On the recurrence and robust properties of Lorenz'63 model

Lie-Poisson structure of the Lorenz'63 system gives a physical insight on its dynamical and statistical behavior considering the evolution of the associated Casimir functions. We study the invariant density and other recurrence features of a Markov expanding Lorenz-like map of the interval arising in the analysis of the predictability of the extreme values reached by particular physical observables evolving in time under the Lorenz'63 dynamics with the classical set of parameters. Moreover, we prove the statistical stability of such an invariant measure. This will allow us to further characterize the SRB measure of the system.Comment: 44 pages, 7 figures, revised version accepted for pubblicatio

Phase Separation of Rigid-Rod Suspensions in Shear Flow

We analyze the behavior of a suspension of rigid rod-like particles in shear flow using a modified version of the Doi model, and construct diagrams for phase coexistence under conditions of constant imposed stress and constant imposed strain rate, among paranematic, flow-aligning nematic, and log-rolling nematic states. We calculate the effective constitutive relations that would be measured through the regime of phase separation into shear bands. We calculate phase coexistence by examining the stability of interfacial steady states and find a wide range of possible ``phase'' behaviors.Comment: 23 pages 19 figures, revised version to be published in Physical Review

Prospectus, February 6, 1980

BUSH BREAKFASTS WITH CHAMPAIGN: FRESH FROM IOWA VICTORY, GEORGE BUSH SPEAKS TO CROWD; College hours are in jeopardy; Week in Review: World, State; Elections today for Stugo; Campus Happenings; Black History Month; Counseling center for choosing careers; Child abuse seminar at Parkland College; Chief Dye: \u27drinking laws tough to enforce\u27; Campus Question: Has raising the drinking age affected your social life?; Letters to the editor: Intramurals for females, also; Between the Tracks: New Wave groups to start off the 80s; Heartbreakers selling big; Free Wheelin\u27 puts out new LP; Classifieds; Champaign Park District counts on donations; Four Cobras win: Trackmen win Chicago Relays meet; U. of I. members help skiers; Exhibit of Olympics at U. of I.; Intramural basketball starts; Mile Relay highlights Cobra\u27s track meet; Cagers upset Kankakee; Bench Warmer: Women cagers look tough; Women slip to 13-6; IM adds volleyballhttps://spark.parkland.edu/prospectus_1980/1039/thumbnail.jp

Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.Comment: 9 pages, 14 figure

Reliability of the beamsplitter based Bell-state measurement

A linear 50/50 beamsplitter, together with a coincidence measurement, has been widely used in quantum optical experiments, such as teleportation, dense coding, etc., for interferometrically distinguishing, measuring, or projecting onto one of the four two-photon polarization Bell-states $|\psi^{(-)}>$. In this paper, we demonstrate that the coincidence measurement at the output of a beamsplitter cannot be used as an absolute identifier of the input state $|\psi^{(-)}>$ nor as an indication that the input photons have projected to the $|\psi^{(-)}>$ state.Comment: 4 pages, two-colum

Sociodemographic Factors Associated with AIDS Knowledge in a Random Sample of University Students

A telephone survey was used to assess knowledge of the transmission, prevalence, and infectivity of acquired immunodeficiency syndrome (AIDS), and the safety of casual contact among 214 randomly selected university students. Males were more knowledgeable than females overall (odds ratio [OR], men/women = 4.8). Although most students understood the dangers of unprotected sex and intravenous needle sharing, up to 30% believed some kinds of casual contact (e.g., shared eating utensils) can transmit AIDS. Older students (≥ 23 yrs) were more knowledgeable than those 17 to 19 years old about the safety of casual contact (OR = 3.8). Students are in need of education programs that stress the ways AIDS is not transmitted. Since most students identified newspapers and television as their main sources of information, these may be effective vehicles for education efforts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73095/1/j.1525-1446.1991.tb00654.x.pd

Breaking of general rotational symmetries by multi-dimensional classical ratchets

We demonstrate that a particle driven by a set of spatially uncorrelated, independent colored noise forces in a bounded, multidimensional potential exhibits rotations that are independent of the initial conditions. We calculate the particle currents in terms of the noise statistics and the potential asymmetries by deriving an n-dimensional Fokker-Planck equation in the small correlation time limit. We analyze a variety of flow patterns for various potential structures, generating various combinations of laminar and rotational flows.Comment: Accepted, Physical Review

Ultrafast carrier relaxation in GaN, In_(0.05)Ga_(0.95)N and an In_(0.05)Ga_(0.95)/In_(0.15)Ga_(0.85)N Multiple Quantum Well

Room temperature, wavelength non-degenerate ultrafast pump/probe measurements were performed on GaN and InGaN epilayers and an InGaN multiple quantum well structure. Carrier relaxation dynamics were investigated as a function of excitation wavelength and intensity. Spectrally-resolved sub-picosecond relaxation due to carrier redistribution and QW capture was found to depend sensitively on the wavelength of pump excitation. Moreover, for pump intensities above a threshold of 100 microJ/cm2, all samples demonstrated an additional emission feature arising from stimulated emission (SE). SE is evidenced as accelerated relaxation (< 10 ps) in the pump-probe data, fundamentally altering the re-distribution of carriers. Once SE and carrier redistribution is completed, a slower relaxation of up to 1 ns for GaN and InGaN epilayers, and 660 ps for the MQW sample, indicates carrier recombination through spontaneous emission.Comment: submitted to Phys. Rev.

The compound Poisson limit ruling periodic extreme behaviour of non-uniformly hyperbolic dynamics

We prove that the distributional limit of the normalised number of returns to small neighbourhoods of periodic points of non-uniformly hyperbolic dynamical systems is compound Poisson. The returns to small balls around a fixed point in the phase space correspond to the occurrence of rare events, or exceedances of high thresholds, so that there is a connection between the laws of Return Times Statistics and Extreme Value Laws. The fact that the fixed point in the phase space is a repelling periodic point implies that there is a tendency for the exceedances to appear in clusters whose average sizes is given by the Extremal Index, which depends on the expansion of the system at the periodic point. We recall that for generic points, the exceedances, in the limit, are singular and occur at Poisson times. However, around periodic points, the picture is different: the respective point processes of exceedances converge to a compound Poisson process, so instead of single exceedances, we have entire clusters of exceedances occurring at Poisson times with a geometric distribution ruling its multiplicity. The systems to which our results apply include: general piecewise expanding maps of the interval (Rychlik maps), maps with indifferent fixed points (Manneville-Pomeau maps) and Benedicks-Carleson quadratic maps.Comment: To appear in Communications in Mathematical Physic