scholarly journals Self-Similar Cosmological Models with a Cosmical Constant

1988 ◽  
Vol 130 ◽  
pp. 516-516
Author(s):  
Robin M. Green ◽  
David Alexander
Keyword(s):  
Analytic Solutions ◽  
Cosmological Models ◽  
Spherically Symmetric ◽  
Self Similarity ◽  
General Behaviour ◽  
Similarity Variable ◽  
Fundamental Scale ◽  
Self Similar

The presence of the cosmical constant introduces a fundamental scale and prevents there being any simple self-symmetry. Henriksen, Emslie and Wesson (HEW), who studied spherically-symmetric models with a positive cosmical constant, have, however, demonstrated the possible existence of a self-similarity of the second kind and identified the similarity variable. They obtained interesting analytic solutions which are homogeneous in density, but not in pressure. We have extended this work and investigated the general behaviour of these cosmological models which possess a self-similarity of the second kind and in which the requirement of homogeneity is relaxed.

ANISOTROPIC SELF-SIMILAR COSMOLOGICAL MODEL WITH DARK ENERGY

2006 ◽  
Vol 15 (07) ◽  
pp. 991-999 ◽  
Author(s):  
P. R. PEREIRA ◽  
M. F. A. DA SILVA ◽  
R. CHAN
Keyword(s):  
Dark Energy ◽  
Energy Conditions ◽  
Anisotropic Fluid ◽  
Accelerating Universe ◽  
Spherically Symmetric ◽  
Einstein Field Equations ◽  
Field Equations ◽  
Self Similarity ◽  
Normal Matter ◽  
Self Similar

We study space–times having spherically symmetric anisotropic fluid with self-similarity of zeroth kind. We find a class of solutions to the Einstein field equations by assuming a shear-free metric and that the fluid moves along time-like geodesics. The energy conditions, and geometrical and physical properties of the solutions are studied and we find that it can be considered as representing an accelerating universe. At the beginning all the energy conditions were fulfilled but beyond a certain time (a maximum geometrical radius) none of them is satisfied, characterizing a transition from normal matter (dark matter, baryon matter and radiation) to dark energy.

scholarly journals SELF-SIMILAR COSMOLOGIES IN 5D: SPATIALLY FLAT ANISOTROPIC MODELS

2009 ◽  
Vol 18 (05) ◽  
pp. 743-762 ◽  
Author(s):  
J. PONCE DE LEON
Keyword(s):  
Extra Dimension ◽  
Riemann Tensor ◽  
Cosmological Models ◽  
Isotropic Case ◽  
Field Equations ◽  
Large Extra Dimension ◽  
Similarity Variable ◽  
Anisotropic Models ◽  
Spatial Coordinates ◽  
Self Similar

In the context of theories of the Kaluza–Klein type, with a large extra dimension, we study self-similar cosmological models in 5D that are homogeneous, anisotropic and spatially flat. The "ladder" to go between the physics in 5D and in 4D is provided by Campbell–Maagard's embedding theorems. We show that the 5D field equations RAB = 0 determine the form of the similarity variable. There are three different possibilities: homothetic, conformal and "wavelike" solutions in 5D. We derive the most general homothetic and conformal solutions to the 5D field equations. They require the extra dimension to be spacelike, and are given in terms of one arbitrary function of the similarity variable and three parameters. The Riemann tensor in 5D is not zero, except in the isotropic limit, which corresponds to the case where the parameters are equal to each other. The solutions can be used as 5D embeddings for a great variety of 4D homogeneous cosmological models, with and without matter, including the Kasner universe. Since the extra dimension is spacelike, the 5D solutions are invariant under the exchange of spatial coordinates. Therefore they also embed a family of spatially inhomogeneous models in 4D. We show that these models can be interpreted as vacuum solutions in braneworld theory. Our work (I) generalizes the 5D embeddings used for FLRW models; (II) shows that anisotropic cosmologies are, in general, curved in 5D, in contrast with FLRW models, which can always be embedded in a 5D Riemann-flat (Minkowski) manifold; and (III) reveals that anisotropic cosmologies can be curved and devoid of matter, both in 5D and in 4D, even when the metric in 5D explicitly depends on the extra coordinate, which is quite different from the isotropic case.

scholarly journals PERTURBED SELF-SIMILAR MASSLESS SCALAR FIELD IN SPHERICALLY SYMMETRIC SPACE–TIMES

2007 ◽  
Vol 22 (25) ◽  
pp. 4695-4708
Author(s):  
M. SHARIF
Keyword(s):  
Scalar Field ◽  
Symmetric Space ◽  
Massless Scalar ◽  
Massless Scalar Field ◽  
Spherically Symmetric ◽  
Field Equations ◽  
Self Similarity ◽  
Linear Perturbations ◽  
Self Similar ◽  
Scalar Field Equations

In this paper, we investigate the linear perturbations of the spherically symmetric space–times with kinematic self-similarity of the second kind. The massless scalar field equations are solved which yield the background and an exact solutions for the perturbed equations. We discuss the boundary conditions of the resulting perturbed solutions. The possible perturbation modes turn out to be stable as well as unstable. The analysis leads to the conclusion that there does not exist any critical solution.

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.

scholarly journals Depressurization-Induced Nucleation in the “Polylactide-Carbon Dioxide” System: Self-Similarity of the Bubble Embryos Expansion

Polymers ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1115
Author(s):  
Dmitry Zimnyakov ◽  
Marina Alonova ◽  
Ekaterina Ushakova
Keyword(s):  
Initial Rate ◽  
Initial Pressure ◽  
External Pressure ◽  
Self Similarity ◽  
Embryo Formation ◽  
Linear Behavior ◽  
Joint Influence ◽  
External Pressures ◽  
Adiabatic Cooling ◽  
Self Similar

Self-similar expansion of bubble embryos in a plasticized polymer under quasi-isothermal depressurization is examined using the experimental data on expansion rates of embryos in the CO2-plasticized d,l-polylactide and modeling the results. The CO2 initial pressure varied from 5 to 14 MPa, and the depressurization rate was 5 × 10−3 MPa/s. The constant temperature in experiments was in a range from 310 to 338 K. The initial rate of embryos expansion varied from ≈0.1 to ≈10 µm/s, with a decrease in the current external pressure. While modeling, a non-linear behavior of CO2 isotherms near the critical point was taken into account. The modeled data agree satisfactorily with the experimental results. The effect of a remarkable increase in the expansion rate at a decreasing external pressure is interpreted in terms of competing effects, including a decrease in the internal pressure, an increase in the polymer viscosity, and an increase in the embryo radius at the time of embryo formation. The vanishing probability of finding the steadily expanding embryos for external pressures around the CO2 critical pressure is interpreted in terms of a joint influence of the quasi-adiabatic cooling and high compressibility of CO2 in the embryos.

scholarly journals Self-similar resistive circuits as fractal-like structures

2017 ◽  
Vol 40 (1) ◽  
Author(s):  
Claudio Xavier Mendes dos Santos ◽  
Carlos Molina Mendes ◽  
Marcelo Ventura Freire
Keyword(s):  
Scale Invariance ◽  
Self Similarity ◽  
General Properties ◽  
Modern Physics ◽  
Resistive Networks ◽  
Self Similar ◽  
And Mathematics ◽  
Definition Of ◽  
The Individual

Fractals play a central role in several areas of modern physics and mathematics. In the present work we explore resistive circuits where the individual resistors are arranged in fractal-like patterns. These circuits have some of the characteristics typically found in geometric fractals, namely self-similarity and scale invariance. Considering resistive circuits as graphs, we propose a definition of self-similar circuits which mimics a self-similar fractal. General properties of the resistive circuits generated by this approach are investigated, and interesting examples are commented in detail. Specifically, we consider self-similar resistive series, tree-like resistive networks and Sierpinski’s configurations with resistors.

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.

Sign in / Sign up

Export Citation Format

Share Document