Accelerating BST Methods for Model Reduction with Graphics Processors

Model order reduction of dynamical linear time-invariant system appears in many scientific and engineering applications. Numerically reliable SVD-based methods for this task require O(n3) floating-point arithmetic operations, with n being in the range 103 − 105 for many practical applications. In this paper we investigate the use of graphics processors (GPUs) to accelerate model reduction of large-scale linear systems via Balanced Stochastic Truncation, by off-loading the computationally intensive tasks to this device. Experiments on a hybrid platform consisting of state-of-the-art general-purpose multi-core processors and a GPU illustrate the potential of this approach

Order reduction approaches for the algebraic Riccati equation and the LQR problem

We explore order reduction techniques for solving the algebraic Riccati equation (ARE), and investigating the numerical solution of the linear-quadratic regulator problem (LQR). A classical approach is to build a surrogate low dimensional model of the dynamical system, for instance by means of balanced truncation, and then solve the corresponding ARE. Alternatively, iterative methods can be used to directly solve the ARE and use its approximate solution to estimate quantities associated with the LQR. We propose a class of Petrov-Galerkin strategies that simultaneously reduce the dynamical system while approximately solving the ARE by projection. This methodology significantly generalizes a recently developed Galerkin method by using a pair of projection spaces, as it is often done in model order reduction of dynamical systems. Numerical experiments illustrate the advantages of the new class of methods over classical approaches when dealing with large matrices

Stability and Manipulation in Representative Democracies

This paper is devoted to the analysis of all constitutions equipped with electoral systems involving two step procedures. First, one candidate is elected in every jurisdiction by the electors in that jurisdiction, according to some aggregation procedure. Second, another aggregation procedure collects the names of the jurisdictional winners in order to designate the final winner. It appears that whenever individuals are allowed to change jurisdiction when casting their ballot, they are able to manipulate the result of the election except in very few cases. When imposing a paretian condition on every jurisdiction?s voting rule, it is shown that, in the case of any finite number of candidates, any two steps voting rule that is not manipulable by movement of the electors necessarily gives to every voter the power of overruling the unanimity on its own. A characterization of the set of these rules is next provided in the case of two candidates

The pursuit of isotopic and molecular fire tracers in the polar atmosphere and cryosphere

We present an overview of recent multidisciplinary, multi-institutional efforts to identify and date major sources of combustion aerosol in the current and paleoatmospheres. The work was stimulated, in part, by an atmospheric particle \u27sample of opportunity\u27 collected at Summit, Greenland in August 1994, that bore the 14C imprint of biomass burning. During the summer field seasons of 1995 and 1996, we collected air filter, surface snow and snowpit samples to investigate chemical and isotopic evidence of combustion particles that had been transported from distant fires. Among the chemical tracers employed for source identification are organic acids, potassium and ammonium ions, and elemental and organic components of carbonaceous particles. Ion chromatography, performed by members of the Climate Change Research Center (University of New Hampshire), has been especially valuable in indicating periods at Summit that were likely to have been affected by the long range transport of biomass burning aerosol. Univariate and multivariate patterns of the ion concentrations in the snow and ice pinpointed surface and snowpit samples for the direct analysis of particulate (soot) carbon and carbon isotopes. The research at NIST is focusing on graphitic and polycyclic aromatic carbon, which serve as almost certain indicators of fire, and measurements of carbon isotopes, especially 14C, to distinguish fossil and biomass combustion sources. Complementing the chemical and isotopic record, are direct \u27visual\u27 (satellite imagery) records and less direct backtrajectory records, to indicate geographic source regions and transport paths. In this paper we illustrate the unique way in which the synthesis of the chemical, isotopic, satellite and trajectory data enhances our ability to develop the recent history of the formation and transport of soot deposited in the polar snow and ice

Constraints on the perturbed mutual motion in Didymos due to impact-induced deformation of its primary after the DART impact

Binary near-Earth asteroid (65803) Didymos is the target of the proposed NASA Double Asteroid Redirection Test (DART), part of the Asteroid Impact & Deflection Assessment (AIDA) mission concept. In this mission, the DART spacecraft is planned to impact the secondary body of Didymos, perturbing mutual dynamics of the system. The primary body is currently rotating at a spin period close to the spin barrier of asteroids, and materials ejected from the secondary due to the DART impact are likely to reach the primary. These conditions may cause the primary to reshape, due to landslides, or internal deformation, changing the permanent gravity field. Here, we propose that if shape deformation of the primary occurs, the mutual orbit of the system would be perturbed due to a change in the gravity field. We use a numerical simulation technique based on the full two-body problem to investigate the shape effect on the mutual dynamics in Didymos after the DART impact. The results show that under constant volume, shape deformation induces strong perturbation in the mutual motion. We find that the deformation process always causes the orbital period of the system to become shorter. If surface layers with a thickness greater than ~0.4 m on the poles of the primary move down to the equatorial region due to the DART impact, a change in the orbital period of the system and in the spin period of the primary will be detected by ground-based measurement.Comment: 8 pages, 7 figures, 2 tables, accepted for publication in MNRA

Generation of spin-wave dark solitons with phase engineering

We generate experimentally spin-wave envelope dark solitons from rectangular high-frequency dark input pulses with externally introduced phase shifts in yttrium-iron garnet magnetic fims. We observe the generation of both odd and even numbers of magnetic dark solitons when the external phase shift varies. The experimental results are in a good qualitative agreement with the theory of the dark-soliton generation in magnetic films developed earlier [Phys. Rev. Lett. 82, 2583 (1999)].Comment: 6 pages, including 7 figures, submitted to Phys. Rev.

Strong anisotropy of superexchange in the copper-oxygen chains of La_{14-x}Ca_{x}Cu_{24}O_{41}

Electron spin resonance data of Cu^{2+} ions in La_{14-x}Ca_{x}Cu_{24}O_{41} crystals (x=9,11,12) reveal a very large width of the resonance line in the paramagnetic state. This signals an unusually strong anisotropy of ~10% of the isotropic Heisenberg superexchange in the Cu-O chains of this compound. The strong anisotropy can be explained by the specific geometry of two symmetrical 90 degree Cu-O-Cu bonds, which boosts the importance of orbital degrees of freedom. Our data show the apparent limitations of the applicability of an isotropic Heisenberg model to the low dimensional cuprates.Comment: 14 pages, 3 figures included, to be published in Phys. Rev. Let

On the Mechanism of Time--Delayed Feedback Control

The Pyragas method for controlling chaos is investigated in detail from the experimental as well as theoretical point of view. We show by an analytical stability analysis that the revolution around an unstable periodic orbit governs the success of the control scheme. Our predictions concerning the transient behaviour of the control signal are confirmed by numerical simulations and an electronic circuit experiment.Comment: 4 pages, REVTeX, 4 eps-figures included Phys. Rev. Lett., in press also available at http://athene.fkp.physik.th-darmstadt.de/public/wolfram.htm

Hachimoji DNA and RNA: A genetic system with eight building blocks

Reported here are DNA and RNA-like systems built from eight (hachi-) nucleotide letters (-moji) that form four orthogonal pairs. This synthetic genetic biopolymer meets the structural requirements needed to support Darwinism, including a polyelectrolyte backbone, predictable thermodynamic stability, and stereoregular building blocks that fit a Schrödinger aperiodic crystal. Measured thermodynamic parameters predict the stability of hachimoji duplexes, allowing hachimoji DNA to double the information density of natural terran DNA. Three crystal structures show that the synthetic building blocks do not perturb the aperiodic crystal seen in the DNA double helix. Hachimoji DNA was then transcribed to give hachimoji RNA in the form of a functioning fluorescent hachimoji aptamer. These results expand the scope of molecular structures that might support life, including life throughout the cosmos