362 research outputs found
Static Analysis of Run-Time Errors in Embedded Real-Time Parallel C Programs
We present a static analysis by Abstract Interpretation to check for run-time
errors in parallel and multi-threaded C programs. Following our work on
Astr\'ee, we focus on embedded critical programs without recursion nor dynamic
memory allocation, but extend the analysis to a static set of threads
communicating implicitly through a shared memory and explicitly using a finite
set of mutual exclusion locks, and scheduled according to a real-time
scheduling policy and fixed priorities. Our method is thread-modular. It is
based on a slightly modified non-parallel analysis that, when analyzing a
thread, applies and enriches an abstract set of thread interferences. An
iterator then re-analyzes each thread in turn until interferences stabilize. We
prove the soundness of our method with respect to the sequential consistency
semantics, but also with respect to a reasonable weakly consistent memory
semantics. We also show how to take into account mutual exclusion and thread
priorities through a partitioning over an abstraction of the scheduler state.
We present preliminary experimental results analyzing an industrial program
with our prototype, Th\'es\'ee, and demonstrate the scalability of our
approach
Approximation for Bessel functions and their application in the computation of Hankel transforms
AbstractWe present rational approximations of the Bessel functions Jv(x), v=0,1,…,10, which can be used to simplify the computation of the Hankel transform to the computation of two Fourier transforms
Effects of P-wave Annihilation on the Angular Power Spectrum of Extragalactic Gamma-rays from Dark Matter Annihilation
We present a formalism for estimating the angular power spectrum of
extragalactic gamma-rays produced by dark matter annihilating with any general
velocity-dependent cross section. The relevant density and velocity
distribution of dark matter is modeled as an ensemble of smooth, universal,
rigid, disjoint, spherical halos with distribution and universal properties
constrained by simulation data. We apply this formalism to theories of dark
matter with p-wave annihilation, for which the relative-velocity-weighted
annihilation cross section is \sigma v=a+bv^2. We determine that this
significantly increases the gamma-ray power if b/a >> 10^6. The effect of
p-wave annihilation on the angular power spectrum is very similar for the
sample of particle physics models we explored, suggesting that the important
effect for a given b/a is largely determined by the cosmic dark matter
distribution. If the dark matter relic from strong p-wave theories is thermally
produced, the intensities of annihilation gamma-rays are strongly p-wave
suppressed, making them difficult to observe. If an angular power spectrum
consistent with a strong p-wave were to be observed, it would likely indicate
non-thermal production of dark matter in the early Universe.Comment: 20 pages, 3 figure
Computation of Fourier and Laplace transforms of singular functions using modified moments
AbstractIn this paper a recurrence formula for the computation of Mk = ∫−1+1 (1 − x)α(1 + x)β exp[−a/(1+x)]Tk(x)dx is presented. The numerical stability is discussed. The starting values are confluent hypergeometric functions which can be evaluated using Luke's results on Chebyshev series expansions and Padé approximations of hypergeometric functions. Applications of this recurrence relation are the evaluation of the Fourier transform of singular functions by modified Clenshaw-Curtis integration, the construction of Gaussian quadrature formulae for Fourier integrals and the numerical inversion of the Laplace transform
Increasing the Reliability of Adaptive Quadrature Using Explicit Interpolants
We present two new adaptive quadrature routines. Both routines differ from
previously published algorithms in many aspects, most significantly in how they
represent the integrand, how they treat non-numerical values of the integrand,
how they deal with improper divergent integrals and how they estimate the
integration error. The main focus of these improvements is to increase the
reliability of the algorithms without significantly impacting their efficiency.
Both algorithms are implemented in Matlab and tested using both the "families"
suggested by Lyness and Kaganove and the battery test used by Gander and
Gautschi and Kahaner. They are shown to be more reliable, albeit in some cases
less efficient, than other commonly-used adaptive integrators.Comment: 32 pages, submitted to ACM Transactions on Mathematical Softwar
A hybrid memory kernel approach for condensed phase non-adiabatic dynamics
The spin-boson model is a simplified Hamiltonian often used to study
non-adiabatic dynamics in large condensed phase systems, even though it has not
been solved in a fully analytic fashion. Herein, we present an exact analytic
expression for the dynamics of the spin-boson model in the infinitely slow bath
limit and generalize it to approximate dynamics for faster baths. We achieve
the latter by developing a hybrid approach that combines the exact slow-bath
result with the popular NIBA method to generate a memory kernel that is
formally exact to second order in the diabatic coupling but also contains
higher-order contributions approximated from the second order term alone. This
kernel has the same computational complexity as NIBA, but is found to yield
dramatically superior dynamics in regimes where NIBA breaks down---such as
systems with large diabatic coupling or energy bias. This indicates that this
hybrid approach could be used to cheaply incorporate higher order effects into
second order methods, and could potentially be generalized to develop alternate
kernel resummation schemes
Numerically improved computational scheme for the optical conductivity tensor in layered systems
The contour integration technique applied to calculate the optical
conductivity tensor at finite temperatures in the case of layered systems
within the framework of the spin-polarized relativistic screened
Korringa-Kohn-Rostoker band structure method is improved from the computational
point of view by applying the Gauss-Konrod quadrature for the integrals along
the different parts of the contour and by designing a cumulative special points
scheme for two-dimensional Brillouin zone integrals corresponding to cubic
systems.Comment: 17 pages, LaTeX + 4 figures (Encapsulated PostScript), submitted to
J. Phys.: Condensed Matter (19 Sept. 2000
Typing Copyless Message Passing
We present a calculus that models a form of process interaction based on
copyless message passing, in the style of Singularity OS. The calculus is
equipped with a type system ensuring that well-typed processes are free from
memory faults, memory leaks, and communication errors. The type system is
essentially linear, but we show that linearity alone is inadequate, because it
leaves room for scenarios where well-typed processes leak significant amounts
of memory. We address these problems basing the type system upon an original
variant of session types.Comment: 50 page
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