On the solution of the equation ut+unux+H(x, t, u)=0

We consider the equation u(t) + u(n)u(x) + H(x, t, u) = 0 and derive a transformation relating it to u(t) + u(n)u(x) = 0. Special cases of the equation appearing in applications are discussed. Initial value problems and asymptotic behaviour of the solution are studied.

3-D Warping in Four-Bar Laminated Linkages

This paper deals with the evaluation of the component-laminate load-carrying capacity, i.e., to calculate the loads that cause the failure of the individual layers and the component-laminate as a whole in four-bar mechanism. The component-laminate load-carrying capacity is evaluated using the Tsai-Wu-Hahn failure criterion for various layups. The reserve factor of each ply in the component-laminate is calculated by using the maximum resultant force and the maximum resultant moment occurring at different time steps at the joints of the mechanism. Here, all component bars of the mechanism are made of fiber reinforced laminates and have thin rectangular cross-sections. They could, in general, be pre-twisted and/or possess initial curvature, either by design or by defect. They are linked to each other by means of revolute joints. We restrict ourselves to linear materials with small strains within each elastic body (beam). Each component of the mechanism is modeled as a beam based on geometrically nonlinear 3-D elasticity theory. The component problems are thus split into 2-D analyses of reference beam cross-sections and nonlinear 1-D analyses along the three beam reference curves. For the thin rectangular cross-sections considered here, the 2-D cross-sectional nonlinearity is also overwhelming. This can be perceived from the fact that such sections constitute a limiting case between thin-walled open and closed sections, thus inviting the nonlinear phenomena observed in both. The strong elastic couplings of anisotropic composite laminates complicate the model further. However, a powerful mathematical tool called the Variational Asymptotic Method (VAM) not only enables such a dimensional reduction, but also provides asymptotically correct analytical solutions to the nonlinear cross-sectional analysis. Such closed-form solutions are used here in conjunction with numerical techniques for the rest of the problem to predict more quickly and accurately than would otherwise be possible. Local 3-D stress, strain and displacement fields for representative sections in the component-bars are recovered, based on the stress resultants from the 1-D global beam analysis. A numerical example is presented which illustrates the failure of each component-laminate and the mechanism as a whole.

Low-Complexity Detection and Performance in Multi-Gigabit High Spectral Efficiency Wireless Systems

Recently, we reported a low-complexity likelihood ascent search (LAS) detection algorithm for large MIMO systems with several tens of antennas that can achieve high spectral efficiencies of the order of tens to hundreds of bps/Hz. Through simulations, we showed that this algorithm achieves increasingly near SISO AWGN performance for increasing number of antennas in Lid. Rayleigh fading. However, no bit error performance analysis of the algorithm was reported. In this paper, we extend our work on this low-complexity large MIMO detector in two directions: i) We report an asymptotic bit error probability analysis of the LAS algorithm in the large system limit, where N-t, N-r -> infinity keeping N-t = N-r, where N-t and N-r are the number of transmit and receive antennas, respectively. Specifically, we prove that the error performance of the LAS detector for V-BLAST with 4-QAM in i.i.d. Rayleigh fading converges to that of the maximum-likelihood (ML) detector as N-t, N-r -> infinity keeping N-t = N-r ii) We present simulated BER and nearness to capacity results for V-BLAST as well as high-rate non-orthogonal STBC from Division Algebras (DA), in a more realistic spatially correlated MIMO channel model. Our simulation results show that a) at an uncoded BER of 10(-3), the performance of the LAS detector in decoding 16 x 16 STBC from DA with N-t = = 16 and 16-QAM degrades in spatially correlated fading by about 7 dB compared to that in i.i.d. fading, and 19) with a rate-3/4 outer turbo code and 48 bps/Hz spectral efficiency, the performance degrades by about 6 dB at a coded BER of 10(-4). Our results further show that providing asymmetry in number of antennas such that N-r > N-t keeping the total receiver array length same as that for N-r = N-t, the detector is able to pick up the extra receive diversity thereby significantly improving the BER performance.

Stretch effects extracted from inwardly and outwardly propagating spherical premixed flames

Unsteady propagation of spherical flames, both inward and outward, are studied numerically extensively for single-step reaction and for different Lewis numbers of fuel/oxidizer. The dependence of flame speed ratio (s) and flame temperature ratio are obtained for a range of Lewis numbers and stretch (kappa) values. These results of s versus kappa show that the asymptotic theory by Frankel and Sivashinsky is reasonable for outward propagation. Other theories are unsatisfactory both quantitatively and qualitatively. The stretch effects are much higher for negative stretch than for positive stretch, as also seen in the theory of Frankel and Sivashinsky. The linearity of the flame speed ratio vs stretch relationship is restricted to nondimensional stretch of +/-0.1. It is shown further that the results from cylindrical flames are identical to the spherical flame on flame speed ratio versus nondimensional stretch plot thus confirming the generality of the concept of stretch. The comparison of the variation of (ds/dkappa)kappa=0 with beta(Lc - 1) show an offset between the computed and the asymptotic results of Matalon and Matkowsky. The departure of negative stretch results from this variation is significant. Several earlier experimental results are analysed and set out in the form of s versus kappa plot. Comparison of the results with experiments seem reasonable for negative stretch. The results for positive stretch are satisfactory qualitatively for a few cases. For rich propane-air, there are qualitative differences pointing to the need for full chemistry calculations in the extraction of stretch effects.

Conjectures about phase turbulence in the complex Ginzburg-Landau equation

In the complex Ginzburg-Landau equation, we consider possible ''phase turbulent'' regimes, where asymptotic correlations are controlled by phase fluctuations rather than by topological defects. Conjecturing that the decay of such correlations is governed by the Kardar-Parisi-Zhang (KPZ) model of growing interfaces, we derive the following results: (1) A scaling ansatz implies that equal-time spatial correlations in 1d, 2d, and 3d decay like e(-Ax2 zeta), where A is a nonuniversal constant, and zeta=1/2 in 1d. (2) Temporal correlations decay as exp(-t(2 beta)h(t/L(z))), with the scaling law <(beta)over bar> = <(zeta)over bar>/z, where z = 3/2, 1.58..., and 1.66..., for d = 1,2, and 3 respectively. The scaling function h(y) approaches a constant as y --> 0, and behaves like y(2(beta-<(beta)over bar>)), for large y. If in 3d the associated KPZ model turns out to be in its weak-coupling (''smooth'') phase, then, instead of the above behavior, the CGLE exhibits rotating long-range order whose connected correlations decay like 1/x in space or 1/t(1/2) in time. (3) For system sizes, L, and times t respectively less than a crossover length, L(c), and time, t(c), correlations are governed by the free-field or Edwards-Wilkinson (EW) equation, rather than the KPZ model. In 1d, we find that L(c) is large: L(c) similar to 35,000; for L < L(c) we show numerical evidence for stretched exponential decay of temporal correlations with an exponent consistent with the EW value beta(EW)= 1/4.

Automated Multi-Agent Search Using Centroidal Voronoi Configuration

This paper addresses the problem of automated multiagent search in an unknown environment. Autonomous agents equipped with sensors carry out a search operation in a search space, where the uncertainty, or lack of information about the environment, is known a priori as an uncertainty density distribution function. The agents are deployed in the search space to maximize single step search effectiveness. The centroidal Voronoi configuration, which achieves a locally optimal deployment, forms the basis for the proposed sequential deploy and search strategy. It is shown that with the proposed control law the agent trajectories converge in a globally asymptotic manner to the centroidal Voronoi configuration. Simulation experiments are provided to validate the strategy. Note to Practitioners-In this paper, searching an unknown region to gather information about it is modeled as a problem of using search as a means of reducing information uncertainty about the region. Moreover, multiple automated searchers or agents are used to carry out this operation optimally. This problem has many applications in search and surveillance operations using several autonomous UAVs or mobile robots. The concept of agents converging to the centroid of their Voronoi cells, weighted with the uncertainty density, is used to design a search strategy named as sequential deploy and search. Finally, the performance of the strategy is validated using simulations.

Free convection in power-law fluids near a three-dimensional stagnation point

Numerical results are presented for the free-convection boundary-layer equations of the Ostwald de-Waele non-Newtonian power-law type fluids near a three-dimensional (3-D) stagnation point of attachment on an isothermal surface. The existence of dual solutions that are three-dimensional in nature have been verified by means of a numerical procedure. An asymptotic solution for very large Prandtl numbers has also been derived. Solutions are presented for a range of values of the geometric curvature parameter c, the power-law index n, and the Prandtl number Pr.

Saturation throughput analysis of an input queueing ATM switch with multiclass bursty traffic

In this paper we consider an N x N non-blocking, space division ATM switch with input cell queueing. At each input, the cell arrival process comprises geometrically distributed bursts of consecutive cells for the various outputs. Motivated by the fact that some input links may be connected to metropolitan area networks, and others directly to B-ISDN terminals, we study the situation where there are two classes of inputs with different values of mean burst length. We show that when inputs contend for an output, giving priority to an input with smaller expected burst length yields a saturation throughput larger than if the reverse priority is given. Further, giving priority to less bursty traffic can give better throughput than if all the inputs were occupied by this less bursty traffic. We derive the asymptotic (as N --> infinity) saturation throughputs for each priority class.

Shear-induced enhancement of self-diffusion in interacting colloidal suspensions

We set up the generalized Langevin equations describing coupled single-particle and collective motion in a suspension of interacting colloidal particles in a shear how and use these to show that the measured self-diffusion coefficients in these systems should be strongly dependent on shear rate epsilon. Three regimes are found: (i) an initial const+epsilon(.2), followed by (ii) a large regime of epsilon(.1/2) behavior, crossing over to an asymptotic power-law approach (iii) D-o - const x epsilon(.-1/2) to the Stokes-Einstein value D-o. The shear dependence is isotropic up to very large shear rates and increases with the interparticle interaction strength. Our results provide a straightforward explanation of recent experiments and simulations on sheared colloids.

Stability of the viscous flow of a fluid through a flexible tube

The stability of the Hagen-Poiseuille flow of a Newtonian fluid in a tube of radius R surrounded by an incompressible viscoelastic medium of radius R < r < HR is analysed in the high Reynolds number regime. The dimensionless numbers that affect the fluid flow are the Reynolds number Re = (rho VR/eta), the ratio of the viscosities of the wall and fluid eta(r) = (eta(s)/eta), the ratio of radii H and the dimensionless velocity Gamma = (rho V-2/G)(1/2). Here rho is the density of the fluid, G is the coefficient of elasticity of the wall and V is the maximum fluid velocity at the centre of the tube. In the high Reynolds number regime, an asymptotic expansion in the small parameter epsilon = (1/Re) is employed. In the leading approximation, the viscous effects are neglected and there is a balance between the inertial stresses in the fluid and the elastic stresses in the medium. There are multiple solutions for the leading-order growth rate s((0)), all of which are imaginary, indicating that the fluctuations are neutrally stable, since there is no viscous dissipation of energy or transfer of energy from the mean flow to the fluctuations due to the Reynolds stress. There is an O(epsilon(1/2)) correction to the growth rate, s((1)), due to the presence of a wall layer of thickness epsilon(1/2)R where the viscous stresses are O(epsilon(1/2)) smaller than the inertial stresses. An energy balance analysis indicates that the transfer of energy from the mean flow to the fluctuations due to the Reynolds stress in the wall layer is exactly cancelled by an opposite transfer of equal magnitude due to the deformation work done at the interface, and there is no net transfer from the mean flow to the fluctuations. Consequently, the fluctuations are stabilized by the viscous dissipation in the wall layer, and the real part of s(1) is negative. However, there are certain values of Gamma and wavenumber k where s((1)) = 0. At these points, the wall layer amplitude becomes zero because the tangential velocity boundary condition is identically satisfied by the inviscid flow solution. The real part of the O(epsilon) correction to the growth rate s((2)) turns out to be negative at these points, indicating a small stabilizing effect due to the dissipation in the bulk of the fluid and the wall material. It is found that the minimum value of s((2)) increases proportional to (H-1)(-2) for (H-1) much less than 1 (thickness of wall much less than the tube radius), and decreases proportional to H-4 for H much greater than 1. The damping rate for the inviscid modes is smaller than that for the viscous wall and centre modes in a rigid tube, which have been determined previously using a singular perturbation analysis. Therefore, these are the most unstable modes in the flow through a flexible tube

Gas-phase controlled mass transfer in a foam-bed reactor

Gas-phase controlled absorption of ammonia in foams made of solutions of sulphuric acid has been studied experimentally. Effects of gas-phase concentration of ammonia and type of surfactant on the performance of the foam-bed reactor are investigated. Gas-phase controlled absorption from a spherical bubble is anaylzed using the asymptotic value of Sherwood number (Sh = 6.58), for both negligible as well as significant changes in the volume of the bubble. The experimental data are shown to be in good agreement with the single-stage model of the foam-bed reactor using these asymptotic sub-models, as well as the diffusion-in-sphere analysis available in literature. Influence of effective diffusivity on the time dependence of fractional gas absorption has been found to be unimportant for foam columns with large times of contact. The asymptotic sub-models have been compared and use of the rigid-sphere asymptotic sub-model is recommended for foam columns of practical relevence.

Multi-installment load distribution in tree networks with delays

This paper presents a new strategy for load distribution in a single-level tree network equipped with or without front-ends. The load is distributed in more than one installment in an optimal manner to minimize the processing time. This is a deviation and an improvement over earlier studies in which the load distribution is done in only one installment. Recursive equations for the general case, and their closed form solutions for a special case in which the network has identical processors and identical links, are derived. An asymptotic analysis of the network performance with respect to the number of processors and the number of installments is carried out. Discussions of the results in terms of some practical issues like the tradeoff relationship between the number of processors and the number of installments are also presented.

Recovery of tropical rainforest avifauna in relation to vegetation succession following shifting cultivation in Mizoram, north-east India

1. Recovery of rainforest bird community structure and composition, in relation to forest succession after slash-and-burn shifting cultivation or jhum was studied in Mizoram, north-east India. Replicate fallow sites abandoned after shifting cultivation 1, 5, 10, 25 and approximate to 100 years ago, were compared with primary evergreen and semi-evergreen forest using transect and quadrat sampling. 2. Vegetation variables such as woody plant species richness, tree density and vertical stratification increased with fallow age in a rapid. nun-linear, asymptotic manner. Principal components analysis of vegetation variables summarized 92.8% of the variation into two axes: PC1 reflecting forest development and woody plant succession (variables such as tree density, woody plant species richness), and PC2 depicting bamboo density, which increased from 1 to 25 years and declined thereafter. 3. Bird species richness, abundance and diversity, increased rapidly and asymptotically during succession paralleling vegetation recovery as shown by positive correlations with fallow age and PC1 scores of sites. Bamboo density reflected by PC2 had a negative effect on bird species richness and abundance. 4. The bird community similarity (Morisita index) of sites with primary forest also increased asymptotically with fallow age indicating sequential species turnover during succession. Bird community similarity of sites with primary forest (or between sites) was positively correlated with both physiognomic and floristic similarities with primary forest (or between sites). 5. The number of bird species in guilds associated with forest development and woody plants (canopy insectivores, frugivores: bark feeders) was correlated with PCI scores of the sites. Species in other guilds (e. g. granivores, understorey insectivores) appeared to dominate during early and mid-succession. 6. The non-linear relationships imply that fallow periods less than a threshold of 25 years for birds, and about 50-75 years for woody plants, are likely to cause substantial community alteration. 7. As 5-10-year rotation periods or jhum cycles prevail in many parts of north-east India. there is a need to protect and conserve tracts of late-successional and primary forest.

Common underlying steering curves for motorcycles in steady turns

We study the steady turn behaviours of some light motorcycle models on circular paths, using the commercial software package ADAMS-Motorcycle. Steering torque and steering angle are obtained for several path radii and a range of steady forward speeds. For path radii much greater than motorcycle wheelbase, and for all motorcycle parameters including tyre parameters held fixed, dimensional analysis can predict the asymptotic behaviour of steering torque and angle. In particular, steering torque is a function purely of lateral acceleration plus another such function divided by path radius. Of these, the first function is numerically determined, while the second is approximated by an analytically determined constant. Similarly, the steering angle is a function purely of lateral acceleration, plus another such function divided by path radius. Of these, the first is determined numerically while the second is determined analytically. Both predictions are verified through ADAMS simulations for various tyre and geometric parameters. In summary, steady circular motions of a given motorcycle with given tyre parameters can be approximately characterised by just one curve for steering torque and one for steering angle.

First-principle description of magnonic PdnFem multilayers

Ab-initio calculations are used to determine the parameters that determine magnonic band structure of PdnFem multilayers (n = 2, m <= 8). We obtain the layer-resolved magnetization, the exchange coupling, and the magnetic anisotropy of the Pd-Fe structures. The Fe moment is 3.0 mu(B) close to the Pd layers and 2.2 mu(B) in the middle of the Fe layers. An intriguing but not usually considered aspect is that the elemental Pd is nonmagnetic, similar to Cu spacer layers in other multilayer systems. This leads to a pre-asymptotic ferromagnetic coupling through the Pd (about 40 mJ/m(2)). Furthermore, the Pd acquires a small moment due to spin polarization by neighboring Fe atoms, which translates into magnetic anisotropy. The anisotropies are large, in the range typical for L1(0) structures, which is beneficial for high-frequency applications. (C) 2011 American Institute of Physics. doi:10.1063/1.3556763]