4,923 research outputs found
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 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 dependence for spectrum VLD,
instead of 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 . 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
is directly depends on , for the HVBK dynamics it
depends on . As a result, for the
disordered case the spectrum coincides with the spectrum . In the
case of the bundle arrangement, the spectrum of the VLD varies (at different
temperatures) from to 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-YMnO
Inelastic neutron scattering has been used to study the magneto-elastic
excitations in the multiferroic manganite hexagonal YMnO. An avoided
crossing is found between magnon and phonon modes close to the Brillouin zone
boundary in the -plane. Neutron polarization analysis reveals that this
mode has mixed magnon-phonon character. An external magnetic field along the
-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 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 spins. This enables us to compute
independent estimates of and 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 -family
equation admits, locally in time, a unique analytic solution. Moreover, if the
initial data is real analytic and it belongs to with , and the
momentum density does not change sign, we prove that the
solution stays analytic globally in time, for . Using pseudospectral
numerical methods, we study, also, the singularity formation for the -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
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