Exact N-Wave Solutions for the Non-Planar Burgers Equation

An exact representation of N-wave solutions for the non-planar Burgers equation u(t) + uu(x) + 1/2ju/t = 1/2deltau(xx), j = m/n, m < 2n, where m and n are positive integers with no common factors, is given. This solution is asymptotic to the inviscid solution for Absolute value of x < square-root (2Q0 t), where Q0 is a function of the initial lobe area, as lobe Reynolds number tends to infinity, and is also asymptotic to the old age linear solution, as t tends to infinity; the formulae for the lobe Reynolds numbers are shown to have the correct behaviour in these limits. The general results apply to all j = m/n, m < 2n, and are rather involved; explicit results are written out for j = 0, 1, 1/2, 1/3 and 1/4. The case of spherical symmetry j = 2 is found to be 'singular' and the general approach set forth here does not work; an alternative approach for this case gives the large time behaviour in two different time regimes. The results of this study are compared with those of Crighton & Scott (1979).

Localization of light in coherently amplifying random media

We derive and analyze the statistics of reflection coefficient of light backscattered coherently from an amplifying and disordered optical medium modeled by a spatially random refractive index having a uniform imaginary part in one dimension. We find enhancement of reflected intensity owing to a synergy between wave confinement by Anderson localization and coherent amplification by the active medium. This is not the same as that due to enhanced optical path lengths expected from photon diffusion in the random active medium. Our study is relevant to the physical realizability of a mirrorless laser by photon confinement due to Anderson localization.

PVU and wave-particle splitting schemes for Euler equations of gas dynamics

A new way of flux-splitting, termed as the wave-particle splitting is presented for developing upwind methods for solving Euler equations of gas dynamics. Based on this splitting, two new upwind methods termed as Acoustic Flux Vector Splitting (AFVS) and Acoustic Flux Difference Splitting (AFDS) methods are developed. A new Boltzmann scheme, which closely resembles the wave-particle splitting, is developed using the kinetic theory of gases. This method, termed as Peculiar Velocity based Upwind (PVU) method, uses the concept of peculiar velocity for upwinding. A special feature of all these methods that the unidirectional and multidirectional parts of the flux vector are treated separately. Extensive computations done using these schemes demonstrate the soundness of the ideas.

Role of multicritical points in addressing some key problems concerning condensed matter science

We illustrate the potential of using higher order critical points in the deeper understanding of several interesting problems of condensed matter science, e.g. critical adsorption, finite size effects, morphology of critical fluctuations, reversible aggregation of colloids, dynamics of the ordering process, etc.

Soft condensed matter: A survey and a proposal

Pn this perspective on the increasingly important field of soft condensed matter science, I make the case for a concentrated multidisciplinary effort to develop the area in India. I base my arguments on its demonstrated potential for new 'emergent' phenomena, interesting table-top experiments, and applications.

A study of over-reflection in Hartmann flow

It is observed that Hartmann flow sustains wave propagation in its centre region for waves whose phase speed is less than the maximum flow speed. Similar to the previous observations it is found that viscous boundary layers around the critical level and at the wall replace the exponential regions and wave sinks required for over-reflection in the inviscid flow. The uniform magnetic field stabilizes the flow for small-wave-number disturbances along thez-direction. Over-reflection is confined to a few ranges of phase speeds for which the two boundary layers are close together rather than widely separated. These ranges correspond exactly to those for which unstable eigenmodes exist. Over-reflection is associated with a wave phase tilt opposite in direction to the shear.

Why should we pursue soft condensed matter

This review highlights the physics aspects of soft condensed matter to show that these are novel systems to explore cooperative behaviour in condensed matter under equilibrium and non-equilibrium conditions. A case is made for focusing research in this-area in our country.

A characteristic based numerical method with tracking for nonlinear wave equations

Many physical problems can be modeled by scalar, first-order, nonlinear, hyperbolic, partial differential equations (PDEs). The solutions to these PDEs often contain shock and rarefaction waves, where the solution becomes discontinuous or has a discontinuous derivative. One can encounter difficulties using traditional finite difference methods to solve these equations. In this paper, we introduce a numerical method for solving first-order scalar wave equations. The method involves solving ordinary differential equations (ODEs) to advance the solution along the characteristics and to propagate the characteristics in time. Shocks are created when characteristics cross, and the shocks are then propagated by applying analytical jump conditions. New characteristics are inserted in spreading rarefaction fans. New characteristics are also inserted when values on adjacent characteristics lie on opposite sides of an inflection point of a nonconvex flux function, Solutions along characteristics are propagated using a standard fourth-order Runge-Kutta ODE solver. Shocks waves are kept perfectly sharp. In addition, shock locations and velocities are determined without analyzing smeared profiles or taking numerical derivatives. In order to test the numerical method, we study analytically a particular class of nonlinear hyperbolic PDEs, deriving closed form solutions for certain special initial data. We also find bounded, smooth, self-similar solutions using group theoretic methods. The numerical method is validated against these analytical results. In addition, we compare the errors in our method with those using the Lax-Wendroff method for both convex and nonconvex flux functions. Finally, we apply the method to solve a PDE with a convex flux function describing the development of a thin liquid film on a horizontally rotating disk and a PDE with a nonconvex flux function, arising in a problem concerning flow in an underground reservoir.

Effect of open joint on stress wave propagation

Stress wave characteristics are drastically altered by joints and other inhomogenities. This paper addresses the effect of an open joint on stress wave transmission. An elastodynamic analysis is developed to supplement and explain some recent observations by Fourney and Dick(1995) on open as well as filled joints. The analytical model developed here assuming spherical symmetry can be extended to filled joints between dissimilar media, but results are presented only for open joints separating identical materials. As a special case, stress wave transmission across a joint with no gap is also addressed.

Scroll-Wave Dynamics in Human Cardiac Tissue: Lessons from a Mathematical Model with Inhomogeneities and Fiber Architecture

Cardiac arrhythmias, such as ventricular tachycardia (VT) and ventricular fibrillation (VF), are among the leading causes of death in the industrialized world. These are associated with the formation of spiral and scroll waves of electrical activation in cardiac tissue; single spiral and scroll waves are believed to be associated with VT whereas their turbulent analogs are associated with VF. Thus, the study of these waves is an important biophysical problem. We present a systematic study of the combined effects of muscle-fiber rotation and inhomogeneities on scroll-wave dynamics in the TNNP (ten Tusscher Noble Noble Panfilov) model for human cardiac tissue. In particular, we use the three-dimensional TNNP model with fiber rotation and consider both conduction and ionic inhomogeneities. We find that, in addition to displaying a sensitive dependence on the positions, sizes, and types of inhomogeneities, scroll-wave dynamics also depends delicately upon the degree of fiber rotation. We find that the tendency of scroll waves to anchor to cylindrical conduction inhomogeneities increases with the radius of the inhomogeneity. Furthermore, the filament of the scroll wave can exhibit drift or meandering, transmural bending, twisting, and break-up. If the scroll-wave filament exhibits weak meandering, then there is a fine balance between the anchoring of this wave at the inhomogeneity and a disruption of wave-pinning by fiber rotation. If this filament displays strong meandering, then again the anchoring is suppressed by fiber rotation; also, the scroll wave can be eliminated from most of the layers only to be regenerated by a seed wave. Ionic inhomogeneities can also lead to an anchoring of the scroll wave; scroll waves can now enter the region inside an ionic inhomogeneity and can display a coexistence of spatiotemporal chaos and quasi-periodic behavior in different parts of the simulation domain. We discuss the experimental implications of our study.

Plane wave analysis of conical and exponential pipes with incompressible mean flow

The general equation for one-dimensional wave propagation at low flow Mach numbers (M less-than-or-equals, slant0·2) is derived and is solved analytically for conical and exponential shapes. The transfer matrices are derived and shown to be self-consistent. Comparison is also made with the relevant data available in the literature. The transmission loss behaviour of conical and exponential pipes, and mufflers involving these shapes, are studied. Analytical expressions of the same are given for the case of a stationary medium. The mufflers involving conical and exponential pipes are shown to be inferior to simple expansion chambers (of similar dimensions) at higher frequencies from the point of view of noise abatement, as was observed earlier experimentally.

Performance analysis of surface acoustic wave matched filters

SAW matched filter is commonly used in spread spectrum communication receivers in order to maximize the SNR prior to detection, At times the receiver would be a mobile one while the signal is processed at the IF level, In that case frequency deviations due to Doppler shift or temperature dependence of the acoustic medium used for SAW device would, severely effect it's performance, The impact of these errors on the receiver performance is analyzed on a generalised basis.

Design and realization of high-performance wave-pipelined 8×8 b multiplier in CMOS technology

Wave pipelining is a design technique for increasing the throughput of a digital circuit or system without introducing pipelining registers between adjacent combinational logic blocks in the circuit/system. However, this requires balancing of the delays along all the paths from the input to the output which comes the way of its implementation. Static CMOS is inherently susceptible to delay variation with input data, and hence, receives a low priority for wave pipelined digital design. On the other hand, ECL and CML, which are amenable to wave pipelining, lack the compactness and low power attributes of CMOS. In this paper we attempt to exploit wave pipelining in CMOS technology. We use a single generic building block in Normal Process Complementary Pass Transistor Logic (NPCPL), modeled after CPL, to achieve equal delay along all the propagation paths in the logic structure. An 8×8 b multiplier is designed using this logic in a 0.8 ?m technology. The carry-save multiplier architecture is modified suitably to support wave pipelining, viz., the logic depth of all the paths are made identical. The 1 mm×0.6 mm multiplier core supports a throughput of 400 MHz and dissipates a total power of 0.6 W. We develop simple enhancements to the NPCPL building blocks that allow the multiplier to sustain throughputs in excess of 600 MHz. The methodology can be extended to introduce wave pipelining in other circuits as well

Diffusing wave spectroscopy of dense colloids: Liquid, crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115µm and 0.089µm results in freezing into a crystalline phase at volume fraction? of 0.1 and into a glassy state at?=0.2. The functional form of the field autocorrelation functiong (1)(t) for the binary fluid phase is fitted to exp[??(6k 0 2 D eff t)1/2] wherek 0 is the magnitude of the incident light wavevector and? is a parameter inversely proportional to the photon transport mean free pathl*. TheD eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg (1)(t) is fitted (only with a moderate success) to exp[??(6k 0 2 W(t))1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameter? for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.

Prediction of nonlocal scaling parameter for armchair and zigzag single-walled carbon nanotubes based on molecular structural mechanics, nonlocal elasticity and wave propagation

Atomic vibration in the Carbon Nanotubes (CNTs) gives rise to non-local interactions. In this paper, an expression for the non-local scaling parameter is derived as a function of the geometric and electronic properties of the rolled graphene sheet in single-walled CNTs. A self-consistent method is developed for the linearization of the problem of ultrasonic wave propagation in CNTs. We show that (i) the general three-dimensional elastic problem leads to a single non-local scaling parameter (e(0)), (ii) e(0) is almost constant irrespective of chirality of CNT in the case of longitudinal wave propagation, (iii) e(0) is a linear function of diameter of CNT for the case of torsional mode of wave propagation, (iv) e(0) in the case of coupled longitudinal-torsional modes of wave propagation, is a function which exponentially converges to that of axial mode at large diameters and to torsional mode at smaller diameters. These results are valid in the long-wavelength limit. (C) 2011 Elsevier Ltd. All rights reserved.