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

Averaged Template Matching Equations

By exploiting an analogy with averaging procedures in fluid dynamics, we present a set of averaged template matching equations. These equations are analogs of the exact template matching equations that retain all the geometric properties associated with the diffeomorphismgrou p, and which are expected to average out small scale features and so should, as in hydrodynamics, be more computationally efficient for resolving the larger scale features. Froma geometric point of view, the new equations may be viewed as coming from a change in norm that is used to measure the distance between images. The results in this paper represent first steps in a longer termpro gram: what is here is only for binary images and an algorithm for numerical computation is not yet operational. Some suggestions for further steps to develop the results given in this paper are suggested

Magnetic ground state and magnon-phonon interaction in multiferroic h-YMnO3_3

Inelastic neutron scattering has been used to study the magneto-elastic excitations in the multiferroic manganite hexagonal YMnO$_3$. An avoided crossing is found between magnon and phonon modes close to the Brillouin zone boundary in the $(a,b)$-plane. Neutron polarization analysis reveals that this mode has mixed magnon-phonon character. An external magnetic field along the $c$-axis is observed to cause a linear field-induced splitting of one of the spin wave branches. A theoretical description is performed, using a Heisenberg model of localized spins, acoustic phonon modes and a magneto-elastic coupling via the single-ion magnetostriction. The model quantitatively reproduces the dispersion and intensities of all modes in the full Brillouin zone, describes the observed magnon-phonon hybridized modes, and quantifies the magneto-elastic coupling. The combined information, including the field-induced magnon splitting, allows us to exclude several of the earlier proposed models and point to the correct magnetic ground state symmetry, and provides an effective dynamic model relevant for the multiferroic hexagonal manganites.Comment: 12 pages, 10 figure

Critical Exponents of the Classical 3D Heisenberg Model: A Single-Cluster Monte Carlo Study

We have simulated the three-dimensional Heisenberg model on simple cubic lattices, using the single-cluster Monte Carlo update algorithm. The expected pronounced reduction of critical slowing down at the phase transition is verified. This allows simulations on significantly larger lattices than in previous studies and consequently a better control over systematic errors. In one set of simulations we employ the usual finite-size scaling methods to compute the critical exponents $\nu,\alpha,\beta,\gamma, \eta$ from a few measurements in the vicinity of the critical point, making extensive use of histogram reweighting and optimization techniques. In another set of simulations we report measurements of improved estimators for the spatial correlation length and the susceptibility in the high-temperature phase, obtained on lattices with up to $100^3$ spins. This enables us to compute independent estimates of $\nu$ and $\gamma$ from power-law fits of their critical divergencies.Comment: 33 pages, 12 figures (not included, available on request). Preprint FUB-HEP 19/92, HLRZ 77/92, September 199

Lombardi Drawings of Graphs

We introduce the notion of Lombardi graph drawings, named after the American abstract artist Mark Lombardi. In these drawings, edges are represented as circular arcs rather than as line segments or polylines, and the vertices have perfect angular resolution: the edges are equally spaced around each vertex. We describe algorithms for finding Lombardi drawings of regular graphs, graphs of bounded degeneracy, and certain families of planar graphs.Comment: Expanded version of paper appearing in the 18th International Symposium on Graph Drawing (GD 2010). 13 pages, 7 figure

Highly turbulent solutions of LANS-alpha and their LES potential

We compute solutions of the Lagrangian-Averaged Navier-Stokes alpha-model (LANS) for significantly higher Reynolds numbers (up to Re 8300) than have previously been accomplished. This allows sufficient separation of scales to observe a Navier-Stokes (NS) inertial range followed by a 2nd LANS inertial range. The analysis of the third-order structure function scaling supports the predicted l^3 scaling; it corresponds to a k^(-1) scaling of the energy spectrum. The energy spectrum itself shows a different scaling which goes as k^1. This latter spectrum is consistent with the absence of stretching in the sub-filter scales due to the Taylor frozen-in hypothesis employed as a closure in the derivation of LANS. These two scalings are conjectured to coexist in different spatial portions of the flow. The l^3 (E(k) k^(-1)) scaling is subdominant to k^1 in the energy spectrum, but the l^3 scaling is responsible for the direct energy cascade, as no cascade can result from motions with no internal degrees of freedom. We verify the prediction for the size of the LANS attractor resulting from this scaling. From this, we give a methodology either for arriving at grid-independent solutions for LANS, or for obtaining a formulation of a LES optimal in the context of the alpha models. The fully converged grid-independent LANS may not be the best approximation to a direct numerical simulation of the NS equations since the minimum error is a balance between truncation errors and the approximation error due to using LANS instead of the primitive equations. Furthermore, the small-scale behavior of LANS contributes to a reduction of flux at constant energy, leading to a shallower energy spectrum for large alpha. These small-scale features, do not preclude LANS to reproduce correctly the intermittency properties of high Re flow.Comment: 37 pages, 17 figure

Inertial Range Scaling, Karman-Howarth Theorem and Intermittency for Forced and Decaying Lagrangian Averaged MHD in 2D

We present an extension of the Karman-Howarth theorem to the Lagrangian averaged magnetohydrodynamic (LAMHD-alpha) equations. The scaling laws resulting as a corollary of this theorem are studied in numerical simulations, as well as the scaling of the longitudinal structure function exponents indicative of intermittency. Numerical simulations for a magnetic Prandtl number equal to unity are presented both for freely decaying and for forced two dimensional MHD turbulence, solving directly the MHD equations, and employing the LAMHD-alpha equations at 1/2 and 1/4 resolution. Linear scaling of the third-order structure function with length is observed. The LAMHD-alpha equations also capture the anomalous scaling of the longitudinal structure function exponents up to order 8.Comment: 34 pages, 7 figures author institution addresses added magnetic Prandtl number stated clearl

Analytic solutions and Singularity formation for the Peakon b--Family equations

Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum

Cluster algorithms

Cluster algorithms for classical and quantum spin systems are discussed. In particular, the cluster algorithm is applied to classical O(N) lattice actions containing interactions of more than two spins. The performance of the multi-cluster and single--cluster methods, and of the standard and improved estimators are compared. (Lecture given at the summer school on `Advances in Computer Simulations', Budapest, July 1996.)Comment: 17 pages, Late

Phytoplankton competition along a gradient of dilution rates

Natural phytoplankton from Lake Constance was used for chemostat competition experiments performed at a variety of dilution rates. In the first series at high Si:P ratios and under uniform phosphorus limitation for all species, Synedra acus outcompeted all other species at all dilution rates up to 1.6 d-1, only at the highest dilution rate (2.0 d-1) Achnanthes minutissima was successful. In the second series in the absence of any Si a green algal replacement series was found, with Mougeotia thylespora dominant at the lowest dilution rates, Scenedesmus acutus at the intermediate ones, and Chlorella minutissima at the highest ones. The outcome of interspecific competition was not in contradiction with the Monod kinetics of P-limited growth of the five species, but no satisfactorily precise prediction of competitive performance can be derived from the Monod kinetics because of insufficient precision in the estimate of k s