Waves of Transverse Stresses under a Plane Impact on the Surface of a Sandwich Panel (Acoustic Approximation)

The wave process arising in a sandwich panel with a free back surface under the action of a short-term dynamic load on the front surface of the upper layer (plane deformation) is investigated. The calculation procedure for displacements, rates, and stresses under a rectangular short-time pulse, whose duration does not exceed the double time of wave travel within a layer, is based on the representation of the solution to the one-dimensional wave equation in terms of characteristics. The transmission and reflection coefficients of the pressure pulses on the contact surfaces of layers with different physical properties are determined. The expressions for tensile stresses in the panel face layers and filler, which are responsible for the material failure by spalling, are presented. The stresses in relation to the geometry and dynamic parameters of the sandwich structure are analyzed. In the case of a symmetric panel structure, the stress pattern in the midlayer and on its contact boundaries is given, which takes into account the branching and superposition of pulses.     

Solvability of a model for monomer–monomer surface reactions

A mathematical model for a monomer–monomer surface reaction is considered taking into account the surface diffusion of adsorbed particles of both reactants. The model is described by a coupled system of parabolic equations where some of them are defined in a domain and the other ones have to be solved on the domain surface. The existence and uniqueness theorem of a classic solution for the time-dependent problem is proved. Non-uniqueness of solutions for the steady-state problem is established.     

Approximation of Surface Measures in a Locally Convex Space

The main result of the paper is an analog of the surface layer theorem for measures given on a locally convex space with a continuously and densely embedded Hilbert subspace (for a surface of finite codimension). Earlier, the surface layer theorem was proved only for Banach spaces: for surfaces of codimension 1 by Uglanov (1979) and for surfaces of an arbitrary finite codimension by Yakhlakov (1990). In these works, the definition of the surface layer and the proof of the theorem essentially use the fact that the original space is equipped with a norm.     

Study of a model of linear biomolecular synthesis with reversible processes

The results are presented of studying a mathematical model of linear biomolecular synthesis which accounts for the reversibility of attaching a monomer to a growing molecule and some spontaneous termination of the synthesis. A previous model of a synthesis ignored the influence of reversibility and sinks. It is shown that if the rate of the monomer attachment (the direct process) exceeds the rate of the monomer removal (the reverse process) then the passage to the limit model with infinitely many stages leads to a delay differential equation. For any other ratios of the rates, the solution reaches a stationary state.     

Certain properties of the surface layer of AG-4V glass-reinforced plastic

It is shown that after a glass-reinforced plastic (GRP) has been molded the properties of the surface layer differ sharply from those of the interior layers of material. The surface layer is stronger and less moisture-absorbent. The properties of the surface layer and its thickness are determined by the parameters of the molding process. The surface layer of the GRP AG-4V is thickest, hardest and least moisture-absorbent after molding at 130° C and 200 kg/cm². In this case the microstructure is characterized by a highly uniform fiber distribution without signs of splitting or other damage.Mekhanika Polimerov, Vol. 1, No. 5, pp. 118–122, 1965     

Combustion wave in a two-layer solid fuel system

We consider the model describing propagation of a combustion wave in a system of two layers of different exothermic reacting materials under conditions of thermal contact between them through a common surface. This system is directly related to synthesis of advanced materials via the Self-propagating High temperature Synthesis technology when one of the reactants serves as a heat source (donor layer) for the other reacting material (acceptor layer) and facilitates the chemical reaction in the latter. The reaction sheet approximation is used and the parametric study of the boundaries of existence and characteristics of combustion waves in the system of layers is undertaken. The parameters of the process are identified which allow to achieve significantly superadiabatic peak temperatures of combustion in the acceptor layer.     

Dynamic responses of shear flows over a deformable porous surface layer in a cylindrical tube

This paper investigates dynamic responses of a viscous fluid flow introduced under a time dependent pressure gradient in a rigid cylindrical tube that is lined with a deformable porous surface layer. With the Darcy’s law and a linear elasticity assumption, we have solved the coupling effect of the fluid movement and the deformation of the porous medium in the Laplace transform space. Governing equations are deduced for the solid displacement and the fluid velocity in the porous layer. Analytical solutions in the transformed domain are derived and the time dependent variables are inverted numerically using Durbin’s algorithm. Interaction between the solid and the fluid phases in the porous layer and its effects on fluid flow in tube are investigated under steady and unsteady flow conditions when the solid phase is either rigid or deformable. Examples are presented for flows driven by a Heaviside or a sinusoid pressure gradient. Significant effects of the porous surface layer on the flow in the tube are observed. The analytical solutions can be used to test more complicated numerical schemes.     

One singularly perturbed Stefan problem describing destruction of the fuel layer in a laser target

A mathematical model of degradation of a deuterium-tritium (D-T) fuel layer located on the interior wall of a spherical shell is proposed. Such a shell with a solid layer frozen on it is a laser target that is employed in controlled thermonuclear fusion. As the laser target is delivered from the cryogenic chamber to the focus of the laser beam, the chamber stays, during a certain time interval, in a warm-gas cloud. During this time interval, the D-T layer degrades, and, in particular, its surface becomes nonideal. The mathematical model is formulated as a Stefan problem for a system of parabolic equations with nonlinear initial-boundary conditions. Small-parameter methods are applied to obtain an analytic solution to this problem, and the time during which the changes in the geometric parameters of the target’s fuel layer do not exceed technologically admissible values is estimated.     

Langevin equation of a fluid particle in wall-induced turbulence

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion equation for admixture dispersion in wall-induced turbulence.     

Time-dependent laser ignition of a combustible stagnant boundary layer

A spatially one-dimensional model for the ignition of a combustiblegas layer adjacent to a plane solid surface is considered. Theeffect of an incident laser beam from the gas side is to raisethe surface temperature; the other boundary is taken to be apoor thermal conductor in the form of an inert gaseous medium.It is assumed that the exothermic chemical reaction within thelayer has a negligible reactant consumption. Three examplesfor the effect of the laser on the solid surface are considered:(a) a large instantaneous temperature rise, (b) a temperaturejump at t=0 which is a linear funtion of time t>0, (c) asurface temperature variation which is a linear function oftime. For (a) and (b) conditions for criticality are obtained.For appropriate states of the system, times to ignition for(a), (b), and (c) have been determined. It is shown that thetheoretical results are in reasonably good agreement with experiment.The kind of physical situation envisaged might occur in a mineshaftwhen a stagnant combustible layer is subject to intense transientlight. Although an idealization, our analysis determines conditionsunder which thermal runaway and subsequent explosion could takeplace.     

Modelling of thermoelastic Rayleigh waves in a solid underlying a fluid layer with varying temperature

The present paper is aimed at to study the propagation of surface waves in a homogeneous isotropic, thermally conducting and elastic solid underlying a layer of viscous liquid with finite thickness in the context of generalized theories of thermoelasticity. The secular equations for non-leaky Rayleigh waves, in compact form are derived after developing the mathematical model. The amplitude ratios of displacements and temperature change in both media at the surface (interface) are also obtained. The liquid layer has successfully been modeled as thermal load in addition to normal (hydrostatic pressure) one, which is the distinctive feature of the present study and missing in earlier researches. Finally, the numerical solution is carried out for aluminum-epoxy composite material solid (half-space) underlying a viscous liquid layer of finite thickness. The computer simulated results for dispersion curves, attenuation coefficient profiles, amplitude ratios of surface displacements and temperature change have been presented graphically, in order to illustrate and compare the theoretical results. The present analysis can be utilized in electronics and navigation applications in addition to surface acoustic wave (SAW) devices.     

Nature of the friction deformation of the surface layers of polymethyl methacrylate

The surface deformation of amorphous thermoplastics (polymethyl methacrylate) by a spherical steel indentor has been investigated at various sliding velocities. Small velocities correspond to elastic and forced-elastic deformation of the surface layers and asperities. At temperatures corresponding to the high-elastic state the deformed surface layer completely recovers its shape. As the sliding velocity increases, the forced-elastic deformation is localized in a thinner layer of plastic. Starting from a certain velocity, depending on the temperature and the activation energy for transition of the chain segments from one equilibrium position to another in the process of thermal motion, the deformation of the surface layers and asperities becomes purely elastic. In the event of elastic deformation at pressures above a certain value the surface layer of plastic suffers brittle fracture in the tensile zone behind the indentor.Mekhanika Polimerov, Vol. 4, No. 1, pp. 90–94, 1968.     

Analysis of the Stress State of the Surface Layer of a Polymeric Mass upon Filling of Bulky Compression Molds

The stress state of the surface layer of a polymeric mass during filling of bulky compression molds is analyzed. It is shown that, at particular rheological characteristics of the mass, temperature, and filling rates, cracking of the surface layer occurs, which leads to defects in the finished products. A physical analysis of this process makes it possible to conclude that the cracks arise due to the normal stresses operating in the front region of the moving polymeric mass. It is found that, under certain flow conditions, areas with a pressure lower than the atmospheric one appear on the surface of the polymer. If the tensile stresses arising in these local regions are higher than the tensile strength of the mass, the continuity of the composition is broken in the direction determined by the greatest rate of the normal deformation. To confirm the reliability of the crack-formation mechanism proposed, the distribution of the pressure and normal stresses over the free surface is calculated based on a numerical method. These calculations show that, by comparing the stress level achieved in the front region with the tensile-strength characteristics of the polymeric composition, it is possible to predict, with a sufficient accuracy, the possibility of crack formation in the surface layer of such a mass under given flow conditions and thus to solve the question on flawless manufacturing of products.     

Use of artificial neural network simulation metamodelling to assess groundwater contamination in a road project

The estimation of the extent of a polluted zone after an accidental spill occurred in road transport is essential to assess the risk of water resources contamination and to design remediation plans. This paper presents a metamodel based on artificial neural networks (ANN) for estimating the depth of the contaminated zone and the volume of pollutant infiltration in the soil in a two-layer soil (a silty cover layer protecting a chalky aquifer) after a pollutant discharge at the soil surface. The ANN database is generated using USEPA NAPL-Simulator. For each case the extent of contamination is computed as a function of cover layer permeability and thickness, water table depth and soil surface–pollutant contact time. Different feedforward artificial neural networks with error backpropagation (BPNN) are trained and tested using subsets of the database, and validated on yet another subset. Their performance is compared with a metamodelling method using multilinear regression approximation. The proposed ANN metamodel is used to assess the risk for a DNAPL pollution to reach the groundwater resource underneath the road axis of a highway project in the north of France.     

The stability of a transonic boundary layer on an elastic surface

The perturbations in the boundary layer over an elastic surface when there is non-stationary free viscous-inviscid interaction at transonic velocities are investigated using a modified three-deck model. The modification consists of retaining the term with the second derivative with respect to time (the singular term of the transonic expansion), which occurs in the model of the Lin–Reissner–Tsien equation when it is derived from the complete equations for the velocity potential. This enables the equations of the model to be improved so that they more accurately describe non-stationary and non-linear phenomena. It is shown that the modified model enables perturbations, ignored when using the classical three-deck model, to be taken into account. The compliance on the surface may lead to a reduction in the perturbation growth rate.     

Perturbations from a source in a two-layer atmosphere bounded by the horizontal terrestrial surface

The problem of internal waves excited by a point source in a two-layer atmosphere is investigated in a linear formulation. The lower layer is bounded by a horizontal surface and, the upper layer is unbounded. It is assumed that the vertical displacements and velocities of the particles vary continuously at the layer boundaries, and that the Brunt Väisälä frequency is constant in each layer but experiences discontinuities at the common boundary of the layers; the source is situated in the lower layer. The asymptotic behaviour of the perturbations in the lower layer at long times is investigated. The solution is found using integral transforms and is expressed in terms of double integrals of many-valued analytic functions. A transformation is proposed which enables the solution to be expressed as the sum of single integrals. The behaviour of these integrals at long times is found by the stationary-phase method. It is shown that a critical cone exists across which the asymptotic behaviour of the system undergoes a change.     

Simulation of the chipping behavior of coated abrasives by cooperating cellular automata

During the production of high-grade wooden components often the conditioning with coated abrasives composes the end of the process train. The chipping process and the resulting wood surface are depending of the scatter pattern parameters (particle size and distribution, …) and their time depending variations. Till now, no models exist concerning the interaction of the scatter pattern with the grinding process, the work piece surface and the clogging. The developed model is based on cooperating cellular automata. One is describing the sandpaper, the other one the work piece. These two automata interacts witch each other. Update rules are designed by physical laws and measurements. The paper shows surprising results with respect of surface structures which are the result of self-organization effects in the boundary layer of wood and sandpaper. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Laminar compressible boundary layer flow at a three-dimensional stagnation point with vectored mass transfer

The effect of surface mass transfer velocities having normal, principal and transverse direction components (‘vectored’ suction and injection) on the steady, laminar, compressible boundary layer at a three-dimensional stagnation point has been investigated both for nodal and saddle points of attachment. The similarity solutions of the boundary layer equations were obtained numerically by the method of parametric differentiation. The principal and transverse direction surface mass transfer velocities significantly affect the skin friction (both in the principal and transverse directions) and the heat transfer. Also the inadequacy of assuming a linear viscosity-temperature relation at low-wall temperatures is shown.     

Thermal radiation effects on magnetohydrodynamic free convection heat and mass transfer from a sphere in a variable porosity regime

A mathematical model is presented for multiphysical transport of an optically-dense, electrically-conducting fluid along a permeable isothermal sphere embedded in a variable-porosity medium. A constant, static, magnetic field is applied transverse to the cylinder surface. The non-Darcy effects are simulated via second order Forchheimer drag force term in the momentum boundary layer equation. The surface of the sphere is maintained at a constant temperature and concentration and is permeable, i.e. transpiration into and from the boundary layer regime is possible. The boundary layer conservation equations, which are parabolic in nature, are normalized into non-similar form and then solved numerically with the well-tested, efficient, implicit, stable Keller-box finite difference scheme. Increasing porosity (ε) is found to elevate velocities, i.e. accelerate the flow but decrease temperatures, i.e. cool the boundary layer regime. Increasing Forchheimer inertial drag parameter (Λ) retards the flow considerably but enhances temperatures. Increasing Darcy number accelerates the flow due to a corresponding rise in permeability of the regime and concomitant decrease in Darcian impedance. Thermal radiation is seen to reduce both velocity and temperature in the boundary layer. Local Nusselt number is also found to be enhanced with increasing both porosity and radiation parameters.     

Modelling the semi-batch vinyl acetate emulsion polymerization in a real-life industrial reactor

A detailed dynamic model of the polymerization reaction of vinyl acetate in a real-life industrial reactor is presented. With the recipe and the operating procedures observed in the factory as inputs, the model predicts with reasonable accuracy the final conversion, the average particle diameter, the solid content and the viscosity. The manual and semi-manual operations, and the decision process followed by the operator, are also modelled in order to replicate closely the process carried out in the factory. The model provides further insight into the reaction kinetics and allows us to make knowledge-based decisions. The model is intended to be used for the optimization of the policy of adding monomer in order to reduce the batch time.