Diffraction of Transient Cylindrical Waves by a Rigid Oscillating Strip

This investigation portrays the transient cylindrical wave diffraction by an oscillating strip. Mathematical analysis of the problem is carried out with the help of an integral transforms and the Wiener–Hopf technique. Using far zone approximation, the scattered field is evaluated by the method of steepest descent. This study takes into consideration the transient cylindrical source and an oscillating strip such that both the source and a scatterer have different oscillating frequencies ω 1 ′ and ω 0 ′ , respectively. The situation under consideration is well supported by graphical results showing the effects of emerging parameters.

Phase Transition to Quadrupolar Vortices in a Spherical Model of the Energy-Enstrophy Theory — Exact Solution

A new energy-enstrophy model for the equilibrium statistical mechanics of barotropic flow on a sphere is introduced and solved exactly for phase transitions to quadrupolar vortices when the kinetic energy level is high. Unlike the Kraichnan theory, which is a Gaussian model, we substitute a microcanonical enstrophy constraint for the usual canonical one, a step which is based on sound physical principles. This yields a spherical model with zero total circulation, a microcanonical enstrophy constraint and a canonical constraint on energy, with angular momentum fixed to zero. A closed-form solution of this spherical model, obtained by the Kac – Berlin method of steepest descent, provides critical temperatures and amplitudes of the symmetry-breaking quadrupolar vortices. This model and its results differ from previous solvable models for related phenomena in the sense that they are not based on a mean-field assumption.

Quantum Fields without Wick Rotation

We discuss the calculation of one-loop effective actions in Lorentzian spacetimes, based on a very simple application of the method of steepest descent to the integral over the field. We show that for static spacetimes this procedure agrees with the analytic continuation of Euclidean calculations. We also discuss how to calculate the effective action by integrating a renormalization group equation. We show that the result is independent of arbitrary choices in the definition of the coarse-graining and we see again that the Lorentzian and Euclidean calculations agree. When applied to quantum gravity on static backgrounds, our procedure is equivalent to analytically continuing time and the integral over the conformal factor.

Development of a strategy for improving organizational and production structures based on methods for non-convex programming

The scientific paper discloses problems of functioning of financial industrial groups, particularly their flexible organizational and production structures. The authors highlight that maintaining sustainability of development of financial industrial groups is oriented towards preserving integrity of their organizational and production structures and keeping a set of parameters within given limits, taking into account internal disturbances and external impacts. Generally, sustainable development of organizational and production structures contemplates concerted actions directed towards accomplishing the following two goals: maximizing indicators displaying results of activities of an organizational and production structure through determining optimal amounts of investments by different directions of activity of its modules, as well as minimizing a probable deviation from planned results by directions of activity. The authors have built a two criteria mathematical model for managing development of prospective directions of activities of organizational and production structures, which takes into account their riskiness and is based on retrospective data. To search the optimal value of a functional, the authors have developed a four-step algorithm for solving the indicated problem. To solve the indicated problem of constrained optimization, the authors have applied the method of steepest descent.

METODE NUMERIK STEPEST DESCENT TERINDUKSI NEWTON DALAM PEMECAHAN MASALAH OPTIMISASI TANPA KENDALA

AbstrakPenelitian teoritis ini mengkaji mengenai metode numerik Stepest Descent yang terinduksi Newton. Penelitian ini dilakukan dengan cara memahami terlebih dahulu mengenai metode numerik Stepest Descent dan Newton, kemudian mengkonstruksi metode baru yang disebut dengan Stepest Descent terinduksi Newton. Pada makalah ini turut disertakan pula contoh perhitungan numerik antara ketiga metode tersebut beserta analisis perhitungannya. AbstractThis research is investigating numerical method of Steepest Descent inducted of Newton. Steps of this research can be described as follows: First, the author has to understand the definition and algorithm of Steepest Descent and Newton methods. After that, the second, author constructing the new method called by Steepest Descent inducted newton. In this paper, author also containing examples of numerical counting among that three methods and analyze them self.

Calculation of Constructions of Variable Thickness by Method of Steepest Descent

The technique of calculation of structural elements of variable thickness is discussed in the article. Such constructive elements are described by differential equations with variable coefficients, for the implementation of which it is necessary to have a reliable calculation method that allows obtaining a fairly accurate solution. The most effective method for calculating such structures is the steepest descent method, developed by L.V. Kantorovich. Within the framework of this article, the idea of the method is set forth in the example of solving problems of bending a beam and a plate of variable thickness. A sequence is given for calculating the design of a variable MSD thickness using the example of a statically indeterminate beam, where the bending equation for a beam of constant cross section was used as the initial approximation. Then this method was generalized to a more complex two-dimensional construction - a plate of variable thickness. The problem of constructing the initial approximation for solving a partial differential equation was solved. As an example, we considered a square plate in plan, hinged on the contour. The results of the calculation were compared with the results obtained by the finite difference method. In solving specific problems by the method of steepest descent, it was revealed that it differs from direct methods, such as, for example, Ritz-Timoshenko, Bubnov-Galerkin, which consists in the fact that successive approximations in solving problems are not obtained in a priori chosen form, but in the form , determined by the problem itself. In the MSD, the solution is corrected qualitatively in the course of implementing the method, and when solving the problem by variational methods, we choose the approximating function and thereby set the solution configuration. The use of the MSD makes it possible to obtain finite formulas for determining the stress-strain state of structures of variable thickness, which will allow them to quickly implement their variant design.

SOLUTION OF NON-LINEAR PROBLEMS OF STRUCTURAL MECHANICS BY METHOD OF STEEPEST DESCENT

The algorithm of application of the method of steepest descent to the solution of problems of structural mechanics and solid mechanics, described by nonlinear differential equations. For application of this method to nonlinear operators are described by a sequence of linear operators in incremental form, unlimited and complex linear operator, in line with the idea of L. V. Kantorovich is limited to a simple linear unbounded operator.

Heat kernel asymptotic expansions for the Heisenberg sub-Laplacian and the Grushin operator

The sub-Laplacian on the Heisenberg group and the Grushin operator are typical examples of sub-elliptic operators. Their heat kernels are both given in the form of Laplace-type integrals. By using Laplace's method, the method of stationary phase and the method of steepest descent, we derive the small-time asymptotic expansions for these heat kernels, which are related to the geodesic structure of the induced geometries.