SU(2) instantons with boundary jumps and spin tunneling in magnetic molecules

Coherent state path integrals are shown in general to contain instantons with jumps at the boundaries, i.e., boundary points lying outside classical phase space. Inclusion of these instantons is shown to resolve the "missing quench paradox" in the magnetic molecule Fe8, i.e., the fact that the tunneling between the ground Zeeman states of this molecule is quenched at only four magnetic field values, instead of the ten that would be expected from the topological Berry phase between interfering instantons. An approximate formula is found for the location of the four remaining quenches.     

Domain pattern in ferroelectric triglycine sulphate using pyroelectric effect

A method to study domain structure in ferroelectrics, using pyroelectric effect is described. Variation of pyroelectric signal from the surface of a triglycine sulphate crystal plate has been studied by scanning the surface of the crystal with a low wattage He-Ne laser beam. The integrated pyroelectric signal is due to two components, namely, (1) the primary component arising out of the change in spontaneous polarization with temperature and (2) the delayed component arising out of the possible polarization reversal. The component of an electric field along the ferroelectric axis due to thermal hemisphere within the crystal plate formed by the laser beam has been calculated and shown to exceed coercive field, making polarization reversal possible. The delayed pyroelectric signal is a measure of polarization reversal within the patch illuminated and its observed variation over the surface yields information of the domain structure.     

Comparative performance study of four nanofiltration membranes in the separation of mercury and chromium

In this paper, four nanofiltration membranes, viz., (1) coating of N,O-carboxymethyl chitosan (NOCC) on polyethersulfone ultrafiltration (PES UF) substrate membrane; (2) chitosan and acrylonitrile butadiene styrene (ABS) in the blend ratio of 0:100 (ABS); (3) diethylenetriamine pentaacetic acid coating via casting method on PES UF substrate membrane (DC50); and (4) NOCC and cellulose acetate (CA) polymer blend solution (0.4?wt%) coated on a glass plate (NOCC?CCA), were selected from our previous work. By using these membranes, separation behaviour of mercury and chromium ions was studied at different operating conditions from their salt solutions. From the experimental data, it is evident that ABS membrane gave highest observed solute rejection (92.88 and 88.67?% for 10?ppm feed concentration of mercury sulphate?Cwater system and chromium sulphate?Cwater system, respectively) and NOCC?CCA membrane gave highest permeate volume flux. But from the rejection as well as permeate volume flux point of view, NOCC?CPES membrane is considered to be the best choice among all the membranes.     

Milling Bifurcations from Structural Asymmetry and Nonlinear Regeneration

This paper investigates multiple modeling choices for analyzing the rich and complex dynamics of high-speed milling processes. Various models are introduced to capture the effects of asymmetric structural modes and the influence of nonlinear regeneration in a discontinuous cutting force model. Stability is determined from the development of a dynamic map for the resulting variational system. The general case of asymmetric structural elements is investigated with a fixed frame and rotating frame model to show differences in the predicted unstable regions due to parametric excitation. Analytical and numerical investigations are confirmed through a series of experimental cutting tests. The principal results are additional unstable regions, hysteresis in the bifurcation diagrams, and the presence of coexisting periodic and quasiperiodic attractors which is confirmed through experimentation.     

Accurate numerical estimation of interphase momentum transfer in Lagrangian–Eulerian simulations of dispersed two-phase flows

The Lagrangian–Eulerian (LE) approach is used in many computational methods to simulate two-way coupled dispersed two-phase flows. These include averaged equation solvers, as well as direct numerical simulations (DNS) and large-eddy simulations (LES) that approximate the dispersed-phase particles (or droplets or bubbles) as point sources. Accurate calculation of the interphase momentum transfer term in LE simulations is crucial for predicting qualitatively correct physical behavior, as well as for quantitative comparison with experiments. Numerical error in the interphase momentum transfer calculation arises from both forward interpolation/approximation of fluid velocity at grid nodes to particle locations, and from backward estimation of the interphase momentum transfer term at particle locations to grid nodes. A novel test that admits an analytical form for the interphase momentum transfer term is devised to test the accuracy of the following numerical schemes: (1) fourth-order Lagrange Polynomial Interpolation (LPI-4), (3) Piecewise Cubic Approximation (PCA), (3) second-order Lagrange Polynomial Interpolation (LPI-2) which is basically linear interpolation, and (4) a Two-Stage Estimation algorithm (TSE). A number of tests are performed to systematically characterize the effects of varying the particle velocity variance, the distribution of particle positions, and fluid velocity field spectrum on estimation of the mean interphase momentum transfer term. Numerical error resulting from backward estimation is decomposed into statistical and deterministic (bias and discretization) components, and their convergence with number of particles and grid resolution is characterized. It is found that when the interphase momentum transfer is computed using values for these numerical parameters typically encountered in the literature, it can incur errors as high as 80% for the LPI-4 scheme, whereas TSE incurs a maximum error of 20%. The tests reveal that using multiple independent simulations and higher number of particles per cell are required for accurate estimation using current algorithms. The study motivates further testing of LE numerical methods, and the development of better algorithms for computing interphase transfer terms.     

Dynamic stability of a curved rail under a moving load

The stability of a curved rail under a constant moving load has been investigated using a linear theory; critical speeds of the moving load, and the dynamic rail deflections and rotation were calculated. The effect of the foundation was included through distributed linear springs. It was assumed that the moving load remains in constant contact with the rail and travels along a fixed path on the rail head.     

Availability analysis of crank-case manufacturing in a two-wheeler automobile industry

The paper describes the availability of crank-case manufacturing system in an automobile industry. The units discussed here fail either directly from normal working state or indirectly through partial failure state. The machines are subjected to both preventive and corrective maintenance. Failure and repair times of the units are independent. The problem is formulated using probability consideration and supplementary variable technique. The system of equations governing the working of system consists of ordinary as well as partial differential equations. Lagrange method and Runge–Kutta method is used to solve partial differential equation and ordinary differential equation respectively. The study reveals that successful program of preventive and routine maintenance will reduce equipment failures, extend the life of the equipment, and increase the system availability to considerable margin.