Giant magnons in the D1-D5 system

We study giant magnons in the the D1-D5 system from both the boundary CFT and as classical solutions of the string sigma model in AdS(3) x S-3 x T-4. Re-examining earlier studies of the symmetric product conformal field theory we argue that giant magnons in the symmetric product are BPS states in a centrally extended SU(1 vertical bar 1) x SU(1 vertical bar 1) superalgebra with two more additional central charges. The magnons carry these additional central charges locally but globally they vanish. Using a spin chain description of these magnons and the extended superalgebra we show that these magnons obey a dispersion relation which is periodic in momentum. We then identify these states on the string theory side and show that here too they are BPS in the same centrally extended algebra and obey the same dispersion relation which is periodic in momentum. This dispersion relation arises as the BPS condition for the extended algebra and is similar to that of magnons in N = 4 Yang-Mills Yang-Mills.

Numerical studies on channel formation and growth during solidification: Effect of process parameters

In the present work, solidification of a hyper-eutectic ammonium chloride solution in a bottom-cooled cavity (i.e. with stable thermal gradient) is numerically studied. A Rayleigh number based criterion is developed, which determines the conditions favorable for freckles formation. This criterion, when expressed in terms of physical properties and process parameters, yields the condition for plume formation as a function of concentration, liquid fraction, permeability, growth rate of a mushy layer and thermophysical properties. Subsequently, numerical simulations are performed for cases with initial and boundary conditions favoring freckle formation. The effects of parameters, such as cooling rate and initial concentration, on the formation and growth of freckles are investigated. It was found that a high cooling rate produced larger and more defined channels which are retained for a longer durations. Similarly, a lower initial concentration of solute resulted in fewer but more pronounced channels. The number and size of channels are also found to be related to the mushy zone thickness. The trends predicted with regard to the variation of number of channels with time under different process conditions are in accordance with the experimental observations reported in the literature.

Evolution of isolated streamwise vortices in the late stages of boundary layer transition

Experiments were conducted with two, smooth hills, lying well within the boundary layer over a flat plate mounted in a wind tunnel. One hill was shallow, with peak height 1.5 mm and width 50 mm; the other, steep, 3 mm high and 30 mm wide. Since the hills occupied one-half of the tunnel span, streamwise vorticity formed near the hills' edge. At a freestream speed of 3.5 m/s, streaks formed with inflectional wall-normal and spanwise velocity profiles but without effecting transition. Transition, observed at 7.5 m/s, took different routes with the two hills. With the steep hill, streamwise velocity signals exhibited the passage of a wave packet which intensified before breakdown to turbulence. With the shallow hill there was a broad range of frequencies present immediately downstream of the hill. These fluctuations grew continuously and transition occurred within a shorter distance. Since the size of the streamwise vorticity generated at the hill edge is of the order of the hill height, the shallow hill generates vorticity closer to the wall and supports an earlier transition, whereas the steep hill creates a thicker vortex and associated streaks which exhibit oscillations due to their own instability as an additional precursor stage before transition.

Quantitative photoacoustic tomography from boundary pressure measurements: noniterative recovery of optical absorption coefficient from the reconstructed absorbed energy map

We describe a noniterative method for recovering optical absorption coefficient distribution from the absorbed energy map reconstructed using simulated and noisy boundary pressure measurements. The source reconstruction problem is first solved for the absorbed energy map corresponding to single- and multiple-source illuminations from the side of the imaging plane. It is shown that the absorbed energy map and the absorption coefficient distribution, recovered from the single-source illumination with a large variation in photon flux distribution, have signal-to-noise ratios comparable to those of the reconstructed parameters from a more uniform photon density distribution corresponding to multiple-source illuminations. The absorbed energy map is input as absorption coefficient times photon flux in the time-independent diffusion equation (DE) governing photon transport to recover the photon flux in a single step. The recovered photon flux is used to compute the optical absorption coefficient distribution from the absorbed energy map. In the absence of experimental data, we obtain the boundary measurements through Monte Carlo simulations, and we attempt to address the possible limitations of the DE model in the overall reconstruction procedure.

Real-coded genetic algorithm for machining condition optimization

In this paper, we consider the machining condition optimization models presented in earlier studies. Finding the optimal combination of machining conditions within the constraints is a difficult task. Hence, in earlier studies standard optimization methods are used. The non-linear nature of the objective function, and the constraints that need to be satisfied makes it difficult to use the standard optimization methods for the solution. In this paper, we present a real coded genetic algorithm (RCGA), to find the optimal combination of machining conditions. We present various issues related to real coded genetic algorithm such as solution representation, crossover operators, and repair algorithm in detail. We also present the results obtained for these models using real coded genetic algorithm and discuss the advantages of using real coded genetic algorithm for these problems. From the results obtained, we conclude that real coded genetic algorithm is reliable and accurate for solving the machining condition optimization models.

Stability of an unsupported vertical circular excavation in clays under undrained condition

By using the axisymmetric finite elements static limit analysis formulation, proposed recently by the authors, the stability numbers (gamma H/c(o)) for an unsupported vertical circular excavation in clays, whose cohesion increases with depth, have been determined under undrained condition; gamma = unit weight, H., height of the excavation and c(o) = cohesion along ground surface. The results are obtained for various values of H/b and m; where b = the radius of the excavation and m = a non-dimensional parameter which accounts for the rate of the increase of cohesion with depth. The values of the stability numbers increase continuously both with increases in H/b and m. The results obtained in this study compare well with those available in literature.(C) 2009 Elsevier Ltd. All rights reserved.

A voltage-sensorless control method to balance the input currents of a three-wire boost rectifier under unbalanced input voltages condition

This paper proposes a control method that can balance the input currents of the three-phase three-wire boost rectifier under unbalanced input voltage condition. The control objective is to operate the rectifier in the high-power-factor mode under balanced input voltage condition but to give overriding priority to the current balance function in case of unbalance in the input voltage. The control structure has been divided into two major functional blocks. The inner loop current-mode controller implements resistor emulation to achieve high-power-factor operation on each of the two orthogonal axes of the stationary reference frame. The outer control loop performs magnitude scaling and phase-shifting operations on current of one of the axes to make it balanced with the current on the other axis. The coefficients of scaling and shifting functions are determined by two closed-loop prportional-integral (PI) controllers that impose the conditions of input current balance as PI references. The control algorithm is simple and high performing. It does not require input voltage sensing and transformation of the control variables into a rotating reference frame. The simulation results on a MATLAB-SIMULINK platform validate the proposed control strategy. In implementation Texas Instrument's digital signal processor TMS320F24OF is used as the digital controller. The control algorithm for high-power-factor operation is tested on a prototype boost rectifier under nominal and unbalanced input voltage conditions.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Boundary value problems for third-order nonlinear ordinary differential equations

In this paper, we describe how to analyze boundary value problems for third-order nonlinear ordinary differential equations over an infinite interval. Several physical problems of interest are governed by such systems. The seminumerical schemes described here offer some advantages over solutions obtained by using traditional methods such as finite differences, shooting method, etc. These techniques also reveal the analytic structure of the solution function. For illustrative purposes, several physical problems, mainly drawn from fluid mechanics, are considered; they clearly demonstrate the efficiency of the techniques presented here.

Secondary flows induced by the rotation of a sphere or coaxial cones in micropolar fluids

The micropolar fluids like Newtonian and Non-Newtonian fluids cannot sustain a simple shearing motion, wherein only one component of velocity is present. They exhibit both primary and secondary motions when the boundaries are subject to slow rotations. The primary motion, as in Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., resembles that of Newtonian fluid for slow steady rotation. We further notice that the micro-rotation becomes identically equal to the vorticity present in the fluid and the condition b) of "Wall vorticity" can alone be satisfied at the boundaries. As regards, the secondary motion, we notice that it can be determined by the above procedure for a special class of fluids, namely that for which j0(n2-n3)=4 n3/l2. Moreover for this class of fluids, the micro-rotation is identical with the vorticity of the fluid everywhere. Also the stream function for the secondary flow is identical with that for the Newtonian fluid with a suitable definition of the Reynolds number. In contrast with the Non-Newtonian fluids, characterized by the equation due to Rivlin-Ericksen, Oldroyd, Walters etc., this class of micropolar fluids does not show separation. This is in conformity with the statement of Condiff and Dahler (3) that in any steady flow, internal spin matches the vorticity everywhere provided that (i) spin boundary conditions are satisfied, (ii) body torques and non-conservative body forces are absent, and (iii) inertial and spin-inertial terms are either negligible or vanish identically.

The influence of Zr/Ti content on the morphotropic phase boundary in the PZT-PZN system

A quantitative structural investigation was carried out on (1-y)PbZrxTi1-xO3-yPbZn(1/3)Nb(2/3)O(3) where y=0.1 and 0.2 ((1-y)PZT-yPZN). High resolution XRD data have been used for quantitative phase analysis. The nominal compositions were prepared by a two-step low temperature calcining solid-state method. The sintered samples show an average grain size of 1-2 mu m. It is demonstrated that the increase in the concentration of PZN leads to the shift of the morphotropic phase boundary (MPB) of PZT towards the PbZrO3 end member. In the present work, an effort has been made to quantitatively determine the MPB phase contents and to regain the coexistence of tetragonal and monoclinic phases by varying the value of x(i.e. Zr/Ti ratio). The width of the MPB becomes considerably larger for y=0.10 and 0.20 as compared to pure PZT. This is attributed to the considerably lower grain size of our samples resulting from the adopted preparation method. (C) 2010 Elsevier B.V. All rights reserved.