Physical Sciences and Mathematics Commons^™

All-Optical Suppression Of Relativistic Self-Focusing Of Laser Beams In Plasmas, Serguei Y. Kalmykov, Sunghwan A. Yi, Gennady Shvets

Serge Youri Kalmykov

It is demonstrated that a catastrophic relativistic self-focusing (RSF) of a high-power laser pulse can be prevented all-optically by a second, much weaker, copropagating pulse. RSF suppression occurs when the difference frequency of the pulses slightly exceeds the electron plasma frequency. The mutual defocusing is caused by the three-dimensional electron density perturbation driven by the laser beat wave slightly above the plasma resonance. A bi-envelope model describing the early stage of the mutual defocusing is derived and analyzed. Later stages, characterized by the presence of a strong electromagnetic cascade, are investigated numerically. Stable propagation of the laser pulse with weakly …

Estimated P-Values In Discrete Models: Asymptotic And Non-Asymptotic Effects, Chris Lloyd

Chris J. Lloyd

The exact null distribution of a P-value typically depends on nuisance parameters unspecified under the null. For discrete models and standard approximate P-values, this dependence can be quite strong. The estimated (or bootstrap) P-value is the exact probability of the P-value being no larger than its observed value, with the null estimate of the nuisance parameter substituted. For continuous models, it is known that such `bootstrap' P-values deviate from uniformity by terms of order m^{-3/2}, where m is a measure of sample size. The main difficulty with discrete models is the breakdown of asymptotics near the boundary. The aim of …

Oscillating Regime In Carbonylation Reaction Of Propargyl Alcohol (In Russian), Sergey N. Gorodsky, Anatoly V. Kurdiukov, Oleg N. Temkin

Sergey N. Gorodsky

No abstract provided.

Modeling Of Fermentation Processes Using Online Kernel Learning Algorithm, Yi Liu

Dr. Yi Liu

No abstract provided.

Adaptive Control Of A Class Of Nonlinear Discrete-Time Systems With Online Kernel Learning, Yi Liu

Dr. Yi Liu

No abstract provided.

A Symbolic Operator Approach To Power Series Transformation-Expansion Formulas, Tian-Xiao He

Tian-Xiao He

In this paper we discuss a kind of symbolic operator method by making use of the defined Sheffer-type polynomial sequences and their generalizations, which can be used to construct many power series transformation and expansion formulas. The convergence of the expansions are also discussed.

Studies Of Laser Wakefield Structures And Electron Acceleration In Underdense Plasmas, Anatoly Maksimchuk, Steven A. Reed, Stepan S. Bulanov, Vladimir Chvykov, Galina Kalintchenko, Takeshi Matsuoka, Christopher Mcguffey, Gerard Mourou, Natalia Naumova, John Nees, Pascal Rousseau, Victor Yanovsky, Karl Krushelnick, Nicholas H. Matlis, Serguei Y. Kalmykov, Gennady Shvets, Michael C. Downer, C. R. Vane, J. R. Beene, Daniel W. Stracener, David R. Schultz

Serge Youri Kalmykov

Experiments on electron acceleration and optical diagnostics of laser wakes were performed on the HERCULES facility in a wide range of laser and plasma parameters. Using frequency domain holography we demonstrated single shot visualization of individual plasma waves, produced by 40 TW, 30 fs laser pulses focused to the intensity of 10^{19} W/cm^2 onto a supersonic He gas jet with plasma densities n_e ~ 10^{19} cm^{−3}. These holographic “snapshots” capture the variation in shape of the plasma wave with distance behind the driver, and resolve wave front curvature seen previously only in simulations. High-energy quasimonoenergetic electron beams were generated using …

Computing Equilibria Of N-Player Games With Arbitrary Accuracy,, Srihari Govindan, Robert B. Wilson

Robert B Wilson

From a variant of Kuhn's triangulation we derive a discrete version of the Global Newton Method that yields an epsilon-equilibrium of an N-player game and then sequentially reduces epsilon toward zero to obtain any desired precision or the best precision for any number of iterations.

Evolution Of Higher-Order Gray Hirota Solitary Waves, Tim Marchant

Tim Marchant

The defocusing Hirota equation has dark and gray soliton solutions which are stable on a background of periodic waves of constant amplitude. In this paper, gray solitary wave evolution for a higher-order defocusing Hirota equation is examined. A direct analysis is used to identify families of higher-order gray Hirota solitary waves, which are embedded for certain parameter values. Soliton perturbation theory is used to detmine the detailed behavior of an evolving higher-order gray Hirota solitary wave. An integral expression for the first-order correction to the wave is found and analytical expressions for the steady-state and transient components of the solitary …

Mathematical Modelling Of Nematicons And Their Interactions, Prof. Tim Marchant

Tim Marchant

The mathematical modelling of guided wave (nematicon) propagation in liquid crystals is considered. Model equations are derived based on suitable trial functions in an averaged Lagrangian. These equations are used to model nematicon interactions.

Undular Bores And The Initial-Boundary Value Problem For The Modified Korteweg-De Vries Equation, Tim Marchant

Tim Marchant

Two types of analytical undular bore solutions, of the initial value problem for the modified Korteweg-de Vries (mKdV), are found. The first, an undular bore composed of cnoidal waves, is qualitatively similar to the bore found for the KdV equation, with solitons occurring at the leading edge and small amplitude linear waves occurring at the trailing edge. The second, a newly identified type of undular bore, consists of finite amplitude sinusiodal waves, which have a rational form. At the leading edge is the mKdV algebraic soliton, while, again, small amplitude linear waves occur at the trailing edge. The initial-boundary value …

Collisionless Shock Resolution In Nematic Liquid Crystals, Tim Marchant

Tim Marchant

The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in a nematic liquid crystal is considered, this material being an example of a self-focusing, nonlocal medium. It is found that the shock is resolved through the formation of an undular bore structure which persists for experimentally relevant propagation distances due to nonlocality delaying the onset of modulational instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semianalytical solution is developed for the line undular bore, approximating it as a train of uniform solitary waves. …

Semi-Analytical Solutions For A Gray-Scott Reaction-Diffusion Cell With An Applied Electric Field, Tim Marchant

Tim Marchant

An ionic version of the Gray–Scott chemical reaction scheme is considered in a reaction–diffusion cell, with an applied electric field, which causes migration of the reactant and autocatalyst in a preferred direction. The Galerkin method is used to reduce the governing partial differential equations to an approximate model consisting of ordinary differential equations. This is accomplished by approximating the spatial structure of the reactant and autocatalyst concentrations. Bifurcation analysis of the semi-analytical model is performed by using singularity theory to analyse the static multiplicity and a stability analysis to determine the dynamic multiplicity. The application of the electric field causes …

Nonlocal Validity Of An Asymptotic One-Dimensional Nematicon Solution, Tim Marchant

Tim Marchant

The propagation of coherent, polarized light in a nematic liquid crystal, governed by the nematicon equations, is considered. It is found that in the special case of 1 + 1 dimensions and the highly nonlocal limit, the nematicon equations have an asymptotic bulk solitary wave solution, termed a nematicon, which is given in terms of Bessel functions. This asymptotic solution gives both the ground state and the symmetric and antisymmetric excited states, which have multiple peaks. Numerical simulations of nematicon evolution, for parameters corresponding to experimental scenarios, are presented. It is found, for experimentally reasonable parameter choices, that the validity …

Bayesian Density Forecasting Of Intraday Electricity Prices Using Multivariate Skew T Distributions, Anastasios Panagiotelis, Michael Smith

Michael Stanley Smith

Electricity spot prices exhibit strong time series properties, including substantial periodicity, both inter-day and intraday serial correlation, heavy tails and skewness. In this paper we capture these characteristics using a first order vector autoregressive model with exogenous effects and a skew t distributed disturbance. The vector is longitudinal, in that it comprises observations on the spot price at intervals during a day. A band two inverse scale matrix is employed for the disturbance, as well as a sparse autoregressive coefficient matrix. This corresponds to a parsimonious dependency structure that directly relates an observation to the two immediately prior, and the …

Dipole Soliton Formation In A Nematic Liquid Crystal In The Non-Local Limit, Tim Marchant

Tim Marchant

The interaction of two symmetric solitary waves, termed nematicons, in a liquid crystal is considered in the limit of nonlocal response of the liquid crystal. This nonlocal limit is the applicable limit for most experimentally available liquid crystals. In this nonlocal limit, two separate cases for the initial separation of the nematicons are considered, these being large and small separation. Both spinning and nonspinning nematicons are considered. It is found that in the case of large initial separation, the nematicons can form a spinning or nonspinning bound state with a finite steady separation, this being called a nematicon dipole, when …

On Existence And Uniqueness Results For The Bbm Equation With Arbitrary Forcing Terms, Timothy A. Smith

Timothy Smith

Padé Spline Functions, Tian-Xiao He

Tian-Xiao He

We present here the definition of Pad´e spline functions, their expressions, and the estimate of the remainders of pad´e spline expansions. Some algorithms are also given.

Convergence To Equilibrium In Experimental Markets, Carolyn A. Galantine Cpa., Phd, Charles W. Swenson

Carolyn A Galantine CPA., PhD

The process by which market prices achieve equilibrium is an important topic, as the price formation process is fundamental to applied economic theory. Recently, economists have been applying complex mathematical functions to study the course of market prices convergence to equilibrium. Studies have made progress in modeling the price convergence process in at least one type of experimental market setting, the double auction. The double auction is of interest not only because of its prevalence in many types of real-world markets (e.g., the New York Stock Exchange), but also because of its extensive use in experimental economics. The double auction …

Cascading Infrastructure Failures: Avoidance And Response, George H. Baker, Cheryl J. Elliott

George H Baker

No critical infrastructure is self-sufficient. The complexity inherent in the interdependent nature of infrastructure systems complicates planning and preparedness for system failures. Recent wide-scale disruption of infrastructure on the Gulf Coast due to weather, and in the Northeast due to electric power network failures, dramatically illustrate the problems associated with mitigating cascading effects and responding to cascading infrastructure failures once they have occurred.

The major challenge associated with preparedness for cascading failures is that they transcend system, corporate, and political boundaries and necessitate coordination among multiple, disparate experts and authorities. This symposium brought together concerned communities including government and industry …