Trapped fermions in a synthetic non-Abelian gauge field

On increasing the coupling strength (lambda) of a non-Abelian gauge field that induces a generalized Rashba spin-orbit interaction, the topology of the Fermi surface of a homogeneous gas of noninteracting fermions of density rho similar to k(F)(3) undergoes a change at a critical value, lambda(T) approximate to k(F) [Phys. Rev. B 84, 014512 ( 2011)]. In this paper we analyze how this phenomenon affects the size and shape of a cloud of spin-1/2 fermions trapped in a harmonic potential such as those used in cold atom experiments. We develop an adiabatic formulation, including the concomitant Pancharatnam-Berry phase effects, for the one-particle states in the presence of a trapping potential and the gauge field, obtaining approximate analytical formulas for the energy levels for some high symmetry gauge field configurations of interest. An analysis based on the local density approximation reveals that, for a given number of particles, the cloud shrinks in a characteristic fashion with increasing.. We explain the physical origins of this effect by a study of the stress tensor of the system. For an isotropic harmonic trap, the local density approximation predicts a spherical cloud even for anisotropic gauge field configurations. We show, via a calculation of the cloud shape using exact eigenstates, that for certain gauge field configurations there is a systematic and observable anisotropy in the cloud shape that increases with increasing gauge coupling lambda. The reasons for this anisotropy are explained using the analytical energy levels obtained via the adiabatic approximation. These results should be useful in the design of cold atom experiments with fermions in non-Abelian gauge fields. An important spin-off of our adiabatic formulation is that it reveals exciting possibilities for the cold-atom realization of interesting condensed matter Hamiltonians by using a non-Abelian gauge field in conjunction with another potential. In particular, we show that the use of a spherical non-Abelian gauge field with a harmonic trapping potential produces a monopole field giving rise to a spherical geometry quantum Hall-like Hamiltonian in the momentum representation.

The generalized Onsager model for the secondary flow in a high-speed rotating cylinder

The generalizations of the Onsager model for the radial boundary layer and the Carrier-Maslen model for the end-cap axial boundary layer in a high-speed rotating cylinder are formulated for studying the secondary gas flow due to wall heating and due to insertion of mass, momentum and energy into the cylinder. The generalizations have wider applicability than the original Onsager and Carrier-Maslen models, because they are not restricted to the limit A >> 1, though they are restricted to the limit R e >> 1 and a high-aspect-ratio cylinder whose length/diameter ratio is large. Here, the stratification parameter A = root m Omega(2)R(2)/2k(B)T). This parameter A is the ratio of the peripheral speed, Omega R, to the most probable molecular speed, root 2k(B)T/m, the Reynolds number Re = rho w Omega R(2)/mu, where m is the molecular mass, Omega and R are the rotational speed and radius of the cylinder, k(B) is the Boltzmann constant, T is the gas temperature, rho(w) is the gas density at wall, and mu is the gas viscosity. In the case of wall forcing, analytical solutions are obtained for the sixth-order generalized Onsager equations for the master potential, and for the fourth-order generalized Carrier-Maslen equation for the velocity potential. For the case of mass/momentum/energy insertion into the flow, the separation-of-variables procedure is used, and the appropriate homogeneous boundary conditions are specified so that the linear operators in the axial and radial directions are self-adjoint. The discrete eigenvalues and eigenfunctions of the linear operators (sixth-order and second-order in the radial and axial directions for the Onsager equation, and fourth-order and second-order in the axial and radial directions for the Carrier-Maslen equation) are determined. These solutions are compared with direct simulation Monte Carlo (DSMC) simulations. The comparison reveals that the boundary conditions in the simulations and analysis have to be matched with care. The commonly used `diffuse reflection' boundary conditions at solid walls in DSMC simulations result in a non-zero slip velocity as well as a `temperature slip' (gas temperature at the wall is different from wall temperature). These have to be incorporated in the analysis in order to make quantitative predictions. In the case of mass/momentum/energy sources within the flow, it is necessary to ensure that the homogeneous boundary conditions are accurately satisfied in the simulations. When these precautions are taken, there is excellent agreement between analysis and simulations, to within 10 %, even when the stratification parameter is as low as 0.707, the Reynolds number is as low as 100 and the aspect ratio (length/diameter) of the cylinder is as low as 2, and the secondary flow velocity is as high as 0.2 times the maximum base flow velocity. The predictions of the generalized models are also significantly better than those of the original Onsager and Carrier-Maslen models, which are restricted to thin boundary layers in the limit of high stratification parameter.

A generalized network alignment for three-source three-destination multiple unicast networks with delays

The concept of interference alignment when extended to three-source three-destination instantaneous multiple unicast network for the case where, each source-destination pair has a min-cut of 1 and zero-interference conditions are not satisfied, is known to achieve a rate of half for every source-destination pair under certain conditions [6]. This was called network alignment. We generalize this concept of network alignment to three-source three-destination multiple unicast (3S-3D-MU) networks with delays, without making use of memory at the intermediate nodes (i.e., nodes other than the sources and destinations) and using time varying Local Encoding Kernels (LEKs). This achieves half the rate corresponding to the individual source-destination min-cut for some classes of 3S-3D-MU network with delays which do not satisfy the zero-interference conditions.

A Generalized Enthalpy Update Scheme for Solidification of a Binary Alloy with Solid Phase Movement

A generalized enthalpy update scheme is presented for evaluating solid and liquid fractions during the solidification of binary alloys, taking solid movement into consideration. A fixed-grid, enthalpy-based method is developed such that the scheme accounts for equilibrium as well as for nonequilibrium solidification phenomena, along with solid phase movement. The effect of solid movement on the solidification interface shape and macrosegregation is highlighted.

Transport processes in one component plasmas using Landau equation

A system of transport equations have been obtained for plasma of electrons and having a background of positive ions in the presence of an electric and magnetic field. The starting kinetic equation is the well-known Landau kinetic equation. The distribution function of the kinetic equation has been expanded in powers of generalized Hermite polynomials and following Grad, a consistent set of transport equations have been obtained. The expressions for viscosity and heat conductivity have been deduced from the transport equation.

On Generalized Reed-Muller Expansions

The generalized Reed-Muller expansions of a switching function are generated using a single Boolean matrix and step-by-step shifting of the principal column.

Measurement of probability-distribution functions sensitive technique for the study of conduction phenomena in liquid dielectrics

The paper outlines a technique for sensitive measurement of conduction phenomena in liquid dielectrics. The special features of this technique are the simplicity of the electrical system, the inexpensive instrumentation and the high accuracy. Detection, separation and analysis of a random function of current that is superimposed on the prebreakdown direct current forms the basis of this investigation. In this case, prebreakdown direct current is the output data of a test cell with large electrodes immersed in a liquid medium subjected to high direct voltages. Measurement of the probability-distribution function of a random fluctuating component of current provides a method that gives insight into the mechanism of conduction in a liquid medium subjected to high voltages and the processes that are responsible for the existence of the fluctuating component of the current.

Noncommutative vortices and instantons from generalized Bose operators

Generalized Bose operators correspond to reducible representations of the harmonic oscillator algebra. We demonstrate their relevance in the construction of topologically non-trivial solutions in noncommutative gauge theories, focusing our attention to flux tubes, vortices, and instantons. Our method provides a simple new relation between the topological charge and the number of times the basic irreducible representation occurs in the reducible representation underlying the generalized Bose operator. When used in conjunction with the noncommutative ADHM construction, we find that these new instantons are in general not unitarily equivalent to the ones currently known in literature.

Generalized method for assessment of compressibility of rockfill material

Examination of experimental data of the modelled rockfill materials using parallel gradation technique has revealed that the plots of logarithm of strain at failure against logarithm of confining pressure are linear. Also, a trend of increase in failure strain with increase in confining pressure and maximum size of the particle have been observed. The approach presented in this paper highlights the prediction of volume change properties of rockfill materials over a range of confining pressures and particle sizes based on the results of only two tests carried out at two different confining pressures for a maximum particle size of modelled material with the use of parallel gradation technique. Two test approach and its application in modelling of rockfill materials to estimate its volume change behaviour is illustrated by means of a selected experimental data available in the literature.

Tensile force distribution along the reinforcement for reinforced soil foundations

In a reinforced soil bed system reinforcement layer is usually placed with or without end anchorage. Since soil is weak in tension reinforcement develop tension under the applied load or the displacement of the footing. This tensile force is distributed along the length of the reinforcement subjected to the end condition. The reinforccement tension helps in distributing the load over a wider area, and becomes more effective at large induced settlements. As a result, vertical componenent of tensile force generated becomes effective in reducing applied load. However, very few studies to quantify the tensile force along the reinforcement have been reported in the literature. In this paper an attempt has been made to obtain the true nature of tensile force distribution along the reinforcement. For a reinforced soil bed below a strip footing this paper brings out induced tensile force distribution along the reinforcement at different load levels and for different types of reinforcements.

Generalized frequent episodes in Event Sequences

Discovering patterns in temporal data is an important task in Data Mining. A successful method for this was proposed by Mannila et al. [1] in 1997. In their framework, mining for temporal patterns in a database of sequences of events is done by discovering the so called frequent episodes. These episodes characterize interesting collections of events occurring relatively close to each other in some partial order. However, in this framework(and in many others for finding patterns in event sequences), the ordering of events in an event sequence is the only allowed temporal information. But there are many applications where the events are not instantaneous; they have time durations. Interesting episodesthat we want to discover may need to contain information regarding event durations etc. In this paper we extend Mannila et al.’s framework to tackle such issues. In our generalized formulation, episodes are defined so that much more temporal information about events can be incorporated into the structure of an episode. This significantly enhances the expressive capability of the rules that can be discovered in the frequent episode framework. We also present algorithms for discovering such generalized frequent episodes.

Chain Length Effects on Helix-Hairpin Distribution in Short Peptides with Aib-(D)Ala and Aib-Aib Segments

The Aib-(D)Ala dipeptide segment has a tendency to form both type-I'/III' and type-I/III beta-turns. The occurrence of prime turns facilitates the formation of beta-hairpin conformations, while type-I/III turns can nucleate helix formation. The octapeptide Boc-Leu-Phe-Val-Aib-(D)Ala-Leu-Phe-Val-OMe (1) has been previously shown to form a beta-hairpin in the crystalline state and in solution. The effects of sequence truncation have been examined using the model peptides Boc-Phe-Val-Aib-Xxx-Leu-Phe-NHMe (2, 6), Boc-Val-Aib-Xxx-Leu-NHMe (3, 7), and Boc-Aib-Xxx-NHMe (4, 8), where Xxx = (D)Ala, Aib. For peptides with central Aib-Aib segments, Boc-Phe-Val-Aib-Aib-Leu-Phe-NHMe (6), Boc-Val-Aib-Aib-Leu-NHMe (7), and Boc-Aib-Aib-NHMe (8) helical conformations have been established by NMR studies in both hydrogen bonding (CD(3)OH) and non-hydrogen bonding (CDCl(3)) solvents. In contrast, the corresponding hexapeptide Boc-Phe-Val-Aib-(D)Ala-Leu-Phe-Val-NHMe (2) favors helical conformations in CDCl(3) and beta-hairpin conformations in CD(3)OH. The beta-turn conformations (type-I'/III) stabilized by intramolecular 4 -> 1 hydrogen bonds are observed for the peptide Boc-Aib-(D)Ala-NHMe (4) and Boc-Aib-Aib-NIiMe (8) in crystals. The tetrapeptide Boc-Val-Aib-Aib-Leu-NHMe (7) adopts an incipient 3(10)-helical conformation stabilized by three 4 -> 1 hydrogen bonds. The peptide Boc-Val-Aib-(D)Ala-Leu-NHMe (3) adopts a novel et-turn conformation, stabilized by three intramolecular hydrogen bonds (two 4 -> 1 and one 5 -> 1). The Aib-L(D)Ala segment adopts a type-I' beta-turn conformation. The observation of an NOE between Val (1) NH <-> HNCH(3) (5) in CD(3)OH suggests, that the solid state conformation is maintained in methanol solutions. (C) 2011 Wiley Periodicals, Inc. Biopolymers (Pept Sci) 96: 744-756, 2011.

Mass Distribution Studies in Effervescent Sprays

An experimental study on liquid mass distribution in effervescent sprays using water and air as working fluids is presented in this paper. Optical patternation and techniques of image processing are employed for analyzing the spray. The flow regime inside the effervescent atomizer largely dictates the mass distribution patterns. The patterns are seen to vary from concentrated, poorly atomized liquid lumps to uniformly distributed, fine droplets as the flow regime changes from bubbly flow to annular flow. A large variety of instantaneous spray patterns are observed in bubbly flow regime indicating a highly unsteady atomization process. However, relatively better consistency in spray patterns is observed at higher gas flow rates. Thus, the degree of unsteadiness gradually diminishes as gas flow rate is increased. The axial evolution of the spray in annular mode shows good mixing of liquid and gas across the interface.

A robust three phase power flow algorithm for radial distribution systems

An efficient load flow solution technique is required as a part of the distribution automation (DA) system for taking various control and operations decisions. This paper presents an efficient and robust three phase power flow algorithm for application to radial distribution networks. This method exploits the radial nature of the network and uses forward and backward propagation to calculate branch currents and node voltages. The proposed method has been tested to analyse several practical distribution networks of various voltage levels and also having high R/X ratio. The results for a practical distribution feeder are presented for illustration purposes. The application of the proposed method is also extended to find optimum location for reactive power compensation and network reconfiguration for planning and day-to-day operation of distribution networks.