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Fluctuation Field (fluctuation + field)

Distribution by Scientific Domains

Physics and Astronomy	75%

Selected Abstracts

Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002
Christian Miehe
Abstract The paper investigates computational procedures for the treatment of a homogenized macro-continuum with locally attached micro-structures of inelastic constituents undergoing small strains. The point of departure is a general internal variable formulation that determines the inelastic response of the constituents of a typical micro-structure as a generalized standard medium in terms of an energy storage and a dissipation function. Consistent with this type of inelasticity we develop a new incremental variational formulation of the local constitutive response where a quasi-hyperelastic micro-stress potential is obtained from a local minimization problem with respect to the internal variables. It is shown that this local minimization problem determines the internal state of the material for finite increments of time. We specify the local variational formulation for a setting of smooth single-surface inelasticity and discuss its numerical solution based on a time discretization of the internal variables. The existence of the quasi-hyperelastic stress potential allows the extension of homogenization approaches of elasticity to the incremental setting of inelasticity. Focusing on macro-strain-driven micro-structures, we develop a new incremental variational formulation of the global homogenization problem where a quasi-hyperelastic macro-stress potential is obtained from a global minimization problem with respect to the fine-scale displacement fluctuation field. It is shown that this global minimization problem determines the state of the micro-structure for finite increments of time. We consider three different settings of the global variational problem for prescribed linear displacements, periodic fluctuations and constant stresses on the boundary of the micro-structure and discuss their numerical solutions based on a spatial discretization of the fine-scale displacement fluctuation field. The performance of the proposed methods is demonstrated for the model problem of von Mises-type elasto-visco-plasticity of the constituents and applied to a comparative study of micro-to-macro transitions of inelastic composites. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Perturbation theory and excursion set estimates of the probability distribution function of dark matter, and a method for reconstructing the initial distribution function

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 1 2008
Tsz Yan Lam
ABSTRACT Non-linear evolution is sometimes modelled by assuming there is a deterministic mapping from initial to final values of the locally smoothed overdensity. However, if an underdense region is embedded in a denser one, then it is possible that its evolution is determined by its surroundings, so the mapping between initial and final overdensities is not as ,local' as one might have assumed. If this source of non-locality is not accounted for, then it appears as stochasticity in the mapping between initial and final densities. Perturbation theory methods ignore this ,cloud-in-cloud' effect, whereas methods based on the excursion set approach do account for it; as a result, one may expect the two approaches to provide different estimates of the shape of the non-linear counts in cells distribution. We show that, on scales where the rms fluctuation is small, this source of non-locality has only a small effect, so the predictions of the two approaches differ only on the small scales on which perturbation theory is no longer expected to be valid anyway. We illustrate our results by comparing the predictions of these approaches when the initial,final mapping is given by the spherical collapse model. Both are in reasonably good agreement with measurements in numerical simulations on scales where the rms fluctuation is of the order of unity or smaller. If the deterministic mapping from initial conditions to final density depends on quantities other than the initial density, then this will also manifest as stochasticity in the mapping from initial density to final. For example, the Zeldovich approximation and the ellipsoidal collapse model both assume that the initial shear field plays an important role in determining the evolution. We compare the predictions of these approximations with simulations, both before and after accounting for the ,cloud-in-cloud' effect. Our analysis accounts approximately for the fact that the shape of a cell at the present time is different from its initial shape; ignoring this makes a noticeable difference on scales where the rms fluctuation in a cell is of the order of unity or larger. On scales where the rms fluctuation is 2 or less, methods based on the spherical model are sufficiently accurate to permit a rather accurate reconstruction of the shape of the initial distribution from the non-linear one. This can be used as the basis for a method for constraining the statistical properties of the initial fluctuation field from the present-day field, under the hypothesis that the evolution was purely gravitational. We illustrate by showing how the highly non-Gaussian non-linear density field in a numerical simulation can be transformed to provide an accurate estimate of the initial Gaussian distribution from which it evolved. [source]

Anisotropic distribution of quantum-vacuum momentum density in a moving electromagnetic medium

ANNALEN DER PHYSIK, Issue 7 2010
J.Q. Shen
Abstract An isotropic electromagnetic medium becomes gyrotropically anisotropic when it moves, and an anisotropic electromagnetic environment can then be created in this motion-induced anisotropic medium. One of the most remarkable features is that the quantum vacuum in the anisotropic electromagnetic environment exhibits a nonzero electromagnetic momentum density, since the universal symmetry of the vacuum fluctuation field is broken, and the anisotropic quantum vacuum mode structure is produced because of the symmetry breaking. This would give rise to a noncompensation effect among the four vacuum eigenmodes (i.e., the forward and backward propagating modes as well as their respective mutually perpendicular polarized components), and leads to an anisotropic correction to the vacuum momentum in the moving medium. The physical significance and the potential applications of the anisotropic quantum vacuum are discussed. This quantum-vacuum effect may be used to develop sensitive sensor techniques and to design new quantum optical and photonic devices. [source]

Cosmic momentum field and mass fluctuation power spectrum

MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY, Issue 2 2000
Changbom Park
We introduce the cosmic momentum field as a new measure of the large-scale peculiar velocity and matter fluctuation fields. The momentum field is defined as the peculiar velocity field traced and weighted by galaxies, and is equal to the velocity field in the linear regime. We show that the radial component of the momentum field can be considered as a scalar field with the power spectrum which is practically one-third of that of the total momentum field. We present a formula for the power spectrum directly calculable from the observed radial peculiar velocity data. The momentum power spectrum is measured for the MAT sample in the Mark III catalogue of peculiar velocities of galaxies. Using the momentum power spectrum we find the amplitude of the matter power spectrum is and at the wavenumbers 0.049 and 0.074 h Mpc,1, respectively, where , is the density parameter. The 68 per cent confidence limits include the cosmic variance. The measured momentum and density power spectra together indicate that the parameter or where bO is the bias factor for optical galaxies. [source]