High accuracy precession measurement with an autometric gyro

High accuracy precession measurement with autometric gyroscope

Computational coarse graining of a randomly forced 1-D Burgers equation

We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, and nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.Comment: 21 pages, 7 figure

On the decay of Burgers turbulence

This work is devoted to the decay ofrandom solutions of the unforced Burgers equation in one dimension in the limit of vanishing viscosity. The initial velocity is homogeneous and Gaussian with a spectrum proportional to $k^n$ at small wavenumbers $k$ and falling off quickly at large wavenumbers. In physical space, at sufficiently large distances, there is an ``outer region'', where the velocity correlation function preserves exactly its initial form (a power law) when $n$ is not an even integer. When $1<n<2$ the spectrum, at long times, has three scaling regions : first, a $|k|^n$ region at very small $k$\ms1 with a time-independent constant, stemming from this outer region, in which the initial conditions are essentially frozen; second, a $k^2$ region at intermediate wavenumbers, related to a self-similarly evolving ``inner region'' in physical space and, finally, the usual $k^{-2}$ region, associated to the shocks. The switching from the $|k|^n$ to the $k^2$ region occurs around a wave number $k_s(t) \propto t^{-1/[2(2-n)]}$, while the switching from $k^2$ to $k^{-2}$ occurs around $k_L(t)\propto t^{-1/2}$ (ignoring logarithmic corrections in both instances). The key element in the derivation of the results is an extension of the Kida (1979) log-corrected $1/t$ law for the energy decay when $n=2$ to the case of arbitrary integer or non-integer $n>1$. A systematic derivation is given in which both the leading term and estimates of higher order corrections can be obtained. High-resolution numerical simulations are presented which support our findings.Comment: In LaTeX with 11 PostScript figures. 56 pages. One figure contributed by Alain Noullez (Observatoire de Nice, France

Phase ordering of two-dimensional symmetric binary fluids: a droplet scaling state

The late-stage phase ordering, in $d=2$ dimensions, of symmetric fluid mixtures violates dynamical scaling. We show however that, even at 50/50 volume fractions, if an asymmetric droplet morphology is initially present then this sustains itself, throughout the viscous hydrodynamic regime, by a `coalescence-induced coalescence' mechanism. Scaling is recovered (with length scale $l \sim t$, as in $d=3$). The crossover to the inertial hydrodynamic regime is delayed even longer than in $d=3$; on entering it, full symmetry is finally restored and we find $l\sim t^{2/3}$, regardless of the initial state.Comment: 4 pages, three figures include

Interplay between the Beale-Kato-Majda theorem and the analyticity-strip method to investigate numerically the incompressible Euler singularity problem

Numerical simulations of the incompressible Euler equations are performed using the Taylor-Green vortex initial conditions and resolutions up to $4096^3$. The results are analyzed in terms of the classical analyticity strip method and Beale, Kato and Majda (BKM) theorem. A well-resolved acceleration of the time-decay of the width of the analyticity strip $\delta(t)$ is observed at the highest resolution for $3.7<t<3.85$ while preliminary 3D visualizations show the collision of vortex sheets. The BKM criterium on the power-law growth of supremum of the vorticity, applied on the same time-interval, is not inconsistent with the occurrence of a singularity around $t \simeq 4$. These new findings lead us to investigate how fast the analyticity strip width needs to decrease to zero in order to sustain a finite-time singularity consistent with the BKM theorem. A new simple bound of the supremum norm of vorticity in terms of the energy spectrum is introduced and used to combine the BKM theorem with the analyticity-strip method. It is shown that a finite-time blowup can exist only if $\delta(t)$ vanishes sufficiently fast at the singularity time. In particular, if a power law is assumed for $\delta(t)$ then its exponent must be greater than some critical value, thus providing a new test that is applied to our $4096^3$ Taylor-Green numerical simulation. Our main conclusion is that the numerical results are not inconsistent with a singularity but that higher-resolution studies are needed to extend the time-interval on which a well-resolved power-law behavior of $\delta(t)$ takes place, and check whether the new regime is genuine and not simply a crossover to a faster exponential decay

Universal decay of scalar turbulence

The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the scalar -- generally non-Gaussian -- with global self-similar evolution in time. Analogous behavior is found numerically with a more realistic flow resulting from an inverse energy cascade.Comment: 4 pages, 3 Postscript figures, submitted to PR

Fluctuations of the vortex line density in turbulent flows of quantum fluids

We present an analytical study of fluctuations of the Vortex Line Density (VLD) $$ in turbulent flows of quantum fluids. Two cases are considered. The first one is the counterflowing (Vinen) turbulence, where the vortex lines are disordered, and the evolution of quantity $\mathcal{L}(t)$ obeys the Vinen equation. The second case is the quasi-classic turbulence, where vortex lines are believed to form the so called vortex bundles, and their dynamics is described by the HVBK equations. The latter case, is of a special interest, since a number of recent experiments demonstrate the $\omega ^{-5/3}$ dependence for spectrum VLD, instead of $\omega ^{1/3}$ law, typical for spectrum of vorticity. In nonstationary situation, in particular, in the fluctuating turbulent flow there is a retardation between the instantaneous value of the normal velocity and the quantity $\mathcal{L}$. This retardation tends to decrease in the accordance with the inner dynamics, which has a relaxation character. In both cases the relaxation dynamics of VLD is related to fluctuations of the relative velocity, however if for the Vinen case the rate of temporal change for $\mathcal{L}(t)$ is directly depends on $\delta \mathbf{v}_{ns}$, for the HVBK dynamics it depends on $\nabla \times \delta \mathbf{v}_{ns}$. As a result, for the disordered case the spectrum $<\delta \mathcal{L}(\omega) \delta \mathcal{L}(-\omega)>$ coincides with the spectrum $\omega ^{-5/3}$. In the case of the bundle arrangement, the spectrum of the VLD varies (at different temperatures) from $\omega ^{1/3}$ to $\omega ^{-5/3}$ dependencies. This conclusion may serve as a basis for the experimental determination of what kind of the turbulence is implemented in different types of generation.Comment: 8 pages, 29 reference

Short to long-range charge-transfer excitations in the zincbacteriochlorin-bacteriochlorin complex: a Bethe-Salpeter study

We study using the Bethe-Salpeter formalism the excitation energies of the zincbacteriochlorinbacteriochlorin dyad, a paradigmatic photosynthetic complex. In great contrast with standard timedependent density functional theory calculations with (semi)local kernels, charge transfer excitations are correctly located above the intramolecular Q-bands transitions found to be in excellent agreement with experiment. Further, the asymptotic Coulomb behavior towards the true quasiparticle gap for charge transfer excitations at long distance is correctly reproduced, showing that the present scheme allows to study with the same accuracy intramolecular and charge transfer excitations at various spatial range and screening environment without any adjustable parameter.Comment: 5 pages, 2 figures, 1 tabl

Interstellar Dust Close to the Sun

The low density interstellar medium (ISM) close to the Sun and inside of the heliosphere provides a unique laboratory for studying interstellar dust grains. Grain characteristics in the nearby ISM are obtained from observations of interstellar gas and dust inside of the heliosphere and the interstellar gas towards nearby stars. Comparison between the gas composition and solar abundances suggests that grains are dominated by olivines and possibly some form of iron oxide. Measurements of the interstellar Ne/O ratio by the Interstellar Boundary Explorer spacecraft indicate that a high fraction of interstellar oxygen in the ISM must be depleted onto dust grains. Local interstellar abundances are consistent with grain destruction in ~150 km/s interstellar shocks, provided that the carbonaceous component is hydrogenated amorphous carbon and carbon abundances are correct. Variations in relative abundances of refractories in gas suggest variations in the history of grain destruction in nearby ISM. The large observed grains, > 1 micron, may indicate a nearby reservoir of denser ISM. Theoretical three-dimensional models of the interaction between interstellar dust grains and the solar wind predict that plumes of about 0.18 micron dust grains form around the heliosphere.Comment: 2011 AGOS Taiwan meeting; accepted for publication in Earth, Planets and Spac

Orientation dependence of the elastic instability on strained SiGe films

At low strain, SiGe films on Si substrates undergo a continuous nucleationless morphological evolution known as the Asaro-Tiller-Grinfeld instability. We demonstrate experimentally that this instability develops on Si(001) but not on Si(111) even after long annealing. Using a continuum description of this instability, we determine the origin of this difference. When modeling surface diffusion in presence of wetting, elasticity and surface energy anisotropy, we find a retardation of the instability on Si(111) due to a strong dependence of the instability onset as function of the surface stiffness. This retardation is at the origin of the inhibition of the instability on experimental time scales even after long annealing.Comment: 3 pages, 4 figure