particle systems. We focus on models such as the contact process which evolve via destruction and autocatalytic creation of particles. At a critical value of the destruction rate there is a continuous phase transition between an active steady state and the vacuum state, which is absorbing. We present several methods for deriving series for the evolution starting from a single seed particle, including expansions for the ultimate survival probability in the super- and subcritical regions, expansions for the average number of particles in the subcritical region, and short-time expansions. Algorithms for computer generation of the various expansions are presented. Rather long series (24 terms or more) and precise estimates of critical parameters are presented.     

Scaling properties of models of nonequilibrium phenomena

The renormalization group method proposed by 't Hooft is developed for the study of scaling properties of some models of nonequilibrium phenomena. For one of two models studied in detail, the Langevin equation for the random variables contains a bilinear streaming velocity and the stationary probability distribution is Gaussian. The time-dependent Ginzburg-Landau model is chosen as a second example because it illustrates the advantage of the 't Hooft method of not having to specify a particular renormalization point. The scaling exponents for a model of the liquid-gas phase transition are calculated in lowest order to illustrate application of the method to a multifield system.     

Analysis of the relaxation of a nonequilibrium gas or plasma in a nozzle

An economical and consistent, in mathematical respects, method of analyzing the flow of a relaxing gas or plasma in a supersonic nozzle is developed. The method is used in analyzing the vibrational relaxation of a two-phase mixture in the nozzle of a combustion gasdynamic laser. It is shown that the use of the Gear method in the numerical integration stage permits passage of the near-equilibrium sections with a large spacing, which substantially cuts down the computing time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 99–104, July, 1979.     

Triplet-triplet transfer of electronic energy upon nonequilibrium vibrational excitation of triplet molecules

The specific features of the triplet-triplet (T-T) transfer of electronic excitation energy in a gas phase upon nonequilibrium vibrational excitation of the triplet molecules of a donor were studied for an anthraquinone-diacetyl donor-acceptor pair using the time-resolved slow fluoresence of anthraquinone and sensitized phosphorescence of diacetyl. It is shown that in the gas phase, which allows regular control of the number of collisions, competition between the processes of T-T transfer and intermolecular vibrational relaxation is observed for nanosecond time resolution. The T-T transfer rate for the molecular system investigated exceeded the rate of intermolecular vibrational relaxation k_V in the triplet state T₁ of the donor. The effectiveness of the T-T transfer of energy by vibrationally excited molecules turned out to be higher than the effectiveness of transfer by thermalized ones, but even the highest of them was much less than unity. An increase in the equilibrium temperature of vapors led to a decrease in the effectiveness of transfer for both vibrationally excited and thermalized triplet molecules, thus indicating the importance of the collisional complex in the intermolecular process studied. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 67, No. 4, pp. 474–479, July–August, 2000.     

Multiple temperature model for the information preservation method and its application to nonequilibrium gas flows

The information preservation (IP) method has been successfully applied to various nonequilibrium gas flows. Comparing with the direct simulation Monte Carlo (DSMC) method, the IP method dramatically reduces the statistical scatter by preserving collective information of simulation molecules. In this paper, a multiple temperature model is proposed to extend the IP method to strongly translational nonequilibrium gas flows. The governing equations for the IP quantities have been derived from the Boltzmann equation based on an assumption that each simulation molecule represents a Gaussian distribution function with a second-order temperature tensor. According to the governing equations, the implementation of IP method is divided into three steps: molecular movement, molecular collision, and update step. With a reasonable multiple temperature collision model and the flux splitting method in the update step, the transport of IP quantities can be accurately modeled. We apply the IP method with the multiple temperature model to shear-driven Couette flow, external force-driven Poiseuille flow and thermal creep flow, respectively. In the former two cases, the separation of different temperature components is clearly observed in the transition regime, and the velocity, temperature and pressure distributions are also well captured. The thermal creep flow, resulting from the presence of temperature gradients along boundary walls, is properly simulated. All of the IP results compare well with the corresponding DSMC results, whereas the IP method uses much smaller sampling sizes than the DSMC method. This paper shows that the IP method with the multiple temperature model is an accurate and efficient tool to simulate strongly translational nonequilibrium gas flows.     

Fluctuations of one dimensional Ginzburg-Landau models in nonequilibrium

We study the fluctuation of one dimensional Ginzburg-Landau models in nonequilibrium along the hydrodynamic (diffusion) limit. The hydrodynamic limit has been proved to be a nonlinear diffusion equation by Fritz, Guo-Papanicolaou-Varadhan, etc. We proved that if the potential is uniformly convex then the fluctuation process is governed by an Ornstein-Uhlenbeck process whose drift term is obtained by formally linearizing the hydrodynamic equation.Work partially supported by the National Science Foundation under grant no. DMS 8806731 and DMS 9101196