Equilibrium distribution of block-structured Markov chains with repeating rows

1990 ◽  
Vol 27 (3) ◽  
pp. 557-576 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Daniel P. Heyman
Keyword(s):  
General Theory ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Transition Matrix ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Block Form ◽  
The Right ◽  
Block Structured

In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

Equilibrium distribution of block-structured Markov chains with repeating rows

1990 ◽  
Vol 27 (03) ◽  
pp. 557-576 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Daniel P. Heyman
Keyword(s):  
General Theory ◽  
Markov Chains ◽  
Boundary Conditions ◽  
Transition Matrix ◽  
Equilibrium Distribution ◽  
Two Dimensional ◽  
Block Form ◽  
The Right ◽  
Block Structured

In this paper we consider two-dimensional Markov chains with the property that, except for some boundary conditions, when the transition matrix is written in block form, the rows are identical except for a shift to the right. We provide a general theory for finding the equilibrium distribution for this class of chains. We illustrate theory by showing how our results unify the analysis of the M/G/1 and GI/M/1 paradigms introduced by M. F. Neuts.

Separation of the 3D stress state of a loaded plate into two-dimensional tasks: bending and symmetric compression of the plate

2021 ◽  
Vol 103 (3) ◽  
pp. 53-62
Author(s):  
Victor Revenko ◽  
Andrian Revenko
Keyword(s):  
Boundary Conditions ◽  
Harmonic Functions ◽  
Three Dimensional ◽  
Partial Solution ◽  
Theory Of Elasticity ◽  
Two Dimensional ◽  
Normal Stresses ◽  
Equilibrium Equations ◽  
Dimensional Boundary ◽  
The Right

The three-dimensional stress-strain state of an isotropic plate loaded on all its surfaces is considered in the article. The initial problem is divided into two ones: symmetrical bending of the plate and a symmetrical compression of the plate, by specified loads. It is shown that the plane problem of the theory of elasticity is a special case of the second task. To solve the second task, the symmetry of normal stresses is used. Boundary conditions on plane surfaces are satisfied and harmonic conditions are obtained for some functions. Expressions of effort were found after integrating three-dimensional stresses that satisfy three equilibrium equations. For a thin plate, a closed system of equations was obtained to determine the harmonic functions. Displacements and stresses in the plate were expressed in two two-dimensional harmonic functions and a partial solution of the Laplace equation with the right-hand side, which is determined by the end loads. Three-dimensional boundary conditions were reduced to two-dimensional ones. The formula was found for experimental determination of the sum of normal stresses via the displacements of the surface of the plate.

scholarly journals On the Horizontal Deviation of a Spinning Projectile Penetrating into Granular Systems

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Waseem Ghazi Alshanti
Keyword(s):  
General Theory ◽  
Dynamical Behavior ◽  
Numerical Approach ◽  
Granular Systems ◽  
Soft Particle ◽  
Impact Point ◽  
Two Dimensional ◽  
Rotation Direction ◽  
Spinning Projectile ◽  
The Right

The absence of a general theory that describes the dynamical behavior of the particulate materials makes the numerical simulations the most current powerful tool that can grasp many mechanical problems relevant to the granular materials. In this paper, based on a two-dimensional soft particle discrete element method (DEM), a numerical approach is developed to investigate the consequence of the orthogonal impact into various granular beds of projectile rotating in both clockwise (CW) and counterclockwise (CCW) directions. Our results reveal that, depending on the rotation direction, there is a significant deviation of the x-coordinate of the final stopping point of a spinning projectile from that of its original impact point. For CW rotations, a deviation to the right occurs while a left deviation has been recorded for CCW rotation case.

scholarly journals Dynamics from Multivariable Longitudinal Data

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Maria Vivien Visaya ◽  
David Sherwell
Keyword(s):  
Longitudinal Data ◽  
Transition Matrix ◽  
Multivalued Map ◽  
Two Dimensional ◽  
Time Step ◽  
Subshift Of Finite Type ◽  
Mathematical Properties ◽  
Dimensional State Space ◽  
The Right ◽  
Time Information

We introduce a method of analysing longitudinal data in n≥1 variables and a population of K≥1 observations. Longitudinal data of each observation is exactly coded to an orbit in a two-dimensional state space Sn. At each time, information of each observation is coded to a point (x,y)∈Sn, where x is the physical condition of the observation and y is an ordering of variables. Orbit of each observation in Sn is described by a map that dynamically rearranges order of variables at each time step, eventually placing the most stable, least frequently changing variable to the left and the most frequently changing variable to the right. By this operation, we are able to extract dynamics from data and visualise the orbit of each observation. In addition, clustering of data in the stable variables is revealed. All possible paths that any observation can take in Sn are given by a subshift of finite type (SFT). We discuss mathematical properties of the transition matrix associated to this SFT. Dynamics of the population is a nonautonomous multivalued map equivalent to a nonstationary SFT. We illustrate the method using a longitudinal data of a population of households from Agincourt, South Africa.

scholarly journals Markov chains, ${\mathscr R}$-trivial monoids and representation theory

2015 ◽  
Vol 25 (01n02) ◽  
pp. 169-231 ◽  
Author(s):  
Arvind Ayyer ◽  
Anne Schilling ◽  
Benjamin Steinberg ◽  
Nicolas M. Thiéry
Keyword(s):  
Markov Chain ◽  
General Theory ◽  
Markov Chains ◽  
Random Walks ◽  
Transition Matrix ◽  
Coxeter Groups ◽  
Mixing Time ◽  
New Class ◽  
Free Tree ◽  
Sandpile Models

We develop a general theory of Markov chains realizable as random walks on [Formula: see text]-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Möbius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom–Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Symbolic computation to estimate two-sided boundary conditions in two-dimensional conduction problems

10.2514/3.920 ◽  
1997 ◽  
Vol 11 ◽  
pp. 472-476
Author(s):  
Henry H. Kerr ◽  
F. C. Frank ◽  
Jae-Woo Lee ◽  
W. H. Mason ◽  
Ching-Yu Yang
Keyword(s):  
Boundary Conditions ◽  
Symbolic Computation ◽  
Two Dimensional

scholarly journals Singular BPS boundary conditions in $$ \mathcal{N} $$ = (2, 2) supersymmetric gauge theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
String Theory ◽  
Boundary Conditions ◽  
Gauge Theories ◽  
Holomorphic Curve ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Special Lagrangian ◽  
Supersymmetric Gauge ◽  
M Theory

Abstract We derive general BPS boundary conditions in two-dimensional $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories. We analyze the solutions of these boundary conditions, and in particular those that allow the bulk fields to have poles at the boundary. We also present the brane configurations for the half- and quarter-BPS boundary conditions of the $$ \mathcal{N} $$ N = (2, 2) supersymmetric gauge theories in terms of branes in Type IIA string theory. We find that both A-type and B-type brane configurations are lifted to M-theory as a system of M2-branes ending on an M5-brane wrapped on a product of a holomorphic curve in ℂ2 with a special Lagrangian 3-cycle in ℂ3.

Adversarial Medical and Scientific Testimony and Lay Jurors: A Proposal for Medical Malpractice Reform

1995 ◽  
Vol 21 (2-3) ◽  
pp. 281-300
Author(s):  
Jody Weisberg Menon
Keyword(s):  
General Theory ◽  
Legal System ◽  
Medical Malpractice ◽  
Common Knowledge ◽  
Common Law ◽  
Expert Witnesses ◽  
Malpractice Reform ◽  
The Right ◽  
Scholarly Attention ◽  
Scientific Testimony

Pleas for reform of the legal system are common. One area of the legal system which has drawn considerable scholarly attention is the jury system. Courts often employ juries as fact-finders in civil cases according to the Seventh Amendment of the Constitution: “In Suits at common law, where the value in controversy shall exceed twenty dollars, the right of trial by jury shall be preserved … .” The general theory behind the use of juries is that they are the most capable fact-finders and the bestsuited tribunal for arriving at the most accurate and just outcomes. This idea, however, has been under attack, particularly by those who claim that cases involving certain difficult issues or types of evidence are an inappropriate province for lay jurors who typically have no special background or experience from which to make informed, fair decisions.The legal system uses expert witnesses to assist triers of fact in understanding issues which are beyond their common knowledge or difficult to comprehend.

scholarly journals A methodology for hygrothermal modelling of imperfect masonry interfaces

2021 ◽  
pp. 174425912198938
Author(s):  
Michael Gutland ◽  
Scott Bucking ◽  
Mario Santana Quintero
Keyword(s):  
Boundary Conditions ◽  
Material Properties ◽  
Structural Integrity ◽  
Bulk Material ◽  
Weather Conditions ◽  
Masonry Wall ◽  
Two Dimensional ◽  
Liquid Transport ◽  
Imperfect Contact ◽  
Moisture Contents

Hygrothermal models are important tools for assessing the risk of moisture-related decay mechanisms which can compromise structural integrity, loss of architectural features and material. There are several sources of uncertainty when modelling masonry, related to material properties, boundary conditions, quality of construction and two-dimensional interactions between mortar and unit. This paper examines the uncertainty at the mortar-unit interface with imperfections such as hairline cracks or imperfect contact conditions. These imperfections will alter the rate of liquid transport into and out of the wall and impede the liquid transport between mortar and masonry unit. This means that the effective liquid transport of the wall system will be different then if only properties of the bulk material were modelled. A detailed methodology for modelling this interface as a fracture is presented including definition of material properties for the fracture. The modelling methodology considers the combined effect of both the interface resistance across the mortar-unit interface and increase liquid transport in parallel to the interface, and is generalisable to various combinations of materials, geometries and fracture apertures. Two-dimensional DELPHIN models of a clay brick/cement-mortar masonry wall were created to simulate this interaction. The models were exposed to different boundary conditions to simulate wetting, drying and natural cyclic weather conditions. The results of these simulations were compared to a baseline model where the fracture model was not included. The presence of fractures increased the rate of absorption in the wetting phase and an increased rate of desorption in the drying phase. Under cyclic conditions, the result was higher peak moisture contents after rain events compared to baseline and lower moisture contents after long periods of drying. This demonstrated that detailed modelling of imperfections at the mortar-unit interface can have a definitive influence on results and conclusions from hygrothermal simulations.

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