Performance bounds for particle filters using the optimal proposal

Particle filters may suffer from degeneracy of the particle weights. For the simplest "bootstrap" filter, it is known that avoiding degeneracy in large systems requires that the ensemble size must increase exponentially with the variance of the observation log-likelihood. The present article shows first that a similar result applies to particle filters using sequential importance sampling and the optimal proposal distribution and, second, that the optimal proposal yields minimal degeneracy when compared to any other proposal distribution that depends only on the previous state and the most recent observations. Thus, the optimal proposal provides performance bounds for filters using sequential importance sampling and any such proposal. An example with independent and identically distributed degrees of freedom illustrates both the need for exponentially large ensemble size with the optimal proposal as the system dimension increases and the potentially dramatic advantages of the optimal proposal relative to simpler proposals. Those advantages depend crucially on the magnitude of the system noise

Feasibility study of aileron and spoiler control systems for large horizontal axis wind turbines

The feasibility of using aileron or spoiler controls as alternates to pitch control for large horizontal axis wind turbines was studied. The NASA Mod-0 100 kw machine was used as the basis for the study. Specific performance studies were conducted for 20% chord ailerons over the outboard 30% span, and for 10% chord spoilers over the same portion of the span. Both control systems utilized control deflections up to 60 deg. Results of the study show that either ailerons or spoilers can provide the control necessary to limit turbine power in high wind conditions. The aileron system, as designed, provides overspeed protection at hurricane wind speeds, low wind speed starting torque of 778 N-m (574 ft. lb) at 3.6 m/sec, and a 1.3 to 1.5% increase in annual energy compared to a fixed pitch rotor. The aileron control system preliminary design study includes aileron loads analysis and the design of a failsafe flyweight actuator for overspeed protection in the event of a hydraulic system failure

Effect of disorder on the thermal transport and elastic properties in thermoelectric Zn4Sb3

Zn4Sb3 undergoes a phase transition from alpha to beta phase at T1[approximate]250 K. The high temperature beta-Zn4Sb3 phase has been widely investigated as a potential state-of-the-art thermoelectric (TE) material, due to its remarkably low thermal conductivity. We have performed electronic and thermal transport measurements exploring the structural phase transition at 250 K. The alpha to beta phase transition manifests itself by anomalies in the resistivity, thermopower, and specific heat at 250 K as well as by a reduction in the thermal conductivity as Zn4Sb3 changes phase from the ordered alpha to the disordered beta-phase. Moreover, measurements of the elastic constants using resonant ultrasound spectroscopy (RUS) reveal a dramatic softening at the order-disorder transition upon warming. These measurements provide further evidence that the remarkable thermoelectric properties of beta-Zn4Sb3 are tied to the disorder in the crystal structure

Wave localization in binary isotopically disordered one-dimensional harmonic chains with impurities having arbitrary cross section and concentration

The localization length for isotopically disordered harmonic one-dimensional chains is calculated for arbitrary impurity concentration and scattering cross section. The localization length depends on the scattering cross section of a single scatterer, which is calculated for a discrete chain having a wavelength dependent pulse propagation speed. For binary isotopically disordered systems composed of many scatterers, the localization length decreases with increasing impurity concentration, reaching a mimimum before diverging toward infinity as the impurity concentration approaches a value of one. The concentration dependence of the localization length over the entire impurity concentration range is approximated accurately by the sum of the behavior at each limiting concentration. Simultaneous measurements of Lyapunov exponent statistics indicate practical limits for the minimum system length and the number of scatterers to achieve representative ensemble averages. Results are discussed in the context of future investigations of the time-dependent behavior of disordered anharmonic chains.Comment: 8 pages, 10 figures, submitted to PR

Shape-changing Collisions of Coupled Bright Solitons in Birefringent Optical Fibers

Wecritically review the recent progress in understanding soliton propagation in birefringent optical fibers.By constructing the most general bright two-soliton solution of the integrable coupled nonlinear Schroedinger equation (Manakov model) we point out that solitons in birefringent fibers can in general change their shape after interaction due to a change in the intensity distribution among the modes even though the total energy is conserved. However, the standard shape-preserving collision (elastic collision) property of the (1+1)-dimensional solitons is recovered when restrictions are imposed on some of the soliton parameters. As a consequence the following further properties can be deduced using this shape-changing collision. (i) The exciting possibility of switching of solitons between orthogonally polarized modes of the birefringent fiber exists. (ii) When additional effects due to periodic rotation of birefringence axes are considered, the shape changing collision can be used as a switch to suppress or to enhance the periodic intensity exchange between the orthogonally polarized modes. (iii) For ultra short optical soliton pulse propagation in non-Kerr media, from the governing equation an integrable system of coupled nonlinear Schroedinger equation with cubic-quintic terms is identified. It admits a nonlocal Poisson bracket structure. (iv) If we take the higher-order terms in the coupled nonlinear Schroedinger equation into account then their effect on the shape-changing collision of solitons, during optical pulse propagation, can be studied by using a direct perturbational approach.Comment: 14 pages, ROMP31, 4 EPS figure

Where are the Hedgehogs in Nematics?

In experiments which take a liquid crystal rapidly from the isotropic to the nematic phase, a dense tangle of defects is formed. In nematics, there are in principle both line and point defects (``hedgehogs''), but no point defects are observed until the defect network has coarsened appreciably. In this letter the expected density of point defects is shown to be extremely low, approximately $10^{-8}$ per initially correlated domain, as result of the topology (specifically, the homology) of the order parameter space.Comment: 6 pages, latex, 1 figure (self-unpacking PostScript)

Contracted Representation of Yang's Space-Time Algebra and Buniy-Hsu-Zee's Discrete Space-Time

Motivated by the recent proposition by Buniy, Hsu and Zee with respect to discrete space-time and finite spatial degrees of freedom of our physical world with a short- and a long-distance scales, $l_P$ and $L,$ we reconsider the Lorentz-covariant Yang's quantized space-time algebra (YSTA), which is intrinsically equipped with such two kinds of scale parameters, $\lambda$ and $R$. In accordance with their proposition, we find the so-called contracted representation of YSTA with finite spatial degrees of freedom associated with the ratio $R/\lambda$, which gives a possibility of the divergence-free noncommutative field theory on YSTA. The canonical commutation relations familiar in the ordinary quantum mechanics appear as the cooperative Inonu-Wigner's contraction limit of YSTA, $\lambda \to 0$ and $R \to \infty.

The Area Quantum and Snyder Space

We show that in the Snyder space the area of the disc and of the sphere can be quantized. It is also shown that the area spectrum of the sphere can be related to the Bekenstein conjecture for the area spectrum of a black hole horizon.Comment: 7 pages, in Press, Physics Letters