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).

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.

Effect of surfactant dispersed in oil on interaction force between an oil film and a steel substrate in water

The oil phase, in an oil-in-water emulsion on a steel substrate, is strongly repelled by the substrate. The oil in this situation does not wet the steel and steel/steel friction is high. In this work we disperse anionic surfactants in an oil film and study the effect of this dispersion on the force of interaction between a silica colloid probe (AFM) carrying the oil film and a steel substrate in water. It is observed that when the surfactant is oil insoluble and the interaction time is short the strong entropic repulsion (without the surfactant) is replaced by a strong attraction. The steel on steel sliding friction in this case is low compared to that what is achieved when the surfactant is soluble in oil. The rationale underlying these interactions is explored here. (C) 2011 Elsevier B.V. All rights reserved.

Use of L matrix to obtain reliable ab initio force constants of polyatomic molecules: ethylene as a test system

Direct use of experimental eigenvalues of the vibrational secular equation on to the ab initio predicted eigenvector space is suggested as a means of obtaining a reliable set of intramolecular force constants. This method which we have termed RECOVES (recovery in the eigenvector space) is computationally simple and free from arbitrariness. The RECOVES force constants, by definition, reproduce the experimental vibrational frequencies of the parent molecule exactly. The ab initio calculations were carried out for ethylene as a test molecule and the force constants obtained by the present procedure also correctly predict the vibrational frequencies of the deuterated species. The RECOVES force constants for ethylene are compared with those obtained by using the SQM procedure.

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.

Investigation of the characteristics of an SF6 rotating arc by a mathematical model

A mathematical model has been developed for predicting the performance of rotating arcs in SF6 gas by considering the energy balance and force balance equations. The finite difference technique has been adopted for the computer simulation of the arc characteristics. This method helps in considering the spatial variation of the transport and radiative properties of the arc. All the three heat loss mechanisms-conduction, convection, and radiation-have been considered. Results obtained over a 10 ms (half cycle of 50 Hz wave) current flow period for 1.4 kA (peak) and 4.2 kA (peak), show that the proposed arc model gives the expected behavior of the arc over the range of currents studied.

Phase Separation in Binary Nearly-Hard-Sphere Colloids: Evidence for the Depletion Force

A binary aqueous suspension of large (L) and small (S) nearly-hard-sphere colloidal polystyrene spheres is shown to segregate spontaneously into L-rich and S-rich regions for suitable choices of volume fraction and size ratio. This is the first observation of such purely entropic phase separation of chemically identical species in which at least one component remains fluid. Simple theoretical arguments are presented to make this effect plausible.

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.

Optical phase conjugation by two-wave mixing in iron-doped lithium niobate

A novel technique to generate forward phase conjugate wave by two-wave mixing (TWM) in photorefractive iron-doped lithium niobate crystal has been demonstrated. An optical beam from a positive transparency was forward phase conjugated by TWM technique. The experimental scheme was then extended to a specific interferometric application.