Time-resolved studies of ultrafast wavepacket dynamics in hydrogen molecules

Recent advances in the study of quantum vibrations and rotations in the fundamental hydrogen molecules are reported. Using the deuterium molecules (D-2(+) and D-2) as exemplars, the application of ultrafast femtosecond pump-probe experiments to study the creation and time-resolved imaging of coherent nuclear wavepackets is discussed. The ability to study the motion of these fundamental molecules in the time-domain is a notable milestone, made possible through the advent of ultrashort intense laser pulses with durations on sub-vibrational (and sub-rotational) timescales. Quantum wavepacket revivals are characterised for both vibrational and rotational degrees of freedom and quantum models are used to provide a detailed discussion of the underlying ultrafast physical dynamics for the specialist and non-specialist alike. (C) 2009 Elsevier B.V. All rights reserved.

Music, Magic, and the Mythic: The Dynamics of Visual and Aural Discourse in Souleymane Cissé’s Yeelen

The 1980s saw a wave of African films that aimed to represent, on both local and international screens, a sophisticated pre-colonial Africa, thus debunking notions of the continent as primitive. Toward this aim the films inscribed the conventions of oral performance within their visual styles, denying spectator identification with the protagonists and emphasising the presence of the narrator. However, some critics argued that these films exoticised Africa, while their use of oral performance’s distancing effect echoed the ‘scientific’ distance structured by the ethnographic film, in which African societies were represented as ‘the other’. Souleymane Cissé’s Yeelen exemplifies this tension, transposing into cinematic form oral storytelling techniques in the depiction of a power struggle within the covert cult of the komo, a Bambara initiation society unfamiliar to most non-Bambara viewers. This paper demonstrates how the film negotiates this tension via music, which interpellates the international spectator by eliciting a greater identification with the protagonists than that determined at a visual level, while encoding a verisimilitude to rituals that may otherwise be read as the superstitious practices of ‘the other’. In this way, music and image in Yeelen operate as parallel, though often overlapping, discourses, bridging the gap between the film’s culturally specific narrative and formal components, and its international spectators.

The feeding dynamics of broiler chickens

Contrary to a commonly held belief that broiler chickens need more space, there is increasing evidence that these birds are attracted to other birds. Indeed, commercially farmed birds exhibit a range of socially facilitated behaviours, such as increased feeding and preening in response to the presence of other birds. Social facilitation can generate feedback loops, whereby the adoption of a particular behaviour can spread rapidly and suddenly through the population. Here, by measuring the rate at which broiler chickens join and leave a feeding trough as a function of the number of birds already there, we quantify social facilitation. We use these measurements to parameterize a simulation model of chicken feeding behaviour. This model predicts, and further observations of broiler chickens confirm, that social facilitation leads to excitatory and synchronized patterns of group feeding. Such models could prove a powerful tool in understanding how feeding patterns depend on broiler house design.

Stability and dynamical behavior in a lake-model and implications for regime shifts in real lakes

A modified abstract version of the Comprehensive Aquatic Simulation Model (CASM) is found to exhibit three types of folded bifurcations due to nutrient loading. The resulting bifurcation diagrams account for nonlinear dynamics such as regime shifts and cyclic changes between clear-water state and turbid state that have actually been observed in real lakes. In particular, pulse-perturbation simulations based on the model presented suggest that temporal behaviors of real lakes after biomanipulations can be explained by pulse-dynamics in complex ecosystems, and that not only the amplitude (manipulated abundance of organisms) but also the phase (timing) is important for restoring lakes by biomanipulation. Ecosystem management in terms of possible irreversible changes in ecosystems induced by regime shifts is also discussed. (c) 2007 Elsevier B.V All rights reserved.

Simplification of structured population dynamics in complex ecological communities

Goldstone's idea of slow dynamics resulting from spontaneously broken symmetries is applied to Hubbell's neutral hypothesis of community dynamics, to efficiently simplify stage-structured multi-species models-introducing the quasi-neutral approximation (QNA). Rather than assuming population-dynamical neutrality in the QNA, deviations from ideal neutrality, thought to be small, drive dynamics. The QNA is systematically derived to first and second order in a two-scale singular perturbation expansion. The total reproductive value of species, as computed from the effective life-history parameters resulting from the non-linear interactions with the surrounding community, emerges as the new dynamic variables in this aggregated description. Using a simple stage-structured community-assembly model, the QNA is demonstrated to accurately reproduce population dynamics in large, complex communities. Further, the utility of the QNA in building intuition for management problems is illustrated by estimating the responses of a fish stock to harvesting and variations in fecundity.

Modeling Multivariate Interest Rates Using Time-Varying Copulas and Reducible Nonlinear Stochastic Differential Equations

We propose a new approach for modeling nonlinear multivariate interest rate processes based on time-varying copulas and reducible stochastic differential equations (SDEs). In the modeling of the marginal processes, we consider a class of nonlinear SDEs that are reducible to Ornstein--Uhlenbeck (OU) process or Cox, Ingersoll, and Ross (1985) (CIR) process. The reducibility is achieved via a nonlinear transformation function. The main advantage of this approach is that these SDEs can account for nonlinear features, observed in short-term interest rate series, while at the same time leading to exact discretization and closed-form likelihood functions. Although a rich set of specifications may be entertained, our exposition focuses on a couple of nonlinear constant elasticity volatility (CEV) processes, denoted as OU-CEV and CIR-CEV, respectively. These two processes encompass a number of existing models that have closed-form likelihood functions. The transition density, the conditional distribution function, and the steady-state density function are derived in closed form as well as the conditional and unconditional moments for both processes. In order to obtain a more flexible functional form over time, we allow the transformation function to be time varying. Results from our study of U.S. and UK short-term interest rates suggest that the new models outperform existing parametric models with closed-form likelihood functions. We also find the time-varying effects in the transformation functions statistically significant. To examine the joint behavior of interest rate series, we propose flexible nonlinear multivariate models by joining univariate nonlinear processes via appropriate copulas. We study the conditional dependence structure of the two rates using Patton (2006a) time-varying symmetrized Joe--Clayton copula. We find evidence of asymmetric dependence between the two rates, and that the level of dependence is positively related to the level of the two rates. (JEL: C13, C32, G12) Copyright The Author 2010. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

Dynamics of Gompertzian tumour growth under environmental fluctuations

We investigate the effect of correlated additive and multiplicative Gaussian white noise oil the Gompertzian growth of tumours. Our results are obtained by Solving numerically the time-dependent Fokker-Planck equation (FPE) associated with the stochastic dynamics. In Our numerical approach we have adopted B-spline functions as a truncated basis to expand the approximated eigenfunctions. The eigenfunctions and eigenvalues obtained using this method are used to derive approximate solutions of the dynamics under Study. We perform simulations to analyze various aspects, of the probability distribution. of the tumour cell populations in the transient- and steady-state regimes. More precisely, we are concerned mainly with the behaviour of the relaxation time (tau) to the steady-state distribution as a function of (i) of the correlation strength (lambda) between the additive noise and the multiplicative noise and (ii) as a function of the multiplicative noise intensity (D) and additive noise intensity (alpha). It is observed that both the correlation strength and the intensities of additive and multiplicative noise, affect the relaxation time.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Weakly nonlinear vertical dust grain oscillations in dusty plasma crystals in the presence of a magnetic field

The weakly nonlinear regime of transverse paramagnetic dust grain oscillations in dusty (complex) plasma crystals is discussed. The nonlinearity, which is related to the sheath electric/magnetic field(s) and to the intergrain (electrostatic/magnetic dipole) interactions, is shown to lead to the generation of phase harmonics and, in the case of propagating transverse dust-lattice modes, to the modulational instability of the carrier wave due to self-interaction. The stability profile depends explicitly on the form of the electric and magnetic fields in the plasma sheath. The long term evolution of the modulated wave packet, which is described by a nonlinear Schrodinger-type equation, may lead to propagating localized envelope structures whose exact forms are presented and discussed. Explicit suggestions for experimental investigations are put forward. (C) 2004 American Institute of Physics.

Lagrangian description of nonlinear dust-ion acoustic waves in dusty plasmas

An analytical model is presented for the description of nonlinear dust-ion-acoustic waves propagating in an unmagnetized, collisionless, three component plasma composed of electrons, ions and inertial dust grains. The formulation relies on a Lagrangian approach of the plasma fluid model. The modulational stability of the wave amplitude is investigated. Different types of localized envelope electrostatic excitations are shown to exist.

Nonlinear Lagrangian theory of envelope electrostatic plasma waves in a two-electron-temperature plasma

An analytical model based on Lagrangian variables is presented for the description of ion-acoustic waves propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions and two thermalized electron populations, characterized by different temperatures. The wave's amplitude is shown to be modulationally unstable. Different types of localized envelope electrostatic excitations are shown to exist, and their forms are analytically and numerically investigated in terms of the plasma dispersion and nonlinearity laws. These results are in qualitative agreement with satellite observations in the magnetosphere. (C) 2004 American Institute of Physics.