Strong shock approximation in the new theory of shock dynamics

This paper investigates the propagation of a strong shock into an inhomogeneous medium using the new theory of shock dynamics. The equations are simple to solve and involve no trial-and-error method commonly used in this case. The results compare favourably with earlier results obtained in the case of self-similar flows, which arise as a special case of this theory.

The actor-critic algorithm as multi-time-scale stochastic approximation

The actor-critic algorithm of Barto and others for simulation-based optimization of Markov decision processes is cast as a two time Scale stochastic approximation. Convergence analysis, approximation issues and an example are studied.

Theory of combined AM and high-harmonic FM mode locked laser

Closed form solutions for a simultaneously AM and high-harmonic FM mode locked laser system is presented. Analytical expressions for the pulsewidth and pulsewidth-bandwidth products are derived in terms of the system parameters. The analysis predicts production of 17 ps duration pulses in a Nd:YAG laser mode locked with AM and FM modulators driven at 80 MHz and 1.76 GHz for 1 W modulator input power. The predicted values of the pulsewidth-bandwidth product lie between the values corresponding to the pure AM and FM mode locking values.

Providing quality of service via opportunistic splitting using stochastic approximation

We consider the problem of wireless channel allocation to multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. Each metric sequence can be Markov. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

Opportunistic splitting for scheduling via stochastic approximation

We consider the problem of scheduling a wireless channel among multiple users. A slot is given to a user with a highest metric (e.g., channel gain) in that slot. The scheduler may not know the channel states of all the users at the beginning of each slot. In this scenario opportunistic splitting is an attractive solution. However this algorithm requires that the metrics of different users form independent, identically distributed (iid) sequences with same distribution and that their distribution and number be known to the scheduler. This limits the usefulness of opportunistic splitting. In this paper we develop a parametric version of this algorithm. The optimal parameters of the algorithm are learnt online through a stochastic approximation scheme. Our algorithm does not require the metrics of different users to have the same distribution. The statistics of these metrics and the number of users can be unknown and also vary with time. We prove the convergence of the algorithm and show its utility by scheduling the channel to maximize its throughput while satisfying some fairness and/or quality of service constraints.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data. (C) 2011 Optical Society of America

Theory of Gas Hydrates: Effect of the Approximation of Rigid Water Lattice

One of the assumptions of the van der Waals and Platteeuw theory for gas hydrates is that the host water lattice is rigid and not distorted by the presence of guest molecules. In this work, we study the effect of this approximation on the triple-point lines of the gas hydrates. We calculate the triple-point lines of methane and ethane hydrates via Monte Carlo molecular simulations and compare the simulation results with the predictions of van der Waals and Platteeuw theory. Our study shows that even if the exact intermolecular potential between the guest molecules and water is known, the dissociation temperatures predicted by the theory are significantly higher. This has serious implications to the modeling of gas hydrate thermodynamics, and in spite of the several impressive efforts made toward obtaining an accurate description of intermolecular interactions in gas hydrates, the theory will suffer from the problem of robustness if the issue of movement of water molecules is not adequately addressed.

Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

Optical diffraction of second-harmonic signals in the LiBO2-Nb2O5 glasses induced by self-organized LiNbO3 crystallites

The nanocrystallites ( ≈ 3 nm) of LiNbO3, evolved in the (100−x)LiBO2-xNb2O5 (5x20, in molar ratio) glass system exhibited intense second-harmonic signals in transmission mode when exposed to infrared (IR) light at λ = 1064 nm. The second-harmonic waves were found to undergo optical diffraction which was attributed to the presence of self-organized submicrometer-sized LiNbO3 crystallites that were grown within the glass matrix along the parallel damage fringes created by the IR laser radiation. Micro-Raman studies carried out on the laser-irradiated samples confirmed the self-organized crystallites to be LiNbO3.

Adaptive Harmonic Elimination Technique in Single Phase PWM Inverters

High frequency PWM inverters produce an output voltage spectrum at the fundamental reference frequency and around the switching frequency. Thus ideally PWM inverters do not introduce any significant lower order harmonics. However, in real systems, due to dead-time effect, device drops and other non-idealities lower order harmonics are present. In order to attenuate these lower order harmonics and hence to improve the quality of output current, this paper presents an \emph{adaptive harmonic elimination technique}. This technique uses an adaptive filter to estimate a particular harmonic that is to be attenuated and generates a voltage reference which will be added to the voltage reference produced by the current control loop of the inverter. This would have an effect of cancelling the voltage that was producing the particular harmonic. The effectiveness and the limitations of the technique are verified experimentally in a single phase PWM inverter in stand-alone as well as g rid interactive modes of operation.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.