A probabilistic constrained nonlinear optimization framework to optimize RED parameters

The random early detection (RED) technique has seen a lot of research over the years. However, the functional relationship between RED performance and its parameters viz,, queue weight (omega(q)), marking probability (max(p)), minimum threshold (min(th)) and maximum threshold (max(th)) is not analytically availa ble. In this paper, we formulate a probabilistic constrained optimization problem by assuming a nonlinear relationship between the RED average queue length and its parameters. This problem involves all the RED parameters as the variables of the optimization problem. We use the barrier and the penalty function approaches for its Solution. However (as above), the exact functional relationship between the barrier and penalty objective functions and the optimization variable is not known, but noisy samples of these are available for different parameter values. Thus, for obtaining the gradient and Hessian of the objective, we use certain recently developed simultaneous perturbation stochastic approximation (SPSA) based estimates of these. We propose two four-timescale stochastic approximation algorithms based oil certain modified second-order SPSA updates for finding the optimum RED parameters. We present the results of detailed simulation experiments conducted over different network topologies and network/traffic conditions/settings, comparing the performance of Our algorithms with variants of RED and a few other well known adaptive queue management (AQM) techniques discussed in the literature.

On the sensitivity of elastic waves due to structural damages:Time-frequency based indexing method

Time-frequency analysis of various simulated and experimental signals due to elastic wave scattering from damage are performed using wavelet transform (WT) and Hilbert-Huang transform (HHT) and their performances are compared in context of quantifying the damages. Spectral finite element method is employed for numerical simulation of wave scattering. An analytical study is carried out to study the effects of higher-order damage parameters on the reflected wave from a damage. Based on this study, error bounds are computed for the signals in the spectral and also on the time-frequency domains. It is shown how such an error bound can provide all estimate of error in the modelling of wave propagation in structure with damage. Measures of damage based on WT and HHT is derived to quantify the damage information hidden in the signal. The aim of this study is to obtain detailed insights into the problem of (1) identifying localised damages (2) dispersion of multifrequency non-stationary signals after they interact with various types of damage and (3) quantifying the damages. Sensitivity analysis of the signal due to scattered wave based on time-frequency representation helps to correlate the variation of damage index measures with respect to the damage parameters like damage size and material degradation factors.

Instabilities and Waves in Thin Films of Living Fluids

We formulate the thin-film hydrodynamics of a suspension of polar self-driven particles and show that it is prone to several instabilities through the interplay of activity, polarity, and the existence of a free surface. Our approach extends, to self-propelling systems, the work of Ben Amar and Cummings [Phys. Fluids 13 1160 (2001)] on thin-film nematics. Based on our estimates the instabilities should be seen in bacterial suspensions and the lamellipodium, and are potentially relevant to the morphology of biofilms. We suggest several experimental tests of our theory.

In search of inorganic nonlinear optical materials for second harmonic generation

In a search for inorganic oxide materials showing second-order nonlinear optical (NLO) susceptibility, we investigated several berates, silicates, and a phosphate containing trans-connected MO6, octahedral chains or MO5 square pyramids, where, M = d(0): Ti(IV), Nb(V), or Ta(V), Our investigations identified two new NLO structures: batisite, Na2Ba(TiO)(2)Si4O12, containing trans-connected TiO5 octahedral chains, and fresnoite, Ba2TiOSi2O7, containing square-pyramidal TiO5. Investigation of two other materials containing square-pyramidal TiO5 viz,, Cs2TiOP2O7 and Na4Ti2Si8O22. 4H(2)O, revealed that isolated TiO5, square pyramids alone do not cause a second harmonic generation (SHG) response; rather, the orientation of TiO5 units to produce -Ti-O-Ti-O- chains with alternating long and short Ti-O distances in the fresnoite structure is most likely the origin of a strong SHG response in fresnoite,

Energy-momentum conserving algorithm for nonlinear transient analysis within the framework of hybrid elements

This work deals with the formulation and implementation of an energy-momentum conserving algorithm for conducting the nonlinear transient analysis of structures, within the framework of stress-based hybrid elements. Hybrid elements, which are based on a two-field variational formulation, are much less susceptible to locking than conventional displacement-based elements within the static framework. We show that this advantage carries over to the transient case, so that not only are the solutions obtained more accurate, but they are obtained in fewer iterations. We demonstrate the efficacy of the algorithm on a wide range of problems such as ones involving dynamic buckling, complicated three-dimensional motions, et cetera.

Influence of non-stoichiometric defects on nonlinear absorption and refraction in Nd:Zn co-doped lithium niobate

Nonlinear absorption and refraction phenomena in stoichiometric lithium niobate (SLN) pure and co-doped with Zn and Nd, and congruent lithium niobate (CLN) were investigated using Z-scan technique. Femtosecond laser pulses from Ti:Sapphire laser (800 nm, 110 fs pulse width and 1 kHz repetition rate) were utilized for the experiment. The process responsible for nonlinear behavior of the samples was identified to be three photon absorption (3PA). This is in agreement with the band gap energies of the samples obtained from the linear absorption cut off and the slope of the plot of Ln(1 − TOA) vs. Ln(I0) using Sutherland’s theory (s = 2.1, for 3PA). The nonlinear refractive index (n2) of Zn doped samples was found to be lower than that of pure samples. Our experiments show that there exists a correlation between the nonlinear properties and the stoichiometry of the samples. The values of n2 fall into the same range as those obtained for the materials of similar band gap.

Surface waves in the presence of external high frequency fields

The system equations of a collisionless, unmagnetized plasma, contained in a box where a high frequency (HF) electric field is incident, are solved in the electrostatic approximation. The surface modes of the plasma in the semi-infinite and box geometry are investigated. In thi high frequency limit, the mode frequencies are not significantly changed by the HF field but their group velocities can be quite different. Two long wavelength low frequency modes, which are not excited in the absence of HF field, are found. These modes are true surface modes (decaying on one wavelength from the surface) unlike the only low frequency ion acoustic mode in the zero field case. In the short wavelength limit the low frequency mode occurs at omega i/ square root 2, omega i being the ion plasma frequency, as a result similar to the case of no HF field.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Mesh-free approximations via the error reproducing kernel method and applications to nonlinear systems developing shocks

Error estimates for the error reproducing kernel method (ERKM) are provided. The ERKM is a mesh-free functional approximation scheme [A. Shaw, D. Roy, A NURBS-based error reproducing kernel method with applications in solid mechanics, Computational Mechanics (2006), to appear (available online)], wherein a targeted function and its derivatives are first approximated via non-uniform rational B-splines (NURBS) basis function. Errors in the NURBS approximation are then reproduced via a family of non-NURBS basis functions, constructed using a polynomial reproduction condition, and added to the NURBS approximation of the function obtained in the first step. In addition to the derivation of error estimates, convergence studies are undertaken for a couple of test boundary value problems with known exact solutions. The ERKM is next applied to a one-dimensional Burgers equation where, time evolution leads to a breakdown of the continuous solution and the appearance of a shock. Many available mesh-free schemes appear to be unable to capture this shock without numerical instability. However, given that any desired order of continuity is achievable through NURBS approximations, the ERKM can even accurately approximate functions with discontinuous derivatives. Moreover, due to the variation diminishing property of NURBS, it has advantages in representing sharp changes in gradients. This paper is focused on demonstrating this ability of ERKM via some numerical examples. Comparisons of some of the results with those via the standard form of the reproducing kernel particle method (RKPM) demonstrate the relative numerical advantages and accuracy of the ERKM.

A comment on the consistency of truncated nonlinear integral equation based theories of freezing

We report the results of two studies of aspects of the consistency of truncated nonlinear integral equation based theories of freezing: (i) We show that the self-consistent solutions to these nonlinear equations are unfortunately sensitive to the level of truncation. For the hard sphere system, if the Wertheim–Thiele representation of the pair direct correlation function is used, the inclusion of part but not all of the triplet direct correlation function contribution, as has been common, worsens the predictions considerably. We also show that the convergence of the solutions found, with respect to number of reciprocal lattice vectors kept in the Fourier expansion of the crystal singlet density, is slow. These conclusions imply great sensitivity to the quality of the pair direct correlation function employed in the theory. (ii) We show the direct correlation function based and the pair correlation function based theories of freezing can be cast into a form which requires solution of isomorphous nonlinear integral equations. However, in the pair correlation function theory the usual neglect of the influence of inhomogeneity of the density distribution on the pair correlation function is shown to be inconsistent to the lowest order in the change of density on freezing, and to lead to erroneous predictions. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.

Studies in Nonlinear Optical Materials: Structure of 3-Menthyl 2-[Bis(dimethylarnino)methylene]-3-oxobutyrate Hemihydrate

C 19Ha4N203.~xH 2 O, Mr= 347.5, monoclinic, C2, a = 15.473 (3), b = 6.963 (2), c = 20.708 (4) ]1, //=108.2(2) ° , V=2119(2)A 3, Z=4, Ox= 1.089 Mg m -3, ,~(Cu Ktx) = 1.5418 ]1, p = 0.523 mm -~, F(000) = 760.0, T= 293 K, R = 0.068 for 1967 unique reflections. The C=C bond length is 1-447 (6)]1, significantly longer than in ethylene, 1.336 (2)]1. The crystal structure is stabilized by O-H...O hydrogen bonding. Explanation for the observed low second-harmonic-generation efficiency (0.5 times that of urea) is provided.

Formation of Standing Waves on Lecher Wires

With a short review of the work on the Lecher wire method of wavelength measurement, this paper describes in detail the wave form of current distribution along wires under a variety of terminal conditions of length and impedances.

Thermal Overstability Of Hydromagnetic Surface-Waves

We investigate the effects of radiative heat losses and thermal conductivity on the hydromagnetic surface waves along a magnetic discontinuity in a plasma of infinite electrical conductivity. We show that the effects of radiative heat losses on such surface waves are appreciable only when values of the plasma pressure on the two sides of the discontinuity are substantially different. Overstability of a surface wave requires that the medium in which it gives larger first-order compression should satisfy the criterion of Field (1965). Possible applications of the study to magnetic discontinuities in solar corona are briefly discussed.

Studies in Nonlinear Optical Materials: Structure of Methyl 2-(4-Ethyl-5-methyl- 2-thioxo-2,3-dihydro-l,3-thiazol- 3-yl) propionate

CIoH15NO282, Mr=245"0, orthorhombic, P21212 ~, a = 6.639 (2), b = 8.205 (2), c = 22.528(6)A, V= I227.2(6)A 3, z=4, Dm= 1.315, Dx= 1.326gem -3, MoKa, 2=0.7107A, 12= 3.63 cm -1, F(000) = 520, T= 293 K, R = 0.037 for 1115 significant reflections. The second-harmonicgeneration (SHG) efficiency of this compound is only 1/10th of the urea standard. The observed low second-order nonlinear response may be attributed to the unfavourable packing of the molecules in the crystal lattice.