Generalized asymptotic expansions for coupled wavenumbers in fluid-filled cylindrical shells

Analytical expressions are found for the coupled wavenumbers in an infinite fluid-filled cylindrical shell using the asymptotic methods. These expressions are valid for any general circumferential order (n).The shallow shell theory (which is more accurate at higher frequencies)is used to model the cylinder. Initially, the in vacua shell is dealt with and asymptotic expressions are derived for the shell wavenumbers in the high-and the low-frequency regimes. Next, the fluid-filled shell is considered. Defining a relevant fluid-loading parameter p, we find solutions for the limiting cases of small and large p. Wherever relevant, a frequency scaling parameter along with some ingenuity is used to arrive at an elegant asymptotic expression. In all cases.Poisson's ratio v is used as an expansion variable. The asymptotic results are compared with numerical solutions of the dispersion equation and the dispersion relation obtained by using the more general Donnell-Mushtari shell theory (in vacuo and fluid-filled). A good match is obtained. Hence, the contribution of this work lies in the extension of the existing literature to include arbitrary circumferential orders(n). (C) 2010 Elsevier Ltd. All rights reserved.

Evolution of polyandry by reduction in progeny number variance in structured populations

When there is a variation in the quality of males in a population, multiple mating can lead to an increase in the genetic fitness of a female by reducing the variance of the progeny number. The extent of selective advantage obtainable by this process is investigated for a population subdivided into structured demes. It is seen that for a wide range of model parameters (deme size, distribution of male quality, local resource level), multiple mating leads to a considerable increase in the fitness. Frequency-dependent selection or a stable coexistence between polyandry and monandry can also result when the possible costs involved in multiple mating are taken into account.

On Finding the Natural Number of Topics with Latent Dirichlet Allocation: Some Observations

It is important to identify the ``correct'' number of topics in mechanisms like Latent Dirichlet Allocation(LDA) as they determine the quality of features that are presented as features for classifiers like SVM. In this work we propose a measure to identify the correct number of topics and offer empirical evidence in its favor in terms of classification accuracy and the number of topics that are naturally present in the corpus. We show the merit of the measure by applying it on real-world as well as synthetic data sets(both text and images). In proposing this measure, we view LDA as a matrix factorization mechanism, wherein a given corpus C is split into two matrix factors M-1 and M-2 as given by C-d*w = M1(d*t) x Q(t*w).Where d is the number of documents present in the corpus anti w is the size of the vocabulary. The quality of the split depends on ``t'', the right number of topics chosen. The measure is computed in terms of symmetric KL-Divergence of salient distributions that are derived from these matrix factors. We observe that the divergence values are higher for non-optimal number of topics - this is shown by a `dip' at the right value for `t'.

Design of speaker identification schemes for large number of speakers (A)

Design of speaker identification schemes for a small number of speakers (around 10) with a high degree of accuracy in controlled environment is a practical proposition today. When the number of speakers is large (say 50–100), many of these schemes cannot be directly extended, as both recognition error and computation time increase monotonically with population size. The feature selection problem is also complex for such schemes. Though there were earlier attempts to rank order features based on statistical distance measures, it has been observed only recently that the best two independent measurements are not the same as the combination in two's for pattern classification. We propose here a systematic approach to the problem using the decision tree or hierarchical classifier with the following objectives: (1) Design of optimal policy at each node of the tree given the tree structure i.e., the tree skeleton and the features to be used at each node. (2) Determination of the optimal feature measurement and decision policy given only the tree skeleton. Applicability of optimization procedures such as dynamic programming in the design of such trees is studied. The experimental results deal with the design of a 50 speaker identification scheme based on this approach.

A Novel, Balanced, and Energy-Efficient Training Method for Receive Antenna Selection

In receive antenna selection (AS), only signals from a subset of the antennas are processed at any time by the limited number of radio frequency (RF) chains available at the receiver. Hence, the transmitter needs to send pilots multiple times to enable the receiver to estimate the channel state of all the antennas and select the best subset. Conventionally, the sensitivity of coherent reception to channel estimation errors has been tackled by boosting the energy allocated to all pilots to ensure accurate channel estimates for all antennas. Energy for pilots received by unselected antennas is mostly wasted, especially since the selection process is robust to estimation errors. In this paper, we propose a novel training method uniquely tailored for AS that transmits one extra pilot symbol that generates accurate channel estimates for the antenna subset that actually receives data. Consequently, the transmitter can selectively boost the energy allocated to the extra pilot. We derive closed-form expressions for the proposed scheme's symbol error probability for MPSK and MQAM, and optimize the energy allocated to pilot and data symbols. Through an insightful asymptotic analysis, we show that the optimal solution achieves full diversity and is better than the conventional method.

Steady incompressible flow of cohesionless granular materials through a wedge-shaped hopper: Frictional 14kinetic solution to the smooth wall, radial gravity problem

Hybrid frictional-kinetic equations are used to predict the velocity, grain temperature, and stress fields in hoppers. A suitable choice of dimensionless variables permits the pseudo-thermal energy balance to be decoupled from the momentum balance. These balances contain a small parameter, which is analogous to a reciprocal Reynolds number. Hence an approximate semi-analytical solution is constructed using perturbation methods. The energy balance is solved using the method of matched asymptotic expansions. The effect of heat conduction is confined to a very thin boundary layer near the exit, where it causes a marginal change in the temperature. Outside this layer, the temperature T increases rapidly as the radial coordinate r decreases. In particular, the conduction-free energy balance yields an asymptotic solution, valid for small values of r, of the form T proportional r-4. There is a corresponding increase in the kinetic stresses, which attain their maximum values at the hopper exit. The momentum balance is solved by a regular perturbation method. The contribution of the kinetic stresses is important only in a small region near the exit, where the frictional stresses tend to zero. Therefore, the discharge rate is only about 2.3% lower than the frictional value, for typical parameter values. As in the frictional case, the discharge rate for deep hoppers is found to be independent of the head of material.

Radiative interactions in boundary layers

A detailed description of radiative interactions in laminar compressible boundary layers for moderate Mach numbers is presented by way of asymptotic analysis and supporting solutions. The radiation field is described by the differential approximation. While the asymptotic analysis is valid for large N (the ratio of photon mean free path to molecular mean free path) and arbitrary Boltzmann number, Bo (the ratio of convective heat flux to radiation heat flux), the solutions are obtained for Bo [double less-than sign] 1, the case of strong radiative interactions. The asymptotic analysis shows the existence of an optically thin boundary layer for large N and all Bo. For Bo [double less-than sign] 1, two outer regions are observed — one optically thin (at short distances from the leading edge) and the other optically thick (at large distances from the leading edge). An interesting feature not pointed out in the previous literature is the existence of a wall layer at large distances from the leading edge where convective heat flux can be ignored to the leading order of approximation. The radiation field in all cases can be very well approximated by a one-dimensional description. The solutions have been constructed using the ideas of matched asymptotic expansions by approximate analytical procedures and numerical methods. It is shown that, to the leading order of approximation, the radiation slip method yields exactly the same result as the more complicated matching procedure. Both the cases of linear and nonlinear radiation have been considered, the former being of interest in developing approximate methods which are subsequently generalized to handle the nonlinear problem. Detailed results are presented for both cases.

Cubicity of Interval Graphs and the Claw Number

Let G(V, E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product l(1) x l(2) x ... x l(b), where each l(i) is a closed interval of unit length on the real line. The cub/city of G, denoted by cub(G), is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way that two vertices are adjacent in G if and only if their assigned cubes intersect. An interval graph is a graph that can be represented as the intersection of intervals on the real line-i.e. the vertices of an interval graph can be mapped to intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals overlap. Suppose S(m) denotes a star graph on m+1 nodes. We define claw number psi(G) of the graph to be the largest positive integer m such that S(m) is an induced subgraph of G. It can be easily shown that the cubicity of any graph is at least log(2) psi(G)]. In this article, we show that for an interval graph G log(2) psi(G)-]<= cub(G)<=log(2) psi(G)]+2. It is not clear whether the upper bound of log(2) psi(G)]+2 is tight: till now we are unable to find any interval graph with cub(G)> (log(2)psi(G)]. We also show that for an interval graph G, cub(G) <= log(2) alpha], where alpha is the independence number of G. Therefore, in the special case of psi(G)=alpha, cub(G) is exactly log(2) alpha(2)]. The concept of cubicity can be generalized by considering boxes instead of cubes. A b-dimensional box is a Cartesian product l(1) x l(2) x ... x l(b), where each I is a closed interval on the real line. The boxicity of a graph, denoted box(G), is the minimum k such that G is the intersection graph of k-dimensional boxes. It is clear that box(G)<= cub(G). From the above result, it follows that for any graph G, cub(G) <= box(G)log(2) alpha]. (C) 2010 Wiley Periodicals, Inc. J Graph Theory 65: 323-333, 2010

Voluntary Energy Harvesting Relays and Selection in Cooperative Wireless Networks

The use of energy harvesting (EH) nodes as cooperative relays is a promising and emerging solution in wireless systems such as wireless sensor networks. It harnesses the spatial diversity of a multi-relay network and addresses the vexing problem of a relay's batteries getting drained in forwarding information to the destination. We consider a cooperative system in which EH nodes volunteer to serve as amplify-and-forward relays whenever they have sufficient energy for transmission. For a general class of stationary and ergodic EH processes, we introduce the notion of energy constrained and energy unconstrained relays and analytically characterize the symbol error rate of the system. Further insight is gained by an asymptotic analysis that considers the cases where the signal-to-noise-ratio or the number of relays is large. Our analysis quantifies how the energy usage at an EH relay and, consequently, its availability for relaying, depends not only on the relay's energy harvesting process, but also on its transmit power setting and the other relays in the system. The optimal static transmit power setting at the EH relays is also determined. Altogether, our results demonstrate how a system that uses EH relays differs in significant ways from one that uses conventional cooperative relays.

2-Dimensional Linear-Stability of Premixed Laminar Flames Under Zero-Gravity

This paper reports on the numerical study of the linear stability of laminar premixed flames under zero gravity. The study specifically addresses the dependence of stability on finite rate chemistry with low activation energy and variable thermodynamic and transport properties. The calculations show that activation energy and details of chemistry play a minor role in altering the linear neutral stability results from asymptotic analysis. Variable specific heat makes a marginal change to the stability. Variable transport properties on the other hand tend to substantially enhance the stability from critical wave number of about 0.5 to 0.20. Also, it appears that the effects of variable properties tend to nullify the effects of non-unity Lewis number. When the Lewis number of a single species is different from unity, as will happen in a hydrogen-air premixed flame, the stability results remain close to that of unity Lewis number.

Pulsatile flow of a viscous fluid in elliptical pipe of variable cross-section

The pulsatile flow of an incompressible viscous fluid in an elliptical pipe of slowly varying cross-section is considered. Asymptotic series solutions for the velocity distribution and pressure gradient are obtained in terms of Mathieu functions for a low Reynold number flow in which the volume flux is prescribed. An expression for shear stress on the boundary is derived. The physically significant quantities governing the flow are computed numerically and analysed for different types of constrictions. The effect of eccentricity and Womerslay parameter on the flow is discussed.