A Circular Inclusion With Circumferentially Inhomogeneous Sliding Interface in Plane Elastostatics

1998 ◽  
Vol 65 (1) ◽  
pp. 30-38 ◽  
Author(s):  
C. Q. Ru
Keyword(s):  
Circular Inclusion ◽  
Form Solution ◽  
Infinite Matrix ◽  
Rigorous Solution ◽  
First Order ◽  
Sliding Interface ◽  
The Mean ◽  
Plane Elastostatics ◽  
Basic Boundary ◽  
General Method

A general method is presented to obtain the rigorous solution for a circular inclusion embedded within an infinite matrix with a circumferentially inhomogeneous sliding interface in plane elastostatics. By virtue of analytic continuation, the basic boundary value problem for four analytic functions is reduced to a first-order differential equation for a single analytic function inside the circular inclusion. The finite form solution is obtained that includes a finite number of unknown constants determined by the analyticity of the solution and certain other auxiliary conditions. With this method, the exact values of the average stresses within the circular inclusion can be calculated without solving the full problem. Several specific examples are used to illustrate the method. The effects of the circumferential variation of the interface parameter on the mean stress at the interface and the average stresses within the inclusion are discussed.

Explicit Solutions of Plane Elastostatics Problems in Heterogeneous Solids

1998 ◽  
Vol 14 (2) ◽  
pp. 67-73 ◽  
Author(s):  
C. K. Chao ◽  
B. Gao
Keyword(s):  
Elastic Moduli ◽  
Homogeneous Problem ◽  
Circular Inclusion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Infinite Matrix ◽  
Heterogeneous Solids ◽  
Arbitrary Loading ◽  
Accuracy Result ◽  
Plane Elastostatics

AbstractThe problem of two circular inclusions of arbitrary radii and of different elastic moduli, which are perfectly bonded to an infinite matrix subjected to arbitrary loading, is solved by the heterogenization technique. This implies that the solution of the heterogeneous problem can be readily obtained from that of the corresponding homogeneous problem by a simple algebraic substitution. Based on the method of successive approximations and the technique of analytical continuation, the solution is formulated in a manner which leads to an approximate, but arbitrary accuracy, result. The present derived solution can be also applied to the problem with straight boundaries. Both the problem of two circular inclusions embedded in an infinite matrix and the problem of a circular inclusion embedded in a half-plane matrix are considered as our examples to demonstrate the use of the present approach.

scholarly journals A circular inclusion with inhomogeneous non-slip imperfect interface in harmonic materials

2016 ◽  
Vol 472 (2190) ◽  
pp. 20160285 ◽  
Author(s):  
D. R. McArthur ◽  
L. J. Sudak
Keyword(s):  
Tangential Direction ◽  
Circular Inclusion ◽  
Imperfect Interface ◽  
Variable Coefficients ◽  
Interface Condition ◽  
Infinite Matrix ◽  
Linear Spring ◽  
Spring Type ◽  
Repeated Use ◽  
Plane Elastostatics

In this work, a rigorous study is presented for the problem associated with a circular inclusion embedded in an infinite matrix in finite plane elastostatics where both the inclusion and matrix are comprised a harmonic material. The inclusion/matrix boundary is treated as a circumferentially inhomogeneous imperfect interface that is described by a linear spring-type imperfect interface model where in the tangential direction, the interface parameter is infinite in magnitude and in the normal direction, the interface parameter is finite in magnitude (the so-called non-slip interface condition). Through the repeated use of the technique of analytic continuation, the boundary value problem for four analytic functions is reduced to solve a single first-order linear ordinary differential equation with variable coefficients for a single analytic function defined within the inclusion. The unknown coefficients of said function are then found via various analyticity requirements. The method is illustrated, using a specific example of a particular class of inhomogeneous non-slip imperfect interface. The results from these calculations are then contrasted with the results from the homogeneous imperfect interface. These comparisons indicate that the circumferential variation of interface damage has a pronounced effect on the average boundary stress.

First passage time for the state of exact chemical equilibrium

1980 ◽  
Vol 45 (3) ◽  
pp. 777-782 ◽  
Author(s):  
Milan Šolc
Keyword(s):  
Chemical Equilibrium ◽  
First Passage Time ◽  
Passage Time ◽  
The State ◽  
Recurrence Time ◽  
First Passage ◽  
First Order ◽  
The Mean ◽  
Passage Times ◽  
Number Of Particles

The establishment of chemical equilibrium in a system with a reversible first order reaction is characterized in terms of the distribution of first passage times for the state of exact chemical equilibrium. The mean first passage time of this state is a linear function of the logarithm of the total number of particles in the system. The equilibrium fluctuations of composition in the system are characterized by the distribution of the recurrence times for the state of exact chemical equilibrium. The mean recurrence time is inversely proportional to the square root of the total number of particles in the system.

The Structure and Photochromism of 2,4,4,6-Tetraphenyl-4H-thiopyran

1992 ◽  
Vol 57 (6) ◽  
pp. 1326-1334 ◽  
Author(s):  
Jaroslav Vojtěchovský ◽  
Jindřich Hašek ◽  
Stanislav Nešpůrek ◽  
Mojmír Adamec
Keyword(s):  
Solid State ◽  
Uv Light ◽  
Order Reaction ◽  
Boat Conformation ◽  
X Rays ◽  
Exponential Time ◽  
First Order ◽  
Double Plane ◽  
The Mean ◽  
Independent Molecules

2,4,4,6-Tetraphenyl-4H-thiopyran, C29H22S, orthorhombic, Pna21, a = 17.980(4), b = 6.956(2), c = 34.562(11) Å, V = 4323(2) Å3, Z = 8, Dx = 1.237 g cm-3, F(000) = 1696, λ(CuKα) = 1.54184 A, μ = 1.372 mm-2, T = 294 K. The final R was 0.050 for the unique set of 3103 observed reflections. The central 4H-thiopyran ring forms a boat conformation for both symmetrically independent molecules with average boat angles 4.4(3) and 6.8(3)° at S and C(sp3), respectively. The mean planes of phenyls at the position 2 and 6 are turned from the double plane of 4H-thiopyran by 42.5(5) and 35.8(3)°, respectively. The investigated material undergoes a photochromic change in the solid state after irradiation with UV light or X-rays. The maximum of the new absorption band is situated at 564 nm. The non-exponential time dependence of photochromic bleaching is analysed in terms of a dispersive first-order reaction.

Towards the Temporal Approach to Abstract Data Types

1988 ◽  
Vol 11 (1) ◽  
pp. 49-63
Author(s):  
Andrzej Szalas
Keyword(s):  
Temporal Logic ◽  
Abstract Data Types ◽  
Data Types ◽  
First Order ◽  
Abstract Data ◽  
Order Completeness ◽  
General Method

In this paper we deal with a well known problem of specifying abstract data types. Up to now there were many approaches to this problem. We follow the axiomatic style of specifying abstract data types (cf. e.g. [1, 2, 6, 8, 9, 10]). We apply, however, the first-order temporal logic. We introduce a notion of first-order completeness of axiomatic specifications and show a general method for obtaining first-order complete axiomatizations. Some examples illustrate the method.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

scholarly journals Diffraction Measurements and Equilibrium Parameters

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Victor A. Sipachev
Keyword(s):  
Low Frequency ◽  
Mean Square ◽  
Structural Studies ◽  
Free Rotation ◽  
Theory Analysis ◽  
First Order ◽  
Internuclear Distances ◽  
The Mean ◽  
Asymmetry Parameters ◽  
First Order Perturbation

Structural studies are largely performed without taking into account vibrational effects or with incorrectly taking them into account. The paper presents a first-order perturbation theory analysis of the problem. It is shown that vibrational effects introduce errors on the order of 0.02 Å or larger (sometimes, up to 0.1-0.2 Å) into the results of diffraction measurements. Methods for calculating the mean rotational constants, mean-square vibrational amplitudes, vibrational corrections to internuclear distances, and asymmetry parameters are described. Problems related to low-frequency motions, including torsional motions that transform into free rotation at low excitation levels, are discussed. The algorithms described are implemented in the program available from the author (free).

Unified uncertainty analysis by the mean value first order saddlepoint approximation

2012 ◽  
Vol 46 (6) ◽  
pp. 803-812 ◽  
Author(s):  
Ning-Cong Xiao ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Yu Liu ◽  
Xiao-Ling Zhang
Keyword(s):  
Uncertainty Analysis ◽  
Saddlepoint Approximation ◽  
Mean Value ◽  
First Order ◽  
The Mean

scholarly journals The colorimetric properties of the spectrum

1931 ◽  
Vol 108 (759) ◽  
pp. 576-576 ◽  
Keyword(s):  
Distribution Curve ◽  
National Physical Laboratory ◽  
Group Of Seven ◽  
Physical Laboratory ◽  
Luminosity Functions ◽  
Direct Measurements ◽  
Energy Distribution Curve ◽  
The Mean ◽  
General Method

The paper describes an investigation carried out at the National Physical Laboratory to determine the colorimetric properties of a group of seven subjects as obtained from direct measurements of the trichromatic coefficients of the spectrum on a trichromatic colorimeter. The “spectral distribution curves of the primaries,” by means of which the colorimetric quality of a heterochromatic stimulus may be computed from its energy distribution curve, are obtained by combining the experimentally determined trichromatic coefficients with the International Standard visibility curve. This procedure is a simplification, applicable to the mean results of a normal group, of a general method by which the chromatic and luminosity functions of any subject or group of subjects can be determined from one set of observations. The general method is described in an Appendix.

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