20,104 research outputs found
Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations
We examine the effects of turbulence on elliptic instability of rotating
stratified incompressible flows, in the context of the Lagragian-averaged
Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba
model alters the instability in a variety of ways for fixed Rossby number and
Brunt-V\"ais\"al\"a frequency. First, it alters the location of the instability
domains in the parameter plane, where is the
angle of incidence the Kelvin wave makes with the axis of rotation and
is the eccentricity of the elliptic flow, as well as the size of the associated
Lyapunov exponent. Second, the model shrinks the width of one instability band
while simultaneously increasing another. Third, the model introduces bands of
unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce
two similarity variables--one is a ratio of the Brunt-V\"ais\"al\"a frequency
to the model parameter , and the other is the
ratio of the adjusted inverse Rossby number to the same model parameter. Here,
is the turbulence correlation length, and is the Kelvin wave
number. We show that by adjusting the Rossby number and Brunt-V\"ais\"al\"a
frequency so that the similarity variables remain constant for a given value of
, turbulence has little effect on elliptic instability for small
eccentricities . For moderate and large eccentricities,
however, we see drastic changes of the unstable Arnold tongues due to the
\laeba model.Comment: 23 pages (sigle spaced w/figure at the end), 9 figures--coarse
quality, accepted by Phys. Fluid
A stochastic large deformation model for computational anatomy
In the study of shapes of human organs using computational anatomy, variations are found to arise from inter-subject anatomical differences, disease-specific effects, and measurement noise. This paper introduces a stochastic model for incorporating random variations into the Large Deformation Diffeomorphic Metric Mapping (LDDMM) framework. By accounting for randomness in a particular setup which is crafted to fit the geometrical properties of LDDMM, we formulate the template estimation problem for landmarks with noise and give two methods for efficiently estimating the parameters of the noise fields from a prescribed data set. One method directly approximates the time evolution of the variance of each landmark by a finite set of differential equations, and the other is based on an Expectation-Maximisation algorithm. In the second method, the evaluation of the data likelihood is achieved without registering the landmarks, by applying bridge sampling using a stochastically perturbed version of the large deformation gradient flow algorithm. The method and the estimation algorithms are experimentally validated on synthetic examples and shape data of human corpora callosa
Two-component {CH} system: Inverse Scattering, Peakons and Geometry
An inverse scattering transform method corresponding to a Riemann-Hilbert
problem is formulated for CH2, the two-component generalization of the
Camassa-Holm (CH) equation. As an illustration of the method, the multi -
soliton solutions corresponding to the reflectionless potentials are
constructed in terms of the scattering data for CH2.Comment: 22 pages, 3 figures, draft, please send comment
Navier-Stokes-alpha model: LES equations with nonlinear dispersion
We present a framework for discussing LES equations with nonlinear
dispersion. In this framework, we discuss the properties of the nonlinearly
dispersive Navier-Stokes-alpha model of incompressible fluid turbulence ---
also called the viscous Camassa-Holm equations and the LANS equations in the
literature --- in comparison with the corresponding properties of large eddy
simulation (LES) equations obtained via the approximate-inverse approach.
In this comparison, we identify the spatially filtered NS-alpha equations
with a class of generalized LES similarity models. Applying a certain
approximate inverse to this class of LES models restores the Kelvin circulation
theorem for the defiltered velocity and shows that the NS-alpha model describes
the dynamics of the defiltered velocity for this class of generalized LES
similarity models. We also show that the subgrid scale forces in the NS-alpha
model transform covariantly under Galilean transformations and under a change
to a uniformly rotating reference frame. Finally, we discuss in the spectral
formulation how the NS-alpha model retains the local interactions among the
large scales, retains the nonlocal sweeping effects of large scales on small
scales, yet attenuates the local interactions of the small scales amongst
themselves.Comment: 15 pages, no figures, Special LES volume of ERCOFTAC bulletin, to
appear in 200
How to mesh up Ewald sums (I): A theoretical and numerical comparison of various particle mesh routines
Standard Ewald sums, which calculate e.g. the electrostatic energy or the
force in periodically closed systems of charged particles, can be efficiently
speeded up by the use of the Fast Fourier Transformation (FFT). In this article
we investigate three algorithms for the FFT-accelerated Ewald sum, which
attracted a widespread attention, namely, the so-called
particle-particle-particle-mesh (P3M), particle mesh Ewald (PME) and smooth PME
method. We present a unified view of the underlying techniques and the various
ingredients which comprise those routines. Additionally, we offer detailed
accuracy measurements, which shed some light on the influence of several tuning
parameters and also show that the existing methods -- although similar in
spirit -- exhibit remarkable differences in accuracy. We propose combinations
of the individual components, mostly relying on the P3M approach, which we
regard as most flexible.Comment: 18 pages, 8 figures included, revtex styl
Continuous and discrete Clebsch variational principles
The Clebsch method provides a unifying approach for deriving variational
principles for continuous and discrete dynamical systems where elements of a
vector space are used to control dynamics on the cotangent bundle of a Lie
group \emph{via} a velocity map. This paper proves a reduction theorem which
states that the canonical variables on the Lie group can be eliminated, if and
only if the velocity map is a Lie algebra action, thereby producing the
Euler-Poincar\'e (EP) equation for the vector space variables. In this case,
the map from the canonical variables on the Lie group to the vector space is
the standard momentum map defined using the diamond operator. We apply the
Clebsch method in examples of the rotating rigid body and the incompressible
Euler equations. Along the way, we explain how singular solutions of the EP
equation for the diffeomorphism group (EPDiff) arise as momentum maps in the
Clebsch approach. In the case of finite dimensional Lie groups, the Clebsch
variational principle is discretised to produce a variational integrator for
the dynamical system. We obtain a discrete map from which the variables on the
cotangent bundle of a Lie group may be eliminated to produce a discrete EP
equation for elements of the vector space. We give an integrator for the
rotating rigid body as an example. We also briefly discuss how to discretise
infinite-dimensional Clebsch systems, so as to produce conservative numerical
methods for fluid dynamics
How Close to Two Dimensions Does a Lennard-Jones System Need to Be to Produce a Hexatic Phase?
We report on a computer simulation study of a Lennard-Jones liquid confined
in a narrow slit pore with tunable attractive walls. In order to investigate
how freezing in this system occurs, we perform an analysis using different
order parameters. Although some of the parameters indicate that the system goes
through a hexatic phase, other parameters do not. This shows that to be certain
whether a system has a hexatic phase, one needs to study not only a large
system, but also several order parameters to check all necessary properties. We
find that the Binder cumulant is the most reliable one to prove the existence
of a hexatic phase. We observe an intermediate hexatic phase only in a
monolayer of particles confined such that the fluctuations in the positions
perpendicular to the walls are less then 0.15 particle diameters, i. e. if the
system is practically perfectly 2d
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