Calculation of an unsteady moving-boundary flow in a porous medium by the generalized method of integral relations

Dorodnicyn’s generalized method of integral relations is used to compute a Verigin-type single-phase unsteady flow in a porous medium. This problem describes the pumping of a gas through a gallery in a bounded horizontal aquifer and is associated with underground gas storage in aquifers. The case of an isothermal process and an ideal gas are considered. The viscosity of the gas is neglected. Sines are used as smoothing functions. The results obtained in the first and third approximations are presented and analyzed. The solution is compared with a finite-difference solution and that produced by the method of integral relations. The results are given in a table.     

Investment–consumption with regime-switching discount rates

This paper considers the problem of consumption and investment in a financial market within a continuous time stochastic economy. The investor exhibits a change in the discount rate. The investment opportunities are a stock and a riskless account. The market coefficients and discount factor switch according to a finite state Markov chain. The change in the discount rate leads to time inconsistencies of the investor’s decisions. The randomness in our model is driven by a Brownian motion and a Markov chain. Following Ekeland and Pirvu (2008) we introduce and characterize the subgame perfect strategies. Numerical experiments show the effect of time preference on subgame perfect strategies and the pre-commitment strategies.     

Non-linear peristaltic transport of a second-order fluid through a porous medium

The present paper investigates phenomena brought about into the classic peristaltic mechanism by inclusion of non-Newtonian effects through a porous space in a channel. The peristaltic motion of a second-order fluid through a porous medium was studied for the case of a planar channel with harmonically undulating extensible walls. The system of the governing nonlinear PDE is solved by using the perturbation method to second-order in dimensionless wavenumber. The analytic solution has been obtained in the form of a stream function from which the axial pressure gradient has been derived. The flow is investigated in a wave frame of reference moving with velocity of the wave. Numerical calculations are carried out for the pressure rise and frictional force. The features of the flow characteristics are analyzed by plotting graphs and discussed in detail.     

On the deformation of an elastic half-space with a thin slit for mixed conditions on its boundary

The problem of the state of stress and strain in an elastic half-space with a cutout in the shape of a circular slot is solved by Kelvin's method /1/. The conditions on the slot are satisfied in a suitable manner by selecting the scalar and vector mass force potentials as generalized functions concentrated at the slot. The problem reduces to a system of Fredholm integral equations of the second kind in a semi-infinite interval. The solution for an elastic space with a slot is obtained in final form in the limiting case, which enables an estimate to be made of the magnitude of the settling of the earth's surface as a result of oil or gas deposit development.     

The out-of-kilter algorithm applied to traffic congestion

The out-of-kilter algorithm finds a minimum cost assignment of flows to a network defined in terms of one-way arcs, each with upper and lower bounds on flow, and a cost. It is a mathematical programming algorithm which exploits the network structure of the data. The objective function, being the sum taken over all the arcs of the products, cost×flow, is linear. The algorithm is applied in a new way to minimise a series of linear functions in a heuristic method to reduce the value of a non-convex quadratic function which is a measure of traffic congestion. The coefficients in these linear functions are chosen in a way which avoids one of the pitfalls occurring when Beale's method is applied to such a quadratic function. The method does not guarantee optimality but has produced optimal results with networks small enough for an integer linear programming method to be feasible.     

Steady-state problem of complex heat transfer

The problem of radiative-conductive-convective heat transfer in a three-dimensional domain is studied. The existence of a weak solution of the problem is proved, and sufficient conditions for the uniqueness of a solution are found. The temperature distribution in a three-dimensional channel is determined in numerical experiments.     

A Small-Parameter Problem from the Theory of Boundary-Value Problems with a Small Nonlinearity

We consider a system of nonlinear equations with a small (in a certain sense) nonlinearity. The existence of a solution is investigated in the presence of a perturbation parameter of small absolute value, and the perturbed solution is required to approach the original solution of the limiting linear system. The sufficient conditions are presented in geometrical and analytical forms. The problem considered in this article arises in connection with nonlinear boundary-value problems for systems of differential equations with a small (in a certain sense) nonlinearity.     

Modeling and numerical analysis of the thread rolling process

The paper presents the physical and mathematical models of deformations (displacements and strains) and the stress in the cold process of the thread rolling. The process is considered as a geometrical and physical nonlinear, initial as well as a boundary value problem. The phenomena of a typical incremental step were described using a step-by-step incremental procedure, in the updated Lagrangian formulation. The state of strains was described by Green-Lagrange's tensor, while the state of stress was described by the second symmetrical Pioli-Kirchhoff's tensor. The object was treated as an elastic (in the reversible zone) and visco-plastic body (in the non-reversible zone) with mixed hardening. The variational equation of the motion in three dimensions for this case was proposed. Then, the finite elements methods (FEM) and dynamic explicit method (DEM) were used to obtain the solution. In a numerical analysis, boundary condition for a displacement increment, was determined in the model investigation. The results of a numerical analysis were compared and verified in an experimental investigation. Examples of calculations of the influence of a friction coefficient on the state of the deformation and stress, and an example application for this method of thread rolling were presented. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Viscoelastic body colliding against a rigid wall with and without dry friction effects

The impact of a body against a rigid wall is studied. The body consists of a rigid block and a viscoelastic rod described by the distributed-order fractional model and in particular its solid-like and fluid-like special cases. Translatory motion of a body is studied in two cases: without and with the influence of dry friction. When present, dry friction is modeled by the Coulomb friction law. The problem is treated analytically by the use of the Laplace transform method and solutions are obtained in a convolution form.     

Ohmic heating of foods during aspetic processing

The problem of heating food by applying a large electrical currentacross it is considered. Various aspects of the problem areconsidered, with emphasis on the electrical and thermal behaviourdue to variations in electrical conductivity of the food. Suchvariations are due to variations in temperature within the foodand differences in material properties of the food. The stabilityof ohmic heating as a method used for processing is consideredfor the simple case of a homogeneous food. The heating of ahomogeneous food in a shear layer close to a wall is analysed.The case of a single spherical solid food particle with temperature-dependentconductivity surrounded by a liquid sauce is considered to modelthe behaviour of a multiphase food.     

An Oligopolistic Investment Model of the Finnish Electricity Market

The investment problem faced by producers in deregulated electricity markets contains high uncertainties about the future. It can also be seen as a game, as only a small number of large players act in the market. A dynamic stochastic oligopoly model to describe the production and investment in such a situation is developed and applied to the Finnish electricity market. The demand growth rate is modeled as a stochastic variable. The strategies of the firms consist of investments and production levels for base and peak load periods. The firms have nuclear, hydro and thermal capacities, but are only allowed to invest in new thermal capacity. Using a so-called sample-path adapted open-loop information structure, the model contributes to the understanding of the dynamics of production, investment and market power in a medium time horizon. The solution method uses recent developments in variational inequality and mixed complementarity problem formulations.     

On the convergence of 2-dimensional markov chains in quadrants with boundary reflection

The aim of this paper is to prove a limit theorem on the weak convergence of a family of rescaled Markov chains in a quadrant with boundary reflection. The limiting process is specified in terms of solutions of a certain submartingale problem in the style used by Varadhan and Williams. The obtained result is then applied to the problem of approximating an arbitrary Brownian motion with oblique reflection in a wedge by a family of Markov chains.     

激波在异种气体中传播及诱导的剪切混合研究

利用二阶迎风TVD格式求解多组分,层流全N－S方程,针对直通道和突扩直通道,研究了马赫数为2和4的激波在H2和空气界面上的传播及诱导的燃料剪切混合,计算结果表明：（1）直通道中,剪切层中的激波阵面要发生畸变,存在对混合起主要作用的卷吸涡,激波马赫数不同,卷吸涡结构和横向混合的尺寸也不同,激波马赫数低,剪切混合效果好,（2）在突扩直通道中,马赫数为2和4的激波在H2中产生不同强度激波,在剪切层中都能产生顺时针,尺度较大的卷吸涡,后台阶增强了剪切层的混合。     

Information in the operations research process

The article deals with information in the OR process. The value of an ‘optimal’ model solution which is not implemented is not very high. Many errors are due to a too narrow formulation of the problem, often a formulation which has focused on purely technical and economic aspects, or a formulation which has been adapted for a standard model. The concepts and models treated in the article take their point of departure in the actual problem. The models can be used as a frame of reference by various individuals and groups which are involved in OR work.     

Optimum strategies for the application of border guard detection devices

A model of the interaction between a violator of a frontier and a sentry guarding it using a certain detection device is considered. The efficiency of the device depends on the moment in time at which it is applied. The interaction between a sentry and a violator of a frontier is formally described by an antagonistic game that has no saddle point in pure strategies in cases of practical interest. The search for equilibrium in mixed strategies is reduced to a maximin problem that is solved using the equalization principle.     

The transmission of a flexural-gravitational wave through a rigid end-stop in a floating plate

An elastic plate is located on the surface of a liquid, in continuous contact with it and rigidly clamped in a support along a certain straight line. The orthogonal incidence of a small amplitude flexural-gravitational wave on the support is considered. Exact expressions are obtained for the wave field in the fluid and the flexural field in the plate. The transmission coefficient of the incident flexural-gravitational wave through the support and its reflection coefficient from it are determined. The forces which arise in the support are found. The investigation is carried out for liquids of finite and infinite depth. The effect of the depth of the liquid on the wave processes is indicated. The liquid is assumed to be inviscid and its friction on the bottom and the lower surface of the plate in the neighbourhood of the support is therefore ignored.     

Motion transformation in a higher order dimensional space

The objective of the work presented in this paper is an attempt at solving and transforming of the known from the classical mechanics two dimensional-plane single mass mechanical and mathematical vibration models in a higher order dimensional space with any virtual sectional curvature-positive or negative, constant or variable. A characterization of the Riemannian manifolds is performed by means of curvature operators. The computer codes Mathematica and MATLAB are used in the numerical simulation. The objects of the investigation are a sphere – with a positive constant sectional curvature, a cylinder-with a zero constant sectional curvature, helicoid-with a negative variable sectional curvature, a torus-with a variable (±) sectional curvature, any virtual surface of second order-with a variable (±) sectional curvature, pseudo-sphere – with a negative constant sectional curvature and a saddle-with a negative variable sectional curvature. The system motion is investigated in a qualitative aspect in time and frequency domain on the cited surfaces. The common algorithm derived in the paper can transform any motion from 3D space to curved manifold. We can derive the trajectory in an explicit form on the curved manifold. We can change the trajectory by a suitable variation of the curved manifold.     

Decision-making in a fuzzy environment with fuzzy termination time

The multistage control of a deterministic and stochastic system in a fuzzy environment is considered. The fuzzy environment is meant as fuzzy constraints imposed on subsequent controls and a fuzzy goal to be attained. The fuzzy decision is assumed to be the intersection of fuzzy constraints and a fuzzy goal. The problem is to find a maximizing decision. The termination time is given as a specified fuzzy set in the space of control stages. For solving the problem, the dynamic programming is applied.     

Influence of particle size on the fracture toughness of a PP-based particulate composite

The main focus of this paper is a numerical investigation of the fracture behavior of a particulate composite (CaCO₃-PP). The composite is modeled as a three-phase continuum and simulated numerically on a microscale by using finite elements. The propagation of a microcrack in a matrix filled with rigid particles covered by an interphase is analyzed. The stress distribution is determined for a variety of particle sizes and material properties of the interphase. The final results, in agreement with experimental data, confirm that the microcrack behavior depends on particle sizes. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 45, No. 3, pp. 411-418, May-June, 2009.