7,305 research outputs found
The Cauchy-Lagrangian method for numerical analysis of Euler flow
A novel semi-Lagrangian method is introduced to solve numerically the Euler
equation for ideal incompressible flow in arbitrary space dimension. It
exploits the time-analyticity of fluid particle trajectories and requires, in
principle, only limited spatial smoothness of the initial data. Efficient
generation of high-order time-Taylor coefficients is made possible by a
recurrence relation that follows from the Cauchy invariants formulation of the
Euler equation (Zheligovsky & Frisch, J. Fluid Mech. 2014, 749, 404-430).
Truncated time-Taylor series of very high order allow the use of time steps
vastly exceeding the Courant-Friedrichs-Lewy limit, without compromising the
accuracy of the solution. Tests performed on the two-dimensional Euler equation
indicate that the Cauchy-Lagrangian method is more - and occasionally much more
- efficient and less prone to instability than Eulerian Runge-Kutta methods,
and less prone to rapid growth of rounding errors than the high-order Eulerian
time-Taylor algorithm. We also develop tools of analysis adapted to the
Cauchy-Lagrangian method, such as the monitoring of the radius of convergence
of the time-Taylor series. Certain other fluid equations can be handled
similarly.Comment: 30 pp., 13 figures, 45 references. Minor revision. In press in
Journal of Scientific Computin
Melt viscosities of lattice polymers using a Kramers potential treatment
Kramers relaxation times and relaxation times and
for the end-to-end distances and for center of mass diffusion are
calculated for dense systems of athermal lattice chains. is defined
from the response of the radius of gyration to a Kramers potential which
approximately describes the effect of a stationary shear flow. It is shown that
within an intermediate range of chain lengths N the relaxation times
and exhibit the same scaling with N, suggesting that N-dependent
melt-viscosities for non-entangled chains can be obtained from the Kramers
equilibrium concept.Comment: submitted to: Journal of Chemical Physic
Lattice Boltzmann Magnetohydrodynamics
Lattice gas and lattice Boltzmann methods are recently developed numerical
schemes for simulating a variety of physical systems. In this paper a new
lattice Boltzmann model for modeling two-dimensional incompressible
magnetohydrodynamics (MHD) is presented. The current model fully utilizes the
flexibility of the lattice Boltzmann method in comparison with previous lattice
gas and lattice Boltzmann
MHD models, reducing the number of moving directions from in other
models to only. To increase computational efficiency, a simple single time
relaxation rule is used for collisions, which directly controls the transport
coefficients.
The bi-directional streaming process of the particle distribution function in
this paper is similar to the original model [ H. Chen and W. H. Matthaeus,
Phys. Rev. Lett., {\bf 58}, 1845(1987), S.Chen, H.Chen, D.Mart\'{\i}nez and
W.H.Matthaeus, Phys. Rev. Lett. {\bf 67},3776 (1991)], but has been greatly
simplified, affording simpler implementation of boundary conditions and
increasing the feasibility of extension into a workable three-dimensional
model. Analytical expressions for the transport coefficients are presented.
Also, as example cases, numerical calculation for the Hartmann flow is
performed, showing a good agreement between the theoreticalComment: 45 pages, to appear in Physics of Plasma
An exact relation between Eulerian and Lagrangian velocity increment statistics
We present a formal connection between Lagrangian and Eulerian velocity
increment distributions which is applicable to a wide range of turbulent
systems ranging from turbulence in incompressible fluids to magnetohydrodynamic
turbulence. For the case of the inverse cascade regime of two-dimensional
turbulence we numerically estimate the transition probabilities involved in
this connection. In this context we are able to directly identify the processes
leading to strongly non-Gaussian statistics for the Lagrangian velocity
increments.Comment: 5 pages, 3 figure
Lagrangian statistics in forced two-dimensional turbulence
We report on simulations of two-dimensional turbulence in the inverse energy
cascade regime. Focusing on the statistics of Lagrangian tracer particles,
scaling behavior of the probability density functions of velocity fluctuations
is investigated. The results are compared to the three-dimensional case. In
particular an analysis in terms of compensated cumulants reveals the transition
from a strong non-Gaussian behavior with large tails to Gaussianity. The
reported computation of correlation functions for the acceleration components
sheds light on the underlying dynamics of the tracer particles.Comment: 8 figures, 1 tabl
Observation of Lasing Mediated by Collective Atomic Recoil
We observe the buildup of a frequency-shifted reverse light field in a
unidirectionally pumped high- optical ring cavity serving as a dipole trap
for cold atoms. This effect is enhanced and a steady state is reached, if via
an optical molasses an additional friction force is applied to the atoms. We
observe the displacement of the atoms accelerated by momentum transfer in the
backscattering process and interpret our observations in terms of the
collective atomic recoil laser. Numerical simulations are in good agreement
with the experimental results.Comment: 4 pages, 3 figure
Photoassociation of a cold atom-molecule pair: long-range quadrupole-quadrupole interactions
The general formalism of the multipolar expansion of electrostatic
interactions is applied to the calculation the potential energy between an
excited atom (without fine structure) and a ground state diatomic molecule at
large separations. Both partners exhibit a permanent quadrupole moment, so that
their mutual quadrupole-quadrupole long-range interaction is attractive enough
to bind trimers. Numerical results are given for an excited Cs(6P) atom and a
ground state Cs2 molecule. The prospects for achieving photoassociation of a
cold atom/dimer pair is thus discussed and found promising. The formalism can
be easily generalized to the long-range interaction between molecules to
investigate the formation of cold tetramers.Comment: 5 figure
Rough-conduit flows and the existence of fully developed turbulence
It is widely believed that at high Reynolds number (Re) all turbulent flows
approach a state of "fully developed turbulence" defined by a unique,
Re-independent statistics of the velocity fluctuations. Yet direct measurements
of the velocity fluctuations have failed to yield clear-cut empirical evidence
of the existence of fully developed turbulence. Here we relate the friction
coefficient () of rough-conduit flows to the statistics of the velocity
fluctuations. In light of experimental measurements of , our results yield
unequivocal evidence of the existence of fully developed turbulence.Comment: 5 pages, 2 figure
The Monge-Ampere equation: various forms and numerical methods
We present three novel forms of the Monge-Ampere equation, which is used,
e.g., in image processing and in reconstruction of mass transportation in the
primordial Universe. The central role in this paper is played by our Fourier
integral form, for which we establish positivity and sharp bound properties of
the kernels. This is the basis for the development of a new method for solving
numerically the space-periodic Monge-Ampere problem in an odd-dimensional
space. Convergence is illustrated for a test problem of cosmological type, in
which a Gaussian distribution of matter is assumed in each localised object,
and the right-hand side of the Monge-Ampere equation is a sum of such
distributions.Comment: 24 pages, 2 tables, 5 figures, 32 references. Submitted to J.
Computational Physics. Times of runs added, multiple improvements of the
manuscript implemented
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