Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The beam mode

Using asymptotics, the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell vibrating in the beam mode (viz. circumferential wave order n = 1) are studied. Initially, the uncoupled wavenumbers of the acoustic fluid and the cylindrical shell structure are discussed. Simple closed form expressions for the structural wavenumbers (longitudinal, torsional and bending) are derived using asymptotic methods for low- and high-frequencies. It is found that at low frequencies the cylinder in the beam mode behaves like a Timoshenko beam. Next, the coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter mu due to the coupling. An asymptotic expansion involving mu is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (as modifications to the uncoupled wavenumbers) separately for low- and high-frequency ranges and further, within each frequency range, for large and small values of mu. Only the flexural wavenumber, the first rigid duct acoustic cut-on wavenumber and the first pressure-release acoustic cut-on wavenumber are considered. The general trend found is that for small mu, the coupled wavenumbers are close to the in vacuo structural wavenumber and the wavenumbers of the rigid-acoustic duct. With increasing mu, the perturbations increase, until the coupled wavenumbers are better identified as perturbations to the pressure-release wavenumbers. The systematic derivation for the separate cases of small and large mu gives more insight into the physics and helps to continuously track the wavenumber solutions as the fluid-loading parameter is varied from small to large values. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. This method of asymptotics is simple to implement using a symbolic computation package (like Maple). (C) 2008 Elsevier Ltd. All rights reserved.

Asymptotic analysis for the coupled wavenumbers in an infinite fluid-filled flexible cylindrical shell: The axisymmetric mode

The coupled wavenumbers of a fluid-filled flexible cylindrical shell vibrating in the axisymmetric mode are studied. The coupled dispersion equation of the system is rewritten in the form of the uncoupled dispersion equation of the structure and the acoustic fluid, with an added fluid-loading term involving a parameter e due to the coupling. Using the smallness of Poisson's ratio (v), a double-asymptotic expansion involving e and v 2 is substituted in this equation. Analytical expressions are derived for the coupled wavenumbers (for large and small values of E). Different asymptotic expansions are used for different frequency ranges with continuous transitions occurring between them. The wavenumber solutions are continuously tracked as e varies from small to large values. A general trend observed is that a given wavenumber branch transits from a rigidwalled solution to a pressure-release solution with increasing E. Also, it is found that at any frequency where two wavenumbers intersect in the uncoupled analysis, there is no more an intersection in the coupled case, but a gap is created at that frequency. Only the axisymmetric mode is considered. However, the method can be extended to the higher order modes.

Generalised regression estimation for domain class frequencies

This study examines the properties of Generalised Regression (GREG) estimators for domain class frequencies and proportions. The family of GREG estimators forms the class of design-based model-assisted estimators. All GREG estimators utilise auxiliary information via modelling. The classic GREG estimator with a linear fixed effects assisting model (GREG-lin) is one example. But when estimating class frequencies, the study variable is binary or polytomous. Therefore logistic-type assisting models (e.g. logistic or probit model) should be preferred over the linear one. However, other GREG estimators than GREG-lin are rarely used, and knowledge about their properties is limited. This study examines the properties of L-GREG estimators, which are GREG estimators with fixed-effects logistic-type models. Three research questions are addressed. First, I study whether and when L-GREG estimators are more accurate than GREG-lin. Theoretical results and Monte Carlo experiments which cover both equal and unequal probability sampling designs and a wide variety of model formulations show that in standard situations, the difference between L-GREG and GREG-lin is small. But in the case of a strong assisting model, two interesting situations arise: if the domain sample size is reasonably large, L-GREG is more accurate than GREG-lin, and if the domain sample size is very small, estimation of assisting model parameters may be inaccurate, resulting in bias for L-GREG. Second, I study variance estimation for the L-GREG estimators. The standard variance estimator (S) for all GREG estimators resembles the Sen-Yates-Grundy variance estimator, but it is a double sum of prediction errors, not of the observed values of the study variable. Monte Carlo experiments show that S underestimates the variance of L-GREG especially if the domain sample size is minor, or if the assisting model is strong. Third, since the standard variance estimator S often fails for the L-GREG estimators, I propose a new augmented variance estimator (A). The difference between S and the new estimator A is that the latter takes into account the difference between the sample fit model and the census fit model. In Monte Carlo experiments, the new estimator A outperformed the standard estimator S in terms of bias, root mean square error and coverage rate. Thus the new estimator provides a good alternative to the standard estimator.

Coherent quasiparticle approximation cQPA and nonlocal coherence

We show that the dynamical Wigner functions for noninteracting fermions and bosons can have complex singularity structures with a number of new solutions accompanying the usual mass-shell dispersion relations. These new shell solutions are shown to encode the information of the quantum coherence between particles and antiparticles, left and right moving chiral states and/or between different flavour states. Analogously to the usual derivation of the Boltzmann equation, we impose this extended phase space structure on the full interacting theory. This extension of the quasiparticle approximation gives rise to a self-consistent equation of motion for a density matrix that combines the quantum mechanical coherence evolution with a well defined collision integral giving rise to decoherence. Several applications of the method are given, for example to the coherent particle production, electroweak baryogenesis and study of decoherence and thermalization.

Monte carlo simulation for molecular gas dynamics

The dynamics of low-density flows is governed by the Boltzmann equation of the kinetic theory of gases. This is a nonlinear integro-differential equation and, in general, numerical methods must be used to obtain its solution. The present paper, after a brief review of Direct Simulation Monte Carlo (DSMC) methods due to Bird, and Belotserkovskii and Yanitskii, studies the details of theDSMC method of Deshpande for mono as well as multicomponent gases. The present method is a statistical particle-in-cell method and is based upon the Kac-Prigogine master equation which reduces to the Boltzmann equation under the hypothesis of molecular chaos. The proposed Markoff model simulating the collisions uses a Poisson distribution for the number of collisions allowed in cells into which the physical space is divided. The model is then extended to a binary mixture of gases and it is shown that it is necessary to perform the collisions in a certain sequence to obtain unbiased simulation.

An accurate numerical integration scheme for finite rotations using rotation vector parametrization

A numerical integration procedure for rotational motion using a rotation vector parametrization is explored from an engineering perspective by using rudimentary vector analysis. The incremental rotation vector, angular velocity and acceleration correspond to different tangent spaces of the rotation manifold at different times and have a non-vectorial character. We rewrite the equation of motion in terms of vectors lying in the same tangent space, facilitating vector space operations consistent with the underlying geometric structure. While any integration algorithm (that works within a vector space setting) may be used, we presently employ a family of explicit Runge-Kutta algorithms to solve this equation. While this work is primarily motivated out of a need for highly accurate numerical solutions of dissipative rotational systems of engineering interest, we also compare the numerical performance of the present scheme with some of the invariant preserving schemes, namely ALGO-C1, STW, LIEMIDEA] and SUBCYC-M. Numerical results show better local accuracy via the present approach vis-a-vis the preserving algorithms. It is also noted that the preserving algorithms do not simultaneously preserve all constants of motion. We incorporate adaptive time-stepping within the present scheme and this in turn enables still higher accuracy and a `near preservation' of constants of motion over significantly longer intervals. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

A thermodynamic protocol for explaining subcriticality and other subtle features in self-deflagrating solids

A novel universal approach to understand the self-deflagration in solids has been attempted by using basic thermodynamic equation of partial differentiation, where burning mte depends on the initial temperature and pressure of the system. Self-deflagrating solids are rare and are reported only in few compounds like ammonium perchlorate (AP), polystyrene peroxide and tetrazole. This approach has led us to understand the unique characteristics of AP, viz. the existence of low pressure deflagration limit (LPL 20 atm), hitherto not understood sufficiently. This analysis infers that the overall surface activation energy comprises of two components governed by the condensed phase and gas phase processes. The most attractive feature of the model is the identification of a new subcritical regime I' below LPL where AP does not burn. The model is aptly supported by the thermochemical computations and temperature-profile analyses of the combustion train. The thermodynamic model is further corroborated from the kinetic analysis of the high pressure (1-30 atm) DTA thermograms which affords distinct empirical decomposition rate laws in regimes I' and 1 (20-60 atm). Using Fourier-Kirchoff one dimensional heat transfer differential equation, the phase transition thickness and the melt-layer thickness have been computed which conform to the experimental data.

Combining Bayes Classification and Point Group Symmetry under Boolean Framework for Enhanced Protein Quaternary Structure Inference

Our ability to infer the protein quaternary structure automatically from atom and lattice information is inadequate, especially for weak complexes, and heteromeric quaternary structures. Several approaches exist, but they have limited performance. Here, we present a new scheme to infer protein quaternary structure from lattice and protein information, with all-around coverage for strong, weak and very weak affinity homomeric and heteromeric complexes. The scheme combines naive Bayes classifier and point group symmetry under Boolean framework to detect quaternary structures in crystal lattice. It consistently produces >= 90% coverage across diverse benchmarking data sets, including a notably superior 95% coverage for recognition heteromeric complexes, compared with 53% on the same data set by current state-of-the-art method. The detailed study of a limited number of prediction-failed cases offers interesting insights into the intriguing nature of protein contacts in lattice. The findings have implications for accurate inference of quaternary states of proteins, especially weak affinity complexes.

Thomas-Fermi Method For Particles Obeying Generalized Exclusion Statistics

We use the Thomas-Fermi method to examine the thermodynamics of particles obeying Haldane exclusion statistics. Specifically, we study Calogero-Sutherland particles placed in a given external potential in one dimension. For the case of a simple harmonic potential (constant density of states), we obtain the exact one-particle spatial density and a {\it closed} form for the equation of state at finite temperature, which are both new results. We then solve the problem of particles in a $x^{2/3} ~$ potential (linear density of states) and show that Bose-Einstein condensation does not occur for any statistics other than bosons.

Nonequilibrium phase transition in the kinetic Ising model: Critical slowing down and the specific-heat singularity

The nonequilibrium dynamic phase transition, in the kinetic Ising model in the presence of an oscillating magnetic field has been studied both by Monte Carlo simulation and by solving numerically the mean-field dynamic equation of motion for the average magnetization. In both cases, the Debye ''relaxation'' behavior of the dynamic order parameter has been observed and the ''relaxation time'' is found to diverge near the dynamic transition point. The Debye relaxation of the dynamic order parameter and the power law divergence of the relaxation time have been obtained from a very approximate solution of the mean-field dynamic equation. The temperature variation of appropriately defined ''specific heat'' is studied by the Monte Carlo simulation near the transition point. The specific heat has been observed to diverge near the dynamic transition point.

Temperature scaling in a dense vibrofluidized granular material

The leading order "temperature" of a dense two-dimensional granular material fluidized by external vibrations is determined. The grain interactions are characterized by inelastic collisions, but the coefficient of restitution is considered to be close to 1, so that the dissipation of energy during a collision is small compared to the average energy of a particle. An asymptotic solution is obtained where the particles are considered to be elastic in the leading approximation. The velocity distribution is a Maxwell-Boltzmann distribution in the leading approximation,. The density profile is determined by solving the momentum balance equation in the vertical direction, where the relation between the pressure and density is provided by the virial equation of state. The temperature is determined by relating the source of energy due to the vibrating surface and the energy dissipation due to inelastic collisions. The predictions of the present analysis show good agreement with simulation results at higher densities where theories for a dilute vibrated granular material, with the pressure-density relation provided by the ideal gas law, sire in error. [:S1063-651X(99)04408-6].

Indian Ocean dipole mode events in an ocean general circulation model

The evolution of the dipole mode (DM) events in the Indian Ocean is examined using an ocean model that is driven by the NCEP fluxes for the period 1975-1998. The positive DM events during 1997, 1994 and 1982 and negative DM events during 1996 and 1984-1985 are captured by the model and it reproduces both the surface and subsurface features associated with these events. In its positive phase, the DM is characterized by warmer than normal SST in the western Indian Ocean and cooler than normal SST in the eastern Indian Ocean. The DM events are accompanied by easterly wind anomalies along the equatorial Indian Ocean and upwelling-favorable alongshore wind anomalies along the coast of Sumatra. The Wyrtki jets are weak during positive DM events, and the thermocline is shallower than normal in the eastern Indian Ocean and deeper in the west. This anomaly pattern reverses during negative DM events. During the positive phase of the DM easterly wind anomalies excite an upwelling equatorial Kelvin wave. This Kelvin wave reflects from the eastern boundary as an upwelling Rossby wave which propagates westward across the equatorial Indian Ocean. The anomalies in the eastern Indian Ocean weaken after the Rossby wave passes. A similar process excites a downwelling Rossby wave during the negative phase. This Rossby wave is much weaker but wind forcing in the central equatorial Indian Ocean amplifies the downwelling and increases its westward phase speed. This Rossby wave initiates the deepening of the thermocline in the western Indian Ocean during the following positive phase of the DM. Rossby wave generated in the southern tropical Indian Ocean by Ekman pumping contributes to this warming. Concurrently, the temperature equation of the model shows upwelling and downwelling to be the most important mechanism during both positive events of 1994 and 1997. (C) 2002 Elsevier Science Ltd. All rights reserved.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

A Simple Charge Model for Symmetric Double-Gate MOSFETs Adapted to Gate-Oxide-Thickness Asymmetry

Surface-potential-based compact charge models for symmetric double-gate metal-oxide-semiconductor field-effect transistors (SDG-MOSFETs) are based on the fundamental assumption of having equal oxide thicknesses for both gates. However, for practical devices, there will always be some amount of asymmetry between the gate oxide thicknesses due to process variations and uncertainties, which can affect device performance significantly. In this paper, we propose a simple surface-potential-based charge model, which is applicable for tied double-gate MOSFETs having same gate work function but could have any difference in gate oxide thickness. The proposed model utilizes the unique so-far-unexplored quasi-linear relationship between the surface potentials along the channel. In this model, the terminal charges could be computed by basic arithmetic operations from the surface potentials and applied biases, and thus, it could be implemented in any circuit simulator very easily and extendable to short-channel devices. We also propose a simple physics-based perturbation technique by which the surface potentials of an asymmetric device could be obtained just by solving the input voltage equation of SDG devices for small asymmetry cases. The proposed model, which shows excellent agreement with numerical and TCAD simulations, is implemented in a professional circuit simulator through the Verilog-A interface and demonstrated for a 101-stage ring oscillator simulation. It is also shown that the proposed model preserves the source/drain symmetry, which is essential for RF circuit design.

Combining heterogeneous classifiers for relational databases

Practical usage of machine learning is gaining strategic importance in enterprises looking for business intelligence. However, most enterprise data is distributed in multiple relational databases with expert-designed schema. Using traditional single-table machine learning techniques over such data not only incur a computational penalty for converting to a flat form (mega-join), even the human-specified semantic information present in the relations is lost. In this paper, we present a practical, two-phase hierarchical meta-classification algorithm for relational databases with a semantic divide and conquer approach. We propose a recursive, prediction aggregation technique over heterogeneous classifiers applied on individual database tables. The proposed algorithm was evaluated on three diverse datasets. namely TPCH, PKDD and UCI benchmarks and showed considerable reduction in classification time without any loss of prediction accuracy. (C) 2012 Elsevier Ltd. All rights reserved.