A new quasi-exactly solvable problem and its connection with an anharmonic oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator had been investigated by methods of KS transformation

The influence of fibre length, diameter and concentration on the strength and strain to failure of glass fibre-reinforced polyamide 6,6

Results of an investigation of the mechanical performance of injection moulded long glass fibre-reinforced polyamide 6,6 composites are presented. The glass fibre content in these composites was varied over the range 10-50% by weight using fibres with average diameters of 10, 14, and 17 μm. Mechanical testing and analysis of the apparent interfacial shear strength was carried out at 23 and 150 °C on dry-as-moulded and boiling water conditioned samples. The results from these composites are compared with standard extrusion compounded short glass fibre materials. The influence of fibre diameter and concentration on the residual fibre length, fibre orientation distribution and composite strength and elongation to failure is presented and discussed in comparison to the predictions of some of the available micromechanical models

Coexistence of single-mode and multi-longitudinal mode emission in the ring laser model

A homogeneously broadened unidirectonal ring laser can emit in several longitudinal modes for large enough pump and cavity length because of Rabi splitting induced gain. This is the so called Risken-Nummedal-Graham-Haken (RNGH) instability. We investigate numerically the properties of the multi-mode solution. We show that this solution can coexist with the single-mode one, and its stability domain can extend to pump values smaller than the critical pump of the RNGH instability. Morevoer, we show that the multi-mode solution for large pump values is affected by two different instabilities: a pitchfork bifurcation, which preserves phase-locking, and a Hopf bifurcation, which destroys it.Comment: 14 pages, 7 figure

Higgs algebraic symmetry of screened system in a spherical geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(\dot{r}=0)$.Comment: 8 pages, 1 fi

Layered Higgs Phase as a Possible Field Localisation on a Brane

So far it has been found by using lattice techniques that in the anisotropic five--dimensional Abelian Higgs model, a layered Higgs phase exists in addition to the expected five--dimensional one. The exploration of the phase diagram has shown that the two Higgs phases are separated by a phase transition from the confining phase. This transition is known to be first order. In this paper we explore the possibility of finding a second order transition point in the critical line which separates the first order phase transition from the crossover region. This is shown to be the case only for the four--dimensional Higgs layered phase whilst the phase transition to the five--dimensional broken phase remains first order. The layered phase serves as the possible realisation of four--dimensional spacetime dynamics which is embedded in a five--dimensional spacetime. These results are due to gauge and scalar field localisation by confining interactions along the extra fifth direction.Comment: 1+15 pages, 12 figure

Enhancement of pair correlation in a one-dimensional hybridization model

We propose an integrable model of one-dimensional (1D) interacting electrons coupled with the local orbitals arrayed periodically in the chain. Since the local orbitals are introduced in a way that double occupation is forbidden, the model keeps the main feature of the periodic Anderson model with an interacting host. For the attractive interaction, it is found that the local orbitals enhance the effective mass of the Cooper-pair-like singlets and also the pair correlation in the ground state. However, the persistent current is depressed in this case. For the repulsive interaction case, the Hamiltonian is non-Hermitian but allows Cooper pair solutions with small momenta, which are induced by the hybridization between the extended state and the local orbitals.Comment: 11 page revtex, no figur

How to determine linear complexity and kk-error linear complexity in some classes of linear recurring sequences

Several fast algorithms for the determination of the linear complexity of $d$-periodic sequences over a finite field \F_q, i.e. sequences with characteristic polynomial $f(x) = x^d-1$, have been proposed in the literature. In this contribution fast algorithms for determining the linear complexity of binary sequences with characteristic polynomial $f(x) = (x-1)^d$ for an arbitrary positive integer $d$, and $f(x) = (x^2+x+1)^{2^v}$ are presented. The result is then utilized to establish a fast algorithm for determining the $k$-error linear complexity of binary sequences with characteristic polynomial $(x^2+x+1)^{2^v}$

The Inert Doublet Model and Inelastic Dark Matter

The annual modulation observed by DAMA/NaI and DAMA/Libra may be interpreted in terms of elastic or inelastic scattering of dark matter particles. In this paper we confront these two scenarios within the framework of a very simple extension of the Standard Model, the Inert Doublet Model (IDM). In this model the dark matter candidate is a scalar, the lightest component of an extra Higgs doublet. We first revisit the case for the elastic scattering of a light scalar WIMP, M_DM~10 GeV, a scenario which requires that a fraction of events in DAMA are channelled. Second we consider the possibility of inelastic Dark Matter (iDM). This option is technically natural in the IDM, in the sense that the mass splitting between the lightest and next-to-lightest neutral scalars may be protected by a Peccei-Quinn (PQ) symmetry. We show that candidates with a mass M_DM between ~535 GeV and ~50 TeV may reproduce the DAMA data and have a cosmic abundance in agreement with WMAP. This range may be extended to candidates as light as ~50 GeV if we exploit the possibility that the approximate PQ symmetry is effectively conserved and that a primordial asymmetry in the dark sector may survive until freeze-out.Comment: 16 pages, 7 figures. v2: minor changes and discussion on the embedding in SO(10) added. v3: matches the published version in JCA

Euler configurations and quasi-polynomial systems

In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework.Comment: 21 pages, 6 figure