20,058 research outputs found
A direct primitive variable recovery scheme for hyperbolic conservative equations: the case of relativistic hydrodynamics
In this article we develop a Primitive Variable Recovery Scheme (PVRS) to
solve any system of coupled differential conservative equations. This method
obtains directly the primitive variables applying the chain rule to the time
term of the conservative equations. With this, a traditional finite volume
method for the flux is applied in order avoid violation of both, the entropy
and "Rankine-Hugoniot" jump conditions. The time evolution is then computed
using a forward finite difference scheme. This numerical technique evades the
recovery of the primitive vector by solving an algebraic system of equations as
it is often used and so, it generalises standard techniques to solve these kind
of coupled systems. The article is presented bearing in mind special
relativistic hydrodynamic numerical schemes with an added pedagogical view in
the appendix section in order to easily comprehend the PVRS. We present the
convergence of the method for standard shock-tube problems of special
relativistic hydrodynamics and a graphical visualisation of the errors using
the fluctuations of the numerical values with respect to exact analytic
solutions. The PVRS circumvents the sometimes arduous computation that arises
from standard numerical methods techniques, which obtain the desired primitive
vector solution through an algebraic polynomial of the charges.Comment: 19 pages, 6 figures, 2 tables. Accepted for publication in PLOS ON
Group implicit concurrent algorithms in nonlinear structural dynamics
During the 70's and 80's, considerable effort was devoted to developing efficient and reliable time stepping procedures for transient structural analysis. Mathematically, the equations governing this type of problems are generally stiff, i.e., they exhibit a wide spectrum in the linear range. The algorithms best suited to this type of applications are those which accurately integrate the low frequency content of the response without necessitating the resolution of the high frequency modes. This means that the algorithms must be unconditionally stable, which in turn rules out explicit integration. The most exciting possibility in the algorithms development area in recent years has been the advent of parallel computers with multiprocessing capabilities. So, this work is mainly concerned with the development of parallel algorithms in the area of structural dynamics. A primary objective is to devise unconditionally stable and accurate time stepping procedures which lend themselves to an efficient implementation in concurrent machines. Some features of the new computer architecture are summarized. A brief survey of current efforts in the area is presented. A new class of concurrent procedures, or Group Implicit algorithms is introduced and analyzed. The numerical simulation shows that GI algorithms hold considerable promise for application in coarse grain as well as medium grain parallel computers
Phonon engineering with superlattices: generalized nanomechanical potentials
Earlier implementations to simulate coherent wave propagation in
one-dimensional potentials using acoustic phonons with gigahertz-terahertz
frequencies were based on coupled nanoacoustic resonators. Here, we generalize
the concept of adiabatic tuning of periodic superlattices for the
implementation of effective one-dimensional potentials giving access to cases
that cannot be realized by previously reported phonon engineering approaches,
in particular the acoustic simulation of electrons and holes in a quantum well
or a double well potential. In addition, the resulting structures are much more
compact and hence experimentally feasible. We demonstrate that potential
landscapes can be tailored with great versatility in these multilayered
devices, apply this general method to the cases of parabolic, Morse and
double-well potentials and study the resulting stationary phonon modes. The
phonon cavities and potentials presented in this work could be probed by
all-optical techniques like pump-probe coherent phonon generation and Brillouin
scattering
Implications and Policy Options of California's Reliance on Natural Gas
Examines existing and currently anticipated infrastructure, rising gas prices, and recurring supply problems, and looks at options to alleviate the problem. Part of a series of research reports that examines energy issues facing California
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