The effect of the finite size of ions and Debye layer overspill on the screened Coulomb interactions between charged flat plates

Screened repulsion between uniformly charged plates with an intervening electrolyte is analyzed for strongly overlapped electrical double layers (EDL), accounting for the steric effect of ions and their expulsion from EDL edges into the surrounding solution. As a generalization of a study by Philipse et al. which does not account for these effects, an analytical expression is derived for the repulsion pressure in the limit of infinitely long plates with a zero-field assumption, which agrees closely with the corresponding numerical solution at low inter-plate separations. Our results show an augmented repulsive pressure for finite-sized ions at strong EDL overlaps. For plates with a finite lateral size, we demonstrate a further extended domain of low inter-plate gaps where the repulsion pressure increases with ion size due to a strong interplay between the steric interaction of ions and the EDL overspill phenomenon, considered earlier in a study by Ghosal & Sherwood limited to the linear Debye-Hückel regime (which cannot account for the steric effect of ions). This investigation on a simple model should enhance our understanding of the interaction between charged particles in electrophoresis, nanoscale self-assembly, active particles, and various other electrokinetic systems.     

The CWKB Method of Particle Production in a Periodic Potential

In this work we study the particle production in time dependent periodic potential using the method of complex time WKB (CWKB) approximation. In the inflationary cosmology at the end of the inflationary stage, the potential becomes time dependent as well as periodic. Reheating occurs due to particle production by the oscillating inflaton field. Using CWKB we obtain almost identical results on catastrophic particle production as obtained by others.     

Morphology of growing interfacial patterns

A study is made of the morphology of the interfacial patterns in the solid-on-solid model evolving from initial states very far from equilibrium. Monte Carlo simulation is used to study the time dependence of the length, the diffuseness, and the width of the interface during such evolution in the absence as well as in the presence of quenched random field. Moreover, the technique of Walsh-Fourier transform is introduced for analyzing the noise level in such interfacial patterns. A quantity is also introduced that characterizes the interfacial structure locally on a very short length scale. Finally, the latter technique is also applied to the kinetic Ising model evolving from a random initial configuration.     

Variational approach to the Hamiltonian structure of a new hierarchy of nonlinear equations

We determine the symplectic Hamiltonian structure associated with the nonlinear evolution equations obtained from two new isospectral problems. We follow the method of variation with respect to the field variables. An explicit example is given to demonstrate the new class of equations that are generated.     

Conventionality of Simultaneity and the Tippe Top Paradox in Relativity

In this paper we critically examine a recently posed paradox (tippe top paradox in relativity) and its suggested resolution. A tippe top when spun on a table, tips over after a few rotations and eventually stands spinning on its stem. The ability of the top to demonstrate this charming feat depends on its geometry (all tops are not tippe tops). To a rocket-bound observer the top geometry should change because of the Lorentz contraction. This gives rise to the possibility that for a sufficiently fast observer the geometry of the top may get altered to such an extent that the top may not tip over! This is certainly paradoxical since a mere change of the observer cannot alter the fact that the top tips over on the table. In an effort to resolve the issue the authors of the paradox compare the equations of motion of the particles of the top from the perspective of the inertial frames of the rocket and the table and observe among other things that (1) the relativity of simultaneity plays an essential role in resolving the paradox and (2) the puzzle in some way is connected with one of the corrolaries of special relativity that the notion of rigidity is inconsistent with the theory. We show here that the question of the incompatibility of the notion of rigidity with special relativity has nothing to do with the current paradox and the role of the lack of synchronization of clocks in the context of the paradox is grossly over-emphasized. The conventionality of simultaneity of special relativity and the notion of the standard (Einstein) synchrony in the Galilean world have been used to throw light on some subtle issues concerning the paradox.     

Higher order contribution to the propagation characteristics of low frequency transverse waves in a dusty plasma

Characteristic features of low frequency transverse wave propagating in a magnetised dusty plasma have been analysed considering the effect of dust-charge fluctuation. The distinctive behaviours of both the left circularly polarised and right circularly polarised waves have been exhibited through the analysis of linear and non-linear dispersion relations. The phase velocity, group velocity, and group travel time for the waves have been obtained and their propagation characteristics have been shown graphically with the variations of wave frequency, dust density and amplitude of the wave. The change in non-linear wave number shift and Faraday rotation angle have also been exhibited with respect to the plasma parameters. It is observed that the effects of dust particles are significant only when the higher order contributions are considered. This may be referred to as the ‘dust regime’ in plasma.     

Energy levels of λx 2k anharmonic oscillators using the quantum normal form

The ground state and first few excited energy levels of the generalized anharmonic oscillator defined by the HamiltonianH=–d ²/dx ²+x ²+x ^2k (k=3, 4,...) have been calculated by employing the method of quantum normal form, which is the quantum mechanical analogue of the classical Birkhoff-Gustavson normal form. The present energy eigenvalues are consistent with other tabulations of the energy levels.     

Periodic and solitary wave solutions of the three-wave problem. A different approach

We consider the inverse problem for a three-wave interaction system in a manner different from Zakharovet al. and of Kaup. Our method is an adaptation of the technique due to Date to a 3 × 3 Lax pair. The analysis leads to a system of ordinary nonlinear equations for the _ivariables linearizable through a suitable definition of differential on a Riemann surface. Next, in the degenerate case, when the _iare equal in pairs, we prove that such a set of equations is exactly integrable and leads to solitary solutions.     

Swinging atwood machine. Far- and near-resonance region

The swinging Atwood machine, a prototype nonlinear dynamical system, is analyzed following an idea of Bogoliubov and Mitropolsky. A series solution is found for the radial and angular displacement as functions of time. The analysis is repeated in the resonance case, when the frequency of the driving force maintains a fixed ratio to that of the free motion. The condition of resonance requires the mass ratio to be equal to 2j ²–1, wherej is an integer not equal to one.     

Determination of oxygen impurity in high purity materials by charged particle activation analysis using alpha projectiles

40 MeV -particles have been used to determine oxygen impurity at ppm levels in silicon, copper, and stainless steel, through the radiochemical separation of¹⁸F from the matrix. The separation of¹⁸F has been carried out by two techniques, viz.(1) distillation of H₂SiF₆ and (2) precipitation of KBF₄ and some modification has been applied in the separation, depending on the nature of interferences from the matrix. Instrumental approach was also carried out to determine the oxygen impurity at 100 ppm in Si matrix because this approach is not possible in Cu and stainless steel samples due to matrix activity.