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The article presents a numerical study of vapor condensation appearing in an ejector. The ejector is a part of a device developed by the authors and used to purify air emissions. The article considers condensation of pure water vapor and condensation of vapor in a mixture of vapor and carrier gas. The system of axisymmetric Navier-Stokes equations and the system of moment equations are considered as a mathematical model for describing two-dimensional non-stationary gas-dynamic processes and processes of phase transitions in the device. The general system of equations is numerically solved using the finite volume method.

The hydrodynamics of nematic liquid crystals in two dimensions are considered, and the existence of global strong solutions of the system is obtained in the article. Some nonlinear stress terms in the moment equations and transport terms in the director equations, together with the Dirichlet boundary condition, induce some difficulties in the analysis. We introduce an elliptic operator for such coupled system to overcome the problems.

The nonlinear recurrence Chapman-Enskog solution for the linearized Grad ten-moment equations is resummed exactly. Using this solution, the stability of higher-order hydrodynamics in various approximations is discussed.

A brief overview is presented of the stochastic methods utilized in the modelling of turbulent plasmas. The microscopic theories based on a kinetic equation for plasmas in the presence of fluctuating fields are first discussed, posing the problem of closure of the moment equations and the renormalization methods. The semi-dynamical methods based on Langevin equations and the associated hybrid kinetic equation are then presented. The occurrence of strange transport is illustrated. Finally, the continuous-time random walk models are briefly discussed.

Closure schemes for the infinite hierarchy of moment equations describing the time evolution of averages of observables over a non-equilibrium ensemble of initial conditions for the logistic map model are derived with the aid the Frobenius-Perron equation in the long-time regime. For the growth parameter r = 4 the approximations compare well with exact results derived for specific initial probability densities.

We show that, under certain conditions of practical interest, radio frequency inductive discharges can exhibit kinetic effects arising from the random thermal motion of electrons. The electrical response of the plasma is altered in this kinetic regime. More power is dissipated than is expected from cold plasma theory and the spatial distributions of the induced currents and fields change. Moment- or fluid-based simulations do not normally include these kinetic effects, but we show that the introduction of an appropriate viscosity into the moment equations can make them accurate in the kinetic regime.

The stability of the first-order and second-order solution moments for a Harrison-type predator–prey model with parametric Gaussian white noise is analyzed in this paper. The moment equations of the system solution are obtained under Ito interpretations. The delay-independent stable condition of the first-order moment is identical to that of the deterministic delayed system, and the delay-independent stable condition of the second-order moment depends on the noise intensities. The corresponding critical time delays are determined once the stabilities of moments lose. Further, when the time delays are greater than the critical time delays, the system solution becomes unstable with the increase of noise intensities. Finally, some numerical simulations are given to verify the theoretical results.

The transport coefficients of the inelastic variable hard sphere are calculated using infinite Maxwellian iterations of Grad’s 14 moment equations and dimensional analysis on the basis of the Chapman‐Enskog expansion. The viscositycoefficient(μ)obtainedusinginfiniteMaxwellianiterationscoincides with that obtained using dimensional analysis on the basis of the Chapman‐ Enskogexpansion.Twotransportcoefficients(κ and η)calculatedusinginfinite Maxwellianiterations,whichdefinetheheatflux,coincidewiththosecalculated using dimensional analysis on the basis of the Chapman‐Enskog expansion, only when κ and η obtained using infinite Maxwellian iterations converge. Divergences of κ and η occur whenever the dissipating rate of the heat flux, via the inelastic collisional term, is equal to or smaller than the characteristic increasingordecreasingrateoftheheatfluxviathedecreaseinthetemperature.

The method of moments (MOM) is a statistically based alternative to sectional and modal methods for aerosol simulation. The MOM is highly efficient as the aerosol distribution is represented by its lower-order moments and only these, not the full distribution itself, are tracked during simulation. Quadrature is introduced to close the moment equations under very general growth laws and to compute aerosol physical and optical properties directly from moments. In this paper the quadrature method of moments (QMOM) is used in a bivariate test tracking of aerosol mixing state. Two aerosol populations, one enriched in soot and the other in sulfate, are allowed to interact through coagulation to form a generally-mixed third particle population. Quadratures of varying complexity (including two candidate schemes for use in climate models) are described and compared with benchmark results obtained by using particle- resolved simulation. Low-order quadratures are found to be highly accurate, and Gauss and Gauss-Radau quadratures appear to give nested lower and upper bounds, respectively, to aerosol mixing rate. These results suggest that the QMOM makes it feasible to represent the generallymixed states of aerosols and track their evolution in climate models.

A theorem is proved on the uniqueness of the solution of the Cauchy problem for the chain of equations for the spatial moments corresponding to smooth solutions of the three-dimensional Navier-Stokes system in the case of any Reynolds numbers. By means of the uniqueness theorem it is proved that any solution of the chain of moment equations belonging to an appropriate function space forms a positive-definite system of moments for any time 0$ SRC=http://ej.iop.org/images/0025-5734/62/2/A09/tex_sm_3249_img1.gif/> if its initial value was positive definite.Bibliography: 11 titles.

The role of the various Grad moment equations in deriving the conductivity tensor for a warm magneto-plasma has been discussed.

The systematic error induced in the readings of neutron moisture gauges by the variation in the dry bulk density of the medium is investigated theoretically. To obtain the correction for dry bulk density in any gauges, two independent measurements have to be performed. The correction is calculated by means of three-group theory with group constants evaluated from multigroup moment equations.