11,107 research outputs found
Full sphere hydrodynamic and dynamo benchmarks
Convection in planetary cores can generate fluid flow and magnetic fields, and a number of sophisticated codes exist to simulate the dynamic behaviour of such systems. We report on the first community activity to compare numerical results of computer codes designed to calculate fluid flow within a whole sphere. The flows are incompressible and rapidly rotating and the forcing of the flow is either due to thermal convection or due to moving boundaries. All problems defined have solutions that allow easy comparison, since they are either steady, slowly drifting or perfectly periodic. The first two benchmarks are defined based on uniform internal heating within the sphere under the Boussinesq approximation with boundary conditions that are uniform in temperature and stress-free for the flow. Benchmark 1 is purely hydrodynamic, and has a drifting solution. Benchmark 2 is a magnetohydrodynamic benchmark that can generate oscillatory, purely periodic, flows and magnetic fields. In contrast, Benchmark 3 is a hydrodynamic rotating bubble benchmark using no slip boundary conditions that has a stationary solution. Results from a variety of types of code are reported, including codes that are fully spectral (based on spherical harmonic expansions in angular coordinates and polynomial expansions in radius), mixed spectral and finite difference, finite volume, finite element and also a mixed Fourier–finite element code. There is good agreement between codes. It is found that in Benchmarks 1 and 2, the approximation of a whole sphere problem by a domain that is a spherical shell (a sphere possessing an inner core) does not represent an adequate approximation to the system, since the results differ from whole sphere results
Nonlinear Modes of Liquid Drops as Solitary Waves
The nolinear hydrodynamic equations of the surface of a liquid drop are shown
to be directly connected to Korteweg de Vries (KdV, MKdV) systems, giving
traveling solutions that are cnoidal waves. They generate multiscale patterns
ranging from small harmonic oscillations (linearized model), to nonlinear
oscillations, up through solitary waves. These non-axis-symmetric localized
shapes are also described by a KdV Hamiltonian system. Recently such ``rotons''
were observed experimentally when the shape oscillations of a droplet became
nonlinear. The results apply to drop-like systems from cluster formation to
stellar models, including hyperdeformed nuclei and fission.Comment: 11 pages RevTex, 1 figure p
Deep inelastic scattering off scalar mesons in the 1/N expansion from the D3D7-brane system
Deep inelastic scattering (DIS) of charged leptons off scalar mesons in the 1/N expansion is studied by using the gauge/gravity duality. We focus on the D3D7-brane system and investigate the corresponding structure functions by considering both the high energy limit and the 1/N expansion. These limits do not commute. From the D7-brane DBI action we derive a Lagrangian at sub-leading order in the D7-brane fluctuations and obtain a number of interactions some of which become relevant for two-hadron final-state DIS. By considering first the high energy limit followed by the large N one, our results fit lattice QCD data within 1.27% for the first three moments of F 2 for the lightest pseudoscalar meson.Fil: Jorrin, David Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Kovensky, Nicolas. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Schvellinger, Martín Alejandro. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin
On anisotropy function in crystal growth simulations using Lattice Boltzmann equation
In this paper, we present the ability of the Lattice Boltzmann (LB) equation,
usually applied to simulate fluid flows, to simulate various shapes of
crystals. Crystal growth is modeled with a phase-field model for a pure
substance, numerically solved with a LB method in 2D and 3D. This study focuses
on the anisotropy function that is responsible for the anisotropic surface
tension between the solid phase and the liquid phase. The anisotropy function
involves the unit normal vectors of the interface, defined by gradients of
phase-field. Those gradients have to be consistent with the underlying lattice
of the LB method in order to avoid unwanted effects of numerical anisotropy.
Isotropy of the solution is obtained when the directional derivatives method,
specific for each lattice, is applied for computing the gradient terms. With
the central finite differences method, the phase-field does not match with its
rotation and the solution is not any more isotropic. Next, the method is
applied to simulate simultaneous growth of several crystals, each of them being
defined by its own anisotropy function. Finally, various shapes of 3D crystals
are simulated with standard and non standard anisotropy functions which favor
growth in -, - and -directions
Matrix Bases for Star Products: a Review
We review the matrix bases for a family of noncommutative products
based on a Weyl map. These products include the Moyal product, as well as the
Wick-Voros products and other translation invariant ones. We also review the
derivation of Lie algebra type star products, with adapted matrix bases. We
discuss the uses of these matrix bases for field theory, fuzzy spaces and
emergent gravity
- …