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.

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).

Self-similarity of decaying two-dimensional turbulence

1996 ◽  
Vol 326 ◽  
pp. 357-372 ◽  
Author(s):  
Peter Bartello ◽  
Tom Warn
Keyword(s):  
Universal Function ◽  
The Self ◽  
Two Dimensional ◽  
Self Similarity ◽  
Important Ingredient ◽  
Similarity Hypothesis ◽  
Coherent Vortices ◽  
Self Similar ◽  
High Reynolds ◽  
The One

Simulations of decaying two-dimensional turbulence suggest that the one-point vorticity density has the self-similar form $P_\omega \sim t\;\;f(\omega t)$implied by Batchelor's (1969) similarity hypothesis, except in the tails. Specifically, similarity holds for |ω| < ωm, while pω falls off rapidly above. The upper bound of the similarity range, ωm, is also nearly conserved in high-Reynolds-number hyperviscosity simulations and appears to be related to the average amplitude of the most intense vortices (McWilliams 1990), which was an important ingredient in the vortex scaling theory of Carnevale et al. (1991).The universal function f also appears to be hyperbolic, i.e. $f(x) \sim c/2\vert x \vert^{1+q_c}$ for |x| > x*, where qc = 0.4 and x* = 70, which along with the truncated similarity form implies a phase transition in the vorticity moments $\langle \vert \omega\vert ^q\rangle \sim \left\{\begin{array}{ll} c_q t^{-q}, & -1 < q < q_c\cr c(q - q_c)^{-1} \omega _m^{q-q_c} t^{-q_c} & q > q_c, \end{array}\right.$ between the self-similar 'background sea' and the coherent vortices. Here Cq and c are universal. Low-order moments are therefore consistent with Batchelor's similarity hypothesis whereas high-order moments are similar to those predicted by Carnevale et al. (1991). A self-similar but less well-founded expression for the energy spectrum is also proposed.It is also argued that ωc = x*/t represents 'mean sea-level', i.e. the (average) threshold separating the vortices and the sea, and that there is a spectrum of vortices with amplitudes in the range (ωs,ωm). The total area occupied by vortices is also found to remain constant in time, with losses due to mergers of large-amplitude vortices being balanced by gains due to production of weak vortices. By contrast, the area occupied by vortices above afixed threshold decays in time as observed by McWilliams (1990).

scholarly journals Onset of the Mach Reflection of Zel’dovich–von Neumann–Döring Detonations

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 314
Author(s):  
Tianyu Jing ◽  
Huilan Ren ◽  
Jian Li
Keyword(s):  
Hot Spot ◽  
Mach Reflection ◽  
Near Field ◽  
The Self ◽  
Small Scale ◽  
Mach Stem ◽  
Self Similarity ◽  
Von Neumann ◽  
Similarity Problem ◽  
Self Similar

The present study investigates the similarity problem associated with the onset of the Mach reflection of Zel’dovich–von Neumann–Döring (ZND) detonations in the near field. The results reveal that the self-similarity in the frozen-limit regime is strictly valid only within a small scale, i.e., of the order of the induction length. The Mach reflection becomes non-self-similar during the transition of the Mach stem from “frozen” to “reactive” by coupling with the reaction zone. The triple-point trajectory first rises from the self-similar result due to compressive waves generated by the “hot spot”, and then decays after establishment of the reactive Mach stem. It is also found, by removing the restriction, that the frozen limit can be extended to a much larger distance than expected. The obtained results elucidate the physical origin of the onset of Mach reflection with chemical reactions, which has previously been observed in both experiments and numerical simulations.

TUBE FORMULAS FOR GRAPH-DIRECTED FRACTALS

Fractals ◽  
2010 ◽  
Vol 18 (03) ◽  
pp. 349-361 ◽  
Author(s):  
BÜNYAMIN DEMÍR ◽  
ALI DENÍZ ◽  
ŞAHIN KOÇAK ◽  
A. ERSIN ÜREYEN
Keyword(s):  
The Self ◽  
Self Similarity ◽  
Complex Dimensions ◽  
Tubular Neighborhoods ◽  
Self Similar ◽  
Tube Formulas

Lapidus and Pearse proved recently an interesting formula about the volume of tubular neighborhoods of fractal sprays, including the self-similar fractals. We consider the graph-directed fractals in the sense of graph self-similarity of Mauldin-Williams within this framework of Lapidus-Pearse. Extending the notion of complex dimensions to the graph-directed fractals we compute the volumes of tubular neighborhoods of their associated tilings and give a simplified and pointwise proof of a version of Lapidus-Pearse formula, which can be applied to both self-similar and graph-directed fractals.

ECCENTRIC DISTANCE SUM OF SIERPIŃSKI GASKET AND SIERPIŃSKI NETWORK

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950016 ◽  
Author(s):  
JIN CHEN ◽  
LONG HE ◽  
QIN WANG
Keyword(s):  
Asymptotic Formula ◽  
Complex Networks ◽  
Sierpinski Gasket ◽  
The Self ◽  
Self Similarity ◽  
Sierpiński Gasket ◽  
Similar Measure ◽  
Self Similar ◽  
Eccentric Distance

The eccentric distance sum is concerned with complex networks. To obtain the asymptotic formula of eccentric distance sum on growing Sierpiński networks, we study some nonlinear integral in terms of self-similar measure on the Sierpiński gasket and use the self-similarity of distance and measure to obtain the exact value of this integral.

Identification of Chaos-Periodic Transitions, Band Merging, and Internal Crisis Using Wavelet-DFA Method

2016 ◽  
Vol 26 (04) ◽  
pp. 1650065 ◽  
Author(s):  
Mahsa Vaghefi ◽  
Ali Motie Nasrabadi ◽  
Seyed Mohammad Reza Hashemi Golpayegani ◽  
Mohammad Reza Mohammadi ◽  
Shahriar Gharibzadeh
Keyword(s):  
Detrended Fluctuation Analysis ◽  
Period Doubling ◽  
Nonstationary Time Series ◽  
The Self ◽  
Fluctuation Analysis ◽  
Scaling Analysis ◽  
Analysis Method ◽  
Self Similarity ◽  
Self Similar ◽  
Detrended Fluctuation

Detrended Fluctuation Analysis (DFA) is a scaling analysis method that can identify intrinsic self-similarity in any nonstationary time series. In contrast, Wavelet Transform (WT) method is widely used to investigate the self-similar processes, as the self-similarity properties exist within the subbands. Therefore, a combination of these two approaches, DFA and WPT, is promising for rigorous investigation of such a system. In this paper a new methodology, so-called wavelet DFA, is introduced and interpreted to evaluate this idea. This approach, further than identifying self-similarity properties, enable us to detect and capture the chaos-periodic transitions, band merging, and internal crisis in systems that become chaotic through period-doubling phenomena. Changes of wavelet DFA exponent have been compared with that of Lyapunov and DFA through Logistic, Sine, Gaussian, Cubic, and Quartic Maps. Furthermore, the potential capabilities of this new exponent have been presented.

Direct numerical simulation of axisymmetric wakes embedded in turbulence

2012 ◽  
Vol 710 ◽  
pp. 482-504 ◽  
Author(s):  
Elad Rind ◽  
Ian P. Castro
Keyword(s):  
Numerical Simulation ◽  
Direct Numerical Simulation ◽  
Decay Rate ◽  
Relative Strength ◽  
Decay Rates ◽  
The Self ◽  
Self Similarity ◽  
Self Similar ◽  
External Turbulence ◽  
Different Levels

AbstractDirect numerical simulation has been used to study the effects of external turbulence on axisymmetric wakes. In the absence of such turbulence, the time-developing axially homogeneous wake is found to have the self-similar properties expected whereas, in the absence of the wake, the turbulence fields had properties similar to Saffman-type turbulence. Merging of the two flows was undertaken for three different levels of external turbulence (relative to the wake strength) and it is shown that the presence of the external turbulence enhances the decay rate of the wake, with the new decay rates increasing with the relative strength of the initial external turbulence. The external turbulence is found to destroy any possibility of self-similarity within the developing wake, causing a significant transformation in the latter as it gradually evolves towards the former.

scholarly journals Bianchi I in scalar and scalar-tensor cosmologies

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
José Belinchón
Keyword(s):  
Perfect Fluid ◽  
Theoretical Models ◽  
Point Of View ◽  
Time Varying ◽  
Self Similarity ◽  
Bianchi I ◽  
Exact Power ◽  
Varying Constants ◽  
Time Varying Constants ◽  
Matter Fields

AbstractWe study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.

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