Quasiperiodic localized oscillating solutions in the discrete nonlinear Schr\"odinger equation with alternating on-site potential

We present what we believe to be the first known example of an exact quasiperiodic localized stable solution with spatially symmetric large-amplitude oscillations in a non-integrable Hamiltonian lattice model. The model is a one-dimensional discrete nonlinear Schr\"odinger equation with alternating on-site energies, modelling e.g. an array of optical waveguides with alternating widths. The solution bifurcates from a stationary discrete gap soliton, and in a regime of large oscillations its intensity oscillates periodically between having one peak at the central site, and two symmetric peaks at the neighboring sites with a dip in the middle. Such solutions, termed 'pulsons', are found to exist in continuous families ranging arbitrarily close both to the anticontinuous and continuous limits. Furthermore, it is shown that they may be linearly stable also in a regime of large oscillations.Comment: 4 pages, 4 figures, to be published in Phys. Rev. E. Revised version: change of title, added Figs. 1(b),(c), 4 new references + minor clarification

Coadjoint orbits of the Virasoro algebra and the global Liouville equation

The classification of the coadjoint orbits of the Virasoro algebra is reviewed and is then applied to analyze the so-called global Liouville equation. The review is self-contained, elementary and is tailor-made for the application. It is well-known that the Liouville equation for a smooth, real field $\phi$ under periodic boundary condition is a reduction of the SL(2,R) WZNW model on the cylinder, where the WZNW field g in SL(2,R) is restricted to be Gauss decomposable. If one drops this restriction, the Hamiltonian reduction yields, for the field $Q=\kappa g_{22}$ where $\kappa\neq 0$ is a constant, what we call the global Liouville equation. Corresponding to the winding number of the SL(2,R) WZNW model there is a topological invariant in the reduced theory, given by the number of zeros of Q over a period. By the substitution $Q=\pm\exp(- \phi/2)$, the Liouville theory for a smooth $\phi$ is recovered in the trivial topological sector. The nontrivial topological sectors can be viewed as singular sectors of the Liouville theory that contain blowing-up solutions in terms of $\phi$. Since the global Liouville equation is conformally invariant, its solutions can be described by explicitly listing those solutions for which the stress-energy tensor belongs to a set of representatives of the Virasoro coadjoint orbits chosen by convention. This direct method permits to study the `coadjoint orbit content' of the topological sectors as well as the behaviour of the energy in the sectors. The analysis confirms that the trivial topological sector contains special orbits with hyperbolic monodromy and shows that the energy is bounded from below in this sector only.Comment: Plain TEX, 48 pages, final version to appear in IJMP

Enhanced spin accumulation in a superconductor

A lateral array of ferromagnetic tunnel junctions is used to inject and detect non-equilibrium quasi-particle spin distribution in a superconducting strip made of Al. The strip width and thickness is kept below the quasi particle spin diffusion length in Al. Non-local measurements in multiple parallel and antiparallel magnetic states of the detectors are used to in-situ determine the quasi-particle spin diffusion length. A very large increase in the spin accumulation in the superconducting state compared to that in the normal state is observed and is attributed to a diminishing of the quasi-particle population by opening of the gap below the transition temperature.Comment: 6 pages, 4 figures; accepted for publication in Journal of Applied Physic

Discrete soliton mobility in two-dimensional waveguide arrays with saturable nonlinearity

We address the issue of mobility of localized modes in two-dimensional nonlinear Schr\"odinger lattices with saturable nonlinearity. This describes e.g. discrete spatial solitons in a tight-binding approximation of two-dimensional optical waveguide arrays made from photorefractive crystals. We discuss numerically obtained exact stationary solutions and their stability, focussing on three different solution families with peaks at one, two, and four neighboring sites, respectively. When varying the power, there is a repeated exchange of stability between these three solutions, with symmetry-broken families of connecting intermediate stationary solutions appearing at the bifurcation points. When the nonlinearity parameter is not too large, we observe good mobility, and a well defined Peierls-Nabarro barrier measuring the minimum energy necessary for rendering a stable stationary solution mobile.Comment: 19 pages, 4 figure

Criteria of efficiency for conformal prediction

We study optimal conformity measures for various criteria of efficiency of classification in an idealised setting. This leads to an important class of criteria of efficiency that we call probabilistic; it turns out that the most standard criteria of efficiency used in literature on conformal prediction are not probabilistic unless the problem of classification is binary. We consider both unconditional and label-conditional conformal prediction.Comment: 31 page

New Relations for Gauge-Theory Amplitudes

We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.Comment: 40 pages, 7 figures, RevTex, v2 minor correction

Survival of Clostridium perfringens During Simulated Transport and Stability of Some Plasmid-borne Toxin Genes under Aerobic Conditions

Clostridium perfringens is a pathogen of great concern in veterinary medicine, because it causes enteric diseases and different types of toxaemias in domesticated animals. It is important that bacteria in tissue samples, which have been collected in the field, survive and for the classification of C. perfringens into the correct toxin group, it is crucial that plasmid-borne genes are not lost during transportation or in the diagnostic laboratory. The objectives of this study were to investigate the survival of C. perfringens in a simulated transport of field samples and to determine the stability of the plasmid-borne toxin genes cpb1 and etx after storage at room temperature and at 4°C. Stability of the plasmid-borne genes cpb1 and etx of C. perfringens CCUG 2035, and cpb2 from C. perfringens CIP 106526, JF 2255 and 6 field isolates in aerobic atmosphere was also studied. Survival of C. perfringens was similar in all experiments. The cpb1 and etx genes were detected in all isolates from samples stored either at room temperature or at 4°C for 24–44 h. Repeated aerobic treatment of C. perfringens CCUG 2035 and CIP 106526 did not result in the loss of the plasmid-borne genes cpb1, cpb2 or etx. Plasmid-borne genes in C. perfringens were found to be more stable than generally reported. Therefore, C. perfringens toxinotyping by PCR can be performed reliably, as the risk of plasmid loss seems to be a minor problem

Physics of Polymorphic Transitions in CeRuSn

We report a detailed study of the polymorphic transitions in ternary stannide CeRuSn on high quality single crystals through a combination of X-ray diffraction experiments conducted at 300, 275 and 120 K, and measurements of the thermal expansion, magnetization, and resistivity, along main crystallographic axes. In addition, the transition was followed as a function of pressure up to 0.8 GPa. The present X-ray diffraction data show that the room temperature polymorph consists of the lattice doubled along the c axis with respect to the CeCoAl-type structure consistent with previous reports. Upon cooling, the compound undergoes two successive transitions, first to a quintuple (290 K) and than to a triple CeCoAl superstructure at 225 K. The transitions are accompanied by a tremendous volume change due to a strong shrinking of the lattice along the c axis, which is clearly observed in thermal expansion. We advance arguments that the volume collapse originates from an increasing number of crystallographically inequivalent Ce sites and the change of ratio between the short and long Ce-Ru bonds. The observed properties of the polymorphic transition in CeRuSn are reminiscent of the transition in elementary Cerium, suggesting that similar physics, i.e., a Kondo influenced transition and strong lattice vibrations might be the driving forces