Journal of Applied and Industrial Mathematics最新文献

We consider an initial–boundary value problem for a semilinear parabolic differentialequation with a time-nonlocal term. This term contains the integral of the solution over the entiretime interval on which the problem is considered. The solvability of the problem inHölder classes is proved. The uniqueness of the solution is established under a constrainton the length of the time interval over which the solution is integrated in the nonlocal term.

A three-vertex subset is called an open triangle (OT) if it induces a subgraph with exactlytwo edges. The problem of finding graphs with maximum number of OTs is considered. It isproved that, in case of sufficiently many vertices, such a graph is unique in the class of graphswith constant difference between the numbers of edges and vertices.

We construct convex continuations of discrete functions defined on the vertices of the( n )-dimensional unit cube( [0,1]^n ), an arbitrary cube( [a,b]^n ), and a parallelepiped( [c_1,d_1]times [c_2,d_2]times dots times [c_n,d_n] ). In each of these cases, we constructively prove that, for any discrete function( f ) defined on the vertices of( mathbb {G} in {[0,1]^n, [a,b]^n, [c_1,d_1]times [c_2,d_2]times dots times [c_n,d_n]} ), first, there exist infinitely many convex continuations to the set( mathbb {G} ), and second, there exists a unique function( f_{DM}colon mathbb {G}to mathbb {R} ) that is the maximum of convex continuations of( f ) to( mathbb {G} ). We also show that the function( f_{DM} ) is continuous on( mathbb {G} ).

In this paper, we computationally study the influence of the initial diameter of a waterdroplet on the dynamics and breakup induction period in the flow behind a passing shock wave.For this purpose, a series of calculations were performed for a fixed Weber number( mathrm {We} = 400 ) and a variable initial diameter( d = 1.4, 2.8, 5.6 ) mm of the water droplet. The numerical technique is based on the VOFmethod, the LES model is used to take into account turbulence, and the technology of adapteddynamic grids is used to describe the behavior of the interfacial boundary at main turbulentscales; this has made it possible to resolve secondary water droplets up to 20( mu )m in size. The droplet shape, the flow structure near and in the droplet wake,and the nature of mass entrainment were investigated. As a result of the calculations, thedependences of the breakup time on the dimensionless droplet diameter were obtained, thebreakup induction time was determined, and the time constant of droplet interaction with the flowwas calculated to estimate the droplet breakup lag.

This paper continues the study of the relationship between the convolution equation of thesecond kind on a finite interval( (0, tau ) ) (which is also called the truncated Wiener–Hopf equation) anda factorization problem (which is also called a vector Riemann–Hilbert boundary value problem ora vector Riemann boundary value problem). The factorization problem is associated with a familyof truncated Wiener–Hopf equations depending on the parameter( tau in (0,infty ) ). The well-posed solvability of this family of equations is shown depending onthe existence of a canonical factorization of some matrix function. In addition, various possibleapplications of the factorization problem and truncated Wiener–Hopf equations are considered.

In this paper, we consider a model of current distribution in a tungsten specimen and theevaporated substance when the surface is heated by an electron beam. The model is based onsolving the equations of electrodynamics and the two-phase Stefan problem for calculating thespecimen area temperature in a cylindrical coordinate system. We use a model temperaturedistribution in a thin layer of evaporated tungsten that replicates the surface temperature.Thermal currents are obtained using approximate temperature dependences of the electricalresistance and thermo emf of tungsten and its vapor. The model parameters are taken fromexperiments at the Beam of Electrons for materials Test Applications (BETA) stand, created atthe Budker Institute of Nuclear Physics of the Siberian Branch of the Russian Academy ofSciences.

We have conducted a computational study of the effect of adding multiwalled carbonnanotubes (MWCNTs) to oil-based drilling fluids on the efficiency of cuttings removal froman annular channel simulating a horizontal section of a well. To simulate the process of sludgetransport in an annular channel, a mathematical model based on the Eulerian approach ofa granular medium for a turbulent flow regime has been developed. The rheology of the drillingfluid modified with MWCNTs was described by the Herschel–Bulkley model with experimentallydetermined rheological coefficients. The base oil-based drilling fluid was an inverse emulsion witha ratio of hydrocarbon and water phases equal to 65/35. The concentration of MWCNTs insolutions varied from 0.1 to 0.5 wt %. The size of the transported sludge particles variedfrom 2 to 7 mm. The flow structure of a two-phase flow in an annular channel for variousconcentrations of MWCNTs has been studied. The dependences of the sludge removal efficiencycoefficient, the average slip speed of sludge particles, and pressure losses on the concentration ofnanotubes are obtained. It has been established that the addition of nanotubes leads to asignificant change in the flow pattern of the drilling fluid and, as a result, to a change in themodes of cuttings transport. Addition of 0.5 wt % of MWCNTs leads to an increase in theefficiency of well flushing by approximately 40%. Thus, based on the results of the computationalstudy, it has been shown that the addition of multiwalled nanotubes to oil-based drilling fluids canlead to an increase in the efficiency of cuttings transport in horizontal wells.

A new cubic version of the least-squares collocation method based on adaptive grids isdeveloped. Approximate values of the solution and its first derivatives at the vertices ofquadrangular cells are the unknowns. This approach has made it possible to eliminate thematching conditions from the global overdetermined system of linear algebraic equationsconsisting of collocation equations and boundary conditions. The preconditioned system is solvedusing the SuiteSparse library by theorthogonal method with the CUDA parallel programming technology. We consider theReissner–Mindlin plate problem in a mixed formulation. A higher accuracy of deflections androtations of the transverse normal in comparison with the isogeometric collocation method as wellas the uniform convergence of shear forces in the case of a thin plate are shown in the proposedmethod. Bending of an annular plate and round plates with an off-center hole is analyzed. Anincrease in the shear force gradient in the vicinity of the hole is shown both with a decrease in theplate thickness and with an increase in the eccentricity. The second order of convergence of thedeveloped method is shown numerically. The results obtained using the Reissner–Mindlin theoryare compared with the ones in the Kirchhoff–Love theory and three-dimensional finite elementsimulation.

A linear game problem for two players is considered. The two players alternately choosetheir strategies from their respective sets. First, player 1 chooses his/her strategy, then player 2,knowing the strategy of player 1, does the same. The set of strategies of player 2 depends on thestrategy of player 1. The goal of player 1 is to choose a strategy to maximize a convex andpiecewise linear function (the minimum function of the strategy of player 2). The goal of player 2is to minimize the linear function. An algorithm is proposed that allows constructing strategies inthis problem, as well as strategies in the dual problem, that satisfy necessary “higher-order”optimality conditions. This algorithm uses a formula for the increment of the objective function inthe dual problem. Theorems that assert the finiteness of the proposed algorithm and itsmodification are proved. An example illustrating the operation of the algorithm is given. Theresults of a numerical experiment on the construction of strategies that satisfy the necessary“higher-order” optimality conditions in problems whose elements were generated by a randomnumber generator are also presented. Based on the results of the numerical experiment, we canconclude that with the proposed algorithm, it is often possible to switch from one locally optimalstrategy of player 1 to another one increasing the objective function.

This paper presents the results of numerical studies of the phase field model for thedevelopment of an electrical breakdown path. The model consists of Maxwell’s equations in thequasi(electro)stationary approximation, the electric charge balance equation, and the Allen–Cahnequation describing the phase field evolution. Several problem settings concerning thedevelopment of a breakdown path in homogeneous as well as macro- and microheterogeneousmedia are considered.