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.

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.

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.

Sound damping in soft particle packings: the interplay between configurational disorder and inelasticity

Soft Matter ◽  
2021 ◽  
Vol 17 (15) ◽  
pp. 4204-4212
Author(s):  
Kuniyasu Saitoh ◽  
Hideyuki Mizuno
Keyword(s):  
Soft Particle ◽  
Two Dimensional ◽  
Particle Packings

We numerically investigate sound damping in disordered two-dimensional soft particle packings. Our findings suggest that sound damping in soft particle packings is determined by the interplay between elastic heterogeneities and inelasticity.

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 On local and integrated stress-tensor commutators

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Mert Besken ◽  
Jan de Boer ◽  
Grégoire Mathys
Keyword(s):  
Stress Tensor ◽  
Free Field ◽  
Virasoro Algebra ◽  
Light Sheet ◽  
Operator Product ◽  
Local Form ◽  
Two Dimensional ◽  
Conformal Embedding ◽  
General Aspects ◽  
The Right

Abstract We discuss some general aspects of commutators of local operators in Lorentzian CFTs, which can be obtained from a suitable analytic continuation of the Euclidean operator product expansion (OPE). Commutators only make sense as distributions, and care has to be taken to extract the right distribution from the OPE. We provide explicit computations in two and four-dimensional CFTs, focusing mainly on commutators of components of the stress-tensor. We rederive several familiar results, such as the canonical commutation relations of free field theory, the local form of the Poincaré algebra, and the Virasoro algebra of two-dimensional CFT. We then consider commutators of light-ray operators built from the stress-tensor. Using simplifying features of the light sheet limit in four-dimensional CFT we provide a direct computation of the BMS algebra formed by a specific set of light-ray operators in theories with no light scalar conformal primaries. In four-dimensional CFT we define a new infinite set of light-ray operators constructed from the stress-tensor, which all have well-defined matrix elements. These are a direct generalization of the two-dimensional Virasoro light-ray operators that are obtained from a conformal embedding of Minkowski space in the Lorentzian cylinder. They obey Hermiticity conditions similar to their two-dimensional analogues, and also share the property that a semi-infinite subset annihilates the vacuum.

ON TWO-DIMENSIONAL DYNAMICAL SYSTEMS ASSOCIATED WITH MEMBRANE KINETICS UNDERLYING CARDIAC ARRHYTHMIAS

2009 ◽  
Vol 19 (05) ◽  
pp. 1709-1732 ◽  
Author(s):  
B. M. BAKER ◽  
M. E. KIDWELL ◽  
R. P. KLINE ◽  
I. POPOVICI
Keyword(s):  
Dynamical Behavior ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
Stimulus Period ◽  
Smooth Maps ◽  
Periodic Stimulation ◽  
Piecewise Smooth Maps ◽  
Dimensional Version ◽  
Bifurcation Law ◽  
The One

We study the orbits, stability and coexistence of orbits in the two-dimensional dynamical system introduced by Kline and Baker to model cardiac rhythmic response to periodic stimulation — as a function of (a) kinetic parameters (two amplitudes, two rate constants) and (b) stimulus period. The original paper focused mostly on the one-dimensional version of this model (one amplitude, one rate constant), whose orbits, stability properties, and bifurcations were analyzed via the theory of skew-tent (hence unimodal) maps; the principal family of orbits were so-called "n-escalators", with n a positive integer. The two-dimensional analog (motivated by experimental results) has led to the current study of continuous, piecewise smooth maps of a polygonal planar region into itself, whose dynamical behavior includes the coexistence of stable orbits. Our principal results show (1) how the amplitude parameters control which escalators can come into existence, (2) escalator bifurcation behavior as the stimulus period is lowered — leading to a "1/n bifurcation law", and (3) the existence of basins of attraction via the coexistence of three orbits (two of them stable, one unstable) at the first (largest stimulus period) bifurcation. We consider the latter result our most important, as it is conjectured to be connected with arrhythmia.

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