Nonstationary Boundary Research Articles

Mixed nonlinear problems for parabolic equations with nonstationary boundary conditions and conditions of conjugacy

Mixed nonlinear problems for parabolic equations with nonstationary boundary conditions and conditions of conjugacy

Non-stationary planetary waves in semirestricted channels

The non-stationary boundary value problem of the propagation of planetary waves (Rossby waves) is semirestricted channels extended in a west to east direction is studied in the β-plane approximation. An explicit solution is obtained and its behaviour at large times is investigated. The results obtained are generalized to the multidimensional case.

Calculation of transients in a microwave amplifier with a dielectric filling

Using as an example the design of a microwave amplifier with a dielectric filling, a numerical algorithm for solving the non-stationary system of Maxwell's equations is described. Integral laws of conservation and variation of momentum and energy are satisfied at the discrete level for the method. The results of a non-linear approach and of the linear theory are compared. The strict statement of non-stationary boundary conditions simulating radiation from a bounded domain is discussed.

Distribution of a nonstationary electron beam in a dense gas

The problem of the temporal and spatial dependences of the parameters of the action of a modulated fast-electron beam on a dense gas is posed on the basis of the transport equation. The problem is simplified by making it nondimensional and by transforming to the Fokker-Planck approximation. A Green's function formalism is developed for this problem and is used to express the solution of the general nonstationary problem in the form of a convolution of a nonstationary boundary flow with a stationary Green's function. The use of the derived equation is illustrated using as an example the solution of a problem with the simplest stationary Green's function corresponding to the “straight-ahead” approximation. This approximation is used to consider a general relativistic case with model scattering cross sections. The methods and results of a numerical computer solution of the nonstationary problem of electron retardation in the upper layer of the atmosphere are surveyed.

Surface diffusion of hydrogen on Ni(100) studied using laser-induced thermal disorption

The surface diffusion coefficient for hydrogen on Ni(100) at low coverage has been measured between 223 and 283 K. A pulsed laser is used to desorb hydrogen from a small, well defined, region on the surface without perturbing the ambient surface temperature. Hydrogen from nearby regions on the surface migrates into the vacant area and the time required to refill that area is determined by subsequent laser-induced-desorption measurements. The diffusion coefficient is obtained using an equation derived from Fick's Second law with non-stationary boundary conditions. The temperature dependence of the diffusion coefficients yields a value of 4.0±0.5 kcal/mol for the energy barrier to diffusion. A value of roughly 3×10 13 s -1 for the site-to-site hopping frequency is derived when the pre-exponential for diffusion is fit to a random-walk mechanism.

Surface diffusion of hydrogen on Ni(100) studied using laser-induced thermal desorption

The surface diffusion coefficient for hydrogen on Ni(100) at low coverage has been measured between 223 and 283 K. A pulsed laser is used to desorb hydrogen from a small, well defined, region on the surface without perturbing the ambient surface temperature. Hydrogen from nearby regions on the surface migrates into the vacant area and the time required to refill that area is determined by subsequent laser-induced-desorption measurements. The diffusion coefficient is obtained using an equation derived from Fick's Second law with non-stationary boundary conditions. The temperature dependence of the diffusion coefficients yields a value of 4.0 ± 0.5 kcal/mol for the energy barrier to diffusion. A value of roughly 3 × 10 13 s −1 for the site-to-site hopping frequency is derived when the pre-exponential for diffusion is fit to a random-walk mechanism.

The flux-ratio equation under nonstationary boundary conditions

Ussing's equation for the ratio of undirectional tracer fluxes, passing in opposite directions through a membrane which has transport properties varying with the distance from a boundary, has recently been extended to include nonstationary fluxes under stationary boundary conditions [Sten-Knudsen and Ussing, J. Membrane Biol. 63:233–242 (1981)]. Using a concise and more generally valid method of proof, that extension is generalized further to include nonstationary boundary values of the tracer concentrations, and to obtain new results useful in the design of experiments.

Laminar boundary layers behind detonation waves

New solutions are presented for non-stationary boundary layers induced by planar, cylindrical and spherical Chapman-Jouguet (C-J) detonation waves. The numerical results show that the Prandtl number ( Pr ) has a very significant influence on the boundary-layer-flow structure. A comparison with available time-dependent heat-transfer measurements in a planar geometry in a 2H 2 + O 2 mixture shows much better agreement with the present analysis than has been obtained previously by others. This lends confidence to the new results on boundary layers induced by cylindrical and spherical detonation waves. Only the spherical-flow analysis is given here in detail for brevity.

Radiation processes in quantum systems with boundary

A study is made of the emission effects in quantum field systems contained in the regions of space with a non-stationary boundary. The back reaction of emission on the boundary is taken into account. The classical equations of motion of a system consisting of a free massless scalar field limited in space by a massive reflecting wall (mirror) are investigated in the two-dimensional case. The system is closed, i.e. external forces are absent. This system is quantised. The effect of the reaction of emission on the trajectory of a mirror is studied. The specific peculiarities of the stimulated emission processes in closed quantum systems with boundary are established and investigated. The results are related to hadronic physics.

Ignition of a gas by a hot horizontal cylinder

The modern thermal theory of ignition makes the assumption that the substance in the heating zone is stationary. However, in describing the process of ignition in liquid and gaseous systems, this assumption is inadmissible. To fully take into account the effect of natural convection, it is necessary to jointly solve the equations describing the ignition process and the equations of motion. The authors consider the problem of the ignition of a chemically reacting gas by a cylindrical body in the presence of natural convection. In order to solve the equations of a nonstationary boundary layer, the method of successive approximations was used. The convective motion in a gaseous system transforms the temperature profiles in the preheating stage of ignition, leading to the localization of ignition. The heating wave is propagated around the circumference of the cylinder at the same time it moves into the medium. Natural convection affects ignition in other ways, influencing the nonstationary ignition characteristics in such a way that there is a considerable reduction in ignition lag as compared with the heat conduction case. It was found that the chemical reaction leads to an increase in the natural convection development time. This is associated with a decreasemore » in the temperature drop between the heated cylindrical surface and the ambient medium, whose temperature rises as a result of chemical heat release.« less

On the resistance law for the nonstationary atmospheric boundary layer

A resistance law for nonstationary conditions is suggested assuming similarity of the non-dimensional Reynold's stress. Equations of motion for the wind velocity deviations are used for the outer layer. In the wall layer, wall similarity is supposed as usual. Then a matching procedure is used for the derivation of the resistance law.

Duhamel integral and the operational-structural method of solution in nonstationary heat-conduction problems for regions of complicated shape

We propose an analytic method for solving nonstationary heat-conduction problems for regions of complicated shape with nonstationary boundary conditions and energy sources.

Laminar boundary layer on an oscillating wedge

A study is made of the nonstationary laminar boundary layer on a sharp wedge over which a compressible perfect gas flows; the wedge executes slow harmonic oscillations about its front point. It is assumed that the perturbations due to the oscillations are small, and the problem is solved in the linear approximation. It is also assumed that the thickness of the boundary layer is small compared with the thickness of the complete perturbed region. Then in a first approximation the influence of the boundary layer on the exterior inviscid flow can be ignored, and the parameters on the outer boundary of the boundary layer can be taken equal to their values on the body for the case of inviscid flow over the wedge. They are determined from the solution to the inviscid problem that is exact in the framework of the linear formulation. The wall is assumed to be isothermal. The dependence of the viscosity on the temperature is linear. Under these assumptions, the problem of calculating the nonstationary perturbations in the boundary layer on the wedge is a self-similar problem.

Wave dynamics of mixed, periodically nonstationary flows of a spontaneously condensing vapor

A study is made of the dynamics of mixed flows of a condensing vapor with nonequilibrium phase transitions and gas-dynamic discontinuities in channels of variable area in the presence of periodically nonstationary boundary conditions at the entrance. The results are given of a numerical investigation of the flows of superheated and spontaneously condensing water vapor in a supersonic nozzle. It is shown that the periodic nonstationarity of the flow at the entrance can lead to a qualitative rearrangement of the flow structure in the presence of spontaneous condensation.

Influence of blowing on the characteristics of the nonstationary boundary layer on an oscillating wedge in a supersonic stream

A study is made of the influence of blowing on the characteristics of a nonstationary boundary layer. For this, we solve the equations of the laminar boundary layer on an infinite wedge moving with supersonic velocity and executing small oscillations about the tip. It is shown that increased blowing improves the damping of the oscillations of the wedge.

An analytic solution of the one-dimensional diffusion equation in a non-stationary boundary layer with an application to inversion rise fumigation

An analytic solution is presented of the one-dimensional, time-dependent diffusion equation in a developing boundary layer. This solution is given in terms of a series of Jacobi polynomials. In its derivation two crucial assumptions are made: The turbulent exchange coefficient is approximated by K = cuz(1 − z h ) and the growth rate of the boundary-layer height h is given by dh dt = αcu , where u is a time-dependent turbulent velocity scale and z is the vertical coordinate (α and c are constants). The asymptotic behaviour of the solution for large values of time leads to a non-uniform concentration distribution across the boundary layer. Subsequently, we calculate the concentration pattern caused by inversion-rise fumigation during morning hours. The results are compared with those of a simple fumigation model.

On the vertical velocity at the top of the planetary boundary layer in nonstationary conditions

The non-stationary planetary boundary layer is parameterized for use in weather forecasting numerical models.

A generalized similarity method with a universal equation in differential form in the theory of a nonstationary boundary layer

The results of the integration of a “segment” of a universal equation in purely differential form for a nonstationary laminar boundary layer are presented and analyzed.

Difference Schemes Derived from the Integral Theorems of Fluid Mechanics

Theme A FAMILY of difference schemes is derived for the calculation of unsteady, compressible flow of an inviscid gas. The schemes can be applied to an arbitrary mesh geometry, and the mesh is allowed to deform in time. Therefore, the mesh can be chosen to coincide with an arbitrary stationary or nonstationary boundary. Also, the schemes can be used to fit shockwaves and contact surfaces by allowing the mesh to deform in concert with these discontinuities. Alternatively, the schemes allow shocks to be calculated by the shock-capturing technique. Recently, several authors' have used a MacCormack scheme, modified for application to arbitrary mesh geometries by using the integral theorems. Schiff 4 extended the method to allow for timevary ing meshes. These schemes, however, suffer from low accuracy if applied to nonCartesian meshes. Even in the relatively simple case of onedimensional, unsteady flow with nonuniform mesh, these schemes have a truncation error of the first order. By contrast, the schemes described in this paper are secondorder accurate in the two-dimensional and first-order accurate in the three-dimensional case. The two-step schemes discussed here are closely related to the LaxWendroff scheme and reduce to it for stationary Cartesian grids.

Investigation of filtration with a nonstationary free boundary

The article indicates an inverse method for constructing filtration flows in the presence of a free surface. It gives concrete series of varying free surfaces, equalizing-out elevations and depressions, and surfaces of a rise or fall of the ground waters as a result of the work of drainage or injection boreholes.