6,756 research outputs found
Symbolic-numeric interface: A review
A survey of the use of a combination of symbolic and numerical calculations is presented. Symbolic calculations primarily refer to the computer processing of procedures from classical algebra, analysis, and calculus. Numerical calculations refer to both numerical mathematics research and scientific computation. This survey is intended to point out a large number of problem areas where a cooperation of symbolic and numerical methods is likely to bear many fruits. These areas include such classical operations as differentiation and integration, such diverse activities as function approximations and qualitative analysis, and such contemporary topics as finite element calculations and computation complexity. It is contended that other less obvious topics such as the fast Fourier transform, linear algebra, nonlinear analysis and error analysis would also benefit from a synergistic approach
Paranoia.Ada: A diagnostic program to evaluate Ada floating-point arithmetic
Many essential software functions in the mission critical computer resource application domain depend on floating point arithmetic. Numerically intensive functions associated with the Space Station project, such as emphemeris generation or the implementation of Kalman filters, are likely to employ the floating point facilities of Ada. Paranoia.Ada appears to be a valuabe program to insure that Ada environments and their underlying hardware exhibit the precision and correctness required to satisfy mission computational requirements. As a diagnostic tool, Paranoia.Ada reveals many essential characteristics of an Ada floating point implementation. Equipped with such knowledge, programmers need not tremble before the complex task of floating point computation
A Study of Speed of the Boundary Element Method as applied to the Realtime Computational Simulation of Biological Organs
In this work, possibility of simulating biological organs in realtime using
the Boundary Element Method (BEM) is investigated. Biological organs are
assumed to follow linear elastostatic material behavior, and constant boundary
element is the element type used. First, a Graphics Processing Unit (GPU) is
used to speed up the BEM computations to achieve the realtime performance.
Next, instead of the GPU, a computer cluster is used. Results indicate that BEM
is fast enough to provide for realtime graphics if biological organs are
assumed to follow linear elastostatic material behavior. Although the present
work does not conduct any simulation using nonlinear material models, results
from using the linear elastostatic material model imply that it would be
difficult to obtain realtime performance if highly nonlinear material models
that properly characterize biological organs are used. Although the use of BEM
for the simulation of biological organs is not new, the results presented in
the present study are not found elsewhere in the literature.Comment: preprint, draft, 2 tables, 47 references, 7 files, Codes that can
solve three dimensional linear elastostatic problems using constant boundary
elements (of triangular shape) while ignoring body forces are provided as
supplementary files; codes are distributed under the MIT License in three
versions: i) MATLAB version ii) Fortran 90 version (sequential code) iii)
Fortran 90 version (parallel code
Numerical simulation code for self-gravitating Bose-Einstein condensates
We completed the development of simulation code that is designed to study the
behavior of a conjectured dark matter galactic halo that is in the form of a
Bose-Einstein Condensate (BEC). The BEC is described by the Gross-Pitaevskii
equation, which can be solved numerically using the Crank-Nicholson method. The
gravitational potential, in turn, is described by Poisson's equation, that can
be solved using the relaxation method. Our code combines these two methods to
study the time evolution of a self-gravitating BEC. The inefficiency of the
relaxation method is balanced by the fact that in subsequent time iterations,
previously computed values of the gravitational field serve as very good
initial estimates. The code is robust (as evidenced by its stability on coarse
grids) and efficient enough to simulate the evolution of a system over the
course of 1E9 years using a finer (100x100x100) spatial grid, in less than a
day of processor time on a contemporary desktop computer.Comment: 13 pages, 1 figure; updated to reflect changes in the published
versio
SHARE with CHARM
SHARE with CHARM program (SHAREv3) implements the statistical hadronization
model description of particle production in relativistic heavy-ion collisions.
Given a set of statistical parameters, SHAREv3 program evaluates yields and
therefore also ratios, and furthermore, statistical particle abundance
fluctuations. The physical bulk properties of the particle source is evaluated
based on all hadrons produced, including the fitted yields. The bulk properties
can be prescribed as a fit input complementing and/or replacing the statistical
parameters. The modifications and improvements in the SHARE suite of programs
are oriented towards recent and forthcoming LHC hadron production results
including charm hadrons. This SHAREv3 release incorporates all features seen
previously in SHAREv1.x and v2.x and, beyond, we include a complete treatment
of charm hadrons and their decays, which further cascade and feed lighter
hadron yields. This article is a complete and self-contained manual explaining
and introducing both the conventional and the extended capabilities of SHARE
with CHARM. We complement the particle list derived from the Particle Data
Group tabulation composed of up, down, strange quarks (including
resonances) with hadrons containing charm quarks. We provide a table
of the charm hadron decays including partial widths. The branching ratios of
each charm hadron decays add to unity, which is achieved by including some
charm hadron decay channels based on theoretical consideration in the absence
of direct experimental information. A very successful interpretation of all
available LHC results has been already obtained using this program.Comment: 41 pages, 5 figures, 3 tables. Associated program available at
http://www.physics.arizona.edu/~gtshare/SHARE/share.html (Computer Physics
Communications in press
Computational Science Revision of the Undergraduate Major
We wish to add courses to the core requirements in order to ease the transition between sophomore and junior/senior level courses and to teach several computational methods and programming concepts in greater depth. We also propose to add a mathematics course (differential equations) to the major requirements. Elective requirements will be reduced so as to not impact total credits
QuantumInformation.jl---a Julia package for numerical computation in quantum information theory
Numerical investigations are an important research tool in quantum
information theory. There already exists a wide range of computational tools
for quantum information theory implemented in various programming languages.
However, there is little effort in implementing this kind of tools in the Julia
language. Julia is a modern programming language designed for numerical
computation with excellent support for vector and matrix algebra, extended type
system that allows for implementation of elegant application interfaces and
support for parallel and distributed computing. QuantumInformation.jl is a new
quantum information theory library implemented in Julia that provides functions
for creating and analyzing quantum states, and for creating quantum operations
in various representations. An additional feature of the library is a
collection of functions for sampling random quantum states and operations such
as unitary operations and generic quantum channels.Comment: 32 pages, 8 figure
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