Use of L matrix to obtain reliable ab initio force constants of polyatomic molecules: ethylene as a test system

Direct use of experimental eigenvalues of the vibrational secular equation on to the ab initio predicted eigenvector space is suggested as a means of obtaining a reliable set of intramolecular force constants. This method which we have termed RECOVES (recovery in the eigenvector space) is computationally simple and free from arbitrariness. The RECOVES force constants, by definition, reproduce the experimental vibrational frequencies of the parent molecule exactly. The ab initio calculations were carried out for ethylene as a test molecule and the force constants obtained by the present procedure also correctly predict the vibrational frequencies of the deuterated species. The RECOVES force constants for ethylene are compared with those obtained by using the SQM procedure.

Phase Separation in Binary Nearly-Hard-Sphere Colloids: Evidence for the Depletion Force

A binary aqueous suspension of large (L) and small (S) nearly-hard-sphere colloidal polystyrene spheres is shown to segregate spontaneously into L-rich and S-rich regions for suitable choices of volume fraction and size ratio. This is the first observation of such purely entropic phase separation of chemically identical species in which at least one component remains fluid. Simple theoretical arguments are presented to make this effect plausible.

SCF and electron correlation studies on structure, force constants and vibrational spectra of borane monoammoniate complex

Effects of basis set and electron correlation on the equilibrium geometry, force constants and vibrational spectra of BH3NH3 have been studied. A series of basis sets ranging from double zeta to triple zeta including polarization and diffuse functions have been utilized. All the SCF based calculations overestimate the dative B-N bond distance and considerable improvement occurs when the treatment for electron correlation is introduced. Detailed vibrational analysis for BH3NH3 has been carried out. The mean absolute percentage deviation of the ab initio predicted vibration frequencies of (BH3NH3)-B-11 from the experiment is about 10% for the SCF based calculations and the MP2 method shows better agreement, the overall deviation being 5-6%. The ground state effective force constants of BH3NH3 were obtained using RECOVES procedure. The RECOVES sets of force constants are found to be highly satisfactory for the prediction of the vibrational frequencies of different isotopomers of BH3NH3. The mean absolute percentage deviation of the calculated frequencies of different isotopomers from the experiment is much less than 1%. The RECOVES-MP2/augDZP set of force constants was found to be the best set among the different sets for this molecule. Theoretical infrared intensities are in fair agreement with the observed spectral features.

Theoretical Analysis of the Electromotive Force of a Cell Incorporating a Composition Gradient Solid Electrolyte

New composition gradient solid electrolytes have been designed for application in high temperature solid-state galvanic sensors and in thermodynamic measurements. The functionally gradient electrolyte consists of a solid solution between two or more ionic conductors with a common ion and gradual variation in composition of the other ionic species. Unequal rates of migration of the ions, caused by the presence of the concentration gradient, may result in the development of space charge, manifesting as diffusion potential. Presented is a theoretical analysis of the EMF of cells incorporating gradient solid electrolytes. An analytical expression is derived for diffusion potential, using the thermodynamics of irreversible processes, for different types of concentration gradients and boundary conditions at the electrode/electrolyte interfaces. The diffusion potential of an isothermal cell incorporating these gradient electrolytes becomes negligible if there is only one mobile ion and the transport numbers of the relatively immobile polyionic species and electrons approach zero. The analysis of the EMF of a nonisothermal cell incorporating a composition gradient solid electrolyte indicates that the cell EMF can be expressed in terms of the thermodynamic parameters at the electrodes and the Seebeck coefficient of the gradient electrolyte under standard conditions when the transport number of one of the ions approaches unity.

On an oscillatory point force in a rotating stratified fluid

The forced oscillations due to a point forcing effect in an infinite or contained, inviscid, incompressible, rotating, stratified fluid are investigated taking into account the density variation in the inertia terms in the linearized equations of motion. The solutions are obtained in closed form using generalized Fourier transforms. Solutions are presented for a medium bounded by a finite cylinder when the oscillatory forcing effect is acting at a point on the axis of the cylinder. In both the unbounded and bounded case, there exist characteristic cones emanating from the point of application of the force on which either the pressure or its derivatives are discontinuous. The perfect resonance existing at certain frequencies in an unbounded or bounded homogeneous fluid is avoided in the case of a confined stratified fluid.

Particle dynamics in a turbulent particle–gas suspension at high Stokes number. Part 2. The fluctuating-force model

A fluctuating-force model is developed for representing the effect of the turbulent fluid velocity fluctuations on the particle phase in a turbulent gas–solid suspension in the limit of high Stokes number, where the particle relaxation time is large compared with the correlation time for the fluid velocity fluctuations. In the model, a fluctuating force is incorporated in the equation of motion for the particles, and the force distribution is assumed to be an anisotropic Gaussian white noise. It is shown that this is equivalent to incorporating a diffusion term in the Boltzmann equation for the particle velocity distribution functions. The variance of the force distribution, or equivalently the diffusion coefficient in the Boltzmann equation, is related to the time correlation functions for the fluid velocity fluctuations. The fluctuating-force model is applied to the specific case of a Couette flow of a turbulent particle–gas suspension, for which both the fluid and particle velocity distributions were evaluated using direct numerical simulations by Goswami & Kumaran (2010). It is found that the fluctuating-force simulation is able to quantitatively predict the concentration, mean velocity profiles and the mean square velocities, both at relatively low volume fractions, where the viscous relaxation time is small compared with the time between collisions, and at higher volume fractions, where the time between collisions is small compared with the viscous relaxation time. The simulations are also able to predict the velocity distributions in the centre of the Couette, even in cases in which the velocity distribution is very different from a Gaussian distribution.

A Flexure-based Deployable Stereo Vision Mechanism and Temperature and Force Sensors for Laparoscopic Tools

This paper presents concepts, designs, and working prototypes of enhanced laparoscopic surgical tools. The enhancements are in equipping the tool with force and temperature sensing as well as image acquisition for stereo vision. Just as the pupils of our eyes are adequately spaced out and the distance between them is adjustable, two minute cameras mounted on a mechanism in our design can be moved closer or farther apart inside the inflated abdomen during the surgery. The cameras are fitted to a deployable mechanism consisting of flexural joints so that they can be inserted through a small incision and then deployed and moved as needed.A temperature sensor and a force sensor are mounted on either of the gripping faces of the surgical grasping tool to measure the temperature and gripping force, which need to be controlled for safe laparoscopic surgery. The sensors are small enough and hence they do not cause interference during surgery and insertion.Prototyping and working of the enhanced laparoscopic tool are presented with details

Closed form solutions for element equilibrium and flexibility matrices of eight node rectangular plate bending element using integrated force method

Closed form solutions for equilibrium and flexibility matrices of the Mindlin-Reissner theory based eight-node rectangular plate bending element (MRP8) using integrated Force Method (IFM) are presented in this paper. Though these closed form solutions of equilibrium and flexibility matrices are applicable to plate bending problems with square/rectangular boundaries, they reduce the computational time significantly and give more exact solutions. Presented closed form solutions are validated by solving large number of standard square/rectangular plate bending benchmark problems for deflections and moments and the results are compared with those of similar displacement-based eight-node quadrilateral plate bending elements available in the literature. The results are also compared with the exact solutions.