Use of ultrasonics in shear layer cavitation control

In this paper we report results from some investigations on the use of ultrasonics in controlling hydrodynamic cavitation in the shear layer downstream of a sudden expansion. Control of this type of cavitation has been achieved by modulating the local pressure that was experienced by a nucleus present in the shear layer. This modulation was made possible by using a piezoelectric device, termed as Ultrasonic Pressure Modulator (UPM). The performance of UPM has been studied at different dissolved gas concentrations with electrolysis bubbles as nuclei. Control of cavitation due to natural nuclei has also been attempted. Efficiency of UPM, in reducing cavitation, was seen to be dependent on the driving frequency employed. Experimental and numerical studies have been conducted to bring out the physics behind this approach of cavitation control. Different measures of cavitation control have been identified and some possible applications of this method have also been outlined.     

Knudsen diffusivity of a hard sphere in a rough slit pore

An analytic theory for the Knudsen self-diffusivity D(s) of hard spheres in an atomically rough slit-shaped pore is presented which quantitatively matches simulation results. The theory assumes that, due to chaotic molecular trajectories caused by surface morphology, collisions of gas molecules with the wall are partly diffuse and partly specular, the relative magnitude of each depending upon the magnitude of the tangential momentum accommodation coefficient f. The theory thus represents a universal Knudsen fluctuation-dissipation correlation between longitudinal momentum loss and diffusivity that can simplify efforts to estimate D(s). It is also found that D(s) computed using Maxwell's theory of slip, in which collisions with the walls are assumed to be purely diffuse or specular, overpredicts the simulated D(s) by a large margin.     

Transfer Thermodynamics of Protein in Denaturing and Stabilizing Media

Free energies of transfer (ΔG_t) of RibonucleaseA (RNaseA) from water to aqueous solutions of urea (4 M, 6 M and 8 M), a protein denaturing solvent as well as ΔG_t of RibonucleaseA, β‐Lactoglobulin, α‐Chymotripsin and ChymotrypsinogenA from water to aqueous glycerol (10%, 20%, 30% and 40%), a protein stabilizing solvent has been dissected into cavity term [ΔG_t(cav)] and interaction term [ΔG_t(int)]. The interaction free energy includes all types of interactions like hard‐soft, hydrogen bonding, electrostatic, etc. The cavity forming free energies have been calculated using the standard version of scaled particle theory (SPT) with well‐reported SPT parameters. It has been found that transfer free energies of cavity terms ΔG_t(cav) for native protein from water to urea‐water and water to aqueous glycerol follow almost opposite trends. This primarily indicates there may be some correlation between cavity creation energies and protein denaturing and stabilizing ability of a solvent. The results are in agreement with those obtained from preferential binding coefficient studies in these media.     

A simple mathematical model for seasonal planktonic blooms

We show how the inclusion of the defense strategy by different species can alter the prediction of simple models. One of the defense strategy by the phytoplankton population against their grazer is the release of toxic chemicals. In turn the zooplankton population reduces there predation rate over toxin producing phytoplankton (TPP) to protect themselves from those toxic chemicals. Thus, when the level of toxicity is high, the grazing pressure is low and when the level of toxicity is low or when the toxin is absent, the grazing pressure is high. Here we have considered a TPP–zooplankton system where the rate of toxin liberation and the predation rate vary with zooplankton abundance. We observe that our proposed model has the potential to show different dynamical behaviour that are similar to that seen in real‐world situations. Further, we consider three different functional forms for the distribution of the toxins and compare them using latin hypercube sampling technique and found that the functional forms seem to have no effect in determining the final outcome of the system. Copyright © 2009 John Wiley & Sons, Ltd.     

Continuation of limit cycles near saddle homoclinic points using splines in phase space

We present a new algorithm for continuation of limit cycles of autonomous systems as a system parameter is varied. The algorithm works in phase space with an ordered set of points on the limit cycle, along with spline interpolation. Currently popular algorithms in bifurcation analysis packages compute time-domain approximations of limit cycles using either shooting or collocation. The present approach seems useful for continuation near saddle homoclinic points, where it encounters a corner while time-domain methods essentially encounter a discontinuity (a relatively short period of rapid variation). Other phase space-based algorithms use rescaled arclength in place of time, but subsequently resemble the time-domain methods. Compared to these, we introduce additional freedom through a variable stretching of arclength based on local curvature, through the use of an auxiliary index-based variable. Several numerical examples are presented. Comparisons with results from the popular package, MATCONT, are favorable close to saddle homoclinic points.