Thermal mechanical coupling analysis of two-dimensional decagonal quasicrystals with elastic elliptical inclusion

2021 ◽  
pp. 108128652110387
Author(s):  
Yuan-Yuan Ma ◽  
Xue-Fen Zhao ◽  
Ting Zhai ◽  
Sheng-Hu Ding
Keyword(s):  
Flow Direction ◽  
Elastic Field ◽  
Cauchy Type ◽  
Two Dimensional ◽  
Elliptic Inclusion ◽  
Riemann Boundary Value Problem ◽  
Decagonal Quasicrystal ◽  
Riemann Boundary ◽  
Linear Temperature ◽  
Mechanical Coupling

In this paper, the thermal mechanical coupling problem of an infinite two-dimensional decagonal quasicrystal matrix containing elastic elliptic inclusion is studied under remote uniform loading and linear temperature variation. Combining with the theory of the sectional holomorphic function, conformal transformation, singularity analysis, Cauchy-type integral and Riemann boundary value problem, the analytic relations among the sectional functions are obtained, and the problem is transformed into a basic complex potential function equation. The closed form solutions of the temperature field and thermo-elastic field in the matrix and inclusion are obtained. The solutions demonstrate that the uniform temperature and remote uniform stresses will induce an internal uniform stress field. Numerical examples show the effects of the thermal conductivity coefficient ratio, the heat flow direction angle and the elastic modulus on the interface stresses. The results provide a valuable reference for the design and application of reinforced quasicrystal materials.

scholarly journals Queues and Risk Models with Simultaneous Arrivals

2014 ◽  
Vol 46 (03) ◽  
pp. 812-831 ◽  
Author(s):  
E. S. Badila ◽  
O. J. Boxma ◽  
J. A. C. Resing ◽  
E. M. M. Winands
Keyword(s):  
Risk Model ◽  
Stochastic Decomposition ◽  
Two Dimensional ◽  
Riemann Boundary Value Problem ◽  
Risk Models ◽  
Riemann Boundary ◽  
Parallel Queues ◽  
The Laplace Transform ◽  
Claim Size Distribution ◽  
Stationary Workload

We focus on a particular connection between queueing and risk models in a multidimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue), we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline of how the two-dimensional risk model with a general two-dimensional claim size distribution (hence, without ordering of claim sizes) is related to a known Riemann boundary-value problem.

The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces

2016 ◽  
Vol 23 (4) ◽  
pp. 551-558 ◽  
Author(s):  
Vakhtang Kokilashvili ◽  
Alexander Meskhi ◽  
Vakhtang Paatashvili
Keyword(s):  
Boundary Value Problem ◽  
Variable Exponent ◽  
Boundary Value ◽  
Function Spaces ◽  
Cauchy Type ◽  
Riemann Boundary Value Problem ◽  
Lebesgue Spaces ◽  
Standard Type ◽  
Riemann Boundary ◽  
Variable Exponent Lebesgue Spaces

AbstractThe present paper deals with the Riemann boundary value problem for analytic functions in the framework of the new function spaces introduced by the first two authors, the so-called grand variable exponent Lebesgue spaces which unify two non-standard type function spaces: variable exponent Lebesgue spaces and grand Lebesgue spaces.

scholarly journals The Riemann boundary value problem related to the time-harmonic Maxwell equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pei Yang ◽  
Liping Wang ◽  
Zuoliang Xu
Keyword(s):  
Boundary Value Problem ◽  
Maxwell Equations ◽  
Boundary Value ◽  
Uniform Boundedness ◽  
Matrix Operator ◽  
Cauchy Type ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Time Harmonic ◽  
Definition Of

AbstractIn this paper, we first give the definition of Teodorescu operator related to the $\mathcal{N}$ N matrix operator and discuss a series of properties of this operator, such as uniform boundedness, Hölder continuity and so on. Then we propose the Riemann boundary value problem related to the $\mathcal{N}$ N matrix operator. Finally, using the intimate relationship of the corresponding Cauchy-type integral between the $\mathcal{N}$ N matrix operator and the time-harmonic Maxwell equations, we investigate the Riemann boundary value problem related to the time-harmonic Maxwell equations and obtain the integral representation of the solution.

Two-dimensional elliptic inclusions

1963 ◽  
Vol 59 (4) ◽  
pp. 811-820 ◽  
Author(s):  
R. D. Bhargava ◽  
H. C. Radhakrishna
Keyword(s):  
Potential Energy ◽  
Elastic Field ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Minimum Potential Energy ◽  
Elliptic Inclusion ◽  
Inclusion Problems ◽  
Equilibrium Size ◽  
The Matrix ◽  
Minimum Potential

AbstractThe simple concept of minimum potential energy of the classical theory of elasticity, first applied to solve inclusion problems (1) by one of the authors (R. D. B.), who considered spherical and circular inclusions, has now been extended to solve elliptic inclusion problems. The complex-variable method of determining the elastic field, first enunciated by A. C. Stevenson in the U.K. and N. I. Muskhelishvili in the U.S.S.R., has been used to determine the elastic field in the infinite material (the matrix) around the inclusion. Strain energies are calculated. The equilibrium size of an elliptic inclusion of elastic (Lamé's) constants λ1 and μ1, differing from those of matrix, for which the constants are λ and μ, has been determined.An independent check on the calculations has been made by testing the continuity of normal and shearing stresses. The results also agree with the known results for the much simpler case when inclusion and matrix are of the same material.

scholarly journals Queues and Risk Models with Simultaneous Arrivals

2014 ◽  
Vol 46 (3) ◽  
pp. 812-831 ◽  
Author(s):  
E. S. Badila ◽  
O. J. Boxma ◽  
J. A. C. Resing ◽  
E. M. M. Winands
Keyword(s):  
Risk Model ◽  
Stochastic Decomposition ◽  
Two Dimensional ◽  
Riemann Boundary Value Problem ◽  
Risk Models ◽  
Riemann Boundary ◽  
Parallel Queues ◽  
The Laplace Transform ◽  
Claim Size Distribution ◽  
Stationary Workload

We focus on a particular connection between queueing and risk models in a multidimensional setting. We first consider the joint workload process in a queueing model with parallel queues and simultaneous arrivals at the queues. For the case that the service times are ordered (from largest in the first queue to smallest in the last queue), we obtain the Laplace-Stieltjes transform of the joint stationary workload distribution. Using a multivariate duality argument between queueing and risk models, this also gives the Laplace transform of the survival probability of all books in a multivariate risk model with simultaneous claim arrivals and the same ordering between claim sizes. Other features of the paper include a stochastic decomposition result for the workload vector, and an outline of how the two-dimensional risk model with a general two-dimensional claim size distribution (hence, without ordering of claim sizes) is related to a known Riemann boundary-value problem.

scholarly journals On one approach to the solution of miscellaneous problems of the theory of elasticity

2021 ◽  
Vol 57 (3) ◽  
pp. 263-273
Author(s):  
V. V. Amel’kin ◽  
M. N. Vasilevich ◽  
L. A. Khvostchinskaya
Keyword(s):  
Theory Of Elasticity ◽  
Singular Points ◽  
Cauchy Type ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Piecewise Constant ◽  
Analytical Functions ◽  
Cauchy Type Integrals ◽  
Upper Half Plane ◽  
Product Of Matrices

Herein, a miscellaneous contact problem of the theory of elasticity in the upper half-plane is considered. The boundary is a real semi-axis separated into four parts, on each of which the boundary conditions are set for the real or imaginary part of two desired analytical functions. Using new unknown functions, the problem is reduced to an inhomogeneous Riemann boundary value problem with a piecewise constant 2 × 2 matrix and four singular points. A differential equation of the Fuchs class with four singular points is constructed, the residue matrices of which are found by the logarithm method of the product of matrices. The single solution of the problem is represented in terms of Cauchy-type integrals when the solvability condition is met.

Coupled Processor: A Second-Order Continuous-State-Space Model

1990 ◽  
Vol 4 (2) ◽  
pp. 277-298 ◽  
Author(s):  
Haruhisa Takahashi
Keyword(s):  
State Space ◽  
State Space Model ◽  
Second Order ◽  
Two Dimensional ◽  
Riemann Boundary Value Problem ◽  
Riemann Boundary ◽  
Space Model ◽  
Continuous State Space ◽  
Continuous State ◽  
Order Continuous

A second-order continuous-state-space model for two-dimensional queueing systems is developed in this article. A particular problem is treated but the results can apply to some other two-dimensional queueing problems directly. The generating function for the model is obtained by applying a Riemann boundary value problem and leads to a computationally feasible solution.

The use of Riemann problems in solving a class of transcendental equations

1973 ◽  
Vol 73 (1) ◽  
pp. 111-118 ◽  
Author(s):  
E. E. Burniston ◽  
C. E. Siewert
Keyword(s):  
Boundary Value Problem ◽  
Closed Form ◽  
Boundary Value ◽  
Explicit Solutions ◽  
Riemann Boundary Value Problem ◽  
Riemann Problems ◽  
Riemann Boundary ◽  
Canonical Solution ◽  
Transcendental Equations ◽  
Explicit Expressions

AbstractA method of finding explicit expressions for the roots of a certain class of transcendental equations is discussed. In particular it is shown by determining a canonical solution of an associated Riemann boundary-value problem that expressions for the roots may be derived in closed form. The explicit solutions to two transcendental equations, tan β = ωβ and β tan β = ω, are discussed in detail, and additional specific results are given.

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