scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

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.

THE NUMERICAL SOLUTION OF THE BOLTZMANN KINETIC EQUATION FOR GRANULAR GASES

2019 ◽  
pp. 25-30
Author(s):  
I. Gapyak
Keyword(s):  
Cauchy Problem ◽  
Kinetic Equation ◽  
Numerical Solution ◽  
Dimensional Space ◽  
Boltzmann Kinetic Equation ◽  
Granular Gases ◽  
Two Dimensional ◽  
System Of Particles ◽  
The Cauchy Problem

For a system of particles with a dissipative interaction we consider the Boltzmann type kinetic equation for granular gases. A numerical solution of the Cauchy problem for the Boltzmann type kinetic equation is constructed in two dimensional space and its stability is investigated.

Quantum dynamical aspects of two-dimensional spaces of constant negative curvature

1989 ◽  
Vol 22 (17) ◽  
pp. 3577-3596 ◽  
Author(s):  
E N Argyres ◽  
C G Papadopoulos ◽  
E Papantonopoulos ◽  
K Tamvakis
Keyword(s):  
Negative Curvature ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Quantum Dynamical

Nonmonocentric Urban Configurations in a Two-Dimensional Space

1989 ◽  
Vol 21 (3) ◽  
pp. 363-374 ◽  
Author(s):  
H Ogawa ◽  
M Fujita
Keyword(s):  
Land Use ◽  
Dimensional Space ◽  
Urban Land ◽  
Urban Land Use ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Circular Symmetry ◽  
One Dimensional ◽  
Urban Configurations ◽  
The One

A one-dimensional model of nonmonocentric urban land use is extended into a two-dimensional space. Under the assumption of circular symmetry, it is shown that the equilibrium urban configurations in the two-dimensional space are essentially the same as those in the one-dimensional space except for the conditions on the parameters.

The effective Lagrangian and the scale anomaly in the nonlinear σ model

1992 ◽  
Vol 70 (6) ◽  
pp. 455-457 ◽  
Author(s):  
D. G. C. McKeon
Keyword(s):  
Dimensional Space ◽  
Two Dimensions ◽  
Feynman Diagrams ◽  
Two Dimensional ◽  
Standard Result ◽  
Weyl Geometry ◽  
Effective Lagrangian ◽  
Need To Evaluate ◽  
The One ◽  
Generally Covariant

We compute the one-loop effective Lagrangian for the generally covariant nonlinear σ model in two dimensions, using a technique of Bukbinder et al. This circumvents the need to evaluate Feynman diagrams and eliminates having to introduce a mass to serve as an infrared regulator. The two-dimensional space is assumed to have Weyl geometry. In the limit that the Weyl geometry becomes Riemannian, the standard result for the anomaly in the trace of the stress tensor is recovered.

Linearized Two-Dimensional Fluid Transients

1984 ◽  
Vol 106 (2) ◽  
pp. 227-232 ◽  
Author(s):  
E. B. Wylie
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Low Velocity ◽  
Flow Problems ◽  
Spatial Dimensions ◽  
Dimensional Space Time ◽  
Fluid Transients ◽  
Explicit Procedure ◽  
The One

A numerical analysis of low-velocity two-dimensional transient fluid flow problems is presented. The method is similar in concept to the one-dimensional method of characteristics, but does not follow the traditional characteristics theory for two spatial dimensions. Distinct paths are defined in the three-dimensional space-time domain along which compatibility equations are integrated. The explicit procedure is explained, and validated by comparisons with analytical solutions.

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