Quantum-networks: master equation and local measurements

Based on the SU(n)-algebra the Markoff master equation in discrete product space is reformulated to explicitly deal with composite systems. The resulting local (single node) and nonlocal (multi-node) state parameters allow a systematic approach to non-classical features of the state, like variance and covariance tensors. For local optical driving forces, inter-node interactions, and local damping channels the solution of the master equation is unraveled into stochastic quantum trajectories. Sampling leads to a joint distribution function in terms of those state parameters. Its linear moments define the ensemble-density matrix. The average variance and covariance are in terms of non-linear moments, which should be distinguished from their entirely statistical counterpairs. Non-classicality of the network dynamics is shown to reflect itself in the luminescence-photonstatistics.     

μSR studies of heavy fermion systems

We have performed both zero field and high transverse field measurements at dilution refrigerator temperatures on a number of heavy electron systems, examining the superconducting and magnetic properties of these interesting materials. Among the materials studied to date are UBe₁₃, URu₂Si₂ and U₆Fe. The magnetic field penetration depth in the superconducting state of UBe₁₃ is greater than 10000 Å, as no increase in the transverse field relaxation rate is observed belowT _c . A sharp increase in the precession frequency is seen, starting atT _c . This frequency shift shows little temperature dependence at low temperature; we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we we found no clear evidence for unconventional superconductivity in this material. Zero field measurements in URu₂Si₂ show the weak antiferromagnetic transition at 17.5 K. Finally, we have observed relaxation in high transverse field due to the formation of a flux lattice in U₆Fe, a material where the electron effective mass is rather lighter than in other heavy fermion systems. The relaxation exhibits a sharp onset atT _c=3.9 K, and is flat at low temperatures as expected for a conventional superconductor.     

Factorisation in the ring of exponential polynomials

We study factorisation in the ring of exponential polynomials and provide a proof of Ritt's factorisation theorem in modern notation and so generalised as to deal with polynomial coefficients as well as with several variables. We do this in the more general context of a group ring of a divisible torsion-free ordered abelian group over a unique factorisation domain.

     

Mesh selection for stiff two-point boundary value problems

This paper is concerned with the mesh selection algorithm of COLSYS, a well known collocation code for solving systems of boundary value problems. COLSYS was originally designed to solve non-stiff and mildly stiff problems only. In this paper we show that its performance for solving extremely stiff problems can be considerably improved by modifying its error estimation and mesh selection algorithms. Numerical examples indicate the superiority of the modified algorithm.Dedicated to John Butcher on the occasion of his sixtieth birthday     

A proof of Howard’s conjecture in homogeneous parallel shear flows

A rigorous mathematical proof of Howard's conjecture which states that the growth rate of an arbitrary unstable wave must approach zero, as the wave length decreases to zero, in the linear instability of nonviscous homogeneous parallel shear flows, is presented here for the first time under the restriction of the boundedness of the second derivative of the basic velocity field with respect to the vertical coordinate in the concerned flow domain.     

On composition of some general fractional integral operators

In the present paper we derive three interesting expressions for the composition of two most general fractional integral oprators whose kernels involve the product of a general class of polynomials and a multivariableH-function. By suitably specializing the coefficients and the parameters in these functions we can get a large number of (new and known) interesting expressions for the composition of fractional integral operators involving classical orthogonal polynomials and simpler special functions (involving one or more variables) which occur rather frequently in problems of mathematical physics. We have mentioned here two special cases of the first composition formula. The first involves product of a general class of polynomials and the Fox’sH-functions and is of interest in itself. The findings of Buschman [1] and Erdélyi [4] follow as simple special cases of this composition formula. The second special case involves product of the Jacobi polynomials, the Hermite polynomials and the product of two multivariableH-functions. The present study unifies and extends a large number of results lying scattered in the lierature. Its findings are general and deep.     

Temperature dependence of the rate constants for reactions of the carbonate radical with organic and inorganic reductants

Rate constants have been measured by pulse radiolysis for the reactions of the carbonate radical, CO₃^·?, with a number of organic and inorganic reactants as a function of temperature, generally over the range 5 to 80°C. The reactants include the substitution-inert cyano complexes of Fe^II, Mo^IV, and W^IV, the simple inorganic anions SO₃^2?, ClO₂^?, NO₂^?, I^?, and SCN^?, several phenolates, ascorbate, tryptophan, cysteine, cystine, methionine, triethylamine, and allyl alcohol. The measured rate constants ranged from less than 10⁵ to 3 × 10⁹ M^?1 s^?1, the activation energies ranged from ?11.4 to 18.8 kJ mol^?1, and the pre-exponential factors ranged from log A = 6.4 to 10.7. The activation energies for the metal complexes and inorganic anions generally decrease with increasing driving force for the reaction, as expected for an outer sphere electron transfer. For highly exothermic reactions, however, the activation energy appears to increase, probably reflecting the temperature dependence of diffusion. For many of the organic reactants, the activation energies were low and independent of driving force, suggesting that the oxidation is via an inner sphere mechanism.     

Features of evolution of the substructure in the creep of dispersion-hardened nickel

A study is made of the laws governing high-temperature creep and the evolution of the substructure in dispersion-hardened alloy Ni — 3 vol. % HfO₂ during its free annealing and creep. The polygonized substructure was formed in the alloy prior to annealing. An analysis is made of structural transformations at different structural levels and the mechanism of high-temperature creep in the alloy. Institute of the Physics of Strength and Materials Science, Siberian Branch of the Russian Academy of Sciences. All-Republic Engineering-Technical Center, Siberian Branch of the Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 83–89, March, 1998.