The Boltzmann equation approach to the shear flow of a granular material

An exact solution of the Boltzmann equation for the shear flow of granular materials is discussed and compared with some related solutions.     

Compression and shear of a layer of granular material

A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.     

Maximizing the bandwidth of coherent,mid-IR supercontinuum using highly nonlinear aperiodic nanofibers

We describe in detail a new procedure of maximizing the bandwidth of mid-infrared (mid-IR) supercontinuum (SC) in highly nonlinear microstructured As₂Se₃ and tellurite aperiodic nanofibers. By introducing aperiodic rings of first and secondary air holes into the cross-sections of our microstructured fiber designs, we achieve flattened and all-normal dispersion profiles over much broader bandwidths than would be possible with simple periodic designs. These fiber designs are optimized for efficient, broadband, and coherent SC generation in the mid-IR spectral region. Numerical simulations show that these designs enable the generation of a SC spanning over 2290?nm extending from 1140 to 3430?nm in 8?cm length of tellurite nanofiber with input energy of E?=?200?pJ and a SC bandwidth of over 4700?nm extending from 1795 to 6525?nm generated in only 8?mm-length of As₂Se₃-based nanofiber with input energy as low as E?=?100?pJ. This work provides a new type of broadband mid-IR SC source with flat spectral shape as well as excellent coherence and temporal properties by using aperiodic nanofibers with all-normal dispersion suitable for applications in ultrafast science, metrology, coherent control, non-destructive testing, spectroscopy, and optical coherence tomography in the mid-IR region.     

Compression and shear of a layer of granular material

A classical problem in metal plasticity is the compression of a block of material between rigid platens. The corresponding problem for a layer of granular material that conforms to the Coulomb-Mohr yield condition and the double-shearing theory for the velocity field has also been solved. A layer of granular material between rough rigid plates that is subjected to both compression and shearing forces is considered. Analytical solutions are obtained for the stress and velocity fields in the layer. The known solutions for steady simple shear and pure compression are recovered as special cases. Yield loads are determined for combined compression and shear in the case of Coulomb friction boundary conditions. Numerical results which describe the stress and velocity fields in terms of the normal and shear forces on the layer at yield are presented for the case in which the surfaces of the platens are perfectly rough. Post-yield behaviour is briefly considered.     

Damping factor to the prandtl equation for the transition portion of a turbulent boundary layer

The semiempirical theory of interaction of molecular and turbulent viscosities [1] is used to calculate the damping factor to the Prandtl equation and the average velocity distribution over the cross section of the transition portion of a turbulent boundary layer.     

Applicability of the rheological equation of state for thermoplastic composites

A simple experimental method for determining the steady-state shear viscosity of thermoplastic composite melts has been used. Using this method, we have determined the steady-state shear viscosity of an automotive thermoplastic composite system, namely, wollastonite-filled poly(ethylene terephthalate) (WFPET), at various temperatures and shear rates. All the viscosity properties investigated can be successfully described and predicted by a thermodynamically based rheological equation of state. The effects of composition and mixing conditions on the steady-state shear viscosity of all the WFPET investigated were also determined using this rheological equation of state.     

Intermittence and structure of the transitional boundary layer at a plate using a laser anemometer

The procedure for investigating the intermittence in a transitional boundary layer using a laser anemometer is described. The distribution of the coefficient of intermittence over the thickness of the boundary layer as a function of the velocity of the oncoming stream is presented.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 43, No. 1, pp. 16–20, July, 1982.     

Computation of the radiation flux emanating from a highly disperse layer

Problems of the radiation of a highly disperse layer and of radiation transfer in a disperse layer-enclosing surface system are examined. The influence is analyzed of nonisothermy on the radiation flux density emanating from the layer. A dependence of this quantity on the system parameters is found.Translated from Inzhenerno-fizicheskii Zhurnal, Vol. 59, No. 4, pp. 586–593, October, 1990.     

On the dispersion equation of Love waves in a porous layer

Summary The paper is concerned with the propagation of Love waves in a porous layer over an inhomogeneous half-space due to a point source. The dispersion equation for Love waves in a porous layer has been derived. The effects of porosity and inhomogeneity in the half-space have been shown graphically on the dispersion curves. The theory pointed out by Biot for the porous medium has been applied to solve the problem with the help of Green's function technique.With 4 Figures     

Wave properties and shear stress of a turbulent boundary layer

The wave theory of turbulence [1–3] is applied to the problem of a turbulent boundary layer near a planar wall. Preliminary results earlier published have been refined.     

A comparative study of subgrid-scale stress models in the context of a transitional boundary layer

In this paper, four important subgrid-scale (SGS) stress models are investigated in order to assess their predictive performance on modeling of the SGS physics. The analysis is conducted using the a priori method based on a comprehensive direct numerical simulation (DNS) data set of a transitional boundary layer flow over a flat plate. The study includes examination of the correlations between the modeled SGS stress tensor and that directly computed from the DNS data, investigation of the effects of filter sizes on modeled SGS stresses, and evaluation of forward and backward scatter of the kinetic energy of the flow in the transitional and turbulent regions.     

Limit form of the equation of anisotropic heat conduction in a layer

Consideration is given to the problem of asymptotic reduction to a two-dimensional equation of an equation that is three-dimensional along the coordinates and describes the process of heat propagation in an anisotropic material. The region of heat transfer is a layer that is thin along one coordinate. It is assumed that the matrix of the thermal diffusivities depends on the spatial coordinates. The effective thermal-diffusivity matrix is represented in the constructed equivalent heat conduction equation.     

Absorption of radiation in a layer of highly porous material

Radiative transfer through a porous layer, modeled by a uniform system of opaque particles fixed in space, is investigated.Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 50, No. 6, pp. 999–1005, June, 1986.     

Unilateral plastic delamination of a thin inclusion in the compressed layer under shear

The analytic solution of the problem of plastic delamination under shear of a plane thin rigid inclusion in the compressed layer is obtained by the methods of the theory of functions of complex variable. The inclusion is normal to the edges of the layer and located symmetrically about these edges. One side of the inclusion is in perfect contact with the medium and the other side suffers the action of friction forces caused by the compression of the layer. We determine both the length of the strips of plastic delamination as a function of the load and the load under which the inclusion becomes completely delaminated. Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 44, No. 6, pp. 47–52, November–December, 2008.     

Solution of a viscoelastic boundary layer equation by orthogonal collocation

Summary The applicability of the method of orthogonal collocation to the solution of Newtonian and viscoelastic boundary layer problems is investigated. To this end, the method is applied to the boundary layer equation describing the flow of a second-order fluid near a two-dimensional stagnation point. The efficiency of a number of different approximating bases is investigated. It is shown that the method is applicable to both Newtonian and weakly viscoelastic fluids, and that it compares very favorably with other weighted residual methods.     

Anti-symmetric motion of a pre-stressed incompressible elastic layer near shear resonance

A two-dimensional model is derived for anti-symmetric motion in the vicinity of the shear resonance frequencies in a pre-stressed incompressible elastic plate. The method of asymptotic integration is used and a second-order solution, for infinitesimal displacement components and incremental pressure, is obtained in terms of the long-wave amplitude. The leading-order hyperbolic governing equation for the long-wave amplitude is observed to be not wave-like for certain pre-stressed states, with time and one of the in-plane spatial variables swapping roles. This phenomenon is shown to be intimately related to the possible existence of negative group velocity at low wave number, i.e. in the vicinity of shear resonance frequencies.     

Description of particle mixing in a boiling layer by a hyperbolic equation

It is shown that the horizontal diffusion coefficients of particles, which are found from the experimental response functions obtained using the parabolic and hyperbolic diffusion equations, are nearly identical.

     

Solution of the boundary layer equation for a power law fluid in magneto-hydrodynamics

Summary The problem of a non-Newtonian power law conducting fluid past a semi-finite plate, in the presence of an external electromagnetic field, is studied. The electric conductivity is taken as a function of the velocity. The method of expansion for a small parameter is used to obtain the solution and for a special form of the free stream velocity, the method of similarity solutions is used to obtain the exact solutions of the boundary layer equations associated with this problem in a closed form. It was found that the presence of the electromagnetic field reduces the velocity of the fluid.     

Approximate solution of the laminar boundary layer equation for a non-Newtonian fluid on a plate

The laminar boundary layer equations for a non-Newtonian fluid on a flat plate are reduced to Prandtl-Mises variables and solved approximately in quadratures. The velocity profiles and the resistance coefficients are given for certain values of n. Agreement with the results of exact calculations is good.