Asymptotic Stability for Equilibria of Nonlinear Semiflows with Applications to Rotating Viscoelastic Rods, Part I

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Stock Market Interdependence: Evidence from Australia

This study examines the relationship between Australia’s stock market and the five largest international markets for the period 1991 through 2001. Preliminary findings, using correlation statistics, indicated potential benefits to international diversification for the Australian investor. Further analysis, conducted in the VAR framework using the Johansen co-integration method, found that the Australian market has short and long run linkages with the United States, while tests with other markets found little evidence of interdependence. Moreover, only the US market was found to Grangercause the Australian market.Interdependence, price linkages, internationalisation.

Values of inland fisheries in the Mekong river basin

This report provides an overview of the biological, economical, social and cultural values of river fisheries in the Lower Mekong Basin (Yunan, Laos, Thailand, Cambodia and Vietnam). The report also identifies the main impacts of environmental changes on these values.Inland fisheries, Socioeconomic aspects, Economic analysis, Asia, ISEW, Vietnam, Mekong River Delta, Mekong Delta,

Quantum Theory of a Resonant Photonic Crystal

We present a quantum model of two-level atoms localized in a 3D lattice, based on the Hopfield theory of exciton polaritons. In addition to a polaritonic gap at the exciton energy, a photonic bandgap opens up at the Brillouin zone boundary. Upon tuning the lattice period or angle of incidence to match the photonic gap with the exciton energy, one obtains a combined polaritonic and photonic gap as a generalization of Rabi splitting. For typical experimental parameters, the size of the combined gap is on the order of 25 cm^{-1}, up to 10^5 times the detuned gap size. The dispersion curve contains a branch supporting slow-light modes with vanishing exciton probability density.Comment: 4 pages, 3 figure

Intrinsically Motivated Learning of Visual Motion Perception and Smooth Pursuit

We extend the framework of efficient coding, which has been used to model the development of sensory processing in isolation, to model the development of the perception/action cycle. Our extension combines sparse coding and reinforcement learning so that sensory processing and behavior co-develop to optimize a shared intrinsic motivational signal: the fidelity of the neural encoding of the sensory input under resource constraints. Applying this framework to a model system consisting of an active eye behaving in a time varying environment, we find that this generic principle leads to the simultaneous development of both smooth pursuit behavior and model neurons whose properties are similar to those of primary visual cortical neurons selective for different directions of visual motion. We suggest that this general principle may form the basis for a unified and integrated explanation of many perception/action loops.Comment: 6 pages, 5 figure

Global dynamics of a harmonically excited oscillator with a play : Numerical studies

This work was supported by the National Secretariat of Science, Technology and Innovation of Ecuador (SENESCYT); the Escuela Superior Politécnica del Litoral of Ecuador (ESPOL); the National Natural Science Foundation of China (11272268, 11572263) and Scholarship of China. A.S.E. Chong and Y. Yue acknowledge the hospitality of the Centre of Applied Dynamics Research at the University of Aberdeen.Peer reviewedPostprin

Phononic Rogue Waves

We present a theoretical study of extreme events occurring in phononic lattices. In particular, we focus on the formation of rogue or freak waves, which are characterized by their localization in both spatial and temporal domains. We consider two examples. The first one is the prototypical nonlinear mass-spring system in the form of a homogeneous Fermi-Pasta-Ulam-Tsingou (FPUT) lattice with a polynomial potential. By deriving an approximation based on the nonlinear Schroedinger (NLS) equation, we are able to initialize the FPUT model using a suitably transformed Peregrine soliton solution of the NLS, obtaining dynamics that resembles a rogue wave on the FPUT lattice. We also show that Gaussian initial data can lead to dynamics featuring rogue wave for sufficiently wide Gaussians. The second example is a diatomic granular crystal exhibiting rogue wave like dynamics, which we also obtain through an NLS reduction and numerical simulations. The granular crystal (a chain of particles that interact elastically) is a widely studied system that lends itself to experimental studies. This study serves to illustrate the potential of such dynamical lattices towards the experimental observation of acoustic rogue waves.Comment: 9 pages, 4 figure

Demonstration of dispersive rarefaction shocks in hollow elliptical cylinder chains

We report an experimental and numerical demonstration of dispersive rarefaction shocks (DRS) in a 3D-printed soft chain of hollow elliptical cylinders. We find that, in contrast to conventional nonlinear waves, these DRS have their lower amplitude components travel faster, while the higher amplitude ones propagate slower. This results in the backward-tilted shape of the front of the wave (the rarefaction segment) and the breakage of wave tails into a modulated waveform (the dispersive shock segment). Examining the DRS under various impact conditions, we find the counter-intuitive feature that the higher striker velocity causes the slower propagation of the DRS. These unique features can be useful for mitigating impact controllably and efficiently without relying on material damping or plasticity effects

Coupling/decoupling between translational and rotational dynamics in a supercooled molecular liquid

We use molecular dynamics computer simulations to investigate the coupling/decoupling between translational and rotational dynamics in a glass-forming liquid of dumbbells. This is done via a careful analysis of the $\alpha$-relaxation time $\tau_{q^{*}}^{\rm C}$ of the incoherent center-of-mass density correlator at the structure factor peak, the $\alpha$-relaxation time $\tau_{2}$ of the reorientational correlator, and the translational ($D_{t}$) and rotational ($D_{r}$) diffusion constants. We find that the coupling between the relaxation times $\tau_{q^{*}}^{\rm C}$ and $\tau_{2}$ increases with decreasing temperature $T$, whereas the coupling decreases between the diffusivities $D_{t}$ and $D_{r}$. In addition, the $T$-dependence of $D_{t}$ decouples from that of $1/\tau_{2}$, which is consistent with previous experiments and has been interpreted as a signature of the "translation-rotation decoupling." We trace back these apparently contradicting observations to the dynamical heterogeneities in the system. We show that the decreasing coupling in the diffusivities $D_{t}$ and $D_{r}$ is only apparent due to the inadequacy of the concept of the rotational diffusion constant for describing the reorientational dynamics in the supercooled state. We also argue that the coupling between $\tau_{q^{*}}^{\rm C}$ and $\tau_{2}$ and the decoupling between $D_{t}$ and $1/\tau_{2}$, both of which strengthen upon cooling, can be consistently understood in terms of the growing dynamic length scale.Comment: revised manuscript, to appear in Phys. Rev. Let