scholarly journals Chaotic ray propagation in corrugated layers

2005 ◽  
Vol 12 (6) ◽  
pp. 1003-1009 ◽  
Author(s):  
M. Bottiglieri ◽  
S. De Martino ◽  
M. Falanga ◽  
C. Godano
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Chaotic Behaviour ◽  
Kam Theorem ◽  
Different Types ◽  
Corrugated Wall

Abstract. The aim of this paper is to study the effects of a corrugated wall on the behaviour of propagating rays. Different types of corrugation are considered, using different distributions of the corrugation heights: white Gaussian, power law, self-affine perturbation. In phase space, a prevalent chaotic behaviour of rays, and the presence of a lot of caustics, are observed. These results entail that the KAM theorem is not fulfilled.

scholarly journals Cosmological constant in chameleon Brans–Dicke theory

2019 ◽  
Vol 28 (01) ◽  
pp. 1950022 ◽  
Author(s):  
Yousef Bisabr
Keyword(s):  
Exact Solution ◽  
Scalar Field ◽  
Cosmological Constant ◽  
Exact Solutions ◽  
Effective Mass ◽  
Potential Function ◽  
Power Law ◽  
Exponential Form ◽  
First Case ◽  
Different Types

We consider a generalized Brans–Dicke model in which the scalar field has a self-interacting potential function. The scalar field is also allowed to couple nonminimally with the matter part. We assume that it has a chameleon behavior in the sense that it acquires a density-dependent effective mass. We consider two different types of matter systems which couple with the chameleon, dust and vacuum. In the first case, we find a set of exact solutions when the potential has an exponential form. In the second case, we find a power-law exact solution for the scale factor. In this case, we will show that the vacuum density decays during expansion due to coupling with the chameleon.

scholarly journals On the apparent power law in CDM halo pseudo-phase space density profiles

2017 ◽  
Vol 470 (1) ◽  
pp. 500-511 ◽  
Author(s):  
Ethan O. Nadler ◽  
S. Peng Oh ◽  
Suoqing Ji
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Phase Space Density ◽  
Fluid Approximation ◽  
Density Profiles ◽  
Space Density ◽  
Scale Free ◽  
Hydrodynamic Calculations

Abstract We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log–log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

scholarly journals On The Critical Phenomena in The Dynamics of Asteroids

1999 ◽  
Vol 172 ◽  
pp. 383-386
Author(s):  
Ivan I. Shevchenko
Keyword(s):  
Phase Space ◽  
Critical Phenomena ◽  
Power Law ◽  
Anomalous Transport ◽  
Selection Effects ◽  
Recurrence Times ◽  
Statistical Selection ◽  
Power Law Decay ◽  
Statistical Effects

AbstractTwo statistical effects in the long-term chaotic asteroidal dynamics are considered, namely the power-law character of the dependence of recurrence times on local Lyapunov times and the power-law decay in the tails of the recurrence distributions. The dependences in both cases are shaped by effects of anomalous transport, due to the presence of the chaos border in phase space, and by statistical selection effects.

scholarly journals Almost additive entropy

2014 ◽  
Vol 11 (05) ◽  
pp. 1450040 ◽  
Author(s):  
Nikos Kalogeropoulos
Keyword(s):  
Phase Space ◽  
Shannon Entropy ◽  
Power Law ◽  
Physical Significance ◽  
Small Deviations ◽  
Phase Space Volume ◽  
Composition Property ◽  
Flat Manifolds ◽  
Special Case ◽  
Space Volume

We explore consequences of a hyperbolic metric induced by the composition property of the Harvda–Charvat/Daróczy/Cressie–Read/Tsallis entropy. We address the special case of systems described by small deviations of the non-extensive parameter q ≈ 1 from the "ordinary" additive case which is described by the Boltzmann/Gibbs/Shannon entropy. By applying the Gromov/Ruh theorem for almost flat manifolds, we show that such systems have a power-law rate of expansion of their configuration/phase space volume. We explore the possible physical significance of some geometric and topological results of this approach.

scholarly journals A generalized q growth model based on nonadditive entropy

2020 ◽  
Vol 34 (29) ◽  
pp. 2050281
Author(s):  
Irving Rondón ◽  
Oscar Sotolongo-Costa ◽  
Jorge A. González ◽  
Jooyoung Lee
Keyword(s):  
Evolution Equation ◽  
Growth Model ◽  
Power Law ◽  
Statistical Physics ◽  
Von Bertalanffy ◽  
Model Based ◽  
General Growth ◽  
Different Types ◽  
Nonadditive Entropy ◽  
Growth Laws

We present a general growth model based on nonextensive statistical physics. We show that the most common unidimensional growth laws such as power law, exponential, logistic, Richards, Von Bertalanffy, Gompertz can be obtained. This model belongs to a particular case reported in (Physica A 369, 645 (2006)). The new evolution equation resembles the “universality” revealed by West for ontogenetic growth (Nature 413, 628 (2001)). We show that for early times the model follows a power law growth as [Formula: see text], where the exponent [Formula: see text] classifies different types of growth. Several examples are given and discussed.

WEAK DISSIPATION IN A HAMILTONIAN MAP

1994 ◽  
Vol 04 (04) ◽  
pp. 921-932 ◽  
Author(s):  
RAÚL J. MONDRAGÓN C. ◽  
PETER H. RICHTER
Keyword(s):  
Phase Space ◽  
Hamiltonian System ◽  
Periodic Orbits ◽  
Adiabatic Invariance ◽  
Bifurcation Tree ◽  
Bouncing Ball ◽  
Different Types ◽  
Weak Dissipation ◽  
Hamiltonian Map

The dynamics of a bouncing ball reflected off a harmonic spring is investigated, with weak dissipation of three different types. The phase space is found to be organized into a system of tubes that wind around the branches of the bifurcation tree of periodic orbits of the Hamiltonian system. Instead of attraction towards special periodic orbits we observe a kind of piecewise adiabatic invariance of the tubes, with jumps occurring when the branches penetrate each other.

scholarly journals -BOUNDS FOR PSEUDO-DIFFERENTIAL OPERATORS ON COMPACT LIE GROUPS

2017 ◽  
Vol 18 (3) ◽  
pp. 531-559 ◽  
Author(s):  
Julio Delgado ◽  
Michael Ruzhansky
Keyword(s):  
Phase Space ◽  
Vector Fields ◽  
Differential Operators ◽  
Compact Lie Group ◽  
Compact Lie Groups ◽  
Pseudo Differential Operators ◽  
Different Types ◽  
Unitary Dual ◽  
Laplacian Operators ◽  
Noncommutative Analogue

Given a compact Lie group$G$, in this paper we establish$L^{p}$-bounds for pseudo-differential operators in$L^{p}(G)$. The criteria here are given in terms of the concept of matrix symbols defined on the noncommutative analogue of the phase space$G\times \widehat{G}$, where$\widehat{G}$is the unitary dual of$G$. We obtain two different types of$L^{p}$bounds: first for finite regularity symbols and second for smooth symbols. The conditions for smooth symbols are formulated using$\mathscr{S}_{\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF}}^{m}(G)$classes which are a suitable extension of the well-known$(\unicode[STIX]{x1D70C},\unicode[STIX]{x1D6FF})$ones on the Euclidean space. The results herein extend classical$L^{p}$bounds established by C. Fefferman on$\mathbb{R}^{n}$. While Fefferman’s results have immediate consequences on general manifolds for$\unicode[STIX]{x1D70C}>\max \{\unicode[STIX]{x1D6FF},1-\unicode[STIX]{x1D6FF}\}$, our results do not require the condition$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$. Moreover, one of our results also does not require$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$. Examples are given for the case of$\text{SU}(2)\cong \mathbb{S}^{3}$and vector fields/sub-Laplacian operators when operators in the classes$\mathscr{S}_{0,0}^{m}$and$\mathscr{S}_{\frac{1}{2},0}^{m}$naturally appear, and where conditions$\unicode[STIX]{x1D70C}>\unicode[STIX]{x1D6FF}$and$\unicode[STIX]{x1D70C}>1-\unicode[STIX]{x1D6FF}$fail, respectively.

HEAT CONDUCTION IN HOMOGENEOUS AND HETEROGENEOUS BILLIARD SYSTEMS

2008 ◽  
Vol 22 (22) ◽  
pp. 3901-3914 ◽  
Author(s):  
JUN-WEN MAO ◽  
YOU-QUAN LI ◽  
LING-YUN DENG
Keyword(s):  
Heat Conduction ◽  
Phase Space ◽  
Power Law ◽  
Heat Conductivity ◽  
Lorentz Gas ◽  
Rotating Disks ◽  
One Dimensional ◽  
Power Law Decay ◽  
The Moment ◽  
Good Agreement

We investigate the heat conduction in a modified Lorentz gas with freely rotating disks periodically placed along one-dimensional channel. The heat conductivity is dependent on the moment of inertia η of the disks, with a power-law decay when η > 1. By plotting the Poincaré surface of the section, we observe a contraction of phase space over the range of η > 1, which is sensitive to the initial condition. We find that the power-law decay of the heat conductivity is relevant to the mixing phase space. As a possible application, we model the heterostructure by connecting the segments of different η, and predict the analytical results of the temperature profiles and the heat conductivity, which are in good agreement with the numerical ones.

scholarly journals Analysis of the velocity distribution in different types of ventilation system ducts

2018 ◽  
Vol 180 ◽  
pp. 02081 ◽  
Author(s):  
Kazimierz Peszyński ◽  
Lukasz Olszewski ◽  
Emil Smyk ◽  
Daniel Perczyński
Keyword(s):  
Velocity Profile ◽  
Velocity Distribution ◽  
Cross Section ◽  
Power Law ◽  
Flow Rate ◽  
Fundamental Problem ◽  
Ventilation System ◽  
Different Types ◽  
Actual Profile ◽  
Ventilation Duct

The paper presents the results obtained during the preliminary studies of circular and rectangular ducts before testing the properties elements (elbows, tees, etc.)of rectangular with rounded corners ducts. The fundamental problem of the studies was to determine the flow rate in the ventilation duct. Due to the size of the channel it was decided to determine the flow rate based on the integration of flow velocity over the considered cross-section. This method requires knowledge of the velocity distribution in the cross section. Approximation of the measured actual profile by the classic and modified Prandtl power-law velocity profile was analysed.

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