scholarly journals Quasi-homologous evolution of self-gravitating systems with vanishing complexity factor

2020 ◽  
Vol 80 (7) ◽  
Author(s):  
L. Herrera ◽  
A. Di Prisco ◽  
J. Ospino
Keyword(s):  
Analytical Models ◽  
Dissipative Systems ◽  
Spherically Symmetric ◽  
Dissipative Fluid ◽  
Gravitating Systems ◽  
Boundary Surfaces ◽  
Israel Condition

Abstract We investigate the evolution of self-gravitating either dissipative or non-dissipative systems satisfying the condition of minimal complexity, and whose areal radius velocity is proportional to the areal radius (quasi-homologous condition). Several exact analytical models are found under the above mentioned conditions. Some of the presented models describe the evolution of spherically symmetric dissipative fluid distributions whose center is surrounded by a cavity. Some of them satisfy the Darmois conditions whereas others present shells and must satisfy the Israel condition on either one or both boundary surfaces. Prospective applications of some of these models to astrophysical scenarios are discussed.

Study of conformally flat polytropes with tilted congruence

2018 ◽  
Vol 27 (07) ◽  
pp. 1850063 ◽  
Author(s):  
M. Sharif ◽  
Sobia Sadiq
Keyword(s):  
Equation Of State ◽  
Matter Content ◽  
Energy Conditions ◽  
Spherically Symmetric ◽  
Conformally Flat ◽  
Flat Condition ◽  
Polytropic Equation ◽  
Dissipative Fluid ◽  
Symmetric Spacetime ◽  
Fluid Configuration

This paper is aimed to study the modeling of spherically symmetric spacetime in the presence of anisotropic dissipative fluid configuration. This is accomplished for an observer moving relative to matter content using two cases of polytropic equation-of-state under conformally flat condition. We formulate the corresponding generalized Tolman–Oppenheimer–Volkoff equation, mass equation, as well as energy conditions for both cases. The conformally flat condition is imposed to find an expression for anisotropy which helps to study spherically symmetric polytropes. Finally, Tolman mass is used to analyze stability of the resulting models.

Evolution of expansion-free spherically symmetric self-gravitating non-dissipative fluids and some analytical solutions

2018 ◽  
Vol 15 (04) ◽  
pp. 1850058 ◽  
Author(s):  
Rajesh Kumar ◽  
Sudhir Kumar Srivastava
Keyword(s):  
Analytical Models ◽  
Fluid Distribution ◽  
Junction Condition ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Minkowski Space Time ◽  
Spherically Symmetric Metric ◽  
Anisotropic Fluids ◽  
Vacuum Cavity ◽  
Dissipative Fluids

We consider the distribution of spherically symmetric self-gravitating non-dissipative (but anisotropic) fluids under the expansion-free condition which requires the existence of vacuum cavity within the fluid distribution. The Darmois junction condition is investigated for matching the spherically symmetric metric to an internal vacuum cavity (Minkowski space-time). We have studied some analytical models, total of three family of solutions out of which two satisfy the junction conditions over both the hypersurfaces. The models are investigated under some known dynamical assumptions which further provide analytical solution in each family.

scholarly journals EXPANSION-FREE CAVITY EVOLUTION: SOME EXACT ANALYTICAL MODELS

2011 ◽  
Vol 20 (12) ◽  
pp. 2351-2367 ◽  
Author(s):  
A. DI PRISCO ◽  
L. HERRERA ◽  
J. OSPINO ◽  
N. O. SANTOS ◽  
V. M. VIÑA-CERVANTES
Keyword(s):  
Analytical Models ◽  
Fluid Distribution ◽  
Expansion Scalar ◽  
Kinematical Condition ◽  
Cavity Evolution ◽  
Central Explosion ◽  
Anisotropic Fluids ◽  
Surrounding Fluid ◽  
Vacuum Cavity ◽  
Boundary Surfaces

We consider spherically symmetric distributions of anisotropic fluids with a central vacuum cavity, evolving under the condition of vanishing expansion scalar. Some analytical solutions are found satisfying Darmois junction conditions on both delimiting boundary surfaces, while some others require the presence of thin shells on either (or both) boundary surfaces. The solutions here obtained model the evolution of the vacuum cavity and the surrounding fluid distribution, emerging after a central explosion, thereby showing the potential of expansion–free condition for the study of that kind of problems. This study complements a previously published work where modeling of the evolution of such kind of systems was achieved through a different kinematical condition.

scholarly journals The Equilibrium Statistical Mechanics of Self-gravitating Systems

1981 ◽  
Vol 34 (3) ◽  
pp. 267 ◽  
Author(s):  
PS Cally
Keyword(s):  
Partition Function ◽  
Particle Distribution ◽  
Distribution Functions ◽  
Continuum Approximation ◽  
Spherically Symmetric ◽  
Relative Order ◽  
Particle Distributions ◽  
Gravitating Systems ◽  
Correction Terms ◽  
The Continuum

The partition function and one- and two-particle distribution functions are calculated fora spherically symmetric self-gravitating system using a method which is exact except for terms of relative order N -1. The results are in agreement with those found in the continuum approximation. First approximations to the correction terms are evaluated with particular emphasis on the form of the pair distribution as compared with the product of two one-particle distributions.

Mechanism of irregular crack-propagation in thermal controlled fracture of ceramics induced by microwave

2020 ◽  
Vol 21 (6) ◽  
pp. 610
Author(s):  
Xiaoliang Cheng ◽  
Chunyang Zhao ◽  
Hailong Wang ◽  
Yang Wang ◽  
Zhenlong Wang
Keyword(s):  
Crack Propagation ◽  
Industrial Application ◽  
Ceramic Materials ◽  
Advanced Technology ◽  
Analytical Models ◽  
Propagation Mechanism ◽  
Unstable Crack ◽  
Fracture Simulation ◽  
Initial Stage ◽  
Controlled Fracture

Microwave cutting glass and ceramics based on thermal controlled fracture method has gained much attention recently for its advantages in lower energy-consumption and higher efficiency than conventional processing method. However, the irregular crack-propagation is problematic in this procedure, which hinders the industrial application of this advanced technology. In this study, the irregular crack-propagation is summarized as the unstable propagation in the initial stage, the deviated propagation in the middle stage, and the non-penetrating propagation in the end segment based on experimental work. Method for predicting the unstable propagation in the initial stage has been developed by combining analytical models with thermal-fracture simulation. Experimental results show good agreement with the prediction results, and the relative deviation between them can be <5% in cutting of some ceramics. The mechanism of deviated propagation and the non-penetrating propagation have been revealed by simulation and theoretical analysis. Since this study provides effective methods to predict unstable crack-propagation in the initial stage and understand the irregular propagation mechanism in the whole crack-propagation stage in microwave cutting ceramics, it is of great significance to the industrial application of thermal controlled fracture method for cutting ceramic materials using microwave.

Classifying the Past: Discriminant Analysis and its Application to Medieval Farming Systems

1996 ◽  
Vol 8 (1) ◽  
pp. 1-10 ◽  
Author(s):  
Ken Bartley
Keyword(s):  
Cluster Analysis ◽  
Discriminant Analysis ◽  
Processing Time ◽  
Farming Systems ◽  
Frame Of Reference ◽  
Analytical Models ◽  
Successful Implementation ◽  
Medieval Period ◽  
The Past ◽  
Livestock Management

This paper discusses the need for nationally based analytical models of the medieval period. The use of cluster analysis as a method for classifying demesne farms, by the crops they grew and their livestock management, is explained. Successful implementation of cluster analysis requires both the existence of a large base sample, to permit isolation of specific groupings within the data, and access to considerable processing time. The paper concludes by demonstrating how discriminant analysis can provide an efficient and systematic way of classifying even a single manor within a national frame of reference.

Transport and fluctuations in nonlinear-dissipative systems: role of interparticle collisions

1999 ◽  
Vol 4 ◽  
pp. 31-86 ◽  
Author(s):  
R. Katilius ◽  
A. Matulionis ◽  
R. Raguotis ◽  
I. Matulionienė
Keyword(s):  
Electric Fields ◽  
Carrier Density ◽  
Experimental Results ◽  
Dissipative Systems ◽  
Doped Semiconductors ◽  
Electron Diffusion ◽  
Electron Collisions ◽  
Electric Noise ◽  
Diffusion Phenomena

The goal of the paper is to overview contemporary theoretical and experimental research of the microwave electric noise and fluctuations of hot carriers in semiconductors, revealing sensitivity of the noise spectra to non-linearity in the applied electric field strength and, especially, in the carrier density. During the last years, investigation of electronic noise and electron diffusion phenomena in doped semiconductors was in a rapid progress. By combining analytic and Monte Carlo methods as well as the available experimental results on noise, it became possible to obtain the electron diffusion coefficients in the range of electric fields where inter-electron collisions are important and Price’s relation is not necessarily valid. Correspondingly, a special attention to the role of inter-electron collisions and of the non-linearity in the carrier density while shaping electric noise and diffusion phenomena in the non-equilibrium states will be paid. The basic and up-to-date information will be presented on methods and advances in this contemporary field - the field in which methods of non-linear analytic and computational analysis are indispensable while seeking coherent understanding and interpretation of experimental results.

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