Shock Wave Structure in a Weakly Ionized Ion Plasma Containing Charged Particles

The shock wave structure in a three-component weakly ionized plasma containing fine metal particles (macroparticles) is considered. The particles are ionized due to thermionic emission and the ejected electrons adhere to molecules of the neutral carrier gas assumed to be electronegative. The resulting ion plasma contains charged components with sharply different masses which are differently decelerated in the shock wave. This leads to charge separation and the generation of self-consistent electric fields which in turn affect the motion of the charged components.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 179–188.Original Russian Text Copyright © 2005 by Bityurin and Klyuchnikov     

Weakly Nonlinear Convection in a Porous Layer with Multiple Horizontal Partitions

We consider convection in a horizontally uniform fluid-saturated porous layer which is heated from below and which is split into a number of identical sublayers by impermeable and infinitesimally thin horizontal partitions. Rees and Genç (Int J Heat Mass Transfer 54:3081–3089, 2010) determined the onset criterion by means of a detailed analytical and numerical study of the corresponding dispersion relation and showed that this layered system behaves like the single-sublayer constant-heat-flux Darcy–Bénard problem when the number of sublayers becomes large. The aim of the present work is to use a weakly nonlinear analysis to determine whether the layered system also shares the property of the single-sublayer constant-heat-flux Darcy–Bénard problem by having square cells, as opposed to rolls, as the preferred planform for convection.     

Ionization and Recombination Kinetics in a Plasma Accelerator Channel

A number of theoretical approaches to the investigation of ionizing gas flows are analyzed and compared with reference to a plasma accelerator channel. The transition from a weakly ionized gas to a plasma is considered within the framework of the complete system of equations. The ionizing gas flow model is based on the magnetogasdynamic equations of a continuum and the equation of ionization and recombination kinetics. The corresponding coefficients are determined both within the framework of the standard theory and within a modified diffusion approximation, including possible variations. In addition, for comparison purposes some results of numerical experiments on the ionization process under conditions of local thermodynamic equilibrium are given.     

An Incompressible Fluid in a Weakly Deformable Shell. Part I: Analysis of the Model

We consider the flow of a viscous incompressible fluid in a pipe when the boundary is a deformable shell of Naghdi type. We prove that the corresponding system of partial differential equations has a solution when the deformation of the shell is smooth and small enough. We propose an algorithm that uncouples the unknowns and prove its convergence.     

Multiple Equilibria and Their Effects on Impact Damage in an Air-Handling Assembly

Nonlinear dynamic systems can have multiple equilibriumstates, which together with the system properties,initial conditions, input. and nonlinear feedback dictatehow nonlinear systems respond. In systems with impacts,stiffness discontinuitiescan lead to deterioration in function and eventual failureafter many vibration cycles. This article demonstrateshow multiple static equilibria can potentially accelerate impactdamage. Based on experimental data and observations froman air-handling assembly with clearance and Coulomb frictionnonlinearities, a low-order model is developed to describethe observed behavior. It is demonstrated that motion inthe neighborhood of an equilibriumpoint causes more severe vibration impact damage due to aloss of tolerance away from the design point.     

Quasi-Neutral Limit for a Model of Viscous Plasma

We perform a rigorous analysis of the quasi-neutral limit for a model of viscous plasma represented by the Navier–Stokes–Poisson system of equations. It is shown that the limit problem is the Navier–Stokes system describing a barotropic fluid flow, with the pressure augmented by a component related to the nonlinearity in the original Poisson equation.     

Conditions of Instability of a Flame Front in a Weakly Inhomogeneous Flow

The stability of a flame front in a combustible gas mixture flow is investigated. The flame is treated as a gasdynamic discontinuity, the gas is assumed to be dynamically incompressible, and the gravity force is neglected. It is assumed that in the undisturbed state the free-stream velocity component u , tangential to the front, is nonzero and can vary along the front; the normal mixture-velocity component u _n is constant along the front. A criterion distinguishing the absolute and convective instability of a skew flame front on which u =const is formulated. It is shown that the condition of instability of an inhomogeneous front on which the tangential component u (x) varies slowly coincides with the condition of absolute instability of a homogeneous front on which u is constant and equal to the u (x) minimum.     

Non-Hyperbolic Equilibria in the Charged Collinear Three-Body Problem

Consider three charged masses moving along the line. For this model we study the solutions near total collision using blow up techniques obtaining that for given masses and charges the vector field on the collision manifold has a non-hyperbolic equilibrium point. To study this situation the vector field is written in normal form and the center manifold theory is used obtaining that all nonzero solutions near the origin escape to infinity.     

Flow of a Weakly Conducting Fluid in a Channel Filled with a Porous Medium

We investigate the fully developed flow in a fluid-saturated porous medium channel with an electrically conducting fluid under the action of a parallel Lorentz force. The Lorentz force varies exponentially in the vertical direction due to low fluid electrical conductivity and the special arrangement of the magnetic and electric fields at the lower plate. Exact analytical solutions are derived for fluid velocity and the results are presented in figures. All these flows are new and are presented for the first time in the literature.     

Propagation of a Stationary Shock Layer in the Presence of a Boundary

We are interested in the large-time behavior of a stationary shock layer in the presence of a boundary effect. It is shown that the stationary shock propagates away from the boundary with speed inversely proportional to the time . Consequently, the location of the wave front is of order . We show therefore that the zero-viscosity and time-asymptotic limits do not commute. Our analysis involves detailed point-wise estimates, which allow us to trace the shock. (Accepted April 16, 1996)     

Large-eddy Simulation of Pilot-assisted Pulverized-coal Combustion in a Weakly Turbulent Jet

Large-eddy simulation has been performed to investigate pilot-assisted pulverized-coal combustion in a weakly turbulent air jet. An advanced pyrolysis model, the chemical percolation devolatilization (CPD) model, has been incorporated into the LES framework to predict the local, instantaneous pyrolysis kinetics of coal particles during the simulation. Prediction on volatile species generation is thus improved, which provides an important initial condition for gas-phase volatile and solid-phase char combustion. For gas-phase combustion, the partially stirred reactor (PaSR) model is employed to model the combustion of volatile species, taking into account subgrid turbulence-chemistry interactions. For heterogeneous solid-phase char combustion, both the intrinsic chemical reaction on the internal surface of a char particle and the diffusion of gaseous oxidant through the film layer around the particle have been incorporated by using a kinetic/diffusion surface reaction model. The LES results show overall good agreements with experimental data. Sensitivity analysis has been performed to better understand the impact of parameter uncertainties on the LES results.     

Equilibria of axially moving beams in the supercritical regime

Equilibria of axially moving beams are computationally investigated in the supercritical transport speed ranges. In the supercritical regime, the pattern of equilibria consists of the straight configuration and of non-trivial solutions that bifurcate with transport speed. The governing equations of coupled planar is reduced to a partial-differential equation and an integro-partial-differential equation of transverse vibration. The numerical schemes are respectively presented for the governing equations and the corresponding static equilibrium equation of coupled planar and the two governing equations of transverse motion for non-trivial equilibrium solutions via the finite difference method and differential quadrature method under the simple support boundary. A steel beam is treated as example to demonstrate the non-trivial equilibrium solutions of three nonlinear equations. Numerical results indicate that the three models predict qualitatively the same tendencies of the equilibrium with the changing parameters and the integro-partial-differential equation yields results quantitatively closer to those of the coupled equations.     

Modeling of a Dynamic Magneto-Fluid Seal in the Presence of a Pressure Drop

The ferrohydrodynamic problem, with a disconnected free surface, of the stability of an annular magneto-fluid seal under the action of centrifugal forces and a pressure drop is solved numerically. The effect of the shaft speed on the critical pressure drop is investigated in relation to the volume of the magneto-fluid plug, the magnetic field strength, the magnetic properties of the fluid, the gap width, and the shaft radius. The flow pattern and the thermal power released in the sealing layer are studied.     

Weakly non-linear waves in a fluid-filled elastic tube with variable prestretch

In the present work, by utilizing the non-linear equations of motion of an incompressible, isotropic thin elastic tube subjected to a variable prestretch both in the axial and the radial directions and the approximate equations of motion of an incompressible inviscid fluid, which is assumed to be a model for blood, we studied the propagation of weakly non-linear waves in such a medium, in the long wave approximation. Employing the reductive perturbation method we obtained the variable coefficient KdV equation as the evolution equation. By seeking a travelling wave solution to this evolution equation, we observed that the wave speed is variable in the axial coordinate and it decreases for increasing circumferential stretch (or radius). Such a result seems to be plausible from physical considerations.     

Onset of Convection with Internal Heating in a Weakly Heterogeneous Porous Medium

Linear stability analysis is applied to the onset of convection due to internal heating in a porous medium with weak vertical and horizontal heterogeneity. It is found that the effect of horizontal heterogeneity of each of permeability and thermal conductivity is slightly destabilizing. Increase of permeability in the upward direction is destabilizing and increase in the downward direction is stabilizing, and the reverse is true for increase of conductivity.     

Weakly perturbed boundary-value problems for differential equations in a Banach space

We consider boundary-value problems for a system of ordinary differential equations with a small parameter ε in the equations and boundary conditions. We establish conditions for the bifurcation of solutions of a weakly perturbed linear boundary-value problem in a Banach space.     

Weakly nonlinear boundary-value problems for differential equations in a Banach space in the critical case

We obtain necessary and sufficient conditions for the existence of solutions of weakly nonlinear boundary-value problems for differential equations in a Banach space. A convergent iterative procedure is proposed for the determination of solutions. We also establish a relationship between necessary and sufficient conditions.     

On the Vibrations of a Simply Supported Square Plate on a Weakly Nonlinear Elastic Foundation

In this paper an initial-boundary value problem for a weakly nonlinear plate equation with a quadratic nonlinearity will be studied. This initial-boundary value problem can be regarded as a simple model describing free oscillations of a simply supported square plate on an elastic foundation. It is assumed that the foundation has a different behavior for compression and for expansion. An approximation for the solution of the initial-boundary value problem will be constructed using a two-timescales perturbation method. The existence and uniqueness of the solution of the problem will be proved. Also the asymptotic validity of the constructed approximations will be shown on long timescales. For specific parameter values, it turns out that complicated internal resonances occur.     

Weakly disturbed steady transonic flows of a vibrationally relaxing gas

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 2, pp. 48–58, March–April, 1992.     

Modeling Nanoparticle Transport in Porous Media in the Presence of a Foam

Transport in Porous Media - Nano-remediation is a promising in situ remediation technology. It consists in injecting reactive nanoparticles (NPs) into the subsurface for the displacement or the...