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.

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.

A Two-Dimensional Model of the Fluid Dynamics of an Air Reverser

1998 ◽  
Vol 65 (1) ◽  
pp. 171-177 ◽  
Author(s):  
S. Mu¨ftu¨ ◽  
T. S. Lewis ◽  
K. A. Cole ◽  
R. C. Benson
Keyword(s):  
Design Guidelines ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Web Handling ◽  
One Dimensional ◽  
Air Supply ◽  
Two Dimensional Model ◽  
The One ◽  
The Web

A theoretical analysis of the fluid mechanics of the air cushion of the air reversers used in web-handling systems is presented. A two-dimensional model of the air flow is derived by averaging the equations of conservation of mass and momentum over the clearance between the web and the reverser. The resulting equations are Euler’s equations with nonlinear source terms representing the air supply holes in the surface of the reverser. The equations are solved analytically for the one-dimensional case and numerically for the two-dimensional case. Results are compared with an empirical formula and the one-dimensional airjet theory developed for hovercraft. Conditions that maximize the air pressure supporting the web are analyzed and design guidelines are deduced.

Approximate methods of solving amplitude-phase problem for continuous signals

2021 ◽  
pp. 37-46
Author(s):  
Ilia V. Boikov ◽  
Yana V. Zelina
Keyword(s):  
Integral Equations ◽  
Collocation Methods ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Phase Problem ◽  
Spline Collocation ◽  
Approximate Methods ◽  
Nonlinear Operator Equations ◽  
One Dimensional

Amplitude and phase problems in physical research are considered. The construction of methods and algorithms for solving phase and amplitude problems is analyzed without involving additional information about the signal and its spectrum. Mathematical models of the amplitude and phase problems in the case of one-dimensional and two-dimensional continuous signals are proposed and approximate methods for their solution are constructed. The models are based on the use of nonlinear singular and bisingular integral equations. The amplitude and phase problems are modeled by corresponding nonlinear singular and bisingular integral equations defined on the numerical axis (in the one-dimensional case) and on the plane (in the two-dimensional case). To solve the constructed nonlinear singular and bisingular integral equations, spline-collocation methods and the method of mechanical quadratures are used. Systems of nonlinear algebraic equations that arise during the application of these methods are solved by the continuous method of solving nonlinear operator equations. A model example shows the effectiveness of the proposed method for solving the phase problem in the two-dimensional case.

scholarly journals Stability analysis of three-dimensional breather solitons in a Bose–Einstein condensate

2005 ◽  
Vol 461 (2063) ◽  
pp. 3561-3574 ◽  
Author(s):  
M Matuszewski ◽  
E Infeld ◽  
G Rowlands ◽  
M Trippenbach
Keyword(s):  
Three Dimensional ◽  
Einstein Condensate ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stability Properties ◽  
Bose Einstein Condensate ◽  
The Stability ◽  
Bose Einstein ◽  
Dimensional Soliton

We investigated the stability properties of breather soliton trains in a three-dimensional Bose–Einstein condensate (BEC) with Feshbach-resonance management of the scattering length. This is done so as to generate both attractive and repulsive interaction. The condensate is confined only by a one-dimensional optical lattice and we consider strong, moderate and weak confinement. By strong confinement we mean a situation in which a quasi two-dimensional soliton is created. Moderate confinement admits a fully three-dimensional soliton. Weak confinement allows individual solitons to interact. Stability properties are investigated by several theoretical methods such as a variational analysis, treatment of motion in effective potential wells, and collapse dynamics. Armed with all the information forthcoming from these methods, we then undertake a numerical calculation. Our theoretical predictions are fully confirmed, perhaps to a higher degree than expected. We compare regions of stability in parameter space obtained from a fully three-dimensional analysis with those from a quasi two-dimensional treatment, when the dynamics in one direction are frozen. We find that in the three-dimensional case the stability region splits into two parts. However, as we tighten the confinement, one of the islands of stability moves toward higher frequencies and the lower frequency region becomes more and more like that for the quasi two-dimensional case. We demonstrate these solutions in direct numerical simulations and, importantly, suggest a way of creating robust three-dimensional solitons in experiments in a BEC in a one-dimensional lattice.

scholarly journals On the notion of the dimension with respect to a dynamical system

1984 ◽  
Vol 4 (3) ◽  
pp. 405-420 ◽  
Author(s):  
Ya. B. Pesin
Keyword(s):  
Dynamical System ◽  
Hausdorff Dimension ◽  
Invariant Sets ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Common Features ◽  
Dynamical Properties ◽  
The One ◽  
Hyperbolic Sets

AbstractFor the invariant sets of dynamical systems a new notion of dimension-the so-called dimension with respect to a dynamical system-is introduced. It has some common features with the general topological notion of the dimension, but it also reflects the dynamical properties of the system. In the one-dimensional case it coincides with the Hausdorff dimension. For multi-dimensional hyperbolic sets formulae for the calculation of our dimension are obtained. These results are generalizations of Manning's results obtained by him for the Hausdorff dimension in the two-dimensional case.

Complex Order from Disorder and from Simple Order in Coarse-Graining Invariant Orbits of Certain Two-Dimensional Linear Cellular Automata

1997 ◽  
Vol 07 (07) ◽  
pp. 1451-1496 ◽  
Author(s):  
André Barbé
Keyword(s):  
Cellular Automata ◽  
Three Dimensional ◽  
Coarse Graining ◽  
Dimensional Case ◽  
Two Dimensional ◽  
One Dimensional ◽  
Complex Order ◽  
Simple Order ◽  
Problems And Solutions ◽  
The One

This paper considers three-dimensional coarse-graining invariant orbits for two-dimensional linear cellular automata over a finite field, as a nontrivial extension of the two-dimensional coarse-graining invariant orbits for one-dimensional CA that were studied in an earlier paper. These orbits can be found by solving a particular kind of recursive equations (renormalizing equations with rescaling term). The solution starts from some seed that has to be determined first. In contrast with the one-dimensional case, the seed has infinite support in most cases. The way for solving these equations is discussed by means of some examples. Three categories of problems (and solutions) can be distinguished (as opposed to only one in the one-dimensional case). Finally, the morphology of a few coarse-graining invariant orbits is discussed: Complex order (of quasiperiodic type) seems to emerge from random seeds as well as from seeds of simple order (for example, constant or periodic seeds).

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