Monotone iterative procedure and systems of a finite number of nonlinear fractional differential equations

The aim of the paper is to present a nontrivial and natural extension of the comparison result and the monotone iterative procedure based on upper and lower solutions, which were recently established in (Wang et al. in Appl. Math. Lett. 25:1019-1024, 2012), to the case of any finite number of nonlinear fractional differential equations.The author is very grateful to the reviewers for the remarks, which improved the final version of the manuscript. This article was financially supported by University of Łódź as a part of donation for the research activities aimed at the development of young scientists, grant no. 545/1117

Temporally stable coherent states in energy degenerate systems: The hydrogen atom

Klauder's recent generalization of the harmonic oscillator coherent states [J. Phys. A 29, L293 (1996)] is applicable only in non-degenerate systems, requiring some additional structure if applied to systems with degeneracies. The author suggests how this structure could be added, and applies the complete method to the hydrogen atom problem. To illustrate how a certain degree of freedom in the construction may be exercised, states are constructed which are initially localized and evolve semi-classically, and whose long time evolution exhibits "fractional revivals."Comment: 9 pages, 3 figure

Skin health in northern Australia

Achieving healthy skin requires the prevention of infectious diseases that affect the skin. Prevention activities range from environmental health improvements to address inequities in living situations, through to community-wide treatment programs to reduce transmission and improve skin health. In this paper we discuss the pathogens that cause and conditions that arise when skin is infected, the burden of disease in northern Australia, and some of the current research underway to address this high burden, which predominantly affects remote-living Aboriginal and Torres Strait Islander children and families

Thermal conductivity and specific heat of the linear chain cuprate Sr2_{2}CuO3_{3}: Evidence for thermal transport via spinons

We report measurements of the specific heat and the thermal conductivity of the model Heisenberg spin-1/2 chain cuprate Sr$_{2}$CuO$_{3}$ at low temperatures. In addition to a nearly isotropic phonon heat transport, we find a quasi one-dimensional excess thermal conductivity along the chain direction, most likely associated with spin excitations (spinons). The spinon energy current is limited mainly by scattering on defects and phonons. Analyzing the specific heat data, the intrachain magnetic exchange $J/k_{B}$ is estimated to be 2650 K.Comment: 4 RevTeX pages, 3 figures, to appear in Phys. Rev.

Effects of anharmonic strain on phase stability of epitaxial films and superlattices: applications to noble metals

Epitaxial strain energies of epitaxial films and bulk superlattices are studied via first-principles total energy calculations using the local-density approximation. Anharmonic effects due to large lattice mismatch, beyond the reach of the harmonic elasticity theory, are found to be very important in Cu/Au (lattice mismatch 12%), Cu/Ag (12%) and Ni/Au (15%). We find that is the elastically soft direction for biaxial expansion of Cu and Ni, but it is for large biaxial compression of Cu, Ag, and Au. The stability of superlattices is discussed in terms of the coherency strain and interfacial energies. We find that in phase-separating systems such as Cu-Ag the superlattice formation energies decrease with superlattice period, and the interfacial energy is positive. Superlattices are formed easiest on (001) and hardest on (111) substrates. For ordering systems, such as Cu-Au and Ag-Au, the formation energy of superlattices increases with period, and interfacial energies are negative. These superlattices are formed easiest on (001) or (110) and hardest on (111) substrates. For Ni-Au we find a hybrid behavior: superlattices along and like in phase-separating systems, while for they behave like in ordering systems. Finally, recent experimental results on epitaxial stabilization of disordered Ni-Au and Cu-Ag alloys, immiscible in the bulk form, are explained in terms of destabilization of the phase separated state due to lattice mismatch between the substrate and constituents.Comment: RevTeX galley format, 16 pages, includes 9 EPS figures, to appear in Physical Review

Scattering of elastic waves by periodic arrays of spherical bodies

We develop a formalism for the calculation of the frequency band structure of a phononic crystal consisting of non-overlapping elastic spheres, characterized by Lam\'e coefficients which may be complex and frequency dependent, arranged periodically in a host medium with different mass density and Lam\'e coefficients. We view the crystal as a sequence of planes of spheres, parallel to and having the two dimensional periodicity of a given crystallographic plane, and obtain the complex band structure of the infinite crystal associated with this plane. The method allows one to calculate, also, the transmission, reflection, and absorption coefficients for an elastic wave (longitudinal or transverse) incident, at any angle, on a slab of the crystal of finite thickness. We demonstrate the efficiency of the method by applying it to a specific example.Comment: 19 pages, 5 figures, Phys. Rev. B (in press

Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains

The magnetic susceptibility chi and specific heat C versus temperature T of the spin-1/2 antiferromagnetic alternating-exchange (J1 and J2) Heisenberg chain are studied for the entire range 0 \leq alpha \leq 1 of the alternation parameter alpha = J2/J1. For the uniform chain (alpha = 1), detailed comparisons of the high-accuracy chi(T) and C(T) Bethe ansatz data of Kluemper and Johnston are made with the asymptotically exact low-T field theory predictions of Lukyanov. QMC simulations and TMRG calculations of chi(alpha,T) are presented. From the low-T TMRG data, the spin gap Delta(alpha)/J1 is extracted for 0.8 \leq alpha \leq 0.995. High accuracy fits to all of the above numerical data are obtained. We examine in detail the theoretical predictions of Bulaevskii for chi(alpha,T) and compare them with our results. Our experimental chi(T) and C(T) data for NaV2O5 single crystals are modeled in detail. The chi(T) data above the spin dimerization temperature Tc = 34 K are not in agreement with the prediction for the uniform Heisenberg chain, but can be explained if there is a moderate ferromagnetic interchain coupling and/or if J changes with T. By fitting the chi(T) data, we obtain Delta(T = 0) = 103(2) K, alternation parameter delta(0) = (1 - alpha)/(1 + alpha) = 0.034(6) and average exchange constant J(0) = 640(80) K. The delta(T) and Delta(T) are derived from the data. A spin pseudogap with a large magnitude \approx 0.4 Delta(0) is consistently found just above Tc, which decreases with increasing T. Analysis of our C(T) data indicates that at Tc, at least 77% of the entropy change due to the transition at Tc and associated order parameter fluctuations arise from the lattice and/or charge degrees of freedom and less than 23% from the spin degrees of freedom.Comment: 53 two-column REVTeX pages, 50 embedded figures, 7 tables. Revisions required due to incorrect Eq. (39) in Ref. 51 which gives the low-T approximation for the specific heat of a S = 1/2 1D system with a spin gap; no conclusions were changed. Additional minor revisions made. Phys. Rev. B (in press

Representations of sport in the revolutionary socialist press in Britain, 1988–2012

This paper considers how sport presents a dualism to those on the far left of the political spectrum. A long-standing, passionate debate has existed on the contradictory role played by sport, polarised between those who reject it as a bourgeois capitalist plague and those who argue for its reclamation and reformation. A case study is offered of a political party that has consistently used revolutionary Marxism as the basis for its activity and how this party, the largest in Britain, addresses sport in its publications. The study draws on empirical data to illustrate this debate by reporting findings from three socialist publications. When sport did feature it was often in relation to high profile sporting events with a critical tone adopted and typically focused on issues of commodification, exploitation and alienation of athletes and supporters. However, readers’ letters, printed in the same publications, revealed how this interpretation was not universally accepted, thus illustrating the contradictory nature of sport for those on the far left

A Cryogenic Silicon Interferometer for Gravitational-wave Detection

The detection of gravitational waves from compact binary mergers by LIGO has opened the era of gravitational wave astronomy, revealing a previously hidden side of the cosmos. To maximize the reach of the existing LIGO observatory facilities, we have designed a new instrument that will have 5 times the range of Advanced LIGO, or greater than 100 times the event rate. Observations with this new instrument will make possible dramatic steps toward understanding the physics of the nearby universe, as well as observing the universe out to cosmological distances by the detection of binary black hole coalescences. This article presents the instrument design and a quantitative analysis of the anticipated noise floor