Enhanced modeling features within TREETOPS

The original motivation for TREETOPS was to build a generic multi-body simulation and remove the burden of writing multi-body equations from the engineers. The motivation of the enhancement was twofold: (1) to extend the menu of built-in features (sensors, actuators, constraints, etc.) that did not require user code; and (2) to extend the control system design capabilities by linking with other government funded software (NASTRAN and MATLAB). These enhancements also serve to bridge the gap between structures and control groups. It is common on large space programs for the structures groups to build hi-fidelity models of the structure using NASTRAN and for the controls group to build lower order models because they lack the tools to incorporate the former into their analysis. Now the controls engineers can accept the hi-fidelity NASTRAN models into TREETOPS, add sensors and actuators, perform model reduction and couple the result directly into MATLAB to perform their design. The controller can then be imported directly into TREETOPS for non-linear, time-history simulation

The Flash Crash: An Examination of Shareholder Wealth and Market Quality

We investigate stock returns, market quality, and options market activity around the flash crash of May 6, 2010. Abnormal returns are negative on the day of and the day after the flash crash for stocks that had trades that executed during the crash subsequently cancelled by either Nasdaq or NYSE Arca. Consistent with studies that suggest that other sources of liquidity withdrew from the markets during the flash crash, we find that the fraction of trades executed by the NYSE increases during this volatile period. Market quality deteriorates following the flash crash as bid-ask spreads increase and quote depths decrease. Evidence from the options markets indicates that investor uncertainty increased around the time of the crash and remained elevated for several days

Dominance of backward stimulated Raman scattering in gas-filled hollow-core photonic crystal fibers

Backward stimulated Raman scattering in gases provides a promising route to compression and amplification of a Stokes seed-pulse by counter-propagating against a pump-pulse, as has been already demonstrated in various platforms, mainly in free-space. However, the dynamics governing this process when seeded by noise has not yet been investigated in a fully controllable collinear environment. Here we report the first unambiguous observation of efficient noise-seeded backward stimulated Raman scattering in a hydrogen-filled hollow-core photonic crystal fiber. At high gas pressures, when the backward Raman gain is comparable with, but lower than, the forward gain, we report quantum conversion efficiencies exceeding 40% to the backward Stokes at 683 nm from a narrowband 532-nm-pump. The efficiency increases to 65% when the backward process is seeded by a small amount of back-reflected forward-generated Stokes light. At high pump powers the backward Stokes signal, emitted in a clean fundamental mode and spectrally pure, is unexpectedly always stronger than its forward-propagating counterpart. We attribute this striking observation to the unique temporal dynamics of the interacting fields, which cause the Raman coherence (which takes the form of a moving fine-period Bragg grating) to grow in strength towards the input end of the fiber. A good understanding of this process, together with the rapid development of novel anti-resonant-guiding hollow-core fibers, may lead to improved designs of efficient gas-based Raman lasers and amplifiers operating at wavelengths from the ultraviolet to the mid-infrared.Comment: 6 pages and 8 figures in the main section. 4 pages and 5 figures in the supplementary sectio

Persistence in q-state Potts model: A Mean-Field approach

We study the Persistence properties of the T=0 coarsening dynamics of one dimensional $q$-state Potts model using a modified mean-field approximation (MMFA). In this approximation, the spatial correlations between the interfaces separating spins with different Potts states is ignored, but the correct time dependence of the mean density $P(t)$ of persistent spins is imposed. For this model, it is known that $P(t)$ follows a power-law decay with time, $P(t)\sim t^{-\theta(q)}$ where $\theta(q)$ is the $q$-dependent persistence exponent. We study the spatial structure of the persistent region within the MMFA. We show that the persistent site pair correlation function $P_{2}(r,t)$ has the scaling form $P_{2}(r,t)=P(t)^{2}f(r/t^{{1/2}})$ for all values of the persistence exponent $\theta(q)$. The scaling function has the limiting behaviour $f(x)\sim x^{-2\theta}$ ($x\ll 1$) and $f(x)\to 1$ ($x\gg 1$). We then show within the Independent Interval Approximation (IIA) that the distribution $n(k,t)$ of separation $k$ between two consecutive persistent spins at time $t$ has the asymptotic scaling form $n(k,t)=t^{-2\phi}g(t,\frac{k}{t^{\phi}})$ where the dynamical exponent has the form $\phi$=max(${1/2},\theta$). The behaviour of the scaling function for large and small values of the arguments is found analytically. We find that for small separations $k\ll t^{\phi}, n(k,t)\sim P(t)k^{-\tau}$ where $\tau$=max($2(1-\theta),2\theta$), while for large separations $k\gg t^{\phi}$, $g(t,x)$ decays exponentially with $x$. The unusual dynamical scaling form and the behaviour of the scaling function is supported by numerical simulations.Comment: 11 pages in RevTeX, 10 figures, submitted to Phys. Rev.

Persistence in One-dimensional Ising Models with Parallel Dynamics

We study persistence in one-dimensional ferromagnetic and anti-ferromagnetic nearest-neighbor Ising models with parallel dynamics. The probability P(t) that a given spin has not flipped up to time t, when the system evolves from an initial random configuration, decays as P(t) \sim 1/t^theta_p with theta_p \simeq 0.75 numerically. A mapping to the dynamics of two decoupled A+A \to 0 models yields theta_p = 3/4 exactly. A finite size scaling analysis clarifies the nature of dynamical scaling in the distribution of persistent sites obtained under this dynamics.Comment: 5 pages Latex file, 3 postscript figures, to appear in Phys Rev.