Time-reversal focusing of an expanding soliton gas in disordered replicas

We investigate the properties of time reversibility of a soliton gas, originating from a dispersive regularization of a shock wave, as it propagates in a strongly disordered environment. An original approach combining information measures and spin glass theory shows that time reversal focusing occurs for different replicas of the disorder in forward and backward propagation, provided the disorder varies on a length scale much shorter than the width of the soliton constituents. The analysis is performed by starting from a new class of reflectionless potentials, which describe the most general form of an expanding soliton gas of the defocusing nonlinear Schroedinger equation.Comment: 7 Pages, 6 Figure

Effects of demographic stochasticity on biological community assembly on evolutionary time scales

We study the effects of demographic stochasticity on the long-term dynamics of biological coevolution models of community assembly. The noise is induced in order to check the validity of deterministic population dynamics. While mutualistic communities show little dependence on the stochastic population fluctuations, predator-prey models show strong dependence on the stochasticity, indicating the relevance of the finiteness of the populations. For a predator-prey model, the noise causes drastic decreases in diversity and total population size. The communities that emerge under influence of the noise consist of species strongly coupled with each other and have stronger linear stability around the fixed-point populations than the corresponding noiseless model. The dynamics on evolutionary time scales for the predator-prey model are also altered by the noise. Approximate $1/f$ fluctuations are observed with noise, while $1/f^{2}$ fluctuations are found for the model without demographic noise

Gas gun shock experiments with single-pulse x-ray phase contrast imaging and diffraction at the Advanced Photon Source

The highly transient nature of shock loading and pronounced microstructure effects on dynamic materials response call for {\it in situ}, temporally and spatially resolved, x-ray-based diagnostics. Third-generation synchrotron x-ray sources are advantageous for x-ray phase contrast imaging (PCI) and diffraction under dynamic loading, due to their high photon energy, high photon fluxes, high coherency, and high pulse repetition rates. The feasibility of bulk-scale gas gun shock experiments with dynamic x-ray PCI and diffraction measurements was investigated at the beamline 32ID-B of the Advanced Photon Source. The x-ray beam characteristics, experimental setup, x-ray diagnostics, and static and dynamic test results are described. We demonstrate ultrafast, multiframe, single-pulse PCI measurements with unprecedented temporal ($<$100 ps) and spatial ($\sim$2 $\mu$m) resolutions for bulk-scale shock experiments, as well as single-pulse dynamic Laue diffraction. The results not only substantiate the potential of synchrotron-based experiments for addressing a variety of shock physics problems, but also allow us to identify the technical challenges related to image detection, x-ray source, and dynamic loading

Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

We present a straightforward and reliable continuous method for computing the full or a partial Lyapunov spectrum associated with a dynamical system specified by a set of differential equations. We do this by introducing a stability parameter beta>0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. We prove that the method is strongly stable when beta > -lambda_k where lambda_k is the k'th Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.Comment: 14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 k

Stretching Instability of Helical Spring

We show that when a gradually increasing tensile force is applied to the ends of a helical spring with sufficiently large ratios of radius to pitch and twist to bending rigidity, the end-to-end distance undergoes a sequence of discontinuous stretching transitions. Subsequent decrease of the force leads to step-like contraction and hysteresis is observed. For finite helices, the number of these transitions increases with the number of helical turns but only one stretching and one contraction instability survive in the limit of an infinite helix. We calculate the critical line that separates the region of parameters in which the deformation is continuous from that in which stretching instabilities occur, and propose experimental tests of our predictions.Comment: 5 pages, 4 figure

Interminiband Rabi oscillations in biased semiconductor superlattices

Carrier dynamics at energy level anticrossings in biased semiconductor superlattices, was studied in the time domain by solving the time-dependent Schroedinger equation. The resonant nature of interminiband Rabi oscillations has been explicitly demonstrated to arise from interference of intrawell and Bloch oscillations. We also report a simulation of direct Rabi oscillations across three minibands, in the high field regime, due to interaction between three strongly coupled minibands.Comment: 13 pages, 16 figure