scholarly journals Runge Solution of the Continuum Equations for Spherical Electrostatic Plasma Probes

1973 ◽  
Vol 26 (2) ◽  
pp. 261 ◽  
Author(s):  
FH Dorman
Keyword(s):  
Initial Conditions ◽  
Particle Density ◽  
Continuum Theory ◽  
Neutral Solution ◽  
Different Types ◽  
Weakly Ionized ◽  
Charged Particle Density ◽  
Convergent Method ◽  
Runge’S Method ◽  
The Continuum

An approximate but convergent method is used to determine the electric potential and charged particle density near non-small spherical probes in a weakly ionized continuum plasma. Quantities determined partly by experiment (e, PP' yp) and partly from continuum theory (J +, J _) are introduced into three continuum differential equations which are then solved using Runge's method. The initial conditions must be estimated iteratively until the sheath solution joins smoothly to the quasi-neutral solution. Two different types of solution curves are discussed.

scholarly journals SATO–CRUTCHFIELD FORMULATION FOR SOME EVOLUTIONARY GAMES

2003 ◽  
Vol 14 (07) ◽  
pp. 963-971 ◽  
Author(s):  
E. AHMED ◽  
A. S. HEGAZI ◽  
A. S. ELGAZZAR
Keyword(s):  
Prisoner's Dilemma ◽  
Initial Conditions ◽  
Evolutionarily Stable Strategy ◽  
Prisoner’S Dilemma ◽  
Evolutionary Games ◽  
Theoretical Explanation ◽  
Battle Of The Sexes ◽  
Different Types ◽  
Evolutionarily Stable ◽  
Rules Of The Game

The Sato–Crutchfield equations are analytically and numerically studied. The Sato–Crutchfield formulation corresponds to losing memory. Then the Sato–Crutchfield formulation is applied for some different types of games including hawk–dove, prisoner's dilemma and the battle of the sexes games. The Sato–Crutchfield formulation is found not to affect the evolutionarily stable strategy of the ordinary games. But choosing a strategy becomes purely random, independent of the previous experiences, initial conditions, and the rules of the game itself. The Sato–Crutchfield formulation for the prisoner's dilemma game can be considered as a theoretical explanation for the existence of cooperation in a population of defectors.

Confirming the continuum theory of dynamic brittle fracture for fast cracks

Nature ◽  
10.1038/16891 ◽  
1999 ◽  
Vol 397 (6717) ◽  
pp. 333-335 ◽  
Author(s):  
Eran Sharon ◽  
Jay Fineberg
Keyword(s):  
Brittle Fracture ◽  
Continuum Theory ◽  
Dynamic Brittle Fracture ◽  
The Continuum

scholarly journals Matrix integrals & finite holography

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Dionysios Anninos ◽  
Beatrix Mühlmann
Keyword(s):  
Critical Exponents ◽  
Continuum Theory ◽  
Point Of View ◽  
Leading Order ◽  
Minimal Models ◽  
Point Evaluation ◽  
Brst Cohomology ◽  
Matrix Integrals ◽  
The Matrix ◽  
The Continuum

Abstract We explore the conjectured duality between a class of large N matrix integrals, known as multicritical matrix integrals (MMI), and the series (2m − 1, 2) of non-unitary minimal models on a fluctuating background. We match the critical exponents of the leading order planar expansion of MMI, to those of the continuum theory on an S2 topology. From the MMI perspective this is done both through a multi-vertex diagrammatic expansion, thereby revealing novel combinatorial expressions, as well as through a systematic saddle point evaluation of the matrix integral as a function of its parameters. From the continuum point of view the corresponding critical exponents are obtained upon computing the partition function in the presence of a given conformal primary. Further to this, we elaborate on a Hilbert space of the continuum theory, and the putative finiteness thereof, on both an S2 and a T2 topology using BRST cohomology considerations. Matrix integrals support this finiteness.

scholarly journals Analysis of the self-similar solutions of a generalized Burger's equation with nonlinear damping

2001 ◽  
Vol 7 (3) ◽  
pp. 253-282 ◽  
Author(s):  
Ch. Srinivasa Rao ◽  
P. L. Sachdev ◽  
Mythily Ramaswamy
Keyword(s):  
Initial Conditions ◽  
Nonlinear Damping ◽  
Nonlinear Ordinary Differential Equation ◽  
The Self ◽  
Similar Reduction ◽  
Generalized Burgers Equation ◽  
Different Types ◽  
Self Similar ◽  
Parameter Ranges ◽  
Similar Solutions

The nonlinear ordinary differential equation resulting from the self-similar reduction of a generalized Burgers equation with nonlinear damping is studied in some detail. Assuming initial conditions at the origin we observe a wide variety of solutions – (positive) single hump, unbounded or those with a finite zero. The existence and nonexistence of positive bounded solutions with different types of decay (exponential or algebraic) to zero at infinity for specific parameter ranges are proved.

Free Energy of Granular Materials in Static Equilibrium

1979 ◽  
Vol 46 (4) ◽  
pp. 944-945 ◽  
Author(s):  
M. Shahinpoor ◽  
G. Ahmadi
Keyword(s):  
Free Energy ◽  
Granular Materials ◽  
Continuum Theory ◽  
Gravitational Effect ◽  
Experimental Results ◽  
Static Equilibrium ◽  
The Continuum

We employ the continuum theory of granular materials due to Goodman and Cowin and some experimental results due to P. G. Nutting to arrive at a functional from for the free energy of granular materials in static equilibrium. The results obtained indicate the dominance of gravitational effect, modify and enlarge the results previously obtained by J. T. Jenkins.

The equations of immiscible viscous displacement in a porous medium

1981 ◽  
Vol 59 (1) ◽  
pp. 45-56 ◽  
Author(s):  
T. J. T. Spanos
Keyword(s):  
Porous Medium ◽  
Statistical Theory ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Continuum Theory ◽  
Immiscible Displacement ◽  
Macroscopic Scale ◽  
Inertial Terms ◽  
Inhomogeneous Porous Medium ◽  
Relative Motions

A statistical theory for the construction of the equations of viscous displacement in a porous medium is considered. This yields a continuum theory for immiscible displacement which can be applied to either a homogeneous or inhomogeneous porous medium. The relative motions of the fluid are considered in terms of the motion of surfaces of constant saturation which are smoothed surfaces at the macroscopic scale considered. The boundary conditions and initial conditions at the injection boundary are considered as well as the boundary conditions and breakthrough conditions at the recovery boundary and the side boundary conditions. The inertial terms are included in the equations and shown to be of importance in describing these initial conditions and the breakthrough conditions.

Satisfaction with democracy and social capital in Greece

2018 ◽  
Vol 45 (4) ◽  
pp. 614-628 ◽  
Author(s):  
Irene Daskalopoulou
Keyword(s):  
Social Capital ◽  
Multivariate Regression Analysis ◽  
Political Organization ◽  
Content Type ◽  
Satisfaction With Democracy ◽  
The Social ◽  
Different Types ◽  
European Values ◽  
The Relationship ◽  
The Continuum

Purpose The purpose of this paper is to investigate how different types of social capital contribute to the satisfaction with democracy (SWD) in Greece. Understanding the relationship between different variants of social capital and SWD allows one to situate the Greek democracy in the continuum of democracy types, from primary to modern. Design/methodology/approach The study uses microdata extracted from the European Values Surveys of 2002-2010 and multivariate regression analysis. Findings The results are compatible with a conception of the Greek political organization as a civil virtue democracy. A change in the nature of the relationship is observed after the recent economic crisis in the country. Research limitations/implications The study contributes to the empirical knowledge regarding the relationship between different variants of social capital and SWD. Originality/value Using a typology approach, the micro-relationship between democracy and social capital is analyzed as embedded in a continuum of different democracy types. In addition, this is the first study that uses microdata to analyze the effect of social capital upon SWD in Greece. The results of the study provide valuable understanding of the social and institutional arrangements that might sustain Greece’s efforts to meet its overall developmental challenges.

Dynamics of Dual-Cell Series Miura-Ori Structures With Different Types of Inter-Cell Connections

2021 ◽  
Author(s):  
Hai Zhou ◽  
Haiping Wu ◽  
Jian Xu ◽  
Hongbin Fang
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Theoretical Basis ◽  
Initial Conditions ◽  
Cell Structure ◽  
Dynamic Responses ◽  
Complex Environment ◽  
Current State ◽  
Different Types ◽  
Cell Series

Abstract Origami-inspired structures and materials have shown remarkable properties and performances originating from the intricate geometries of folding. Origami folding could be a dynamic process and origami structures could possess rich dynamic characteristics under external excitations. However, the current state of dynamics of origami has mostly focused on the dynamics of a single cell. This research has performed numerical simulations on multi-stable dual-cell series Miura-Ori structures with different types of inter-cell connections based on a dynamic model that does not neglect in-plane mass. We introduce a concept of equivalent constraint stiffness k* to distinguish different types of inter-cell connections. Results of numerical simulations reveal the multi-stable dual-cell structure will exhibit a variety of complex nonlinear dynamic responses with the increasing of connection stiffness because of the deeper energy well it has. The connection stiffness has a strong effect on the steady-state dynamic responses under different excitation amplitudes and a variety of initial conditions. This effect makes us able to adjust the dynamic behaviors of dual-cell series Miura-Ori structure to our needs in a complex environment. Furthermore, the results of this research could provide us a theoretical basis for the dynamics of origami folding and serve as guidelines for designing dynamic applications of origami metastructures and metamaterials.

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