Axialisation, cooling and quenching of ions in a Penning trap

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems. Received: 17 February 1997 / Revised: 3 September 1997 / Accepted: 13 October 1997     

The Laplacian of a Graph as a Density Matrix: A Basic Combinatorial Approach to Separability of Mixed States

We study entanglement properties of mixed density matrices obtained from combinatorial Laplacians. This is done by introducing the notion of the density matrix of a graph. We characterize the graphs with pure density matrices and show that the density matrix of a graph can be always written as a uniform mixture of pure density matrices of graphs. We consider the von Neumann entropy of these matrices and we characterize the graphs for which the minimum and maximum values are attained. We then discuss the problem of separability by pointing out that separability of density matrices of graphs does not always depend on the labelling of the vertices. We consider graphs with a tensor product structure and simple cases for which combinatorial properties are linked to the entanglement of the state. We calculate the concurrence of all graphs on four vertices representing entangled states. It turns out that for these graphs the value of the concurrence is exactly fractional. Received July 28, 2004     

Inverse geophysical problems for some noncompactly supported inhomogeneities

Let[²+k²n(x₁,x₃)]u(x₁,x₂,x₃)=−δ(x₁,y₁δ(x₂,y₂)δ(x₃,y₃) in R³₊. Assume that u(x₁,x₂,x₃=0,y₁,y₂=0,y₃=0,k) is measured at the plane P {x:x₃=0} for all positions of the source on the line y = (y₁,y₂ = 0,y₃ = 0), -∞ < y₁ < ∞, and receiver on the plane(x₁,x₂,x₃ − <x₁,x₂ < ∞, and for low-frequencies 0 < k <k₀, k₀ > 0 is an arbitrary small wave number. Assume thatn(x₁,x₃) is an arbitrary bounded piecewise-continuous function. The basic result is: the above low-frequency surface data determinen(x₁,x₃)uniquely.     

Stability measurements on cored cables in normal and superfluid helium

The relative stability of LHC type cables has been measured by the direct heating of one of the individual strands with a short duration current pulse. The minimum energy required to initiate a quench has been determined for a number of cables which have a central core to increase the effective inter-strand cross-over resistance. Experiments were performed in both normal helium at 4.4 K and superfluid at 1.9 K. Conductors in general are less stable at the lower temperature when measured at the same fraction of critical current. Results show that the cored-cables, even when partially filled with solder or with a ‘porous-metal' filler exhibit a relatively low stability at currents close to the critical current. It is speculated that the high inter-strand electrical and thermal resistance inherent in these cables may affect the stability at high currents.     

Ketal-tethered ring-closing metathesis. An unconventional approach to constructing spiroketals and total synthesis of an insect pheromone

An unconventional approach to constructing spiroketals via ring-closing metathesis of cyclic ketals is described here. This method possesses good generality with no loss of stereochemical integrity at the spiro center under standard RCM conditions. This approach has been applied to the synthesis of an insect pheromone to demonstrate its synthetic potential.     

On the equivalence of slip-line fields and work principles for rigid–plastic body in plane strain

Extremum/work principles for a rigid–plastic body have been discussed in classical theory of plasticity to be of immense significance. Unfortunately, till now, these extremum theorems have been used only as a crude method of obtaining the limit load of a rigid–plastic body, using successive approximations by upper and lower bound estimates. On the other hand slip-line fields (SLF) have been extensively used not only for evaluation of limit load but also for obtaining sufficiently accurate estimates of stresses in the plastic region as well as in the vicinity of crack tip. Till now, these two methods of plastic analyses, that is, the work principles and SLF have remained more or less independent apart from the fact that both are upper bounds as they use kinematically admissible velocity fields. Recently, a new load bounding technique, modified upper bound (MUB) Approach, was proposed by Khan and Ghosh [Khan, I.A., Ghosh, A.K., 2007. A modified upper bound approach to limit analysis for plane strain deeply cracked specimens. International Journal of Solids and Structures 44 (10), 3114–3135]. In this article, a rigorous mathematical basis of this load bounding technique is presented and it is demonstrated that the method is actually a new form of the general extremum/work principles. The equivalence of this new form of work principle, that is, MUB with the classical SLF analysis, for a rigid–plastic material in plane strain, has been discussed in detail. Since plastic deformation fields depend on specimen geometry and type of loading specific cases have been considered. Both cracked and uncracked configurations have been analysed to establish this equivalence in general. Various simplifications resulting from the use of this new load bounding technique over SLF method has been demonstrated. Several standard problems of plane strain analysed by SLF method and validated by experiments in past have been considered in this article. As a novel application of the proposed method, single-edge-cracked plate under combined bending and tensile load has been analysed. For this specimen SLF solutions are available only for bending with small tensile load (defined in Section 3.2.4) while classical upper bound solutions are valid for bending with large tensile load. In this work a completely analytical formulation for yield locus for the entire range of tensile and bending load has been obtained. Apart from accurate evaluation of limit load, detailed evaluation of crack tip stresses and hence constraint near the crack tip has been performed using this new form of work principles.     

Enhanced optoelectronic properties of UV-light-induced photodegraded TPD

We report UV-light-induced photodegradation of N,N’-diphenyl-N,N’-bis(3-methylphenyl)-1,1’-biphenyl-4,4’ diamine (TPD) dye. When a halomethane solution of TPD is exposed to UV light it first oxidizes TPD and subsequently with further exposure leads to irreversible transformation of TPD to an acridine derivative as photoproduct. Exclusive use of halomethane solvents like chloroform and dichloromethane suggests solvent radical initiated photochemical transformation of TPD to a stable acridine-based photoproduct. The resultant photoproduct of TPD showed broad-band dual (both blue and green) emissions in various solvents and also from the sublimed thin film. Based on solvent- and concentration-dependent photoluminescence (PL) of the photoproduct, PL excitation and lifetimes of blue and green bands, the origin of emission in the green region is due to an intermolecular excimer/aggregate of acridine-based photoproduct. A film of acridine-based photoproduct dispersed in polystyrene also showed substantial improvement in electrical conductivity compared to the parent compound TPD. The technique of UV-light-induced molecule structure transformation and material processing under specific environmental conditions may be considered as an efficient means of obtaining materials with enhanced optoelectronic properties. PACS 61.82.Pv; 72.80.Le; 82.50.-m; 82.30.Lp; 33.50.-j     

Kinetic and mechanistic studies on the interaction of adenosine with hydroxopentaaquarhodium(III) ion

The kinetics of the title reaction have been studied spectrophotometrically as a function of pH, [substrate], [adenosine] and temperature (50–65°C) by monitoring the appearance of a characteristic peak of the adenosine substituted product (λ_max = 289 nm). The reaction rate is pH dependent in the 3.0–4.3 range. With increase in [adenosine] the rate was found to increase and approached a limit at a higher adenosine concentration. The following rate law has been established at pH 4.3: d[Rh(H₂O)₃(OH)(adenosine)²⁺]/dt = k _a K _E[Rh(H₂O)₅(OH)²⁺]_total[adenosine]/ (1 + K _E[adenosine]) Rate and activation parameters are consistent with an associative interchange mechanism. Experimental results are discussed with reference to literature data for analogous systems. This revised version was published online in June 2006 with corrections to the Cover Date.