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 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.

Particle temperature distribution in a dust flame

2010 ◽  
Vol 224 (2) ◽  
pp. 363-367
Author(s):  
A S Shahrbabaki ◽  
M Dodangeh
Keyword(s):  
Particle Size ◽  
Heat Conduction ◽  
Temperature Profile ◽  
Particle Temperature ◽  
Transient Heat Conduction ◽  
Order Model ◽  
Conduction Model ◽  
One Dimensional ◽  
Dust Flame ◽  
Good Agreement

An unsteady one-dimensional heat conduction model is used to determine the particle temperature profile in suspension fuels by using a perturbation method. A second-order model is presented for transient heat conduction in a spherical particle. The radiation term is considered in the boundary conditions, which plays an important role in the dust flame. The effects of particle size and Biot number on the temperature profile are investigated. The results are in good agreement with the numerical solution.

On Standard Eigenvalues of Variable-Coefficient Heat and Rod Equations

1989 ◽  
Vol 56 (1) ◽  
pp. 146-148 ◽  
Author(s):  
H. P. W. Gottlieb
Keyword(s):  
Heat Equation ◽  
Power Law ◽  
Heat Conductivity ◽  
Variable Coefficient ◽  
Continuous Case ◽  
Coefficient Function ◽  
Heat Conductivity Coefficient ◽  
One Dimensional ◽  
Variable Heat ◽  
The One

Forms of the variable-heat-conductivity coefficient function in the one-dimensional heat equation are determined which yield a standard harmonic eigenvalue sequence as in the case of homogeneity. The continuous case is found to correspond to a four-thirds power law dependence on coordinate. For the stepped case, the condition on the ratio of segmental heat conductivities in terms of the junction location is presented.

scholarly journals One-dimensional quantum walks via generating function and the CGMV method

2014 ◽  
Vol 14 (13&14) ◽  
pp. 1165-1186
Author(s):  
Norio Konno ◽  
Etsuo Segawa
Keyword(s):  
Limit Theorem ◽  
Weak Convergence ◽  
Generating Function ◽  
Power Law ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Linear Scaling ◽  
One Dimensional ◽  
Power Law Decay ◽  
Quantum Coin

We treat quantum walk (QW) on the line whose quantum coin at each vertex tends to the identity as the distance goes to infinity. We obtain a limit theorem that this QW exhibits localization with not an exponential but a ``power-law" decay around the origin and a ``strongly" ballistic spreading called bottom localization in this paper. This limit theorem implies the weak convergence with linear scaling whose density has two delta measures at $x=0$ (the origin) and $x=1$ (the bottom) without continuous parts.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

Transient convective diffusion to a uniformly accessible surface under aparent slip conditions

1991 ◽  
Vol 56 (2) ◽  
pp. 334-343
Author(s):  
Ondřej Wein
Keyword(s):  
Power Law ◽  
Analytical Solutions ◽  
Convective Diffusion ◽  
Active Surface ◽  
Velocity Profiles ◽  
One Dimensional ◽  
Slip Conditions ◽  
Accessible Surface ◽  
Diffusion Problems

Analytical solutions are given to a class of unsteady one-dimensional convective-diffusion problems assuming power-law velocity profiles close to the transport-active surface.

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