9,766 research outputs found
Testing a theory of gravity in celestial mechanics: a new method and its first results for a scalar theory
A new method of post-Newtonian approximation (PNA) for weak gravitational
fields is presented together with its application to test an alternative,
scalar theory of gravitation. The new method consists in defining a
one-parameter family of systems, by applying a Newtonian similarity
transformation to the initial data that defines the system of interest. This
method is rigorous. Its difference with the standard PNA is emphasized. In
particular, the new method predicts that the internal structure of the bodies
does have an influence on the motion of the mass centers. The translational
equations of motion obtained with this method in the scalar theory are adjusted
in the solar system, and compared with an ephemeris based on the standard PNA
of GR.Comment: v2: links to quoted arXiv papers. LaTeX, 28 pages including 2
figures. This is a revised version of a lecture given at the 8th. Conf.
``Physical Interpretations of Relativity Theory'' (London, September 2002),
organized by the British Society for the Philosophy of Sciences. The initial
version will appear in the proceedings of that conference (M. C. Duffy, ed.
An inventory of Lattice Boltzmann models of multiphase flows
This document reports investigations of models of multiphase flows using
Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog
techniques the corresponding macroscopic equations. The singular interface
(Young-Laplace-Gauss) model is described briefly, with a discussion of its
limitations. The diffuse interface theory is discussed in more detail, and
shown to lead to the singular interface model in the proper asymptotic limit.
The Lattice Boltzmann method is presented in its simplest form appropriate for
an ideal gas. Four different Lattice Boltzmann models for non-ideal
(multi-phase) isothermal flows are then presented in detail, and the resulting
macroscopic equations derived. Partly in contradiction with the published
literature, it is found that only one of the models gives physically fully
acceptable equations. The form of the equation of state for a multiphase system
in the density interval above the coexistance line determines surface tension
and interface thickness in the diffuse interface theory. The use of this
relation for optimizing a numerical model is discussed. The extension of
Lattice Boltzmann methods to the non-isothermal situation is discussed
summarily.Comment: 59 pages, 5 figure
Lattice Fluid Dynamics from Perfect Discretizations of Continuum Flows
We use renormalization group methods to derive equations of motion for large
scale variables in fluid dynamics. The large scale variables are averages of
the underlying continuum variables over cubic volumes, and naturally live on a
lattice. The resulting lattice dynamics represents a perfect discretization of
continuum physics, i.e. grid artifacts are completely eliminated. Perfect
equations of motion are derived for static, slow flows of incompressible,
viscous fluids. For Hagen-Poiseuille flow in a channel with square cross
section the equations reduce to a perfect discretization of the Poisson
equation for the velocity field with Dirichlet boundary conditions. The perfect
large scale Poisson equation is used in a numerical simulation, and is shown to
represent the continuum flow exactly. For non-square cross sections we use a
numerical iterative procedure to derive flow equations that are approximately
perfect.Comment: 25 pages, tex., using epsfig, minor changes, refernces adde
Singular solutions of a modified two-component Camassa-Holm equation
The Camassa-Holm equation (CH) is a well known integrable equation describing
the velocity dynamics of shallow water waves. This equation exhibits
spontaneous emergence of singular solutions (peakons) from smooth initial
conditions. The CH equation has been recently extended to a two-component
integrable system (CH2), which includes both velocity and density variables in
the dynamics. Although possessing peakon solutions in the velocity, the CH2
equation does not admit singular solutions in the density profile. We modify
the CH2 system to allow dependence on average density as well as pointwise
density. The modified CH2 system (MCH2) does admit peakon solutions in velocity
and average density. We analytically identify the steepening mechanism that
allows the singular solutions to emerge from smooth spatially-confined initial
data. Numerical results for MCH2 are given and compared with the pure CH2 case.
These numerics show that the modification in MCH2 to introduce average density
has little short-time effect on the emergent dynamical properties. However, an
analytical and numerical study of pairwise peakon interactions for MCH2 shows a
new asymptotic feature. Namely, besides the expected soliton scattering
behavior seen in overtaking and head-on peakon collisions, MCH2 also allows the
phase shift of the peakon collision to diverge in certain parameter regimes.Comment: 25 pages, 11 figure
A multidimensional finite element method for CFD
A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers
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