scholarly journals Negativity of the Casimir Self-Entropy in Spherical Geometries

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 214 ◽  
Author(s):  
Yang Li ◽  
Kimball A. Milton ◽  
Prachi Parashar ◽  
Lujun Hong
Keyword(s):  
Physical Meaning ◽  
Thermal Fluctuations ◽  
Numerical Results ◽  
The Self ◽  
Surprising Result ◽  
Total Entropy ◽  
Negative Interaction ◽  
Conducting Sphere ◽  
Mathematical Techniques

It has been recognized for some time that, even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self-entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper, we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel–Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

scholarly journals Negativity of the Casimir Self-Entropy in Spherical Geometries

2021 ◽  
Author(s):  
Yang Li ◽  
Kimball Milton ◽  
Prachi Parashar ◽  
Lujan Hong
Keyword(s):  
Physical Meaning ◽  
Thermal Fluctuations ◽  
Numerical Results ◽  
The Self ◽  
Surprising Result ◽  
Total Entropy ◽  
Negative Interaction ◽  
Conducting Sphere ◽  
Mathematical Techniques

It has been recognized for some time that even for perfect conductors, the interaction Casimir entropy, due to quantum/thermal fluctuations, can be negative. This result was not considered problematic because it was thought that the self-entropies of the bodies would cancel this negative interaction entropy, yielding a total entropy that was positive. In fact, this cancellation seems not to occur. The positive self entropy of a perfectly conducting sphere does indeed just cancel the negative interaction entropy of a system consisting of a perfectly conducting sphere and plate, but a model with weaker coupling in general possesses a regime where negative self-entropy appears. The physical meaning of this surprising result remains obscure. In this paper we re-examine these issues, using improved physical and mathematical techniques, partly based on the Abel-Plana formula, and present numerical results for arbitrary temperatures and couplings, which exhibit the same remarkable features.

scholarly journals ON NONCOMMUTATIVE SOLITONS

2000 ◽  
Vol 15 (36) ◽  
pp. 2205-2218 ◽  
Author(s):  
A. SOLOVYOV
Keyword(s):  
Field Theory ◽  
Scalar Field ◽  
Exact Solutions ◽  
Physical Meaning ◽  
Symmetric Solution ◽  
Numerical Results ◽  
Scalar Field Theory ◽  
Radially Symmetric Solution

We consider (2+1)-dimensional classical noncommutative scalar field theory. The general ansatz for a radially symmetric solution is obtained. Some exact solutions are presented. Their possible physical meaning is discussed. The case of finite θ is discussed qualitatively and illustrated by some numerical results.

scholarly journals Scattering of a Plane Wave by an Anisotropic Plasma-Coated Conducting Sphere

2011 ◽  
Vol 2011 ◽  
pp. 1-6 ◽  
Author(s):  
You-Lin Geng
Keyword(s):  
Plane Wave ◽  
Electromagnetic Fields ◽  
Anisotropic Medium ◽  
Free Space ◽  
Numerical Results ◽  
Wave Functions ◽  
Vector Wave ◽  
Homogeneous Plasma ◽  
Conducting Sphere ◽  
Spherical Vector

The electromagnetic field in homogeneous plasma anisotropic medium can be expressed as the addition of the first and second spherical vector wave functions in plasma anisotropic medium. The tangential electromagnetic fields are continued in the boundary between the homogeneous plasma anisotropic medium and free space, and the tangential electrical field is zero in the surface of conducting sphere. The coefficients of electromagnetic fields in plasma anisotropic medium expanded in terms of spherical vector wave functions in plasma anisotropic medium are derived, and then the coefficients of scattering fields in terms of spherical vector functions in free space can be obtained. Numerical results between this paper and hybrid finite element-boundary integral-multilevel fast multipole algorithm (FE-BI-MLFMA) are given, and they are in agreement very well. Some new numerical results of a plane wave scattering by an anisotropic plasma-coated conducting sphere are obtained.

scholarly journals VIII. Numerical results of the theory of the diffraction of a plane electromagnetic wave by a perfectly conducting sphere

1918 ◽  
Vol 217 (549-560) ◽  
pp. 279-314 ◽  
Keyword(s):  
Electromagnetic Wave ◽  
Plane Electromagnetic Wave ◽  
Numerical Results ◽  
Subsequent Work ◽  
Conducting Sphere ◽  
Derivatives Of

1. At the suggestion of Dr. Bromwich, I began the computations leading to this paper nearly three years ago. Using tables constructed by Lord Rayleigh and Prof. A. Lodge, I obtained results for k a = 1, 2, 10 and θ = 0°, 180°; 90°; 45°, 135°; 20°,160°; 70°, 110°; in this order. From the results for 1 and 2, graphs of Y 1 , Y 2 , Z 1 , Z 2 could be constructed with some confidence, but such graphs were entirely impossible in the case of k a = 10, owing to the large number of their undulations. (For the graphs of these functions, as finally drawn, see figs. 1, 3, 18, 20, 22, 24.) I then handed over the work to Messrs. Doodson and Kennedy, and the whole of the results as they now appear are due to them. Mr. Doodson first constructed tables for Bessel’s functions of half-integral orders, and Mr. Kennedy constructed tables for the derivatives of Legendre's functions. These two sets of tables, together with those of Lodge already quoted, are what have been used in all the subsequent work.

Study on Biodegradability of Xenobiotic Polymer with Numerical Simulation Based on Experimental Outcome

2021 ◽  
Vol 1026 ◽  
pp. 136-141
Author(s):  
Masaji Watanabe ◽  
Fusako Kawai
Keyword(s):  
Numerical Simulation ◽  
Inverse Analysis ◽  
Microbial Population ◽  
Numerical Results ◽  
Experimental Results ◽  
Simulation Based ◽  
Mathematical Techniques

This study demonstrates application of mathematical techniques such as modeling, inverse analysis, and numerical simulation to biodegradation of xenobiotic polymer. In particular, this paper presents results of numerical simulation based on experimental results. Numerical results and experimental results show the behavior of microbial population in exogenous type depolymerization processes.

scholarly journals Experimental and Numerical Study of Heat Transfer Performance for an Engine Representative Two-Pass Rotating Internal Cooling Channel

2016 ◽  
Author(s):  
Zhi Wang ◽  
Roque Corral ◽  
Francois Chedevergne
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Heat Transfer Performance ◽  
Numerical Results ◽  
Test Facility ◽  
Design Parameters ◽  
Internal Cooling ◽  
Surprising Result ◽  
Transfer Performance ◽  
Cooling Channel

This paper investigates, both experimentally and computationally, the heat transfer performance on an engine representative varying aspect ratio two-pass internal cooling channel, in both stationary and rotating conditions. The test geometry and design parameters were suggested by SNECMA as a representative HPT blade two-pass internal cooling channel. The cooling channel has radially outward flow in the first passage with an aspect ratio of 1:2.25 and after a 180 degree sharp turn, a radially inward flow in the second passage with an aspect ratio of 1:1.85. One side of the two passages is equipped with 45 degree angled rib turbulators with a rib spacing P/e=7 and blockage ratio e/Dh =0.116. The other side is smooth in order to have optical access for experiment. The experiment was performed at three Reynolds numbers: 15,000, 25,000, and 35,000. Both forward and backward rotating directions were tested in order to study the heat transfer performance of the ribbed surface as trailing wall or leading wall individually. The tested Rotation numbers were Ro=±0.3 at Re=15,000 and Re=25,000, whereas the Rotation number was reduced to ±0.22 at Re=35,000, due to restrictions of the test facility. Infrared thermography technology is used to capture the temperature field for further evaluation of heat transfer performance. Numerical simulations for all experimental cases were conducted using the same geometry including the air feeding system, applying the experimental wall temperature distribution in order to properly capture inlet and buoyancy effects, with the k–ω–SST turbulence model. Numerical results show overall agreement and similar trends than the experimental data. Numerical results also show that the rotation effects alter the internal flow significantly, resulting in different surface heat transfer distributions. Particularly, it is shown that heat transfer performance of the pressure side is not enhanced by the rotation in this study, which is a surprising result. This behavior was captured both in the experiments and the numerical predictions.

Calculations of self-excited impinging jet flow

1986 ◽  
Vol 163 ◽  
pp. 69-98 ◽  
Author(s):  
Samuel Ohring
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Low Frequency ◽  
Numerical Results ◽  
The Self ◽  
Experimental Results ◽  
Number Range ◽  
Planar Jet ◽  
Reynolds Number Range ◽  
Stream Function Formulation

This paper presents numerical calculations of the self-excited oscillations of an incompressible planar jet impinging upon a wedge for a Reynolds-number range of 250–650. For this Reynolds-number range these flows are experimentally observed to be two-dimensional and laminar. A finite-difference vorticity/stream-function formulation of the Navier-Stokes equations is employed. The self-sustained flow oscillations result in not just one but several well-defined flow frequency components due to nonlinear interaction of two primary components: the most unstable frequency (β) of the jet shear layer and a low-frequency modulating component ($\frac{1}{3}\beta $). The modulating component results from vortex-vortex interaction at the impingement edge of both like and counter-rotating vortices. Although the interaction pattern varies through the Reynolds-number range studied, the pattern adjusts itself to maintain the modulating component $\frac{1}{3}\beta $ which has a strong upstream influence. The numerical results, in agreement with experimental results, strongly suggest the occurrence of such phenomena as frequency jumps and hysteresis. Pressure at the wedge surface has been calculated and compared with experimental results. Numerical results for wedge torque and lift, which have not been experimentally measured, have also been obtained.

scholarly journals Fluctuations of work in realistic equilibrium states of quantum systems with conserved quantities

2020 ◽  
Author(s):  
Jordi Mur-Petit ◽  
Armando Relaño ◽  
Rafael A. Molina ◽  
Dieter Jaksch
Keyword(s):  
Thermal Fluctuations ◽  
Quantum Systems ◽  
Numerical Results ◽  
Equilibrium States ◽  
Conserved Quantities ◽  
Body System ◽  
Equilibrium Dynamics ◽  
Relaxation To Equilibrium ◽  
Open Questions ◽  
The Impact

The out-of-equilibrium dynamics of quantum systems is one of the most fascinating problems in physics, with outstanding open questions on issues such as relaxation to equilibrium. An area of particular interest concerns few-body systems, where quantum and thermal fluctuations are expected to be especially relevant. In this contribution, we present numerical results demonstrating the impact of conserved quantities (or ‘charges’) in the outcomes of out-of-equilibrium measurements starting from realistic equilibrium states on a few-body system implementing the Dicke model.

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