Journal of Applied and Industrial Mathematics最新文献

Using two-dimensional cylindrically symmetric physical and mathematical model and analgorithm, a numerical investigation of the problem of irradiating a volumetric aluminum targetwith a single femtosecond laser pulse is carried out. The problem has a number of fundamentaland practical applications related to the hardening effect of residual plastic deformations after thepassage of a laser-induced shock wave, in particular, laser shock hardening technology, also knownin the literature as laser forging, laser riveting, or laser peening. The axial symmetry of laser beampermits one to reduce the dimension of the problem from three to two and save considerablecomputational resources. Semiempirical equation of state of aluminum in theMie–Grüneisen form is used with the adjustment of parameters according to the coldcurve of the metal and the data of shock-wave experiments. The law of shock wave propagationand attenuation is investigated, and the stages of (1) single, (2) transient, and (3) hemisphericalshock wave propagation are identified. The size and shape of the area on which the strengtheningeffect can be carried out by a single femtosecond laser pulse are described.

We propose an algorithm for solving the inverse problem of forming structural membersunder creep conditions using the Nelder–Mead algorithm. The initial problem of finding the forcesthat must be applied to obtain the desired curvature of a part is reduced to a sequence ofauxiliary direct problems of modeling the stress-strain state of pure bending of rectangular beams.This model, taking into account the difference in the properties of the material in tension andcompression as well as the presence of accumulated damage in the material during creep, wasverified by numerical methods and implemented in the finite element program MSC Marc.

The paper describes an implemented algorithm for solving the problem of vibrationalconvection in a rectangular domain filled with an unevenly heated incompressible fluid. Themathematical model is based on the solution of the Simonenko–Zenkovskaya equations obtainedby averaging the Navier-Stokes equations under the assumption that the volume of liquid executeshigh-frequency translational vibrations. To solve the Poisson equations, an algebraic multigridmethod is implemented in combination with a highly efficient dynamic programming method(based on R. Bellman’s optimal control principle) and fast Fourier transform. Mathematicalsoftware written in C/C++ hasbeen developed. Examples of solving model problems with various directions of the heating flow ofa square domain relative to the vibration vector are given.

The interaction of a liquid drop with a copper surface is studied. The substrate is assumedto be superhydrophobic with a wetting angle of( 150^circ ). Based on the volume of the drop, the Bond and Weber numbers areapproximately 0.23 and 1.6, respectively. The temperature of the surface and the surrounding airis 298 K, and the temperature of the liquid drop is 5K lower. Simulation of conjugate heattransfer is performed using an axisymmetric coordinate system. The Kistler contact line model isused to determine the dynamic contact angle of a drop during spreading. The change in the shearstress on the substrate and the heat flux induced during the propagation of the drop as a functionof time is studied.

The paper presents the equations of the linear moment theory of elasticity for the case ofarbitrary anisotropy of material tensors of the fourth rank. Symmetric and skew-symmetriccomponents are distinguished in the defining relations. Some simplified versions of linear definingrelations are considered. The possibility of Cauchy elasticity is allowed when material tensors ofthe fourth rank do not have the main symmetry. For material tensors that determine force andcouple stresses, we introduce eigenmoduli and eigenstates that are invariant characteristics of anelastic moment medium. For the case of plane deformation and constrained rotation, an exampleof a complete solution of the two-dimensional problem is given when there are only shear stresses.The solutions turn out to be significantly different for anisotropic and isotropic elastic media.

For the wave equation containing a nonlinearity in the form of an( n )th order polynomial, we study the problem of determining the coefficients ofthe polynomial depending on the variable( xin mathbb {R}^3 ). We consider plane waves that propagate in a homogeneous medium in thedirection of a unit vector( boldsymbol nu ) with a sharp front and incident on an inhomogeneity localized inside acertain ball( B(R) ). It is assumed that the solutions of the problems can be measured at thepoints of the boundary of this ball at the instants of time close to the arrival of the wavefront forall possible values of the vector( boldsymbol nu ). It is shown that the solution of the inverse problem is reduced to a series ofX-ray tomography problems.

A two-dimensional flow of a viscous fluid in a cell of finite size is studied numerically. Theflow arises as a result of an inverse cascade supported by a constant pumping. Several distinctstates are observed. One of them is dominated by a large eddy with a well-defined average velocityprofile. In the second state, strong chaotic large-scale fluctuations predominate. A laminar flow isobserved in the third state. The nature of the resulting state depends on the fluid kinematicviscosity coefficient, the magnitude of the external pumping force wave vector, and the value ofthe bottom friction factor. When the values of the kinematic viscosity and wave vector are fixed, asmall value of the bottom friction factor leads to the appearance of the first state. As thecoefficient of the bottom friction factor increases, there occurs a transition from a flow with onelarge vortex to a laminar flow through a series of states with several unstable vortices, which wecall chaotic motion. The paper presents the results of numerical simulation of a weaklycompressible viscous fluid flow in a closed cell with no-slip boundary conditions on the walls.Pumping is carried out by a static force periodic in space in two directions. The simulation iscarried out for various values of the bottom friction factor.

The Nash equilibrium problem with nonconcave quadratic payoff functions is considered.We analyze conditions that provide quasiconcavity of payoff functions in their own variables onthe respective strategy sets and hence guarantee the existence of an equilibrium point. One suchcondition is that the matrix of every payoff function has exactly one positive eigenvalue; thiscondition is viewed as a basic assumption in the paper. We propose an algorithm that eitherconverges to an equilibrium point or declares that the game has no equilibria. It is shown thatsome stages of the algorithm are noticeably simplified for quasiconcave games. The algorithm istested on small-scale instances.

In this paper, mathematical modeling of the suspension flow in a complex system offractures, when the main fracture is crossed by the secondary one, is carried out. Themathematical model of the process is constructed in the one-fluid approximation and includes thecontinuity equation for the suspension, the system of equations of suspension motion, and themass conservation equation in the form of a convective—diffusion transfer equation for the volumeconcentration of particles. The solution to the problem in a 3D formulation is implemented in theOpenFOAM software package. Thedynamics of the distribution of solid spherical particles in the network of fractures is studieddepending on the ratio of the characteristic Reynolds numbers for the flow and particles, as well ason the ratio of the lengths of the main and secondary fractures.

Mathematical modeling of heat transfer processes in a room with a gas infrared emitter,an air exchange system, a horizontal panel simulating equipment, and a local fence has beencarried out. The system of radiative heat transfer, energy, and Navier–Stokes equations for air andheat equations for solid elements was solved. The temperature and air velocity fields obtained as aresult of modeling illustrate the possibility of controlling the thermal regime of the local workingarea when a special fence is installed at its boundary. It was established that by changing thefence height and material one can change the local and average air temperatures in the localworking area. The results of numerical studies suggest that by varying the local fence parametersone can create more comfortable temperature conditions in the local working area when gasinfrared emitters operate under sufficiently intense air exchange conditions.