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

Reversible jump sampler for autoregressive time series

We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

A stochastic jump and deterministic dynamics model of impact failure evolution with rate effect

Motivated by the observation of the rate effect on material failure, a model of nonlinear and nonlocal evolution is developed, that includes both stochastic and dynamic effects. In phase space a transitional region prevails, which distinguishes the failure behavior from a globally stable one to that of catastrophic. Several probability functions are found to characterize the distinctive features of evolution due to different degrees of nucleation, growth and coalescence rates. The results may provide a better understanding of material failure.

The concentration-jump coefficient in a rarefied binary gas-mixture

The results presented are obtained from sound velocity measurements, uniaxial compression tests, Brazilian tests and three-point bending tests. The density of microcracks in the heated rock is studied by means of optical microscopy, SEM and differential strain analysis (DSA).

The concentration-jump coefficient in a rarefied binary gas-mixture

The problem of the concentration jump of a vapour in the vicinity of a plane wall, which consists of the condensed phase of the vapour, in a rarefied gas mixture of that vapour (A) and another 'inert' gas (B), is considered. The general formulation of the problem of determining the concentration-jump coefficient for dA is given. In the Knudsen layer the simplest model of Boley-Yip theory is used to simplify the Boltzmann equations for the binary gas mixture. The numerical calculation of the concentration jump coefficient for dA for various values of evaporation coefficient of A is illustrated for the case of the equilibrium concentration of B being much greater than that of A, for which experimental data are available.

A numerical model for predicting the jump of lift force on an oscillating cylinder

The fluid force coefficients on a transversely oscillating cylinder are calculated by applying two- dimensional large eddy simulation method. Considering the ‘‘jump’’ phenomenon of the amplitude of lift coefficient is harmful to the security of the submarine slender structures, the characteristics of this ‘‘jump’’ are dissertated concretely. By comparing with experiment results, we establish a numerical model for predicting the jump of lift force on an oscillating cylinder, providing consultation for revising the hydrodynamic parameters and checking the fatigue life scale design of submarine slender cylindrical structures.