Two-dimensional shear Alfvén-wave turbulence in a plasma with arbitrary β

1996 ◽  
Vol 55 (1) ◽  
pp. 121-130 ◽  
Author(s):  
G. Brodin
Keyword(s):  
Dimensional Space ◽  
Alfven Wave ◽  
Dimensional Case ◽  
Wave Turbulence ◽  
Two Dimensional ◽  
One Dimensional ◽  
Coupled Equations ◽  
Parallel Propagation ◽  
Derivative Nonlinear Schrödinger Equation ◽  
Space Dependence

Two-dimensional shear Alfvén-wave turbulence is investigated for a plasma with arbitrary β value. A set of three equations, which reduces to the derivative nonlinear Schrödinger equation in the limit of parallel propagation, is derived. The genuinely two-dimensional case is governed by two coupled equations. For a non-parallel one-dimensional space dependence, the nonlinearity is shown to vanish to all orders.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

Regions-based Two-dimensional Continua: The Euclidean Case

2018 ◽  
Author(s):  
Geoffrey Hellman ◽  
Stewart Shapiro
Keyword(s):  
Mathematical Induction ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Entire Space ◽  
Euclidean Case ◽  
Free Basis ◽  
One Dimensional ◽  
Archimedean Property ◽  
The One

This chapter develops a Euclidean, two-dimensional, regions-based theory. As with the semi-Aristotelian account in Chapter 2, the goal here is to recover the now orthodox Dedekind–Cantor continuum on a point-free basis. The chapter derives the Archimedean property for a class of readily postulated orientations of certain special regions, what are called “generalized quadrilaterals” (intended as parallelograms), by which the entire space is covered. Then the chapter generalizes this to arbitrary orientations, and then establishes an isomorphism between the space and the usual point-based one. As in the one-dimensional case, this is done on the basis of axioms which contain no explicit “extremal clause”, and we have no axiom of induction other than ordinary numerical (mathematical) induction.

A Graphical Exposition of the Ising Problem

1971 ◽  
Vol 12 (3) ◽  
pp. 365-377 ◽  
Author(s):  
Frank Harary
Keyword(s):  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Higher Dimensional ◽  
The One

Ising [1] proposed the problem which now bears his name and solved it for the one-dimensional case only, leaving the higher dimensional cases as unsolved problems. The first solution to the two dimensional Ising problem was obtained by Onsager [6]. Onsager's method was subsequently explained more clearly by Kaufman [3]. More recently, Kac and Ward [2] discovered a simpler procedure involving determinants which is not logically complete.

scholarly journals Cluster Structure of Optimal Solutions in Bipartitioning of Small Worlds

Entropy ◽  
2020 ◽  
Vol 22 (11) ◽  
pp. 1319
Author(s):  
Adam Lipowski ◽  
António L. Ferreira ◽  
Dorota Lipowska
Keyword(s):  
Cluster Structure ◽  
Finite Size ◽  
Lattice Models ◽  
Square Lattice ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Small Worlds ◽  
Replica Symmetry ◽  
One Dimensional ◽  
Optimal Partitions

Using simulated annealing, we examine a bipartitioning of small worlds obtained by adding a fraction of randomly chosen links to a one-dimensional chain or a square lattice. Models defined on small worlds typically exhibit a mean-field behavior, regardless of the underlying lattice. Our work demonstrates that the bipartitioning of small worlds does depend on the underlying lattice. Simulations show that for one-dimensional small worlds, optimal partitions are finite size clusters for any fraction of additional links. In the two-dimensional case, we observe two regimes: when the fraction of additional links is sufficiently small, the optimal partitions have a stripe-like shape, which is lost for a larger number of additional links as optimal partitions become disordered. Some arguments, which interpret additional links as thermal excitations and refer to the thermodynamics of Ising models, suggest a qualitative explanation of such a behavior. The histogram of overlaps suggests that a replica symmetry is broken in a one-dimensional small world. In the two-dimensional case, the replica symmetry seems to hold, but with some additional degeneracy of stripe-like partitions.

scholarly journals AN ALTERNATIVE DIMENSIONAL REDUCTION PRESCRIPTION

1996 ◽  
Vol 11 (13) ◽  
pp. 1037-1045 ◽  
Author(s):  
J.D. EDELSTEIN ◽  
C. NÚÑEZ ◽  
F.A. SCHAPOSNIK ◽  
J.J. GIAMBIAGI
Keyword(s):  
Dimensional Reduction ◽  
Dimensional Space ◽  
Dimensional Case ◽  
Green Functions ◽  
Two Dimensional ◽  
Spatial Coordinate ◽  
Higher Dimensional

We propose an alternative dimensional reduction prescription which in respect with Green functions corresponds to dropping the extra spatial coordinate. From this, we construct the dimensionally reduced Lagrangians both for scalars and fermions, discussing bosonization and supersymmetry in the particular two-dimensional case. We argue that our proposal is in some situations more physical in the sense that it maintains the form of the interactions between particles thus preserving the dynamics corresponding to the higher-dimensional space.

scholarly journals Chaotic Attractor Generation via Space Function Controls

2011 ◽  
Vol 2011 ◽  
pp. 1-11
Author(s):  
Hong Shi ◽  
Guangming Xie ◽  
Desheng Liu
Keyword(s):  
Linear Systems ◽  
Chaotic Attractor ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Underlying Mechanism ◽  
Two Dimensional ◽  
One Dimensional ◽  
Suitable Space ◽  
Space Function ◽  
Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

How Long Is Its Projection?

2004 ◽  
Vol 9 (8) ◽  
pp. 444-448
Author(s):  
Sandra Davis Trowell ◽  
Anne Reynolds
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Dimensional Space ◽  
Digital Age ◽  
Two Dimensional ◽  
One Dimensional ◽  
Teaching And Learning Mathematics ◽  
Learning Mathematics ◽  
Important Idea ◽  
Principles And Standards

PRINCIPLES AND STANDARDS FOR SCHOOL MATHEMATICS (NCTM 2000) is designed around the idea of integrating content and process skills in teaching and learning mathematics. A curriculum is envisioned in which the content is taught through problem solving, communicating, and making connections. In the Grade 6–8 Standards, one key idea that connects much of the content is proportionality: “Proportionality connects many of the mathematics topics studied in grades 6–8” (NCTM 2000, p. 217). For example, in this digital age, numerous students have access to equipment for enhancing photographs, including stretching and shrinking. Proportional reasoning is an important idea in the manipulation of such objects and involves distinguishing between changes that occur in both one-dimensional, or linear (length), and two-dimensional space (area) as well as the development of the mathematics of similarity. Textbooks typically equate proportions with the cross-products rule, which states that the “product of the extremes equals the product of the means.” In other words, if a/b = c/d, then a × d = b × c.

SOME PECULIAR PROPERTIES OF THE DARWIN’S LAGRANGIAN

1995 ◽  
Vol 09 (23) ◽  
pp. 3069-3083 ◽  
Author(s):  
I.P. PAVLOTSKY ◽  
M. STRIANESE
Keyword(s):  
Phase Space ◽  
Dimensional Case ◽  
Minimal Distance ◽  
Rectilinear Motion ◽  
Two Dimensional ◽  
Singular Surfaces ◽  
One Dimensional ◽  
Local Singularity ◽  
Dynamical Properties

In the post-Galilean approximation the Lagrangians are singular on a submanifold of the phase space. It is a local singularity, which differs from the ones considered by Dirac. The dynamical properties are essentially peculiar on the studied singular surfaces. In the preceding publications,1,2,3 two models of singular relativistic Lagrangians and the rectilinear motion of two electrons, determined by Darwin’s Lagrangian, were examined. In the present paper we study the peculiar dynamical properties of the two-dimensional Darwin’s Lagrangian. In particular, it is shown that the minimal distance between two electrons (the so called “radius of electron”) appears in the two-dimensional motion as well as in one-dimensional case. Some new peculiar properties are discovered.

scholarly journals Revisiting the 1D and 2D Laplace Transforms

2020 ◽  
Author(s):  
Manuel Duarte Ortigueira ◽  
José Tenreiro Machado
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Linear Systems ◽  
Laplace Transforms ◽  
Dimensional Case ◽  
Initial Condition ◽  
Two Dimensional ◽  
One Dimensional ◽  
The One

This paper reviews the unilateral and bilateral, one- and two-dimensional Laplace transforms. The unilateral and bilateral Laplace transforms are compared in the one-dimensional case, leading to the formulation of the initial-condition theorem. This problem is solved with all generality in the one- and two-dimensional cases with the bilateral Laplace transform. General two-dimensional linear systems are introduced and the corresponding transfer function defined.

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