scholarly journals The Dirichlet quotient of point vortex interactions on the surface of the sphere examined by Monte Carlo experiments

2004 ◽  
Vol 5 (1) ◽  
pp. 125-136
Author(s):  
Joseph Nebus
Keyword(s):  
Monte Carlo ◽  
Point Vortex ◽  
Vortex Interactions ◽  
Monte Carlo Experiments

Chaos in body–vortex interactions

2010 ◽  
Vol 466 (2119) ◽  
pp. 1871-1891 ◽  
Author(s):  
Johan Roenby ◽  
Hassan Aref
Keyword(s):  
Body Shape ◽  
Mass Density ◽  
Relative Equilibrium ◽  
Large Body ◽  
Point Vortex ◽  
Cylindrical Body ◽  
The Body ◽  
Body Motion ◽  
Single Vortex ◽  
Vortex Interactions

The model of body–vortex interactions, where the fluid flow is planar, ideal and unbounded, and the vortex is a point vortex, is studied. The body may have a constant circulation around it. The governing equations for the general case of a freely moving body of arbitrary shape and mass density and an arbitrary number of point vortices are presented. The case of a body and a single vortex is then investigated numerically in detail. In this paper, the body is a homogeneous, elliptical cylinder. For large body–vortex separations, the system behaves much like a vortex pair regardless of body shape. The case of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos.

scholarly journals Statistical Tests of Symbolic Dynamics

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 817
Author(s):  
Fernando López ◽  
Mariano Matilla-García ◽  
Jesús Mur ◽  
Manuel Ruiz Marín
Keyword(s):  
Monte Carlo ◽  
Symbolic Dynamics ◽  
Null Hypothesis ◽  
Statistical Tests ◽  
General Applicability ◽  
Monte Carlo Experiments ◽  
The Mean ◽  
Theoretical Application ◽  
New Statistics ◽  
General Method

A novel general method for constructing nonparametric hypotheses tests based on the field of symbolic analysis is introduced in this paper. Several existing tests based on symbolic entropy that have been used for testing central hypotheses in several branches of science (particularly in economics and statistics) are particular cases of this general approach. This family of symbolic tests uses few assumptions, which increases the general applicability of any symbolic-based test. Additionally, as a theoretical application of this method, we construct and put forward four new statistics to test for the null hypothesis of spatiotemporal independence. There are very few tests in the specialized literature in this regard. The new tests were evaluated with the mean of several Monte Carlo experiments. The results highlight the outstanding performance of the proposed test.

Recovering cointegration via wavelets in the presence of non-linear patterns

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Jorge Martínez Compains ◽  
Ignacio Rodríguez Carreño ◽  
Ramazan Gençay ◽  
Tommaso Trani ◽  
Daniel Ramos Vilardell
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Gross National Product ◽  
Structural Breaks ◽  
Low Frequency ◽  
Cointegration Test ◽  
Seasonal Adjustment ◽  
Traditional Use ◽  
Monte Carlo Experiments ◽  
Non Linear

Abstract Johansen’s Cointegration Test (JCT) performs remarkably well in finding stable bivariate cointegration relationships. Nonetheless, the JCT is not necessarily designed to detect such relationships in presence of non-linear patterns such as structural breaks or cycles that fall in the low frequency portion of the spectrum. Seasonal adjustment procedures might not detect such non-linear patterns, and thus, we expose the difficulty in identifying cointegrating relations under the traditional use of JCT. Within several Monte Carlo experiments, we show that wavelets can empower more the JCT framework than the traditional seasonal adjustment methodologies, allowing for identification of hidden cointegrating relationships. Moreover, we confirm these results using seasonally adjusted time series as US consumption and income, gross national product (GNP) and money supply M1 and GNP and M2.

Stepping stone models of finite length

1970 ◽  
Vol 2 (02) ◽  
pp. 229-258 ◽  
Author(s):  
Takeo Maruyama
Keyword(s):  
Monte Carlo ◽  
Population Structure ◽  
Finite Length ◽  
Correlation Coefficients ◽  
Gene Frequencies ◽  
Explicit Formulas ◽  
Stepping Stone ◽  
Monte Carlo Experiments ◽  
Stepping Stone Models ◽  
Stepping Stone Model

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.

scholarly journals Vortex Interactions Subjected to Deformation Flows: A Review

Fluids ◽  
2019 ◽  
Vol 4 (1) ◽  
pp. 14 ◽  
Author(s):  
Konstantin Koshel ◽  
Eugene Ryzhov ◽  
Xavier Carton
Keyword(s):  
Review Paper ◽  
Point Vortex ◽  
Passive Scalar ◽  
Dynamical System Theory ◽  
Single Vortex ◽  
Vortex Interactions ◽  
Rotational Components ◽  
Coherent Vortices ◽  
Numerical And Analytical Methods ◽  
Submerged Obstacles

Deformation flows are the flows incorporating shear, strain and rotational components. These flows are ubiquitous in the geophysical flows, such as the ocean and atmosphere. They appear near almost any salience, such as isolated coherent structures (vortices and jets) and various fixed obstacles (submerged obstacles and continental boundaries). Fluid structures subject to such deformation flows may exhibit drastic changes in motion. In this review paper, we focus on the motion of a small number of coherent vortices embedded in deformation flows. Problems involving isolated one and two vortices are addressed. When considering a single-vortex problem, the main focus is on the evolution of the vortex boundary and its influence on the passive scalar motion. Two vortex problems are addressed with the use of point vortex models, and the resulting stirring patterns of neighbouring scalars are studied by a combination of numerical and analytical methods from the dynamical system theory. Many dynamical effects are reviewed with emphasis on the emergence of chaotic motion of the vortex phase trajectories and the scalars in their immediate vicinity.

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