Spatial B-jump at sudden channel enlargements with abrupt drop

An analytical and experimental study of the hydraulic jump in stilling basins with abrupt drop and sudden enlargement, called the spatial B-jump here, is carried out for finding the sequent depth ratio and resulting energy dissipation. The spatial B-jump studied has its toe downstream of the expansion section, and the stream lines at the toe are characterized by downward curvature. An expression is obtained for the sequent depth ratio based on the momentum equation with suitable assumptions for the extra pressure force term because of the abrupt drop in the bed and sudden enlargement in the basin width. Predictions compare favorably with experiments. It is shown that the spatial B-jump needs less tailwater depth, thereby enhancing the stability of the jump when compared either with spatial jump, which forms in sudden expanding channels, or with B-jump, which forms in a channel with an abrupt drop in bed. It is also shown that there is a significant increase in relative energy loss for the spatial B-jump compared to either the spatial jump or B-jump alone.

Proline ring conformations corresponding to a bistable jump model from 13C spin-lattice relaxation times

A formalism for extracting the conformations of a proline ring based on the bistable jump model of R. E. London [(1978) J. Am. Chem. Soc. 100, 2678-2685] from 13C spin-lattice relaxation times (T1) is given. The method is such that the relaxation data are only partially used to generate the conformations; these conformations are constrained to satisfy the rest of the relaxation data and to yield acceptable ring geometry. An alternate equation for T1 of 13C nuclei to that of London is given. The formalism is illustrated through an example.

Jump Reorientation of Water Molecules Confined in Narrow Carbon Nanotubes

We used molecular dynamics (MD) simulations to study the reorientational dynamics of water molecules confined inside narrow carbon nanotubes immersed in a bath of water. Our simulations show that the confined water molecules exhibit bistability in their reorientational relaxation, which proceeds by angular jumps between the two stable states. The angular jump of a water molecule in the bulk involves the breaking of a hydrogen bond with one of its neighbors and the formation of a hydrogen bond with a different neighbor. In contrast, the angular jump of a confined water molecule corresponds to an interchange of the two hydrogen atoms that can form a hydrogen bond with the same neighbor. The free energy barrier between these two states is a few k(B)T. The analytic solution of a simplified two-state jump model that qualitatively explains the reorientational behavior observed in simulations is also presented.

The jump in vorticity across a shock wave in relativistic hydrodynamics

Using the singular surface theory, an expression for the jump in vorticity across a shock wave of arbitrary shape propagating in a uniform, perfect fluid occupying the space-time of special relativity, has been derived. It has been shown that the jump in vorticity across a shock of given strength and curvature depends only on the velocity of the medium ahead of the shock.

Analytical and numerical solutions of inward spherical solidification of a superheated melt with radiative-convective heat transfer and density jump at freezing front

Analytical and numerical solutions of a general problem related to the radially symmetric inward spherical solidification of a superheated melt have been studied in this paper. In the radiation-convection type boundary conditions, the heat transfer coefficient has been taken as time dependent which could be infinite, at time,t=0. This is necessary, for the initiation of instantaneous solidification of superheated melt, over its surface. The analytical solution consists of employing suitable fictitious initial temperatures and fictitious extensions of the original region occupied by the melt. The numerical solution consists of finite difference scheme in which the grid points move with the freezing front. The numerical scheme can handle with ease the density changes in the solid and liquid states and the shrinkage or expansions of volumes due to density changes. In the numerical results, obtained for the moving boundary and temperatures, the effects of several parameters such as latent heat, Boltzmann constant, density ratios, heat transfer coefficients, etc. have been shown. The correctness of numerical results has also been checked by satisfying the integral heat balance at every timestep.

Relaxation and jump dynamics of water at the mica interface

The orientational relaxation dynamics of water confined between mica surfaces is investigated using molecular dynamics simulations. The study illustrates the wide heterogeneity that exists in the dynamics of water adjacent to a strongly hydrophilic surface such as mica. Analysis of the survival probabilities in different layers is carried out by normalizing the corresponding relaxation times with bulk water layers of similar thickness. A 10-fold increase in the survival times is observed for water directly in contact with the mica surface and a non-monotonic variation in the survival times is observed moving away from the mica surface to the bulk-like interior. The orientational relaxation time is highest for water in the contact layer, decreasing monotonically away from the surface. In all cases the ratio of the relaxation times of the 1st and 2nd rank Legendre polynomials of the HH bond vector is found to lie between 1.5 and 1.9 indicating that the reorientational relaxation in the different water layers is governed by jump dynamics. The orientational dynamics of water in the contact layer is particularly novel and is found to undergo distinct two-dimensional hydrogen bond jump reorientational dynamics with an average waiting time of 4.97 ps. The waiting time distribution is found to possess a long tail extending beyond 15 ps. Unlike previously observed jump dynamics in bulk water and other surfaces, jump events in the mica contact layer occur between hydrogen bonds formed by the water molecule and acceptor oxygens on the mica surface. Despite slowing down of the water orientational relaxation near the surface, life-times of water in the hydration shell of the K ion are comparable to that observed in bulk salt solutions. (C) 2012 American Institute of Physics. http://dx.doi.org/10.1063/1.4717710]

Motion Analysis for Short and Long Jump

Motion analysis is very essential in sport activities to enhance the performance of an athlete and to ensure the correctness of regimes. Expensive methods of motion analysis involving the use of sophisticated technology has led to limited application of motion analysis in sports. Towards this, in this paper we have integrated a low-cost method for motion analysis using three axis accelerometer, three axis magnetometer and microcontroller which are very accurate and easy to use. Seventeen male subjects performed two experiments, standing short jumps and long jumps over a wide range of take-off angles. During take-off and landing the acceleration and angles at different joints of the body are recorded using accelerometers and magnetometers, and the data is captured using Lab VIEW software. Optimum take-off angle in these jumps are calculated using the recorded data, to identify the optimum projection angle that maximizes the distance achieved in a jump. The results obtained for optimum take off angle in short jump and long jump is in agreement with those obtained using other methodologies and theoretical calculations assuming jump to be a projectile motion. The impact force (acceleration) is also analysed and is found to progressively decrease from foot to neck.

Phase-field elasticity model based on mechanical jump conditions

Computational models based on the phase-field method typically operate on a mesoscopic length scale and resolve structural changes of the material and furthermore provide valuable information about microstructure and mechanical property relations. An accurate calculation of the stresses and mechanical energy at the transition region is therefore indispensable. We derive a quantitative phase-field elasticity model based on force balance and Hadamard jump conditions at the interface. Comparing the simulated stress profiles calculated with Voigt/Taylor (Annalen der Physik 274(12):573, 1889), Reuss/Sachs (Z Angew Math Mech 9:49, 1929) and the proposed model with the theoretically predicted stress fields in a plate with a round inclusion under hydrostatic tension, we show the quantitative characteristics of the model. In order to validate the elastic contribution to the driving force for phase transition, we demonstrate the absence of excess energy, calculated by Durga et al. (Model Simul Mater Sci Eng 21(5):055018, 2013), in a one-dimensional equilibrium condition of serial and parallel material chains. To validate the driving force for systems with curved transition regions, we relate simulations to the Gibbs-Thompson equilibrium condition

Helmholtz Instability In Stratified Shear Flows With Magnetic-Fields

The stability characteristics of a Helmholtz velocity profile in a stratified Boussinesq fluid in the presence of a rigid boundary is studied, A jump in the magnetic field is introduced at a level different from the velocity discontinuity. New unstable modes in addition to the Kelvin-Helmhottz mode are found. The wavelengths of these unstable modes are close to the wavelengths of internal Alfv6n gravity waves in the atmospher.

Non-stationary signal analysis by least mean fourth (LMF) adaptive algorithm

A modified least mean fourth (LMF) adaptive algorithm applicable to non-stationary signals is presented. The performance of the proposed algorithm is studied by simulation for non-stationarities in bandwidth, centre frequency and gain of a stochastic signal. These non-stationarities are in the form of linear, sinusoidal and jump variations of the parameters. The proposed LMF adaptation is found to have better parameter tracking capability than the LMS adaptation for the same speed of convergence.

Instabilities of a compressible stratified fluid in horizontal sheared motion

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible atmosphere in the presence of a lower boundary are studied. A jump in the Brunt–Väisälä frequency is introduced and the level at which this jump occurs is assumed to be different from the shear zone, to simulate sharp temperature discontinuities in the atmosphere. The results are compared with those of Pellacani, Tebaldi, and Tosi and Lindzen and Rosenthal. In the present configuration, new unstable modes with larger growth rates are found. The wavelengths of the most unstable gravity waves for the parameters pertaining to observed cases of clear air turbulence agree quite closely with the experimental values. Physics of Fluids is copyrighted by The American Institute of Physics

Instabilities induced by variation of Brunt-Vaisala frequency in compressible stratified shear flows

The stability characteristics of a Helmholtz velocity profile in a stably stratified, compressible fluid in the presence of a lower rigid boundary are studied. A jump in the Brunt-Vaisala frequency at a level different from the shear zone is introduced and the variation of the Brunt-Vaisala frequency with respect to the vertical coordinate in the middle layer of the three-layered model is considered. An analytic solution in each of the layers is obtained, and the dispersion relation is solved numerically for parameters relevant to the model. The effect of shear in the lowermost layer of the three-layered model for a Boussinesq fluid is discussed. The results are compared with the earlier studies of Lindzen and Rosenthal, and Sachdev and Satya Narayanan. In the present model, new unstable modes with larger growth rates are obtained and the most unstable gravity wave modes are found to agree closely with the observed ones at various heights. Physics of Fluids is copyrighted by The American Institute of Physics.

On the propagation of a weak shock front: Theory and application

In this paper the kinematics of a weak shock front governed by a hyperbolic system of conservation laws is studied. This is used to develop a method for solving problems, involving the propagation of nonlinear unimodal waves. It consists of first solving the nonlinear wave problem by moving along the bicharacteristics of the system and then fitting the shock into this solution field, so that it satisfies the necessary jump conditions. The kinematics of the shock leads in a natural way to the definition of ldquoshock-raysrdquo, which play the same role as the ldquoraysrdquo in a continuous flow. A special case of a circular cylinder introduced suddenly in a constant streaming flow is studied in detail. The shock fitted in the upstream region propagates with a velocity which is the mean of the velocities of the linear and the nonlinear wave fronts. In the downstream the solution is given by an expansion wave.