Unified Solution of the Expected Maximum of a Discrete Time Random Walk and the Discrete Flux to a Spherical Trap

Two random-walk related problems which have been studied independently in the past, the expected maximum of a random walker in one dimension and the flux to a spherical trap of particles undergoing discrete jumps in three dimensions, are shown to be closely related to each other and are studied using a unified approach as a solution to a Wiener-Hopf problem. For the flux problem, this work shows that a constant c = 0.29795219 which appeared in the context of the boundary extrapolation length, and was previously found only numerically, can be derived analytically. The same constant enters in higher-order corrections to the expected-maximum asymptotics. As a byproduct, we also prove a new universal result in the context of the flux problem which is an analogue of the Sparre Andersen theorem proved in the context of the random walker's maximum.     

The Quantum-Classical Comparison of the Arrival-Time Distribution Through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.     

Analysis of Low-energy α-4He Elastic Scattering Process in Direct Channel Regge-Pole Formalism

The elastic scattering of low-energy α-particles by a ⁴He target has been analysed within the frame-work of a modified Regge-Pole model which reproduces the partial wave phaseshifts in an elegant and simple way and describes all other relevant features of the scattering phenomena.     

Synthesis of indole derivatives. Part III. Extension of the amine oxide rearrangement

The synthesis of N,N-bis(4-aryloxy-2-butynyl)anilines and their rearrangement to 1,2,3-trisub-stituted indoles is described.     

On axisymmetric stokes flow past a torus

A method is presented for determining the exact solution of the Stokes equation for axisymmetric streaming flow past a torus. By solving directly for the velocity and pressure fields rather than introducing a stream function, the problem is reduced to the solution of a second order difference equation for a coefficient sequence. The force acting on the torus is evaluated for a number of values of the parameter defining the torus geometry.

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Zusammenfassung In dieser Arbeit wird eine Methode entwickelt um die exakte Lösung der Stokes' schen Gleichung für einen axisymmetrischen Fluss um einen Torus zu erhalten. Indem man direkt Geschwindgkeits- und Druckverteilung ausrechnet (statt eine Stromfunktion einzuführen) wird das Problem auf die Lösung einer Differenzengleichung zweiter Ordnung für eine Folge von Koeffizienten reduziert. Die am Torus wirksame Kraft wird dann für mehrere Parameterwerte der Torusgeometrie bestimmt.

     

Unsteady flow of an elastico-viscous fluid in tubes of uniform cross-section

In this paper, the uniqueness of solution for internal bounded unsteady flows of a shortmemory fluid is first established. Closed-form solutions are then obtained for the equations characterizing flows of such fluids in circular and rectangular tubes of uniform cross-section under an arbitrary pressure gradient. Special cases including the oscillatory flow between two parallel plates are discussed.     

Temporary mechanoluminescence of certain organic and inorganic crystals

The present paper reports the temporary mechanoluminescence of certain organic and inorganic crystals. The rate constant of the decrease in mechanoluminescence is different for different crystals and it increases with the temperature of the crystals. The mechanoluminescence spectra of As₂O₃ crystals also change with the age of the crystals. It is concluded that the phase transformation may be responsible for the temporary mechanoluminescence in the crystals.