Scale Factor Of Universe Research Articles

Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.

The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos. As many as 13 period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a self-similar behavior that is demonstrated and used to compute a universal scaling factor, which arises also from the theory of nonlinear maps and can enable continuation of the solution into a chaotic regime. Aperiodic solutions alternate with periodic ones after chaos sets in, and we show the existence of a period six solution separated by chaotic regions.

Influence of asymmetry on multifractal properties of maps.

It is shown that the multifractal properties of a period-doubling attractor and of repellers associated with symmetric unimodal maps are affected if an asymmetry is introduced in the zth derivative of the map at its maximum of order z. For a quadratic map, a universal scaling factor associated with the period-doubling attractor is calculated as a function of an asymmetry parameter. Expansions of multifractal functions in terms of an asymmetry parameter are obtained.

Perturbative analysis of quasiperiodic route to chaos in the circle map

The perturbative analysis developed recently to evaluate the universal parameters in the period-doubling route to chaos in one hump maps, is applied to the transition from quasiperiodicity to chaos observed in the sine circle map,θn + 1 = θ + Ω – K/2π sin 2 πθnThe universal scale factor α and δ associated with this transition for K = 1 as well as the universal function g(x) are evaluated analytically. It is found that there is good convergence for α and δ to the numerical values as higher and higher orders of approximation are considered. The behaviour of g(x) is also discussed.

Relativistic stochastic Boltzmann equation and fluctuations in general relativity

Using the Klimontovich method (1982) of microscopic phase densities, a relativistic stochastic Boltzmann equation leading to a fluctuating energy-momentum tensor is derived. Via Einstein's equations the metric quantities themselves become random. They fulful relations of the type of fluctuation-dissipation theorems as is demonstrated for fluctuations of the cosmic scale factor of a flat Friedman universe.

Wave function of the Universe as a leaking system.

We propose a path-integral formulation for the wave function of the Universe which requires neither the Euclidean nor the conformal rotation. The boundary condition is taken to be that ``all possible boundaries are included.'' The resulting wave function in a simple model is shown to have the following properties: (i) the wave function tends to zero as the scale factor of the Universe tends to zero; (ii) in the semiclassical regime, it contains only the expanding component; (iii) it favors inflation.

The transverse viscomagnetic effect in N2 and N2-noble gas mixtures in the near hydrodynamic regime

The influence of a magnetic field on the shear viscosity of N2 and N2-noble gas mixtures was measured at 295 K in the moderately rarefied gas regime, where the mean free path is non-negligible. For all systems a similar pressure dependence was observed with the Knudsen number providing a universal scaling factor. For pure N2 it was found that the theory of Waldmann and Vestner describes the pressure dependence very well as long as the boundary layers are well separated (Knudsen number ⪅0.15).

Expansion of a Thin Shell around a Void in Expanding Universe. II

Motion of a compressed shell in the dust universe model is investigated in a fully relativistic manner under the approximation of infinitesimally thin shell: All voids smaller than the horizon size expand similarly, but the voids larger than the horizon do not expand appreciably until the horizon encompasses their sizes. In the open universe model, the enlargement of the void stops actually after some period. In the flat universe, the void expands forever faster than the background and its radius R behaves asymptotically as R/a ∝t0.130, where a is the scale factor of the background universe. In the closed universe, the void expands much faster and tends to the light velocity at the final stage.

Universal spectral property in higher dimensional dynamical systems

The universal scaling factor is computed for several multi-dimensional dissipative systems and it is found to agree with the theoretical value of Nauenberg and Rudnick.

Gravitational vacuum hypothesis and cosmology with variable particle number

We discuss a heurisitic model of gravitational vacuum as a set of virtual, radiating planckeons, particles with Planck size (L) and mass (ħ/cL). Combined with Dirac's large number hypothesis, this gives the minimum universe scale factor valuea min∼10−13 cm, the strong interaction length (a = L just whena=a min ). Taking this state as an initial one using standard quantum techniques, we consider particle creation by planckeons. Under some reasonable assumptions we obtain the present number of particles with nucleon mass close to observations,N ∼ 1080. A criterion for gravitational stability of particles is formulated and some applications of the corresponding mass formula are considered. In particular, Fermi's weak interaction constant is expressed in terms ofa andL and a finite value for the neutrino mass is obtained.

Pressure dependence of elastic constants and optical phonon frequencies in Se and Te. A study of the homological relationship between the vibrational modes in these materials

AbstractThe hydrostatic pressure coefficients for the elastic constants of Se and Te are shown to be large and positive in contrast to the negative mode Grüneisen parameters reported earlier for the optical vibrations. These results can be understood on the basis of the idea that the hydrostatic pressure promotes transfer of electrons from intrachain bonding orbitals to interchain bonding states. This strengthens the interchain “elastic” force constants while simultaneously weakening the intrachain “optic” force constants. The great similarity in the Se and Te lattices suggests that their vibrational spectra can be related by homology. Of the three lattice parameters describing each crystal, the intrachain bond angle is nearly identical and relatively pressure insensitive in the two lattices. Therefore, by a two‐step transformation in which the c/a‐ratio is first made equal by applying hydrostatic pressure, and secondly by properly scaling the mass and the unit cell, the two lattices can be made structurally identical. With this transformation and the available pressure data all zone centre phonons studied in the two materials could be related by a universal scaling factor for the “mode” force constants. Rough estimates for the higher‐order pressure coefficients can also be made.

Position determination from hyperbolic navigation systems

A method based on Sodano's inverse solution of geodesics for determining geodetic positions from hyperbolic navigation time differences is derived to an accuracy of 0.005 sec of arc. The inverse problem is also solved. Hyperbolic coordinates can be transformed directly to universal transverse Mercator coordinates by proper application of the universal transverse Mercator scale factor.

The fine-structure constant α=e 2/hc as a universal scaling factor

The fine-structure constant α=e 2/hc as a universal scaling factor

A non-linear theory of strong interactions

A non-linear theory of mesons, nucleons and hyperons is proposed. The three independent fields of the usual symmetrical pseudo-scalar pion field are replaced by the three directions of a four-component field vector of constant length, conceived in an Euclidean four-dimensional isotopic spin space. This length provides the universal scaling factor, all other constants being dimensionless; the mass of the meson field is generated by a ϕ 4 term; this destroys the continuous rotation group in the iso-space, leaving a ‘cubic’ symmetry group. Classification of states by this group introduces quantum numbers corresponding to isotopic spin and to ‘strangeness’; one consequence is that, at least in elementary interactions, charge is only conserved modulo 4. Furthermore, particle states have not a well-defined parity, but parity is effectively conserved for meson-nucleon interactions. A simplified model, using only two dimensions of space and iso-space, is considered further; the non-linear meson field has solutions with particle character, and an indication is given of the way in which the particle field variables might be introduced as collective co-ordinates describing the dynamics of these particular solutions of the meson field equations, suggesting a unified theory based on the meson field alone.