13,436 research outputs found
Flux-corrected transport techniques for transient calculations of strongly shocked flows
New flux-corrected transport algorithms are described for solving generalized continuity equations. These techniques were developed by requiring that the finite difference formulas used ensure positivity for an initially positive convected quantity. Thus FCT is particularly valuable for fluid-like problems with strong gradients or shocks. Repeated application of the same subroutine to mass, momentum, and energy conservation equations gives a simple solution of the coupled time-dependent equations of ideal compressible fluid dynamics without introducing an artificial viscosity. FCT algorithms span Eulerian, sliding-rezone, and Lagrangian finite difference grids in several coordinate systems. The latest FCT techniques are fully vectorized for parallel/pipeline processing
Analysis of error propagation in particle filters with approximation
This paper examines the impact of approximation steps that become necessary
when particle filters are implemented on resource-constrained platforms. We
consider particle filters that perform intermittent approximation, either by
subsampling the particles or by generating a parametric approximation. For such
algorithms, we derive time-uniform bounds on the weak-sense error and
present associated exponential inequalities. We motivate the theoretical
analysis by considering the leader node particle filter and present numerical
experiments exploring its performance and the relationship to the error bounds.Comment: Published in at http://dx.doi.org/10.1214/11-AAP760 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Integrability via geometry: dispersionless differential equations in three and four dimensions
We prove that the existence of a dispersionless Lax pair with spectral
parameter for a nondegenerate hyperbolic second order partial differential
equation (PDE) is equivalent to the canonical conformal structure defined by
the symbol being Einstein-Weyl on any solution in 3D, and self-dual on any
solution in 4D. The first main ingredient in the proof is a characteristic
property for dispersionless Lax pairs. The second is the projective behaviour
of the Lax pair with respect to the spectral parameter. Both are established
for nondegenerate determined systems of PDEs of any order. Thus our main result
applies more generally to any such PDE system whose characteristic variety is a
quadric hypersurface.Comment: 26 pages, v2 substantially expanded and restructured, with new
theorem on projective property of Lax pair in 3
New Multiplier Sequences via Discriminant Amoebae
In their classic 1914 paper, Polya and Schur introduced and characterized two
types of linear operators acting diagonally on the monomial basis of R[x],
sending real-rooted polynomials (resp. polynomials with all nonzero roots of
the same sign) to real-rooted polynomials. Motivated by fundamental properties
of amoebae and discriminants discovered by Gelfand, Kapranov, and Zelevinsky,
we introduce two new natural classes of polynomials and describe diagonal
operators preserving these new classes. A pleasant circumstance in our
description is that these classes have a simple explicit description, one of
them coinciding with the class of log-concave sequences.Comment: 11 pages, 6 figures. Submitted for publicatio
Fluid-loop reaction system
An improved fluid actuating system for imparting motion to a body such as a spacecraft is disclosed. The fluid actuating system consists of a fluid mass that may be controllably accelerated through at least one fluid path whereby an opposite acceleration is experienced by the spacecraft. For full control of the spacecraft's orientation, the system would include a plurality of fluid paths. The fluid paths may be circular or irregular, and the fluid paths may be located on the interior or exterior of the spacecraft
Design and development of a high-stiffness, high-resolution torque sensor
A sensor has been designed and tested for precise pointing applications. The device is able to sense extremely small rotary motion and is immune to cross-axis forces. The hardware and design characteristics of the torque sensor are presented. Test data, integrated control methodology, and future applications are included
Continued fractions and transcendental numbers
It is widely believed that the continued fraction expansion of every
irrational algebraic number either is eventually periodic (and we know
that this is the case if and only if is a quadratic irrational), or it
contains arbitrarily large partial quotients. Apparently, this question was
first considered by Khintchine. A preliminary step towards its resolution
consists in providing explicit examples of transcendental continued fractions.
The main purpose of the present work is to present new families of
transcendental continued fractions with bounded partial quotients. Our results
are derived thanks to new combinatorial transcendence criteria recently
obtained by Adamczewski and Bugeaud
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