Search results for "Exponent"

Cosmological data analysis of f(R) gravity models

2009

A class of well-behaved modified gravity models with long enough matter domination epoch and a late-time accelerated expansion is confronted with SNIa, CMB, SDSS, BAO and H(z) galaxy ages data, as well as current measurements of the linear growth of structure. We show that the combination of geometrical probes and growth data exploited here allows to rule out f(R) gravity models, in particular, the logarithmic of curvature model. We also apply solar system tests to the models in agreement with the cosmological data. We find that the exponential of the inverse of the curvature model satisfies all the observational tests considered and we derive the allowed range of parameters. Current data s…

Experimental investigation of resonant activation

2000

We experimentally investigate the escape from a metastable state over a fluctuating barrier of a physical system. The system is switching between two states under electronic control of a dichotomous noise. We measure the escape time and its probability density function as a function of the correlation rate of the dichotomous noise in a frequency interval spanning more than 4 frequency decades. We observe resonant activation, namely a minimum of the average escape time as a function of the correlation rate. We detect two regimes in the study of the shape of the escape time probability distribution: (i) a regime of exponential and (ii) a regime of non-exponential probability distribution.

Late time approach to Hawking radiation: Terms beyond leading order

2019

Black hole evaporation is studied using wave packets for the modes. These allow for approximate frequency and time resolution. The leading order late time behavior gives the well known Hawking radiation that is independent of how the black hole formed. The focus here is on the higher order terms and the rate at which they damp at late times. Some of these terms carry information about how the black hole formed. A general argument is given which shows that the damping is significantly slower (power law) than what might be naively expected from a stationary phase approximation (exponential). This result is verified by numerical calculations in the cases of 2D and 4D black holes that form from…

Excitation spectra of solitary waves in scalar field models with polynomial self-interaction

2016

We study excitations of solitary waves -- the kinks -- in scalar models with degree eight polynomial self-interaction in (1+1) dimensions. We perform numerical studies of scattering of two kinks with an exponential asymptotic off each other and analyse the occurring resonance phenomena. We connect these phenomena to the energy exchange between the translational and the vibrational modes of the colliding kinks. We also point out that the interaction of two kinks with power-law asymptotic can lead to a long-range interaction between the two kinks.

Semi-Lorentz invariance, unitarity, and critical exponents of symplectic fermion models

2007

We study a model of N-component complex fermions with a kinetic term that is second order in derivatives. This symplectic fermion model has an Sp(2N) symmetry, which for any N contains an SO(3) subgroup that can be identified with rotational spin of spin-1/2 particles. Since the spin-1/2 representation is not promoted to a representation of the Lorentz group, the model is not fully Lorentz invariant, although it has a relativistic dispersion relation. The hamiltonian is pseudo-hermitian, H^\dagger = C H C, which implies it has a unitary time evolution. Renormalization-group analysis shows the model has a low-energy fixed point that is a fermionic version of the Wilson-Fisher fixed points. T…

Comparing estimators of the galaxy correlation function

1999

We present a systematic comparison of some usual estimators of the 2--point correlation function, some of them currently used in Cosmology, others extensively employed in the field of the statistical analysis of point processes. At small scales, it is known that the correlation function follows reasonably well a power--law expression $\xi(r) \propto r^{-\gamma}$. The accurate determination of the exponent $\gamma$ (the order of the pole) depends on the estimator used for $\xi(r)$; on the other hand, its behavior at large scale gives information on a possible trend to homogeneity. We study the concept, the possible bias, the dependence on random samples and the errors of each estimator. Erro…

Monte Carlo renormalization group methods

2014

Universality in Fragmentation

1999

Fragmentation of a two-dimensional brittle solid by impact and ``explosion,'' and a fluid by ``explosion'' are all shown to become critical. The critical points appear at a nonzero impact velocity, and at infinite explosion duration, respectively. Within the critical regimes, the fragment-size distributions satisfy a scaling form qualitatively similar to that of the cluster-size distribution of percolation, but they belong to another universality class. Energy balance arguments give a correlation length exponent that is exactly one-half of its percolation value. A single crack dominates fragmentation in the slow-fracture limit, as expected.

A general nonexistence result for inhomogeneous semilinear wave equations with double damping and potential terms

2021

Abstract We investigate the large-time behavior of solutions for a class of inhomogeneous semilinear wave equations involving double damping and potential terms. Namely, we first establish a general criterium for the absence of global weak solutions. Next, some special cases of potential and inhomogeneous terms are studied. In particular, when the inhomogeneous term depends only on the variable space, the Fujita critical exponent and the second critical exponent in the sense of Lee and Ni are derived.

Fluctuations in mesoscopic systems

1992

Abstract Electronic wavefunctions in weakly disordered systems have been studied within the Anderson model of localization. The eigenstates calculated by means of the Lanczos diagonalization algorithm display characteristic spatial fluctuations that can be described by a multifractal analysis. For increasing disorder or energy the observed curdling of the wavefunction reflects the stronger localization, but no exponential decay can be observed. This is reflected in the set of generalized fractal dimensions and the singularity spectrum of the fractal measure.