Characterization of the space shuttle reaction control system engine

A computer program was developed and written in FORTRAN 5 which predicts the transient and steady state performance and heat transfer characteristics of a pulsing GO2/GH2 rocket engine. This program predicts the dynamic flow and ignition characteristics which, when combined in a quasi-steady state manner with the combustion and mixing analysis program, will provide the thrust and specific impulse of the engine as a function of time. The program also predicts the transient and steady state heat transfer characteristics of the engine using various cooling concepts. The computer program, test case, and documentation are presented. The program is applicable to any system capable of utilizing the FORTRAN 4 or FORTRAN 5 language

Universality in Systems with Power-Law Memory and Fractional Dynamics

There are a few different ways to extend regular nonlinear dynamical systems by introducing power-law memory or considering fractional differential/difference equations instead of integer ones. This extension allows the introduction of families of nonlinear dynamical systems converging to regular systems in the case of an integer power-law memory or an integer order of derivatives/differences. The examples considered in this review include the logistic family of maps (converging in the case of the first order difference to the regular logistic map), the universal family of maps, and the standard family of maps (the latter two converging, in the case of the second difference, to the regular universal and standard maps). Correspondingly, the phenomenon of transition to chaos through a period doubling cascade of bifurcations in regular nonlinear systems, known as "universality", can be extended to fractional maps, which are maps with power-/asymptotically power-law memory. The new features of universality, including cascades of bifurcations on single trajectories, which appear in fractional (with memory) nonlinear dynamical systems are the main subject of this review.Comment: 23 pages 7 Figures, to appear Oct 28 201

From Random Matrices to Stochastic Operators

We propose that classical random matrix models are properly viewed as finite difference schemes for stochastic differential operators. Three particular stochastic operators commonly arise, each associated with a familiar class of local eigenvalue behavior. The stochastic Airy operator displays soft edge behavior, associated with the Airy kernel. The stochastic Bessel operator displays hard edge behavior, associated with the Bessel kernel. The article concludes with suggestions for a stochastic sine operator, which would display bulk behavior, associated with the sine kernel.Comment: 41 pages, 5 figures. Submitted to Journal of Statistical Physics. Changes in this revision: recomputed Monte Carlo simulations, added reference [19], fit into margins, performed minor editin

Random Matrix Theory Analysis of Cross Correlations in Financial Markets

We confirm universal behaviors such as eigenvalue distribution and spacings predicted by Random Matrix Theory (RMT) for the cross correlation matrix of the daily stock prices of Tokyo Stock Exchange from 1993 to 2001, which have been reported for New York Stock Exchange in previous studies. It is shown that the random part of the eigenvalue distribution of the cross correlation matrix is stable even when deterministic correlations are present. Some deviations in the small eigenvalue statistics outside the bounds of the universality class of RMT are not completely explained with the deterministic correlations as proposed in previous studies. We study the effect of randomness on deterministic correlations and find that randomness causes a repulsion between deterministic eigenvalues and the random eigenvalues. This is interpreted as a reminiscent of ``level repulsion'' in RMT and explains some deviations from the previous studies observed in the market data. We also study correlated groups of issues in these markets and propose a refined method to identify correlated groups based on RMT. Some characteristic differences between properties of Tokyo Stock Exchange and New York Stock Exchange are found.Comment: RevTex, 17 pages, 8 figure

Probability of local bifurcation type from a fixed point: A random matrix perspective

Results regarding probable bifurcations from fixed points are presented in the context of general dynamical systems (real, random matrices), time-delay dynamical systems (companion matrices), and a set of mappings known for their properties as universal approximators (neural networks). The eigenvalue spectra is considered both numerically and analytically using previous work of Edelman et. al. Based upon the numerical evidence, various conjectures are presented. The conclusion is that in many circumstances, most bifurcations from fixed points of large dynamical systems will be due to complex eigenvalues. Nevertheless, surprising situations are presented for which the aforementioned conclusion is not general, e.g. real random matrices with Gaussian elements with a large positive mean and finite variance.Comment: 21 pages, 19 figure

On the possibility to supercool molecular hydrogen down to superfluid transition

Recent calculations by Vorobev and Malyshenko (JETP Letters, 71, 39, 2000) show that molecular hydrogen may stay liquid and superfluid in strong electric fields of the order of $4\times 10^7 V/cm$. I demonstrate that strong local electric fields of similar magnitude exist beneath a two-dimensional layer of electrons localized in the image potential above the surface of solid hydrogen. Even stronger local fields exist around charged particles (ions or electrons) if surface or bulk of a solid hydrogen crystal is statically charged. Measurements of the frequency shift of the $1 \to 2$ photoresonance transition in the spectrum of two-dimensional layer of electrons above positively or negatively charged solid hydrogen surface performed in the temperature range 7 - 13.8 K support the prediction of electric field induced surface melting. The range of surface charge density necessary to stabilize the liquid phase of molecular hydrogen at the temperature of superfluid transition is estimated.Comment: 5 pages, 2 figure