General classical theory of spinning particles in a meson field

An exact classical theory of the motion of a point dipole in a meson field is given which takes into account the effects of the reaction of the emitted meson field. The meson field is characterized by a constant $\chi =\mu /\hslash $ of the dimensions of a reciprocal length, $\mu $ being the meson mass, and as $\chi \rightarrow $ 0 the theory of this paper goes over continuously into the theory of the preceding paper for the motion of a spinning particle in a Maxwell field. The mass of the particle and the spin angular momentum are arbitrary mechanical constants. The field contributes a small finite addition to the mass, and a negative moment of inertia about an axis perpendicular to the spin axis. A cross-section (formula (88 a)) is given for the scattering of transversely polarized neutral mesons by the rotation of the spin of the neutron or proton which should be valid up to energies of 10$^{9}$ eV. For low energies E it agrees completely with the old quantum cross-section, having a dependence on energy proportional to p$^{4}$/E$^{2}$ (p being the meson momentum). At higher energies it deviates completely from the quantum cross-section, which it supersedes by taking into account the effects of radiation reaction on the rotation of the spin. The cross-section is a maximum at E $\sim $ 3$\cdot $5$\mu $, its value at this point being 3 $\times $ 10$^{-26}$ cm.$^{2}$, after which it decreases rapidly, becoming proportional to E$^{-2}$ at high energies. Thus the quantum theory of the interaction of neutrons with mesons goes wrong for E $\gtrsim $ 3$\mu $. The scattering of longitudinally polarized mesons is due to the translational but not the rotational motion of the dipole and is at least twenty thousand times smaller. With the assumption previously made by the present author that the heavy partilesc may exist in states of any integral charge, and in particular that protons of charge 2e and - e may occur in nature, the above results can be applied to charged mesons. Thus transversely polarised mesons should undergo a very big scattering and consequent absorption at energies near 3$\cdot $5$\mu $. Hence the energy spectrum of transversely polarized mesons should fall off rapidly for energies below about 3$\mu $. Scattering plays a relatively unimportant part in the absorption of longitudinally polarized mesons, and they are therefore much more penetrating. The theory does not lead to Heisenberg explosions and multiple processes.

Experimental Studies on High-Pressure Spray Structure of Biofuels

The high-pressure spray characteristics of biofuels, specifically, Pongamia oil and its blends with diesel are studied for various gas pressures. Two single-hole solenoid injectors with nozzle diameters of 200 and 260 mu m are used along with a high-pressure common-rail direct-injection system to inject fuel into a high-pressure spray visualization chamber. The spray structure is characterized using a high-speed laser-based shadowgraphy technique. The spray structure of Pongamia oil revealed the presence of an intact liquid core at low gas pressure. At high gas pressures, the spray atomization of the Pongamia oil showed marked improvement. The spray tip penetration of Pongamia oil and its blends with diesel is higher compared to that of diesel for all test conditions. The spray cone angle of Pongamia oil and 50% Pongamia oil blend with diesel is lower as compared to that of diesel. Both these observations are attributed to the presence of large droplets carrying higher momentum in oil and blend. The droplet size is measured at an injection pressure of 1000 bar and gas pressure of 30 bar at 25 mm below the nozzle tip using the particle/droplet image.analysis (PDIA) method. The droplet size measurements have shown that the Sauter mean diameter (SMD) in the spray core of Pongamia oil is more than twice that of diesel. The spray tip penetration of the 20% blend of Pongamia with diesel (P20) is similar to that of diesel but the SMD is 50% higher. Based on experimental data, appropriate spray tip penetration correlation is proposed for the vegetable oil fuels such as Pongamia.

Quenching across quantum critical points in periodic systems: Dependence of scaling laws on periodicity

We study the quenching dynamics of a many-body system in one dimension described by a Hamiltonian that has spatial periodicity. Specifically, we consider a spin-1/2 chain with equal xx and yy couplings and subject to a periodically varying magnetic field in the (z) over cap direction or, equivalently, a tight-binding model of spinless fermions with a periodic local chemical potential, having period 2q, where q is a positive integer. For a linear quench of the strength of the magnetic field (or chemical potential) at a rate 1/tau across a quantum critical point, we find that the density of defects thereby produced scales as 1/tau(q/(q+1)), deviating from the 1/root tau scaling that is ubiquitous in a range of systems. We analyze this behavior by mapping the low-energy physics of the system to a set of fermionic two-level systems labeled by the lattice momentum k undergoing a nonlinear quench as well as by performing numerical simulations. We also show that if the magnetic field is a superposition of different periods, the power law depends only on the smallest period for very large values of tau, although it may exhibit a crossover at intermediate values of tau. Finally, for the case where a zz coupling is also present in the spin chain, or equivalently, where interactions are present in the fermionic system, we argue that the power associated with the scaling law depends on a combination of q and the interaction strength.

Rashbons: properties and their significance

In the presence of a synthetic non-Abelian gauge field that produces a Rashba-like spin-orbit interaction, a collection of weakly interacting fermions undergoes a crossover from a Bardeen-Cooper-Schrieffer (BCS) ground state to a Bose-Einstein condensate (BEC) ground state when the strength of the gauge field is increased (Vyasanakere et al 2011 Phys. Rev. B 84 014512). The BEC that is obtained at large gauge coupling strengths is a condensate of tightly bound bosonic fermion pairs. The properties of these bosons are solely determined by the Rashba gauge field-hence called rashbons. In this paper, we conduct a systematic study of the properties of rashbons and their dispersion. This study reveals a new qualitative aspect of the problem of interacting fermions in non-Abelian gauge fields, i.e. that the rashbon state ceases to exist when the center-of-mass momentum of the fermions exceeds a critical value that is of the order of the gauge coupling strength. The study allows us to estimate the transition temperature of the rashbon BEC and suggests a route to enhance the exponentially small transition temperature of the system with a fixed weak attraction to the order of the Fermi temperature by tuning the strength of the non-Abelian gauge field. The nature of the rashbon dispersion, and in particular the absence of the rashbon states at large momenta, suggests a regime in parameter space where the normal state of the system will be a dynamical mixture of uncondensed rashbons and unpaired helical fermions. Such a state should show many novel features including pseudogap physics.

Wrinkled and slack membranes: nonlinear 3D elasticity solutions via smooth DMS-FEM and experiment

The smooth DMS-FEM, recently proposed by the authors, is extended and applied to the geometrically nonlinear and ill-posed problem of a deformed and wrinkled/slack membrane. A key feature of this work is that three-dimensional nonlinear elasticity equations corresponding to linear momentum balance, without any dimensional reduction and the associated approximations, directly serve as the membrane governing equations. Domain discretization is performed with triangular prism elements and the higher order (C1 or more) interelement continuity of the shape functions ensures that the errors arising from possible jumps in the first derivatives of the conventional C0 shape functions do not propagate because the ill-conditioned tangent stiffness matrices are iteratively inverted. The present scheme employs no regularization and exhibits little sensitivity to h-refinement. Although the numerically computed deformed membrane profiles do show some sensitivity to initial imperfections (nonplanarity) in the membrane profile needed to initiate transverse deformations, the overall patterns of the wrinkles and the deformed shapes appear to be less so. Finally, the deformed profiles, computed through the DMS FEM-based weak formulation, are compared with those obtained through an experiment on an ultrathin Kapton membrane, wherein wrinkles form because of the applied boundary displacement conditions. Comparisons with a reported experiment on a rectangular membrane are also provided. These exercises lend credence to the feasibility of the DMS FEM-based numerical route to computing post-wrinkled membrane shapes. Copyright (c) 2012 John Wiley & Sons, Ltd.

Study of Fluid Flow and Mixing Behaviour of a Vacuum Degasser

In recent times the demand of ultra-low carbon steel (ULCS) with improved mechanical properties such as good ductility and good workability has been increased as it is used to produce cold-rolled steel sheets for automobiles. For producing ULCS efficiently, it is necessary to improve the productivity of the vacuum degassers such as RH, DH and tank degasser. Recently, it has been claimed that using a new process, called REDA (revolutionary degassing activator), one can achieve the carbon content below 10 ppm in less time. As such, REDA process has not been studied thoroughly in terms of fluid flow and mass transfer which is a necessary precursor to understand and design this process. Therefore, momentum and mass transfer of the process has been studied by solving momentum and species balance equations along with k-epsilon turbulent model in two-dimension (2D) for REDA process. Similarly, computational fluid dynamic studies have been made in 2D for tank and RH degassers to compare them with REDA process. Computational results have been validated with published experimental and theoretical data. It is found that REDA process is the most efficient among all these processes in terms of mixing efficiency. Fluid flow phenomena have been studied in details for REDA process by varying gas flow rate, depth of immersed snorkel in the steel, diameter of the snorkel and change in vacuum pressure. It is found that design of snorkel affects the melt circulation in the bath significantly.

Stabilized SPH-based simulations of impact dynamics using acceleration-corrected artificial viscosity

Artificial viscosity in SPH-based computations of impact dynamics is a numerical artifice that helps stabilize spurious oscillations near the shock fronts and requires certain user-defined parameters. Improper choice of these parameters may lead to spurious entropy generation within the discretized system and make it over-dissipative. This is of particular concern in impact mechanics problems wherein the transient structural response may depend sensitively on the transfer of momentum and kinetic energy due to impact. In order to address this difficulty, an acceleration correction algorithm was proposed in Shaw and Reid (''Heuristic acceleration correction algorithm for use in SPH computations in impact mechanics'', Comput. Methods Appl. Mech. Engrg., 198, 3962-3974) and further rationalized in Shaw et al. (An Optimally Corrected Form of Acceleration Correction Algorithm within SPH-based Simulations of Solid Mechanics, submitted to Comput. Methods Appl. Mech. Engrg). It was shown that the acceleration correction algorithm removes spurious high frequency oscillations in the computed response whilst retaining the stabilizing characteristics of the artificial viscosity in the presence of shocks and layers with sharp gradients. In this paper, we aim at gathering further insights into the acceleration correction algorithm by further exploring its application to problems related to impact dynamics. The numerical evidence in this work thus establishes that, together with the acceleration correction algorithm, SPH can be used as an accurate and efficient tool in dynamic, inelastic structural mechanics. (C) 2011 Elsevier Ltd. All rights reserved.

LOCAL TWO-DIMENSIONAL PARTICLE-IN-CELL SIMULATIONS OF THE COLLISIONLESS MAGNETOROTATIONAL INSTABILITY

The magnetorotational instability (MRI) is a crucial mechanism of angular momentum transport in a variety of astrophysical accretion disks. In systems accreting at well below the Eddington rate, such as the central black hole in the Milky Way (Sgr A*), the plasma in the disk is essentially collisionless. We present a nonlinear study of the collisionless MRI using first-principles particle-in-cell plasma simulations. We focus on local two-dimensional (axisymmetric) simulations, deferring more realistic three-dimensional simulations to future work. For simulations with net vertical magnetic flux, the MRI continuously amplifies the magnetic field, B, until the Alfven velocity, v(A), is comparable to the speed of light, c (independent of the initial value of v(A)/c). This is consistent with the lack of saturation of MRI channel modes in analogous axisymmetric MHD simulations. The amplification of the magnetic field by the MRI generates a significant pressure anisotropy in the plasma (with the pressure perpendicular to B being larger than the parallel pressure). We find that this pressure anisotropy in turn excites mirror modes and that the volume-averaged pressure anisotropy remains near the threshold for mirror mode excitation. Particle energization is due to both reconnection and viscous heating associated with the pressure anisotropy. Reconnection produces a distinctive power-law component in the energy distribution function of the particles, indicating the likelihood of non-thermal ion and electron acceleration in collisionless accretion disks. This has important implications for interpreting the observed emission-from the radio to the gamma-rays-of systems such as Sgr A*.

Cumulus clouds and convective boundary layers: a tropical perspective on two turbulent shear flows

This paper is a review prepared for the second Marseille Colloquium on the mechanics of turbulence, held in 2011, 50 years after the first. The review covers recent developments in our understanding of the large-scale dynamics of cumulus cloud flows and of the atmospheric boundary layer in the low-wind convective regime that is often encountered in the tropics. It has recently been shown that a variety of cumulus cloud forms and life cycles can be experimentally realized in the laboratory, with the transient diabatic plume taken as the flow model for a cumulus cloud. The plume is subjected to diabatic heating scaled to be dynamically similar to heat release from phase changes in clouds. The experiments are complemented by exact numerical solutions of the Navier-Stokes-Boussinesq equations for plumes with scaled off-source heating. The results show that the Taylor entrainment coefficient first increases with heating, reaches a positive maximum and then drops rapidly to zero or even negative values. This reduction in entrainment is a consequence of structural changes in the flow, smoothing out the convoluted boundaries in the non-diabatic plume, including the tongues engulfing the ambient flow. This is accompanied by a greater degree of mixedness in the core flow because of lower dilution by the ambient fluid. The cloud forms generated depend strongly on the history of the diabatic heating profile in the vertical direction. The striking effects of heating on the flow are attributable to the operation of the baroclinic torque due to the temperature field. The mean baroclinic torque is shown to peak around a quasi-cylindrical sheet situated midway between the axis of the flow and the edges. This torque is shear-enhancing and folds down the engulfment tongues. The increase in mixedness can be traced to an explosive growth in the enstrophy, triggered by a strong fluctuating baroclinic torque that acts as a source, especially at the higher wave numbers, thus enhancing the mixedness. In convective boundary layers field measurements show that, under conditions prevailing in the tropics, the eddy fluxes of momentum and energy do not follow the Monin-Obukhov similarity. Instead, the eddy momentum flux is found to be linear in the wind speed at low winds; and the eddy heat flux is, to a first approximation, governed by free convection laws, with wind acting as a small perturbation on a regime of free convection. A new boundary layer code, based on heat flux scaling rather than wall-stress scaling, shows promising improvements in predictive skills of a general circulation model.

Scaling Analysis of Solidification of Liquid Aluminum Alloy Flowing on Cooling Slope

Among all methods of metal alloy slurry preparation, the cooling slope method is the simplest in terms of design and process control. The method involves pouring of the melt from top, down an oblique and channel shaped plate cooled from bottom by counter flowing water. The melt, while flowing down, partially solidifies and forms columnar dendrites on plate wall. These dendrites are broken into equiaxed grains and are washed away with melt. The melt, together with the equiaxed grains, forms semisolid slurry collected at the slope exit and cast into billets having non-dendritic microstructure. The final microstructure depends on several process parameters such as slope angle, slope length, pouring superheat, and cooling rate. The present work involves scaling analysis of conservation equations of momentum, energy and species for the melt flow down a cooling slope. The main purpose of the scaling analysis is to obtain a physical insight into the role and relative importance of each parameter in influencing the final microstructure. For assessing the scaling analysis, the trends predicted by scaling are compared against corresponding numerical results using an enthalpy based solidification model with incorporation of solid phase movement.

A model for growth and engulfment of gas microporosity during aluminum alloy solidification process

A new coupled approach is presented for modeling the hydrogen bubble evolution and engulfment during an aluminum alloy solidification process in a micro-scale domain. An explicit enthalpy scheme is used to model the solidification process which is coupled with a level-set method for tracking the hydrogen bubble evolution. The volume averaging techniques are used to model mass, momentum, energy and species conservation equations in the chosen micro-scale domain. The interaction between the solid, liquid and gas interfaces in the system have been studied. Using an order-of-magnitude study on growth rates of bubble and solid interfaces, a criterion is developed to predict bubble elongation which can occur during the engulfment phase. Using this model, we provide further evidence in support of a conceptual thought experiment reported in literature, with regard to estimation of final pore shape as a function of typical casting cooling rates. The results from the proposed model are qualitatively compared with in situ experimental observations reported in literature. The ability of the model to predict growth and movement of a hydrogen bubble and its subsequent engulfment by a solidifying front has been demonstrated for varying average cooling rates encountered in typical sand, permanent mold, and various casting processes. (C) 2012 Elsevier B.V. All rights reserved.

Analysis of large-amplitude stratospheric mountain wave event observed from the AIRS and MLS sounders over the western Himalayan region

Mountain waves in the stratosphere have been observed over elevated topographies using both nadir-looking and limb-viewing satellites. However, the characteristics of mountain waves generated over the Himalayan Mountain range and the adjacent Tibetan Plateau are relatively less explored. The present study reports on three-dimensional (3-D) properties of a mountain wave event that occurred over the western Himalayan region on 9 December 2008. Observations made by the Atmospheric Infrared Sounder on board the Aqua and Microwave Limb Sounder on board the Aura satellites are used to delineate the wave properties. The observed wave properties such as horizontal (lambda(x), lambda(y)) and vertical (lambda(z)) wavelengths are 276 km (zonal), 289 km (meridional), and 25 km, respectively. A good agreement is found between the observed and modeled/analyzed vertical wavelength for a stationary gravity wave determined using the Modern Era Retrospective Analysis for Research and Applications (MERRA) reanalysis winds. The analysis of both the National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis and MERRA winds shows that the waves are primarily forced by strong flow across the topography. Using the 3-D properties of waves and the corrected temperature amplitudes, we estimated wave momentum fluxes of the order of similar to 0.05 Pa, which is in agreement with large-amplitude mountain wave events reported elsewhere. In this regard, the present study is considered to be very much informative to the gravity wave drag schemes employed in current general circulation models for this region.

Spin injection into a metal from a topological insulator

We study a junction of a topological insulator with a thin two-dimensional nonmagnetic or partially polarized ferromagnetic metallic film deposited on a three-dimensional insulator. We show, by deriving generic boundary conditions applicable to electrons traversing the junction, that there is a finite spin-current injection into the film whose magnitude can be controlled by tuning a voltage V applied across the junction. For ferromagnetic films, the direction of the component of the spin current along the film magnetization can also be tuned by tuning the barrier potential V-0 at the junction. We point out the role of the chiral spin-momentum locking of the Dirac electrons behind this phenomenon and suggest experiments to test our theory.

Path-integral formulation for Levy flights: Evaluation of the propagator for free, linear, and harmonic potentials in the over- and underdamped limits

Levy flights can be described using a Fokker-Planck equation, which involves a fractional derivative operator in the position coordinate. Such an operator has its natural expression in the Fourier domain. Starting with this, we show that the solution of the equation can be written as a Hamiltonian path integral. Though this has been realized in the literature, the method has not found applications as the path integral appears difficult to evaluate. We show that a method in which one integrates over the position coordinates first, after which integration is performed over the momentum coordinates, can be used to evaluate several path integrals that are of interest. Using this, we evaluate the propagators for (a) free particle, (b) particle subjected to a linear potential, and (c) harmonic potential. In all the three cases, we have obtained results for both overdamped and underdamped cases. DOI: 10.1103/PhysRevE.86.061105

Effect of pouring temperature on cooling slope casting of semi-solid Al-Si-Mg alloy

Present trend of semi-solid processing is directed towards rheocasting route which allows manufacturing of near-net-shape cast components directly from the prepared semi-solid slurry. Generation of globular equi-axed grains during solidification of rheocast components, compared to the columnar dendritic structure of conventional casting routes, facilitates the manufacturing of components with improved mechanical properties and structural integrity. In the present investigation, a cooling slope has been designed and indigenously fabricated to produce semi solid slurry of Al-Si-Mg (A356) alloy and successively cast in a metallic mould. The scope of the present work discusses about development of a numerical model to simulate the liquid metal flow through cooling slope using Eulerian two-phase flow approach and to investigate the effect of pouring temperature on cooling slope semi-solid slurry generation process. The two phases considered in the present model are liquid metal and air. Solid fraction evolution of the solidifying melt is tracked at different locations of the cooling slope, following Schiel's equation. The continuity equation, momentum equation and energy equation are solved considering thin wall boundary condition approach. During solidification of the liquid metal, a modified temperature recovery scheme has been employed taking care of the latent heat release and change of fraction of liquid. The results obtained from simulations are compared with experimental findings and good agreement has been found.