3,968 research outputs found
On model checking data-independent systems with arrays without reset
A system is data-independent with respect to a data type X iff the operations
it can perform on values of type X are restricted to just equality testing. The
system may also store, input and output values of type X. We study model
checking of systems which are data-independent with respect to two distinct
type variables X and Y, and may in addition use arrays with indices from X and
values from Y . Our main interest is the following parameterised model-checking
problem: whether a given program satisfies a given temporal-logic formula for
all non-empty nite instances of X and Y . Initially, we consider instead the
abstraction where X and Y are infinite and where partial functions with finite
domains are used to model arrays. Using a translation to data-independent
systems without arrays, we show that the u-calculus model-checking problem is
decidable for these systems. From this result, we can deduce properties of all
systems with finite instances of X and Y . We show that there is a procedure
for the above parameterised model-checking problem of the universal fragment of
the u-calculus, such that it always terminates but may give false negatives. We
also deduce that the parameterised model-checking problem of the universal
disjunction-free fragment of the u-calculus is decidable. Practical motivations
for model checking data-independent systems with arrays include verification of
memory and cache systems, where X is the type of memory addresses, and Y the
type of storable values. As an example we verify a fault-tolerant memory
interface over a set of unreliable memories.Comment: Appeared in Theory and Practice of Logic Programming, vol. 4, no.
5&6, 200
Active rc networks of low sensitivity for integrated circuit transfer function
Active RC network is capable of extremely high Q performance with exceptional stability and has independently adjustable zeros and poles. The circuit consists of two integrators and two summers that are interconnected to produce a complete second-order numerator and a second-order denominator
Mini-Conference on Hamiltonian and Lagrangian Methods in Fluid and Plasma Physics
A mini-conference on Hamiltonian and Lagrangian methods in fluid and plasma
physics was held on November 14, 2002, as part of the 44th meeting of the
Division of Plasma Physics of the American Physical Society. This paper
summarizes the material presented during the talks scheduled during the
Mini-Conference, which was held to honor Allan Kaufman on the occasion of his
75th birthday.Comment: 14 pages, conference summar
An approximation scheme for an Eikonal Equation with discontinuous coefficient
We consider the stationary Hamilton-Jacobi equation where the dynamics can
vanish at some points, the cost function is strictly positive and is allowed to
be discontinuous. More precisely, we consider special class of discontinuities
for which the notion of viscosity solution is well-suited. We propose a
semi-Lagrangian scheme for the numerical approximation of the viscosity
solution in the sense of Ishii and we study its properties. We also prove an
a-priori error estimate for the scheme in an integral norm. The last section
contains some applications to control and image processing problems
MHD Memes
The celebration of Allan Kaufman's 80th birthday was an occasion to reflect
on a career that has stimulated the mutual exchange of ideas (or memes in the
terminology of Richard Dawkins) between many researchers. This paper will
revisit a meme Allan encountered in his early career in magnetohydrodynamics,
the continuation of a magnetohydrodynamic mode through a singularity, and will
also mention other problems where Allan's work has had a powerful
cross-fertilizing effect in plasma physics and other areas of physics and
mathematics.Comment: Submitted for publication in IOP Journal of Physics: Conference
Series for publication in "Plasma Theory, Wave Kinetics, and Nonlinear
Dynamics", Proceedings of KaufmanFest, 5-7 October 2007, University of
California, Berkeley, US
On the Dynamical Stability of the Solar System
A long-term numerical integration of the classical Newtonian approximation to
the planetary orbital motions of the full Solar System (sun + 8 planets),
spanning 20 Gyr, was performed. The results showed no severe instability
arising over this time interval. Subsequently, utilizing a bifurcation method
described by Jacques Laskar, two numerical experiments were performed with the
goal of determining dynamically allowed evolutions for the Solar System in
which the planetary orbits become unstable. The experiments yielded one
evolution in which Mercury falls onto the Sun at ~1.261Gyr from now, and
another in which Mercury and Venus collide in ~862Myr. In the latter solution,
as a result of Mercury's unstable behavior, Mars was ejected from the Solar
System at ~822Myr. We have performed a number of numerical tests that confirm
these results, and indicate that they are not numerical artifacts. Using
synthetic secular perturbation theory, we find that Mercury is destabilized via
an entrance into a linear secular resonance with Jupiter in which their
corresponding eigenfrequencies experience extended periods of commensurability.
The effects of general relativity on the dynamical stability are discussed. An
application of the bifurcation method to the outer Solar System (Jupiter,
Saturn, Uranus, and Neptune) showed no sign of instability during the course of
24Gyr of integrations, in keeping with an expected Uranian dynamical lifetime
of 10^(18) years.Comment: 37 pages, 18 figures, accepted for publication in the Astrophysical
Journa
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