43,176 research outputs found
Discrete mechanics and variational integrators
This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic partitioned RungeâKutta schemes are presented
A simulation of the instrument pointing system for the Astro-1 mission
NASA has recently completed a shuttle-borne stellar ultraviolet astronomy mission known as Astro-1. A three axis instrument pointing system (IPS) was employed to accurately point the science instruments. In order to analyze the pointing control system and verify pointing performance, a simulation of the IPS was developed using the multibody dynamics software TREETOPS. The TREETOPS IPS simulation is capable of accurately modeling the multibody IPS system undergoing large angle, nonlinear motion. The simulation is documented and example cases are presented demonstrating disturbance rejection, fine pointing operations, and multiple target pointing and slewing of the IPS
Microbial Effects on Repository Performance
This report presents a critical review of the international literature on microbial effects
in and around a deep geological repository for higher activity wastes. It is aimed at
those who are familiar with the nuclear industry and radioactive waste disposal, but
who are not experts in microbiology; they may have a limited knowledge of how
microbiology may be integrated into and impact upon radioactive waste disposal
safety cases and associated performance assessments (PA)
Canonical and non-canonical equilibrium distribution
We address the problem of the dynamical foundation of non-canonical
equilibrium. We consider, as a source of divergence from ordinary statistical
mechanics, the breakdown of the condition of time scale separation between
microscopic and macroscopic dynamics. We show that this breakdown has the
effect of producing a significant deviation from the canonical prescription. We
also show that, while the canonical equilibrium can be reached with no apparent
dependence on dynamics, the specific form of non-canonical equilibrium is, in
fact, determined by dynamics. We consider the special case where the thermal
reservoir driving the system of interest to equilibrium is a generator of
intermittent fluctuations. We assess the form of the non-canonical equilibrium
reached by the system in this case. Using both theoretical and numerical
arguments we demonstrate that Levy statistics are the best description of the
dynamics and that the Levy distribution is the correct basin of attraction. We
also show that the correct path to non-canonical equilibrium by means of
strictly thermodynamic arguments has not yet been found, and that further
research has to be done to establish a connection between dynamics and
thermodynamics.Comment: 13 pages, 6 figure
Predictive control for energy management in all/more electric vehicles with multiple energy storage units
The paper describes the application of Model Predictive Control (MPC) methodologies for application to electric and hybrid-electric vehicle drive-train formats incorporating multiple energy/power sources. Particular emphasis is given to the co-ordinated management of energy flow from the multiple sources to address issues of extended vehicle range and battery life-time for all-electric drive-trains, and emissions reduction and drive-train torsional oscillations, for hybrid-electric counterparts, whilst accommodating operational constraints and, ultimately, generic non-standard driving cycles
Probability flux as a method for detecting scaling
We introduce a new method for detecting scaling in time series. The method
uses the properties of the probability flux for stochastic self-affine
processes and is called the probability flux analysis (PFA). The advantages of
this method are: 1) it is independent of the finiteness of the moments of the
self-affine process; 2) it does not require a binning procedure for numerical
evaluation of the the probability density function. These properties make the
method particularly efficient for heavy tailed distributions in which the
variance is not finite, for example, in Levy alpha-stable processes. This
utility is established using a comparison with the diffusion entropy (DE)
method
Variational integrators, the Newmark scheme, and dissipative systems
Variational methods are a class of symplectic-momentum integrators for ODEs. Using
these schemes, it is shown that the classical Newmark algorithm is structure preserving in a
non-obvious way, thus explaining the observed numerical behavior. Modifications to variational
methods to include forcing and dissipation are also proposed, extending the advantages
of structure preserving integrators to non-conservative systems
Asynchronous Variational Integrators
We describe a new class of asynchronous variational integrators (AVI) for nonlinear
elastodynamics. The AVIs are distinguished by the following attributes: (i)
The algorithms permit the selection of independent time steps in each element, and
the local time steps need not bear an integral relation to each other; (ii) the algorithms
derive from a spacetime form of a discrete version of Hamiltonâs variational
principle. As a consequence of this variational structure, the algorithms conserve
local momenta and a local discrete multisymplectic structure exactly.
To guide the development of the discretizations, a spacetime multisymplectic
formulation of elastodynamics is presented. The variational principle used incorporates
both configuration and spacetime reference variations. This allows a unified
treatment of all the conservation properties of the system.A discrete version of reference
configuration is also considered, providing a natural definition of a discrete
energy. The possibilities for discrete energy conservation are evaluated.
Numerical tests reveal that, even when local energy balance is not enforced
exactly, the global and local energy behavior of the AVIs is quite remarkable, a
property which can probably be traced to the symplectic nature of the algorith
Galaxy Orientations in the Coma Cluster
We have examined the orientations of early-type galaxies in the Coma cluster
to see whether the well-established tendency for brightest cluster galaxies to
share the same major axis orientation as their host cluster also extends to the
rest of the galaxy population. We find no evidence of any preferential
orientations of galaxies within Coma or its surroundings. The implications of
this result for theories of the formation of clusters and galaxies
(particularly the first-ranked members) are discussed.Comment: Accepted for publication in the Astrophysical Journal Letters. 4
pages, 4 figure
- âŠ