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.     

Spectroscopic studies on nanodispersions of CdS, HgS, their core-shells and composites prepared in micellar medium

CdS is a large band gap material compared to HgS. Both are interesting from academic and technological points of view. The nanodispersions (colloids) of CdS and HgS as well their core-shell products and composites (co-colloids) were prepared by varied modes of precursor addition in micellar solution of cationic surfactant cetyltrimethylammonium bromide (CTAB). The prepared dispersions were studied by spectroscopic and electron microscopic techniques.     

Magnetic moment distributions and form factors in ferromagnetic nickel-ruthenium alloys

Using polarised neutrons, the full three-dimensional magnetic structure amplitudes in the Ni_1?c Ru _c single crystals forc = 0·027, 0·033 and 0·046 were measured. Moment density maps in various portions of the Wigner-Seitz cell were obtained. It is seen from these maps that unlike Ni-based alloys with 3d impurities, the introduction of Ru to the Ni matrix produces extensive perturbations in the diffuse moment density, giving rise to a netpositive diffuse moment which tends to increase with Ru concentration. The asphericity of the host moment at first increases and then decreases with increasing Ru content. Another significant outcome of the present study is the evidence for the reversal of the sign of the Ru moment, from negative to positive, obtained by comparing the shape of the spherical site form factors of the three-alloy concentrations with the Ni spherical form factor itself. The sign reversal of the impurity moment is confirmed by the form factor analyses. Strong local environmental effects seem to play a major role in this alloy system.     

A polarised neutron study of magnetic moment density in Cu2MnAl

A polarised neutron study of the ferromagnetic Heusler alloy Cu₂Mn_0.863Al_1.057 has been made. It has been concluded that the magnetic moment density is primarily situated on the Mn ions. On assigning the Mn-moment value, the observed magnetic form factor is found to be in good agreement with the Mn²⁺ free ion form factor calculated by Watson and Freeman. A slight asphericity has been observed in the moment density. It is estimated that there are about 3% excess 3d-electrons in the Eg states compared to spherical distribution. There is evidence of a very small positive polarisation of the Cu atoms. No appreciable conduction electron polarisation is found.     

The influence of ultrasonic waves on manganese dioxide sol in the atmosphere of nitrogen

Summary The influence of ultrasonic waves at 1 MC/sec and 225 watts/cm² power on the negatively charged manganese dioxide sol has been investigated in an atmosphere of nitrogen and thereby excluding oxygen. The stability of the sol on exposure to ultrasonic waves is affected in a similar way as in presence of air but the extent to which the sol gets unstable on exposure is less in the absence of oxygen than in its presence. The specific conductivity increases but hydrogen ion concentration remains practically constant as the time of exposure increases.

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Zusammenfassung Der Einflu? von Ultraschall (1 mHz, 225 W/cm²) auf negativ geladenes Mangandioxidsol wurde unter Stickstoff unter Ausschlu? von Sauerstoff untersucht. Die Stabilit?t des Sols ist in gleicher Weise wie bei Gegenwart von Luft ver?ndert, nur wird das Sol bei Ausschlu? von Sauerstoff weniger instabil. Die spezifische Leitf?higkeit steigt mit steigender Expositionszeit, w?hrend die Wasserstoffionenkonzentration praktisch konstant bleibt.

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The authors are thankful to the Council of Scientific and Industrial Research for the award of scholarship for this work.     

Influence of ultrasonic waves on cobaltous hydroxide sol

Summary Ultrasonic agency (1 Mc/s 225 watts per sq. cm. output) can be successfully utilised for the preparation of rather a stable colloidal cobaltous hydroxide sol bearing a positive charge. On exposing this sol to ultrasonic waves, it becomes more stable. The specific conductivity and hydrogen ion concentration of the sol continuously increases with the time of exposure to ultrasonic waves. The viscosity of the sol decreases with the time of exposure to ultrasonic waves. The optical density and coagulation values with electrolytes also increase on exposing the sol to ultrasonic waves. The stability of the sol is probably due to the increase in positive charge on the colloidal particles as the hydrogen ion concentration of the sol has increased on exposure. The change in colour is due to transformation of cobaltous to cobaltic hydroxide by ultrasonic waves.

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Zusammenfassung Ultraschallbestrahlung (1 MHz, 225 Watt/cm²) kann erfolgreich zur Pr?paration stabiler kolloidaler Kobaltohydroxydsole mit positiver Ladung angewandt werden. Bei einer solchen Bestrahlung wird das Sol stabiler. Die spez. Leitf?higkeit und die Wasserstoffionen-Konzentrationen des Sols steigt kontinuierlich mit der Zeit der Ultraschallbestrahlung. Die Viskosit?t des Sols nimmt entsprechend ab. Die optische Dichte und die Koagulationswerte mit Elektrolyten steigen ebenfalls mit der Bestrahlung. Die Stabilit?t des Sols ist wahrscheinlich der Erh?hung der positiven Ladung der Kolloidpartikel zuzuschreiben, da die Wasserstoffionen-Konzentration des Sols mit Bestrahlung steigt. Der Wechsel in der Farbe ist der Umformung von Kobalto- zu Kobaltihydroxyd durch die Ultraschallwellen zuzuschreiben.

     

On the feasibility of using thermal gradients for active control of interlaminar stresses in laminated composites

In this paper, a method is proposed to actively control interlaminar stresses near the free edges of laminated composites by though-thickness thermal gradients. Theoretical solutions are given for optimal steady-state through-thickness temperature distributions under uniaxial loading that are required to eliminate or reduce the interlaminar stresses below a prescribed level. The optimal solutions are obtained by minimizing appropriate performance indices that are functions of the far-field properties, with respect to the through-thickness temperature differences. In the second part, an experimental investigation is conducted on a glass/epoxy cross-ply laminate with embedded piezoelectric sensors and a thermal heater. Through the experiment, the feasibility of the thermal control of interlaminar stresses is demonstrated.     

The influence of ultrasonic waves on the hydrogen ion concentration and the stability of colloidal solutions

Summary The ultrasonic waves causes the cerie hydroxide sol to set to a gel. This change has been followed by measuring viscosity, conductivity and hydrogen ion concentration. It has been shown that the extent of hydrogen peroxide formed under the action of ultrasonic waves on water is not alone sufficient to explain for the increase in viscosity, nor at such concentrations it would set the sol to a gel.

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Zusammenfassung Ultraschall verursacht in Cerhydroxyd-Solen Gelierung. Dieses Ver?nderung wurde durch Messen der Viskosit?t, Leitf?higkeit und der Wasserstoffkonzentration verfolgt. Es hat sich gezeigt, da? der Betrag an Wasserstoffperoxydbildung unter Einwirkung des Ultraschalles auf Wasser nicht allein ausreichend ist, den Anstieg in der Viskosit?t oder hinsichtlich der Konzentration zu erkl?ren, um die Gelierung zu deuten.

     

Interaction-driven real-space condensation

We study real-space condensation in a broad class of stochastic mass transport models. We show that the steady state of such models has a pair-factorized form which generalizes the standard factorized steady states. The condensation in this class of models is driven by interactions which give rise to a spatially extended condensate that differs fundamentally from the previously studied examples. We present numerical results as well as a theoretical analysis of the condensation transition and show that the criterion for condensation is related to the binding-unbinding transition of solid-on-solid interfaces.