Evolution of an N-level system via automated vectorization of the Liouville equations and application to optically controlled polarization rotation

The Liouville equation governing the evolution of the density matrix for an atomic/molecular system is expressed in terms of a commutator between the density matrix and the Hamiltonian, along with terms that account for decay and redistribution. For finding solutions of this equation, it is convenient first to reformulate the Liouville equation by defining a vector corresponding to the elements of the density operator, and determining the corresponding time-evolution matrix. For a system of N energy levels, the size of the evolution matrix is N2xN2. When N is very large, evaluating the elements of these matrices becomes very cumbersome. We describe a novel algorithm that can produce the evolution matrix in an automated fashion for an arbitrary value of N. As a non-trivial example, we apply this algorithm to a fifteen-level atomic system used for producing optically controlled polarization rotation. We also point out how such a code can be extended for use in an atomic system with arbitrary number of energy levels

NbSe3: Effect of Uniaxial Stress on the Threshold Field and Fermiology

We have measured the effect of uniaxial stress on the threshold field ET for the motion of the upper CDW in NbSe3. ET exhibits a critical behavior, ET ~ (1 - e/ec)^g, wher e is the strain, and ec is about 2.6% and g ~ 1.2. This ecpression remains valid over more than two decades of ET, up to the highest fields of about 1.5keV/m. Neither g nor ec is very sensitive to the impurity concentraction. The CDW transition temperature Tp decreases linearly with e at a rate dTp/de = -10K/%, and it does not show any anomaly near ec. Shubnikov de-Haas measurements show that the extremal area of the Fermi surface decreases with increasing strain. The results suggest that there is an intimate relationship between pinning of the upper CDW and the Fermiology of NbSe3.Comment: 4 pages, 5 figure

Further SEASAT SAR coastal ocean wave analysis

Analysis techniques used to exploit SEASAT synthetic aperture radar (SAR) data of gravity waves are discussed and the SEASAT SAR's ability to monitor large scale variations in gravity wave fields in both deep and shallow water is evaluated. The SAR analysis techniques investigated included motion compensation adjustments and the semicausal model for spectral analysis of SAR wave data. It was determined that spectra generated from fast Fourier transform analysis (FFT) of SAR wave data were not significantly altered when either range telerotation adjustments or azimuth focus shifts were used during processing of the SAR signal histories, indicating that SEASAT imagery of gravity waves is not significantly improved or degraded by motion compensation adjustments. Evaluation of the semicausal (SC) model using SEASAT SAR data from Rev. 974 indicates that the SC spectral estimates were not significantly better than the FFT results

Door-to-door travel times in RP departure time choice models: An approximation method based on GPS data

A common way to determine values of travel time and schedule delay is by estimating departure time choice models using revealed preference (RP) data. The estimation of such models requires that (expected) travel times are known for both chosen as well as unchosen departure time alternatives. As the availability of such data is limited, most departure time choice studies only take into account travel times on trip segments rather than door-to-doortravel times, or use very rough measures of door-to-door travel times. We show that ignoring the temporal and spatial variation of travel times, and in particular, the correlation of travel times across links may lead to biased estimates of the value of time. To approximate door-to-door travel times for which no complete measurement is possible, we develop a model that relates travel times on links with continuous speed measurements to travel times on links where relatively sparse GPS-based speed measurements are available. We use geographically weighted regression to estimate the location-specific relation between the speeds on these two types of links, which is then used for travel time prediction at different locations, days, and times of the day. This method is not only useful for the calculation of door-to-door travel times in departure time choice models but is generally relevant for predicting travel times in situations where continuous speed measurementsshould be enriched with GPS data

Exact Hybrid Covariance Thresholding for Joint Graphical Lasso

This paper considers the problem of estimating multiple related Gaussian graphical models from a $p$-dimensional dataset consisting of different classes. Our work is based upon the formulation of this problem as group graphical lasso. This paper proposes a novel hybrid covariance thresholding algorithm that can effectively identify zero entries in the precision matrices and split a large joint graphical lasso problem into small subproblems. Our hybrid covariance thresholding method is superior to existing uniform thresholding methods in that our method can split the precision matrix of each individual class using different partition schemes and thus split group graphical lasso into much smaller subproblems, each of which can be solved very fast. In addition, this paper establishes necessary and sufficient conditions for our hybrid covariance thresholding algorithm. The superior performance of our thresholding method is thoroughly analyzed and illustrated by a few experiments on simulated data and real gene expression data

Long-Run vs. Short-Run Perspectives on Consumer Scheduling: Evidence from a Revealed-Preference Experiment among Peak-Hour Road Commuters

Theoretical and empirical studies of consumer scheduling behavior usually ignore that consumers have more flexibility to adjust their schedule in the long run than in the short run. We are able to distinguish between long-run choices of travel routines and short-run choices of departure times due to an extensive panel dataset of commuters who participate in a real-life peak avoidance experiment. We find that the participants, who obtain a monetary reward for not traveling along a camera-observed highway link during the morning peak, value travel time higher in the long-run context compared to the short run, as changes in travel time are more permanent and can be exploited better through the adjustment of routines. Schedule delays are, in contrast, valued higher inthe short-run model, reflecting that scheduling restrictions are typically more binding in the short run. Since the short-run and the long-run shadow prices differ by factors ranging from 2 to 5 in our basic model, our results may have substantial impacts on optimal choices for transport policies such as pricing and investment

Engineered swift equilibration of a Brownian particle

A fundamental and intrinsic property of any device or natural system is its relaxation time relax, which is the time it takes to return to equilibrium after the sudden change of a control parameter [1]. Reducing $tau$ relax , is frequently necessary, and is often obtained by a complex feedback process. To overcome the limitations of such an approach, alternative methods based on driving have been recently demonstrated [2, 3], for isolated quantum and classical systems [4--9]. Their extension to open systems in contact with a thermostat is a stumbling block for applications. Here, we design a protocol,named Engineered Swift Equilibration (ESE), that shortcuts time-consuming relaxations, and we apply it to a Brownian particle trapped in an optical potential whose properties can be controlled in time. We implement the process experimentally, showing that it allows the system to reach equilibrium times faster than the natural equilibration rate. We also estimate the increase of the dissipated energy needed to get such a time reduction. The method paves the way for applications in micro and nano devices, where the reduction of operation time represents as substantial a challenge as miniaturization [10]. The concepts of equilibrium and of transformations from an equilibrium state to another, are cornerstones of thermodynamics. A textbook illustration is provided by the expansion of a gas, starting at equilibrium and expanding to reach a new equilibrium in a larger vessel. This operation can be performed either very slowly by a piston, without dissipating energy into the environment, or alternatively quickly, letting the piston freely move to reach the new volume

Adaptive sliding-mode observer for second order discrete-time MIMO nonlinear systems based on recurrent neural-networks

This manuscript introduces a novel methodology to solve the state estimation of discrete-time multi-input multi-output (MIMO) nonlinear systems with uncertain dynamics. The mathematical model of the nonlinear systems considered in this paper satisfies the usual Lagrangian structure that characterizes many mechanical, electrical or electromechanical systems. A recurrent neural network (RNN) estimates the uncertain dynamics of the MIMO system with an updating law based on a particular variant of the discrete-time version of the super-twisting algorithm (DSTA). A Lyapunov stability analysis defines the convergence zone for the state estimation error throughout the solution of a matrix inequality. The convergence zone for the estimation is smaller when the DSTA and the RNN work together in an observer. Numerical examples demonstrate how the adaptive observer reduces the zone of convergence and the oscillations in the steady state compared with a discrete version of the STA with additional linear correcting terms. An experimental implementation shows how the observer estimates the unknown states of a Van Der Pol Oscillator. A comparison against some variations of the DSTA justifies the advantages of the mixed DSTA-RNN observer

Modelling Unsteady Processes with the Direct Simulation Monte Carlo Technique

Over the past 40 years, the Direct Simulation Monte Carlo (DSMC) technique has been developed into a flexible and effective solver for flow problems in the rarefied to near continuum regime. However, even with modern parallelised code, the efficient computation of unsteady near-continuum flows, which are important in processes such as Pulsed Pressure Chemical Vapour Deposition (PP-CVD), remains a challenge. We have developed an unsteady parallel DSMC code (PDSC) utilising advanced features such as transient adaptive sub-cells to ensure nearest neighbour collisions and a temporal-variable time step to reduce computation time. This technique is combined with a unique post-processor called the DMSC Rapid Ensemble Averaging Method (DREAM) which reduces the statistical scatter in the data sets produced by PDSC. The combined method results in a significant memory and computational reduction over ensemble averaging DSMC, while maintaining low statistical scatter in the results. The unsteady code has been validated by simulation of shock-tube flow and unsteady Couette flow, and a number of test cases have been demonstrated including shock impingement on wedges. The technique is currently being used to model the development of an underexpanded jet in a PP-CVD reactor