Hasil untuk "Analytic mechanics"

P. Vijayalakshmi, K. Karuppasamy

Let G = (V,E) be a finite, simple, and undirected graph without an isolated vertex. A dominating subset D ⊆ V (G) is a restrained pitchfork dominating set if 1 ≤ |N(u) ∩ V − D| ≤ 2 for every u ∈ D and every vertex not in D is adjacent to at least one vertex in the same set. The cardinality of a minimum restrained pitchfork dominating set is the restrained pitchfork domination number γrpf(G). In the course of this investigation, we undertake an examination of the restrained pitchfork domination number within various path-related graphs. This analysis encompasses a range of graph structures, including the coconut tree, double star, banana tree, binomial tree, thorn path, thorn graph, and the square of the path denoted as Pn.

Zhaoyu Shi, Seyed Morteza Habibi Khorasani, Heesoo Shin et al.

Efficient tools for predicting the drag of rough walls in turbulent flows would have a tremendous impact. However, accurate methods for drag prediction rely on experiments or numerical simulations which are costly and time consuming. Data-driven regression methods have the potential to provide a prediction that is accurate and fast. We assess the performance and limitations of linear regression, kernel methods and neural networks for drag prediction using a database of 1000 homogeneous rough surfaces. Model performance is evaluated using the roughness function obtained at a friction Reynolds number $Re_\tau$ of 500. With two trainable parameters, the kernel method can fully account for nonlinear relations between the roughness function $\Delta U^+$ and surface statistics (roughness height, effective slope, skewness, etc.). In contrast, linear regression cannot account for nonlinear correlations and displays large errors and high uncertainty. Multilayer perceptron and convolutional neural networks demonstrate performance on par with the kernel method but have orders of magnitude more trainable parameters. For the current database size, the networks’ capacity cannot be fully exploited, resulting in reduced generalizability and reliability. Our study provides insight into the appropriateness of different regression models for drag prediction. We also discuss the remaining steps before data-driven methods emerge as useful tools in applications.

Katsushi Ito, Hongfei Shu

Abstract We study the spectral problem in deformed supersymmetric quantum mechanics with polynomial superpotential by using the exact WKB method and the TBA equations. We apply the ODE/IM correspondence to the Schrödinger equation with an effective potential deformed by integrating out the fermions, which admits a continuous deformation parameter. We find that the TBA equations are described by the ℤ4-extended ones. For cubic superpotential corresponding to the symmetric double-well potential, the TBA system splits into the two D 3-type TBA equations. We investigate in detail this example based on the TBA equations and their analytic continuation as well as the massless limit. We find that the energy spectrum obtained from the exact quantization condition is in good agreement with the diagonalization approach of the Hamiltonian.

М.Т. Космакова, А.Н. Хамзеева, Л.Ж. Касымова

In the article, the boundary value problem for the wave equation with a fractional time derivative and with initial conditions specified in the form of a fractional derivative in the Riemann-Liouville sense is solved. The definition domain of the desired function is the upper half-plane (x,t). To solve the problem, the Fourier transform with respect to the spatial variable was applied, then the Laplace transform with respect to the time variable was used. After applying the inverse Laplace transform, the solution to the transformed problem contains a two-parameter Mittag-Leffler function. Using the inverse Fourier transform, a solution to the problem was obtained in explicit form, which contains the Wright function. Next, we consider limiting cases of the fractional derivative’s order which is included in the equation of the problem.

Edward Nelson

V.I. Senashov, I.A. Paraschuk

The article discusses the possibility of recognizing a group by the bottom layer, that is, by the set of its elements of prime orders. The paper gives examples of groups recognizable by the bottom layer, almost recognizable by the bottom layer, and unrecognizable by the bottom layer. Results are obtained for recognizing a group by the bottom layer in the class of infinite groups under some additional restrictions. The notion of recognizability of a group by the bottom layer was introduced by analogy with the recognizability of a group by its spectrum (the set of orders of its elements). It is proved that all finite simple nonAbelian groups are recognizable by spectrum and bottom layer simultaneously in the class of finite simple non-Abelian groups.

A.T. Assanova, S.S. Zhumatov, S.T. Mynbayeva et al.

The paper proposes a constructive method to solve a nonlinear boundary value problem for a Fredholm integro-differential equation. Using D.S. Dzhumabaev parametrization method, the problem under consideration is transformed into an equivalent boundary value problem for a system of nonlinear integrodifferential equations with parameters on the subintervals. When applying the parametrization method to a nonlinear Fredholm integro-differential equation, the intermediate problem is a special Cauchy problem for a system of nonlinear integro-differential equations with parameters. By substitution the solution to the special Cauchy problem with parameters into the boundary condition and the continuity conditions of the solution to the original problem at the interior partition points, we construct a system of nonlinear algebraic equations in parameters. It is proved that the solvability of this system provides the existence of a solution to the original boundary value problem. The iterative methods are used to solve both the constructed system of algebraic equations in parameters and the special Cauchy problem. An algorithm for solving boundary value problem under consideration is provided.

A.R. Yeshkeyev, I.O. Tungushbayeva, M.T. Kassymetova

The paper aims to study the model-theoretic properties of differentially closed fields of zero and positive characteristics in framework of study of Jonsson theories. The main attention is paid to the amalgam and joint embedding properties of DCF theory as specific features of Jonsson theories, namely, the implication of JEP from AP. The necessity is identified and justified by importance of information about the mentioned properties for certain theories to obtain their detailed model-theoretic description. At the same time, the current apparatus for studying incomplete theories (Jonsson theories are generally incomplete) is not sufficiently developed. The following results have been obtained: The subclasses of Jonsson theories are determined from the point of view of joint embedding and amalgam properties. Within the exploration of one of these classes, namely the AP-theories, that the theories of differential and differentially closed fields of characteristic 0, differentially perfect and differentially closed fields of fixed positive characteristic are shown to be Jonsson and perfect. Along with this, the theory of differential fields of positive characteristic is considered as an example of an AP-theory that is not Jonsson, but has the model companion, which is perfect Jonsson theory, and the sufficient condition for the theory of differential fields is formulated in the context of being Jonsson.

M. Tabor

R. Gordon

M.T. Jenaliyev, M.G. Yergaliyev, A.A. Assetov et al.

We consider some initial boundary value problems for the Burgers equation in a rectangular domain, which in a sense can be taken as a model one. The fact is that such a problem often arises when studying the Burgers equation in domains with moving boundaries. Using the methods of functional analysis, priori estimates, and Faedo-Galerkin in Sobolev spaces and in a rectangular domain, we show the correctness of the initial boundary value problem for the Burgers equation with nonlinear boundary conditions of the Neumann type.

Michael Schaefer and, M. Karplus

P. Steif, F. Spaepen, J. Hutchinson

B.T. Kalimbetov, A.N. Temirbekov, B.I. Yeskarayeva

This paper is devoted to the study of internal boundary layer. Such motions are often associated with effect of boundary layer, i.e. low flow viscosity affects only in a narrow parietal layer of a streamlined body, and outside this zone the flow is as if there is no viscosity - the so-called ideal flow. Number of exponentials in the boundary layer is determined by the number of non-zero points of the limit operator spectrum. In the paper we consider the case when spectrum of the limit operator vanishes at the point To study the problem the Lomov regularization method is used. The original problem is regularized and the main term of asymptotics of the problem solution is constructed as the low viscosity tends to zero. Numerical results of solutions are obtained for different values of low viscosity.

A.T. Assanova, Zh.S. Tokmurzin

A semi-periodic initial boundary-value problem for a fourth-order system of partial differential equations is considered. Using the method of functional parametrization, an additional parameter is carried out and the studied problem is reduced to the equivalent semi-periodic problem for a system of integro-differential equations of hyperbolic type second order with functional parameters and integral relations. An interrelation between the semi-periodic problem for the system of integro-differential equations of hyperbolic type and a family of Cauchy problems for a system of ordinary differential equations is established. Algorithms for finding of solutions to an equivalent problem are constructed and their convergence is proved. Sufficient conditions of a unique solvability to the semi-periodic initial boundary value problem for the fourth order system of partial differential equations are obtained.

M.T. Jenaliyev, M.I. Ramazanov, A.A. Assetov

The paper is devoted to the questions of solvability in the Sobolev classes for boundary value problem for the Burgers equation with boundary conditions of the Solonnikov-Fasano type in degenerating domain with degenerate point at the origin. By applying the Galerkin methods and a priori estimates we prove the Existence and Uniqueness Theorems for the solution of the considered boundary value problem, as well as its regularity with increasing smoothness of given functions.

Pablo Martin, Fernando Maass, Daniel Diaz-Almeida

Precise analytic approximations have been found for the eigenvalues of the ground state in the anharmonic potentials x2+λx8. Rational functions combined with fractional powers are used to determine the new approximations. First, power series in the parameter has been found using an extension of the quantum mechanics perturbation technique recently published. Modifications of these new technologies has been also developed to obtain asymptotic expansions in λ. The analytic functions here determined are just a bridge between both expansions. The maximum relative error of the best analytic approximation here determined is 0.006 (less than 1%). However, most of the relative errors for other values of λ, are smaller than 0.3%. Positive values of λ are only considered.

Robert E. Kearney, Ian W. Hunter

H. Motohashi, T. Suyama, Masahide Yamaguchi

A bstractWe construct no-ghost theories of analytic mechanics involving arbitrary higher-order derivatives in Lagrangian. It has been known that for theories involving at most second-order time derivatives in the Lagrangian, eliminating linear dependence of canonical momenta in the Hamiltonian is necessary and sufficient condition to eliminate Ostrogradsky ghost. In the previous work we showed for the specific quadratic model involving third-order derivatives that the condition is necessary but not sufficient, and linear dependence of canonical coordinates corresponding to higher time-derivatives also need to be removed appropriately. In this paper, we generalize the previous analysis and establish how to eliminate all the ghost degrees of freedom for general theories involving arbitrary higher-order derivatives in the Lagrangian. We clarify a set of degeneracy conditions to eliminate all the ghost degrees of freedom, under which we also show that the Euler-Lagrange equations are reducible to a second-order system.

L. Barbieri, R. Massabò, C. Berggreen

The effects of shear on energy release rate and mode mixity in a symmetric sandwich beam with isotropic layers and a debond crack at the face sheet/core interface are investigated through a semi-analytic approach based on two-dimensional elasticity and linear elastic fracture mechanics. Semi-analytic expressions are derived for the shear components of energy release rate and mode mixity phase angle which depend on four numerical coefficients derived through accurate finite element analyses. The expressions are combined with earlier results for three-layer configurations subjected to bending-moments and axial forces to obtain solutions for sandwich beams under general loading conditions and for an extensive range of geometrical and material properties. The results are applicable to laboratory specimens used for the characterization of the fracture properties of sandwich composites for civil, marine, energy and aeronautical applications, provided the lengths of the crack and the ligament ahead of the crack tip are above minimum lengths. The physical and mechanical significance of the terms of the energy release rate which depend on the shear forces are explained using structural mechanics concepts and introducing crack tip root rotations to account for the main effects of the near tip deformations.