Minimum error solutions of the Boltzmann equation for shock structure

‘Best’ solutions for the shock-structure problem are obtained by solving the Boltzmann equation for a rigid sphere gas by applying minimum error criteria on the Mott-Smith ansatz. The use of two such criteria minimizing respectively the local and total errors, as well as independent computations of the remaining error, establish the high accuracy of the solutions, although it is shown that the Mott-Smith distribution is not an exact solution of the Boltzmann equation even at infinite Mach number. The minimum local error method is found to be particularly simple and efficient. Adopting the present solutions as the standard of comparison, it is found that the widely used v2x-moment solutions can be as much as a third in error, but that results based on Rosen's method provide good approximations. Finally, it is shown that if the Maxwell mean free path on the hot side of the shock is chosen as the scaling length, the value of the density-slope shock thickness is relatively insensitive to the intermolecular potential. A comparison is made on this basis of present results with experiment, and very satisfactory quantitative agreement is obtained.

String-like propagation of the 5-coordinated defect state in supercooled water: molecular origin of dynamic and thermodynamic anomalies

We find that at low temperature water, large amplitude (similar to 60 degrees) rotational jumps propagate like a string, with the length of propagation increasing with lowering temperature. The strings are formed by mobile 5-coordinated water molecules which move like a Glarum defect (J. Chem. Phys., 1960, 33, 1371), causing water molecules on the path to change from 4-coordinated to 5-coordinated and again back to 4-coordinated water, and in the process cause the tagged water molecule to jump, by following essentially the Laage-Hynes mechanism (Science, 2006, 311, 832-835). The effects on relaxation of the propagating defect causing large amplitude jumps are manifested most dramatically in the mean square displacement (MSD) and also in the rotational time correlation function of the O-H bond of the molecule that is visited by the defect (transient transition to the 5-coordinated state). The MSD and the decay of rotational time correlation function, both remain quenched in the absence of any visit by the defect, as postulated by Glarum long time ago. We establish a direct connection between these propagating events and the known thermodynamic and dynamic anomalies in supercooled water. These strings are found largely in the regions that surround the relatively rigid domains of 4-coordinated water molecules. The propagating strings give rise to a noticeable dynamical heterogeneity, quantified here by a sharp rise in the peak of the four-point density response function, chi(4)(t). This dynamics heterogeneity is also responsible for the breakdown of the Stokes-Einstein relation.

Multi-hop Cooperative Wireless Networks: Diversity Multiplexing Tradeoff and Optimal Code Design

We consider single-source single-sink (ss-ss) multi-hop relay networks, with slow-fading links and single-antenna half-duplex relay nodes. While two-hop cooperative relay networks have been studied in great detail in terms of the diversity-multiplexing tradeoff (DMT), few results are available for more general networks. In this paper, we identify two families of networks that are multi-hop generalizations of the two-hop network: K-Parallel-Path (KPP)networks and layered networks.KPP networks, can be viewed as the union of K node-disjoint parallel relaying paths, each of length greater than one. KPP networks are then generalized to KPP(I) networks, which permit interference between paths and to KPP(D) networks, which possess a direct link from source to sink. We characterize the DMT of these families of networks completely for K > 3. Layered networks are networks comprising of layers of relays with edges existing only between adjacent layers, with more than one relay in each layer. We prove that a linear DMT between the maximum diversity dmax and the maximum multiplexing gain of 1 is achievable for single-antenna fully-connected layered networks. This is shown to be equal to the optimal DMT if the number of relaying layers is less than 4.For multiple-antenna KPP and layered networks, we provide an achievable DMT, which is significantly better than known lower bounds for half duplex networks.For arbitrary multi-terminal wireless networks with multiple source-sink pairs, the maximum achievable diversity is shown to be equal to the min-cut between the corresponding source and the sink, irrespective of whether the network has half-duplex or full-duplex relays. For arbitrary ss-ss single-antenna directed acyclic networks with full-duplex relays, we prove that a linear tradeoff between maximum diversity and maximum multiplexing gain is achievable.Along the way, we derive the optimal DMT of a generalized parallel channel and derive lower bounds for the DMT of triangular channel matrices, which are useful in DMT computation of various protocols. We also give alternative and often simpler proofs of several existing results and show that codes achieving full diversity on a MIMO Rayleigh fading channel achieve full diversity on arbitrary fading channels. All protocols in this paper are explicit and use only amplify-and-forward (AF) relaying. We also construct codes with short block-lengths based on cyclic division algebras that achieve the optimal DMT for all the proposed schemes.Two key implications of the results in the paper are that the half-duplex constraint does not entail any rate loss for a large class of cooperative networks and that simple AF protocols are often sufficient to attain the optimal DMT

Effect of strain path change on the evolution of texture and microstructure during rolling of copper and nickel

The effect of strain path change during rolling has been investigated for copper and nickel using X-ray diffraction and electron back scatter diffraction as well as crystal plasticity simulations. Four different strain paths namely: (i) unidirectional rolling; (ii) reverse rolling; (iii) two-step cross rolling and (iv) multi-step cross rolling were employed to decipher the effect of strain path change on the evolution of deformation texture and microstructure. The cross rolled samples showed weaker texture with a prominent Bs {1 1 0}< 1 1 2 > and P(B(ND)) {1 1 0}< 1 1 1 > component in contrast to the unidirectional and reverse rolled samples where strong S {1 2 3}< 6 3 4 > and Cu {1 1 2}< 1 1 1 > components were formed. This was more pronounced for copper samples compared to nickel. The cross rolled samples were characterized by lower anisotropy and Taylor factor as well as less variation in Lankford parameter. Viscoplastic self-consistent simulations indicated that slip activity on higher number of octahedral slip systems can explain the weaker texture as well as reduced anisotropy in the cross rolled samples. (C) 2011 Elsevier B.V. All rights reserved.

Speech segmentation using extrema based signal track length measure

We introduce a novel temporal feature of a signal, namely extrema-based signal track length (ESTL) for the problem of speech segmentation. We show that ESTL measure is sensitive to both amplitude and frequency of the signal. The short-time ESTL (ST_ESTL) shows a promising way to capture the significant segments of speech signal, where the segments correspond to acoustic units of speech having distinct temporal waveforms. We compare ESTL based segmentation with ML and STM methods and find that it is as good as spectral feature based segmentation, but with lesser computational complexity.

Length of near-wall plumes in turbulent convection

We present planforms of line plumes formed on horizontal surfaces in turbulent convection, along with the length of line plumes measured from these planforms, in a six decade range of Rayleigh numbers (10(5) < Ra < 10(11)) and at three Prandtl numbers (Pr = 0.7, 5.2, 602). Using geometric constraints on the relations for the mean plume spacings, we obtain expressions for the total length of near-wall plumes on horizontal surfaces in turbulent convection. The plume length per unit area (L(p)/A), made dimensionless by the near-wall length scale in turbulent convection (Z(w)), remains constant for a given fluid. The Nusselt number is shown to be directly proportional to L(p)H/A for a given fluid layer of height H. The increase in Pr has a weak influence in decreasing L(p)/A. These expressions match the measurements, thereby showing that the assumption of laminar natural convection boundary layers in turbulent convection is consistent with the observed total length of line plumes. We then show that similar relationships are obtained based on the assumption that the line plumes are the outcome of the instability of laminar natural convection boundary layers on the horizontal surfaces.

Performance of Tuned Half-Wave-Length Power Transmission Lines

The basic concepts of tuned half-wave lines were covered by Hubert and Gent [1]. In this paper the problem of overvoltages during faults and the stability of the system incorporating such tuned lines are discussed. The type of tuning bank and the line arrangements that will be satisfactory from the point of view of stability are suggested. The behavior of a line tuned by distributed capacitor is analyzed, and its performance is compared with the other type of tuned line.

Analysis of Natural Half-Wave-Length Power Transmission Lines

This paper provides additional theoretical information on half-wave-length power transmission. The analysis is rendered more general by consideration of a natural half-wave line instead of a short line tuned to half-wave. The effects of line loading and its power factor on the voltage and current profiles of the line and ganerator excitation have been included. Some of the operating problems such as charging of the line and synchronization of the half-wave system are also discussed. The inevitability of power-frequency overvoltages during faults is established. Stability studies have indicated that the use of switching stations is not beneficial. Typical swing curves are also presented.