Journal of Applied and Industrial Mathematics最新文献

A numerical study of the process of cooling a substrate under the conditions ofevaporation of pure vapor from the surface of a liquid film and droplets was carried out. Thelattice Boltzmann method was used for modeling such a two-phase system taking into account thethermal conductivity of the substance and the evaporation. We used the van der Waals equationof state describing the liquid–vapor phase transition. A new method is proposed for setting theboundary conditions on a flat surface for modeling the contact wetting angles in the latticeBoltzmann method. The latent heat of phase transition is taken into account. It is shown that theprocess depends on the film thickness and the rate of vapor removal from the film surface. Thecases of forced outflow of vapor, as well as the method of vapor condensation on a cooledcondenser are considered. It is shown that the heat flux from the substrate increases sharply inthe vicinity of the droplet contact lines. A comparison is made of the heat fluxes during theevaporation of the film and droplets on substrates with different wettabilities.

We describe a mathematical model of the functioning of the central regulatory circuit ofgene networks for the morphogenesis of Drosophila mechanoreceptors taking into accountmutations of the genes included in it. Computational experiments have been carried out showingthe existence of a hierarchy of effects of CRC gene mutations on the production of ASC proteins.

In this paper, we obtain exact analytical solutions of equations of continuousmathematical models of tumor growth and invasion based on the model introduced by Chaplainand Lolas for the case of one spatial dimension. The models consist of a system of three nonlinearreaction–diffusion–taxis partial differential equations describing the interactions between cancercells, the matrix degrading enzyme and the tissue. The obtained solutions are smooth nonnegativefunctions depending on the traveling wave variable with certain conditions imposed on modelparameters.

The continuation problem for the heat equation is considered. Determining the heat fluxon an inaccessible boundary reduces to an inverse problem. An implicit difference scheme is usedfor the numerical solution of the inverse problem. At each time step, the heat flux on theinaccessible boundary is calculated for the difference analog of the elliptic equation byan economical direct method. The proposed algorithm substantially expands the range ofproblems being solved and can be used to create devices capable of real-time determination of theheat flux on parts of inhomogeneous structures inaccessible for measurements, for example, on theinner radius of pipes made of various materials.

The paper addresses the analysis of a boundary value problem with an unknown contactarea that describes equilibrium of two-dimensional elastic bodies with a thin weakly curvedjunction. It is assumed that the junction exfoliates from the elastic bodies to form interfacialcracks. Nonlinear boundary conditions in the form of inequalities are set on the crack faces andexclude the mutual penetration of the edges. The unique solvability of the boundary valueproblem is established. The analysis of passages to the limit as the junction stiffness parametertends to infinity and to zero is carried out, and limit models are investigated.

We consider two problems that are close in terms of formulation. The first one is that ofclustering, i.e., partitioning the set of( d )-dimensional Euclidean vectors into a given number of clusters with differenttypes of centers so that the total variance would be minimum. Here, by variance we mean the sumof squared distances between the elements of the clusters and their centers. There are three typesof centers: an arbitrary point (clearly, the centroid is the best choice), a point of the initial set(the so-called medoid), or a fixed point of the space given in advance.. The sizes of the clusters arealso given as part of the input. The second problem under consideration is the problem ofchoosing a subset of vectors of fixed cardinality having the minimum sum of squared distancesbetween its elements and the centroid. Polynomial-time approximation schemes (PTAS) areconstructed for each of these problems.

Structural formulas in the theory of mechanisms are formulas expressing the number ofdegrees of freedom of a device in terms of the numbers of its links and kinematic pairs. It is wellknown that they are not always true. Mathematical graph theory helps to understand thisphenomenon. The validity of structural formulas in the case of generic frameworks is completelydetermined by their structure, described by graphs. The present paper considers two models ofplanar frameworks with rotational pairs. The first model is a construction made up of straightrods (levers) bearing hinges at the ends. Such devices are naturally associated with a graph( G ) with vertices corresponding to hinges and edges corresponding to levers. Inthe theory of mechanisms, it is customary to consider another graph( cal G ) whose vertices correspond to links and the edges correspond to kinematicpairs. It turns out that the use of the graph( G ) to describe the structure both in the first model and in the second one, whichcontains all planar constructions with rotational pairs, is preferable to the graph( cal G ). In particular, it allows one to provide a criterion for the applicability ofstructural formulas for generic devices of a given structure.

A modification of the quadratic interpolation method for finding the root of a continuousfunction is proposed. Two quadratic interpolation polynomials are simultaneously constructed. Itis shown that if the third derivative of the original function does not change sign on the consideredinterval of localization of the required root, then the root lies between the roots of the quadraticfunctions. This allows one to substantially narrow the localization interval and reduce the numberof steps to calculate the root with a given accuracy. The proposed modification of the quadraticinterpolation method is used in the problem of calculating isolines when modeling the hill diagramof hydraulic turbines.

The paper considers ray transforms of the moments of symmetric tensor fields of arbitraryrank given in the unit disk. The basic geometric and differential properties of mixed raytransforms of tensor fields and mixed ray transforms of the moments of tensor fields areestablished. A simple algorithm for reconstructing a low-rank tensor field from known mixed raytransforms of its moments is proposed and justified.

We consider a stochastic process whose trajectories are characterized by alternate lineargrowth and linear decrease over time intervals of random length, while the process can alsomaintain its value unchanged for random periods of time between growth and decrease. Thisprocess can be considered as a mathematical model of accumulation and consumption ofmaterials, where random periods of time for accumulation, consumption, and interruptions inoperation are combined. We study the mean value( mathbf {E} N ) of the time of first achievement of a fixed level by trajectories of this process,including finding exact formulas for( mathbf {E} N ), producing an upper bound in the form of an inequality, and obtaining theasymptotics of( mathbf {E} N ) under the conditions of an infinitely receding level.