Transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space in a mode-locked fiber laser near the transition to multi-pulsing. Increasing cavity energy drives the dynamics through a periodic instability to chaotic dynamics. © 2010 Optical Society of America.

Characterizing the transition dynamics for multi-pulsing in mode-locked lasers

We consider experimentally and theoretically a refined parameter space near the transition to multi-pulse modelocking. Near the transition, the onset of instability is initiated by a Hopf (periodic) bifurcation. As cavity energy is increased, the band of unstable, oscillatory modes generates a chaotic behavior between single- and multi-pulse operation. Both theory and experiment are in good qualitative agreement and they suggest that the phenomenon is of a universal nature in mode-locked lasers at the onset of multi-pulsing from N to N + 1 pulses per round trip. This is the first theoretical and experimental characterization of the transition behavior, made possible by a highly refined tuning of the gain pump level. © 2010 Copyright SPIE - The International Society for Optical Engineering.

Dynamics of mode transitions in inductively-coupled plasmas

The dynamics of transitions between the electrostatic and electromagnetic discharge modes of the low-frequency (460 kHz) inductively coupled plasma (LF ICP) reactor is studied. A series of images of plasma glows in Ar and N2 gases taken in the process of continuous variation of the input power confirms the discharge bistability and hysteresis. The operation regimes and parameters making the LF ICP reactor attractive for materials synthesis and processing applications are discussed.

Explaining the Transition Between Exchange Rate Regimes

This paper studies the transition between exchange rate regimes using a Markov chain model with time-varying transition probabilities. The probabilities are parameterized as nonlinear functions of variables suggested by the currency crisis and optimal currency area literature. Results using annual data indicate that inflation, and to a lesser extent, output growth and trade openness help explain the exchange rate regime transition dynamics.

Tracking adversarial targets

We study linear control problems with quadratic losses and adversarially chosen tracking targets. We present an efficient algorithm for this problem and show that, under standard conditions on the linear system, its regret with respect to an optimal linear policy grows as O(log^2 T), where T is the number of rounds of the game. We also study a problem with adversarially chosen transition dynamics; we present an exponentiallyweighted average algorithm for this problem, and we give regret bounds that grow as O(sqtr p T).

On the origin of the inflectional instability of a laminar separation bubble

This is an experimental and theoretical Study of a laminar separation bubble and the associated linear stability mechanisms. Experiments were performed over a flat plate kept in a wind tunnel, with an imposed pressure gradient typical of an aerofoil that would involve a laminar separation bubble. The separation bubble was characterized by measurement of surface-pressure distribution and streamwise velocity using hot-wire anemometry. Single component hot-wire anemometry was also used for a detailed study of the transition dynamics. It was foundthat the so-called dead-air region in the front portion of the bubble corresponded to a region of small disturbance amplitudes, with the amplitude reaching a maximum value close to the reattachment point. An exponential growth rate of the disturbance was seen in the region upstream of the mean maximum height of the bubble, and this was indicative of a linear instability mechanism at work. An infinitesimal disturbance was impulsively introduced into the boundary layer upstream of separation location, and the wave packet was tracked (in an ensemble-averaged sense) while it was getting advected downstream. The disturbance was found to be convective in nature. Linear stability analyses (both the Orr-Sommerfeld and Rayleigh calculations) were performed for mean velocity profiles, starting from an attached adverse-pressure-gradient boundary layer all the way up to the front portion of the separation-bubble region (i.e. up to the end of the dead-air region in which linear evolution of the disturbance could be expected). The conclusion from the present work is that the primary instability mechanism in a separation bubble is inflectional in nature, and its origin can be traced back to upstream of the separation location. In other words, the inviscid inflectional instability of the separated shear layer should be logically seen as an extension of the instability of the upstream attached adverse-pressure-gradient boundary layer. This modifies the traditional view that pegs the origin of the instability in a separation bubble to the detached shear layer Outside the bubble, with its associated Kelvin-Helmholtz mechanism. We contendthat only when the separated shear layer has moved considerably away from the wall (and this happens near the maximum-height location of the mean bubble), a description by the Kelvin-Helmholtz instability paradigm, with its associated scaling principles, Could become relevant. We also propose a new scaling for the most amplified frequency for a wall-bounded shear layer in terms of the inflection-point height and the vorticity thickness and show it to be universal.

Simultaneous perturbation methods for adaptive labor staffing in service systems

We consider the problem of optimizing the workforce of a service system. Adapting the staffing levels in such systems is non-trivial due to large variations in workload and the large number of system parameters do not allow for a brute force search. Further, because these parameters change on a weekly basis, the optimization should not take longer than a few hours. Our aim is to find the optimum staffing levels from a discrete high-dimensional parameter set, that minimizes the long run average of the single-stage cost function, while adhering to the constraints relating to queue stability and service-level agreement (SLA) compliance. The single-stage cost function balances the conflicting objectives of utilizing workers better and attaining the target SLAs. We formulate this problem as a constrained parameterized Markov cost process parameterized by the (discrete) staffing levels. We propose novel simultaneous perturbation stochastic approximation (SPSA)-based algorithms for solving the above problem. The algorithms include both first-order as well as second-order methods and incorporate SPSA-based gradient/Hessian estimates for primal descent, while performing dual ascent for the Lagrange multipliers. Both algorithms are online and update the staffing levels in an incremental fashion. Further, they involve a certain generalized smooth projection operator, which is essential to project the continuous-valued worker parameter tuned by our algorithms onto the discrete set. The smoothness is necessary to ensure that the underlying transition dynamics of the constrained Markov cost process is itself smooth (as a function of the continuous-valued parameter): a critical requirement to prove the convergence of both algorithms. We validate our algorithms via performance simulations based on data from five real-life service systems. For the sake of comparison, we also implement a scatter search based algorithm using state-of-the-art optimization tool-kit OptQuest. From the experiments, we observe that both our algorithms converge empirically and consistently outperform OptQuest in most of the settings considered. This finding coupled with the computational advantage of our algorithms make them amenable for adaptive labor staffing in real-life service systems.

Bayesian inference and learning in Gaussian process state-space models with Particle MCMC

State-space models are successfully used in many areas of science, engineering and economics to model time series and dynamical systems. We present a fully Bayesian approach to inference and learning (i.e. state estimation and system identification) in nonlinear nonparametric state-space models. We place a Gaussian process prior over the state transition dynamics, resulting in a flexible model able to capture complex dynamical phenomena. To enable efficient inference, we marginalize over the transition dynamics function and, instead, infer directly the joint smoothing distribution using specially tailored Particle Markov Chain Monte Carlo samplers. Once a sample from the smoothing distribution is computed, the state transition predictive distribution can be formulated analytically. Our approach preserves the full nonparametric expressivity of the model and can make use of sparse Gaussian processes to greatly reduce computational complexity.

Branching ratios of x-ray photons from dielectronic recombination processes in H-like titanium ions

In dielectronic recombination of hydrogenlike ions an intermediate doubly excited heliumlike ion is formed. Since the K shell is empty, both excited electrons can decay sequentially to the ground state. In this paper we analyze the x-ray radiation emitted from doubly and singly excited heliumlike titanium ions produced inside the Tokyo electron beam ion trap. Theoretical population densities of the singly excited states after the first transition and the transition probabilities of these states into the ground state were also calculated. This allowed theoretical branching ratios to be determined for each manifold. These branching ratios are compared to the experimentally obtained x-ray distribution by fitting across the relevant peak using a convolution of the theoretically obtained resonance strengths and energies. By taking into account 2E1 transitions which are not observed in the experiment, the measured and calculated ratios agree well. This method provides a valuable insight into the transition dynamics of excited highly charged ions.

Atomistic Insights into Rhodopsin Activation from a Dynamic Model

Rhodopsin, the light sensitive receptor responsible for blue-green vision, serves as a prototypical G protein-coupled receptor (GPCR). Upon light absorption, it undergoes a series of conformational changes that lead to the active form, metarhodopsin II (META II), initiating a signaling cascade through binding to the G protein transducin (G(t)). Here, we first develop a structural model of META II by applying experimental distance restraints to the structure of lumi-rhodopsin (LUMI), an earlier intermediate. The restraints are imposed by using a combination of biased molecular dynamics simulations and perturbations to an elastic network model. We characterize the motions of the transmembrane helices in the LUMI-to-META II transition and the rearrangement of interhelical hydrogen bonds. We then simulate rhodopsin activation in a dynamic model to study the path leading from LUMI to our META II model for wild-type rhodopsin and a series of mutants. The simulations show a strong correlation between the transition dynamics and the pharmacological phenotypes of the mutants. These results help identify the molecular mechanisms of activation in both wild type and mutant rhodopsin. While static models can provide insights into the mechanisms of ligand recognition and predict ligand affinity, a dynamic model of activation could be applicable to study the pharmacology of other GPCRs and their ligands, offering a key to predictions of basal activity and ligand efficacy.

Influence of the anion on the electrical conductivity and glass formation of 1-butyl-3-methylimidazolium ionic liquids

Six ionic liquids based on the 1-butyl-3-methylimidazolium cation have been studied. As anions Cl-, Br-, I-, [NCS](-), [N(CN)(2)](-), and [BF4](-) were selected. The electrical conductivities were determined between 173 and 393 K based on impedance measurements in the frequency range from 0.1 to 10(7) Hz. The electrical conductivity increases, whereas the glass transition temperature, the fragility, and the low temperature activation energy decrease with increasing anion size. The results can be understood from the changing anion-cation interaction strength with changing anion size and from the energy landscape interpretation of the glass transition dynamics. (C) 2010 American Institute of Physics. [doi:10.1063/1.3455892]

When Casimir meets Kibble-Zurek

Verification of the dynamical Casimir effect (DCE) in optical systems is still elusive due to the very demanding requirements for its experimental implementation. This typically requires very fast changes in the boundary conditions of the problem. We show that an ensemble of two-level atoms collectively coupled to the electromagnetic field of a cavity, driven at low frequencies and close to a quantum phase transition, stimulates the production of photons from the vacuum. This paves the way for an effective simulation of the DCE through a mechanism that has recently found experimental demonstration. The spectral properties of the emitted radiation reflect the critical nature of the system and allow us to link the detection of DCE to the Kibble-Zurek mechanism for the production of defects when crossing a continuous phase transition.