A note on the Berry phase for systems having one degree of freedom

A one-dimensional arbitrary system with quantum Hamiltonian H(q, p) is shown to acquire the 'geometric' phase gamma (C)=(1/2) contour integral c(Podqo-qodpo) under adiabatic transport q to q+q+qo(t) and p to p+po(t) along a closed circuit C in the parameter space (qo(t), po(t)). The non-vanishing nature of this phase, despite only one degree of freedom (q), is due ultimately to the underlying non-Abelian Weyl group. A physical realisation in which this Berry phase results in a line spread is briefly discussed.

On the Fekete-Szego problem for concave univalent functions

We consider the Fekete-Szego problem with real parameter lambda for the class Co(alpha) of concave univalent functions. (C) 2010 Elsevier Inc. All rights reserved.

Effect of interface friction on the mechanics of indentation of a finite layer resting on a rigid substrate

Copper strips of 2.5 mm thickness resting on stainless steel anvils were normally indented by wedges under nominal plane strain conditions. Inflections in the hardness-penetration characteristics were identified. Inflections separate stages where each stage has typical mechanics of deformation. These are arrived at by studying the distortion of 0.125 mm spaced grids inscribed on the deformation plane of the strip. The sensitivity of hardness and deformation mechanics to wedge angle and the interfacial friction between strip and anvil were investigated within the framework of existing slip line field models of indentation of semi-infinite and finite blocks.

On the improvement of diversity-multiplexing gain tradeoff in a training based TDD-simo system

This paper investigates the diversity-multiplexing gain tradeoff (DMT) of a time-division duplex (TDD) single-input multiple-output (SIMO) system with perfect channel state information (CSI) at the receiver (CSIR) and partial CSI at the transmitter (CSIT). The partial CSIT is acquired through a training sequence from the receiver to the transmitter. The training sequence is chosen in an intelligent manner based on the CSIR, to reduce the training length by a factor of r, the number of receive antennas. We show that, for the proposed training scheme and a given channel coherence time, the diversity order increases linearly with r for nonzero multiplexing gain. This is a significant improvement over conventional orthogonal training schemes.

A polynomial bound on the number of light cycles in an undirected graph

Let G be an undirected graph with a positive real weight on each edge. It is shown that the number of minimum-weight cycles of G is bounded above by a polynomial in the number of edges of G. A similar bound holds if we wish to count the number of cycles with weight at most a constant multiple of the minimum weight of a cycle of G.

Graphics Processing Units for the Real-time Linear Elastostatic Simulation of Liver

Biomedical engineering solutions like surgical simulators need High Performance Computing (HPC) to achieve real-time performance. Graphics Processing Units (GPUs) offer HPC capabilities at low cost and low power consumption. In this work, it is demonstrated that a liver which is discretized by about 2500 finite element nodes, can be graphically simulated in realtime, by making use of a GPU. Present work takes into consideration the time needed for the data transfer from CPU to GPU and back from GPU to CPU. Although behaviour of liver is very complicated, present computer simulation assumes linear elastostatics. One needs to use the commercial software ANSYS to obtain the global stiffness matrix of the liver. Results show that GPUs are useful for the real-time graphical simulation of liver, which in turn is needed in simulators that are used for training surgeons in laparoscopic surgery. Although the computer simulation should involve rendering also, neither rendering, nor the time needed for rendering and displaying the liver on a screen, is considered in the present work. The present work is just a demonstration of a concept; the concept is not really implemented and validated. Future work is to develop software which can accomplish real-time and very realistic graphical simulation of liver, with rendered image of liver on the screen changing in real-time according to the position of the surgical tool tip approximated as the mouse cursor in 3D.

On the incoming water waves against a vertical cliff

The problems of obliquely incident surface water waves against a vertical cliff have been handled in both the cases of water of infinite as well as finite depth by straightforward uses of appropriate Havelock-type expansion theorems. The logarithmic singularity along the shore-line has been incorporated in a direct manner, by suitably representing the Dirac's delta function.

On the water-induced critical double point in a polymer solution: the role of isotopic substitution

This paper examines the effect of substitution of water by heavy water in a polymer solution of polystyrene (molecular weight = 13000) and acetone. A critical double point (CDP), at which the upper and the lower partially-miscible regions merge, occurs at nearly the same coordinates as for the system [polystyrene + acetone + water]. The shape of the critical line for [polystyrene + acetone + heavy water] is highly asymmetric. An explanation for the occurrence of the water-induced CDP in [polystyrene + acetone] is advanced in terms of the interplay between contact energy dissimilarity and free-volume disparity of the polymer and the solvent. The question of the possible existence of a one-phase hole in an hourglass phase diagram is addressed in [polystyrene + acetone + water]. Our data exclude such a possibility.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

Experimental Investigation on the Effect of Advanced Bus-Clamping Pulsewidth Modulation on Motor Acoustic Noise

Voltage source inverters (VSIs) supply nonsinusoidal voltages to induction motor drives, leading to line current distortion and torque pulsation. Conventional space vector pulsewidth modulation (PWM) techniques are widely used in VSIs on the account of good waveform quality and high dc bus utilization. In a conventional space vector PWM technique, the switching sequence begins with one zero state and ends with the other zero state in a subcycle. Some novel switching sequences have been proposed, which employ only one zero state but apply one of the two active states twice in a subcycle. One pair of such special switching sequences has recently been shown to reduce the pulsating torque considerably. In this paper, the conventional and special switching sequences are compared experimentally in terms of acoustic noise. In the low-and medium-speed ranges, the special switching sequence is seen to reduce the amplitude of the tonal component of noise at the switching frequency considerably and is also found to result in spread spectrum.

On the dynamic contact angle in simulation of impinging droplets with sharp interface methods

Effects of dynamic contact angle models on the flow dynamics of an impinging droplet in sharp interface simulations are presented in this article. In the considered finite element scheme, the free surface is tracked using the arbitrary Lagrangian-Eulerian approach. The contact angle is incorporated into the model by replacing the curvature with the Laplace-Beltrami operator and integration by parts. Further, the Navier-slip with friction boundary condition is used to avoid stress singularities at the contact line. Our study demonstrates that the contact angle models have almost no influence on the flow dynamics of the non-wetting droplets. In computations of the wetting and partially wetting droplets, different contact angle models induce different flow dynamics, especially during recoiling. It is shown that a large value for the slip number has to be used in computations of the wetting and partially wetting droplets in order to reduce the effects of the contact angle models. Among all models, the equilibrium model is simple and easy to implement. Further, the equilibrium model also incorporates the contact angle hysteresis. Thus, the equilibrium contact angle model is preferred in sharp interface numerical schemes.

``On-the-fly'' kinetics of enzymatic racemization using deuterium NMR in DNA-based chiral oriented media

We report the in situ and real-time monitoring of the interconversion of L- and D-alanine-d(3) by alanine racemase from Bacillus stearothermophilus directly observed by H-2 NMR spectroscopy in anisotropic phase. The enantiomers are distinguished by the difference of their H-2 quadrupolar splittings in a chiral liquid crystal containing short DNA fragments. The proof-of-principle, the reliability, and the robustness of this new method is demonstrated by the determination of the turnover rates of the enzyme using the Michaelis Menten model.

Experimental Studies on the Kinematics of Cutting in Granular Materials

Slow flow in granular materials is characterized by high solid fraction and sustained inter-particle interaction. The kinematics of trawling or cutting is encountered in processes such as locomotion of organisms in sand; trawl gear movement on a soil deposit; plow movement; movement of rovers, earth moving equipment etc. Additionally, this configuration is very akin to shallow drilling configuration encountered in the mining and petroleum industries. An experimental study has been made in order to understand velocity and deformation fields in cutting of a model rounded sand. Under nominal plane strain conditions, sand is subjected to orthogonal cutting at different tool-rake angles. High-resolution optical images of the region of cutting were obtained during the flow of the granular ensemble around the tool. Interesting kinematics underlying the formation of a chip and the evolution of the deformation field is seen in these experiments. These images are also analyzed using a PIV algorithm and detailed information of the deformation parameters such as velocity, strain rate and volume change is obtained.

SC-FDMA for multiuser communication on the downlink

Single-carrier frequency division multiple access (SC-FDMA) has become a popular alternative to orthogonal frequency division multiple access (OFDMA) in multiuser communication on the uplink. This is mainly due to the low peak-to-average power ratio (PAPR) of SC-FDMA compared to that of OFDMA. Long-term evolution (LTE) uses SC-FDMA on the uplink to exploit this PAPR advantage to reduce transmit power amplifier backoff in user terminals. In this paper, we show that SC-FDMA can be beneficially used for multiuser communication on the downlink as well. We present SC-FDMA transmit and receive signaling architectures for multiuser communication on the downlink. The benefits of using SC-FDMA on the downlink are that SC-FDMA can achieve i) significantly better bit error rate (BER) performance at the user terminal compared to OFDMA, and ii) improved PAPR compared to OFDMA which reduces base station (BS) power amplifier backoff (making BSs more green). SC-FDMA receiver needs to do joint equalization, which can be carried out using low complexity equalization techniques. For this, we present a local neighborhood search based equalization algorithm for SC-FDMA. This algorithm is very attractive both in complexity as well as performance. We present simulation results that establish the PAPR and BER performance advantage of SC-FDMA over OFDMA in multiuser SISO/MIMO downlink as well as in large-scale multiuser MISO downlink with tens to hundreds of antennas at the BS.

Impact of substrate nitridation on the photoluminescence and photovoltaic characteristics of GaN grown on p-Si (100) by molecular beam epitaxy

This report focuses on the structural and optical properties of the GaN films grown on p-Si (100) substrates along with photovoltaic characteristics of GaN/p-Si heterojunctions fabricated with substrate nitridation and in absence of substrate nitridation. The high resolution X-ray diffraction (HRXRD), atomic force microscopy (AFM), Raman and photoluminescence (PL) spectroscopic studies reveal that the significant enhancement in the structural as well as in the optical properties of GaN epifilms grown with silicon nitride buffer layer when compared with the sample grown without silicon nitride buffer layer. The low temperature PL shows a free excitonic (FX) emission peak at 3.51 eV at the temperature of 5 K with a very narrow line width of 35 meV. Temperature dependent PL spectra follow the Varshni equation well and peak energy blue shifts by similar to 63 meV from 300 to 5 K. Raman data confirms the strain free nature and reasonably good crystallinity of the films. The GaN/p-Si heterojunctions fabricated without substrate nitridation show a superior photovoltaic performance compared to the devices fabricated in presence of substrate nitridation. The discussions have been carried out on the junction properties. Such single junction devices exhibit a promising fill factor and conversion efficiency of 23.36 and 0.12 %, respectively, under concentrated AM1.5 illumination.