The statistical self‐similarity hypothesis in grain growth and particle coarsening

1986 ◽  
Vol 59 (4) ◽  
pp. 1341-1349 ◽  
Author(s):  
W. W. Mullins
Keyword(s):  
Grain Growth ◽  
Self Similarity ◽  
Particle Coarsening ◽  
Similarity Hypothesis

scholarly journals Self-similar cosmological solutions in f(R,T) gravity theory

2021 ◽  
pp. 2150206
Author(s):  
José Antonio Belinchón ◽  
Carlos González ◽  
Sami Dib
Keyword(s):  
Exact Solutions ◽  
The Self ◽  
Exact Form ◽  
Field Equations ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Geometrical Quantity ◽  
Cosmological Solutions ◽  
Self Similar ◽  
Matter Collineation

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.

scholarly journals and Models: A Self-Similar Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
José Antonio Belinchón
Keyword(s):  
The Self ◽  
Exact Form ◽  
Field Equations ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Scale Factors ◽  
Self Similar ◽  
Frw Metric ◽  
Similar Solutions ◽  
Bianchi Types

We study the models and their particular case, the so-called -models under the self-similarity hypothesis. In particular, we calculate the exact form that each quantity may take in order that field equations (FEs) admit self-similar solutions. The methods employed allow us to obtain general results that are valid not only for the FRW metric, but also for all the Bianchi types as well as for the Kantowski-Sachs model (under the self-similarity hypothesis and the power-law hypothesis for the scale factors).

scholarly journals BIANCHI I WITH VARIABLE G AND Λ: SELF-SIMILAR APPROACH

2008 ◽  
Vol 23 (31) ◽  
pp. 5021-5036 ◽  
Author(s):  
JOSÉ ANTONIO BELINCHÓN
Keyword(s):  
Equation Of State ◽  
Perfect Fluid ◽  
Weyl Tensor ◽  
The Self ◽  
Variable G And Λ ◽  
Self Similarity ◽  
Similarity Hypothesis ◽  
Bianchi I ◽  
Self Similar ◽  
Variable G

In this paper we show how to study under the self-similarity hypothesis a perfect fluid Bianchi I model with variables G and Λ, but under the condition div T≠0. We arrive to the conclusion that: G and Λ are decreasing time functions (the sign of Λ depends on the equation of state), while the exponents of the scale factor must satisfy the conditions [Formula: see text] and [Formula: see text], ∀ω ∈ (-1, 1), relaxing in this way the Kasner conditions. We also show the connection between the behavior of G and the Weyl tensor.

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