Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.Comment: Accepted for publication in American Journal of Physics. 9 pages, 6 figure

The total mass of super-Brownian motion upon exiting balls and Sheu's compact support condition

We study the total mass of a d-dimensional super-Brownian motion as it first exits an increasing sequence of balls. The process of the total mass is a time-inhomogeneous continuous-state branching process, where the increasing radii of the balls are taken as the time parameter. We are able to characterise its time-dependent branching mechanism and show that it converges, as time goes to infinity, towards the branching mechanism of the total mass of a one-dimensional super-Brownian motion as it first crosses above an increasing sequence of levels. Our results allow us to identify the compact support criterion given in Sheu (1994) as a classical Grey condition (1974) for the aforementioned limiting branching mechanism.Comment: 28 pages, 2 figure

R-process and alpha-elements in the Galactic disk: Kinematic correlations

Recent studies of elemental abundances in the Galactic halo and in the Galactic disk have underscored the possibility to kinematically separate different Galactic subcomponents. Correlations between the galactocentric rotation velocity and various element ratios were found, providing an important means to link different tracers of star formation and metal enrichment to the Galactic components of different origin (collapse vs. accretion). In the present work we determine stellar kinematics for a sample of 124 disk stars, which we derive from their orbits based on radial velocities and proper motions from the the literature. Our stars form a subsample of the Edvardsson et al. (1993) sample and we concentrate on three main tracers: (i) Europium as an r-process element is predominantly produced in Supernovae of type II. (ii) Likewise, alpha-elements, such as Ca, Si, Mg, are synthesised in SNe II, contrary to iron, which is being produced preferentially in SNe Ia. (iii) The s-process element Barium is a measure of the relative contribution of AGB stars to the Galaxy's enrichment history and has been shown to be an indicator for distinguishing between thin and thick disk stars. All such studies reveal, basically, that stars with low galactocentric rotational velocity tend to have high abundances of alpha-elements and Eu, but lower abundances of, e.g., Ba.Comment: 5 pages, 2 figures, Poster contribution to appear in "Planets To Cosmology: Essential Science In Hubble's Final Years", proceedings of the May 2004 STScI Symposium, M. Livio (ed.), (Cambridge University Press

Diffraction and near-zero transmission of flexural phonons at graphene grain boundaries

Graphene grain boundaries are known to affect phonon transport and thermal conductivity, suggesting that they may be used to engineer the phononic properties of graphene. Here, the effect of two buckled grain boundaries on long-wavelength flexural acoustic phonons has been investigated as a function of angle of incidence using molecular dynamics. The flexural acoustic mode has been chosen due to its importance to thermal transport. It is found that the transmission through the boundaries is strongly suppressed for incidence angles close to 35$^\circ$. Also, the grain boundaries are found to act as diffraction gratings for the phonons

Nematicity, magnetism and superconductivity in FeSe

Iron-based superconductors are well known for their complex interplay between structure, magnetism and superconductivity. FeSe offers a particularly fascinating example. This material has been intensely discussed because of its extended nematic phase, whose relationship with magnetism is not obvious. Superconductivity in FeSe is highly tunable, with the superconducting transition temperature, $T_\mathrm{c}$, ranging from 8 K in bulk single crystals at ambient pressure to almost 40 K under pressure or in intercalated systems, and to even higher temperatures in thin films. In this topical review, we present an overview of nematicity, magnetism and superconductivity, and discuss the interplay of these phases in FeSe. We focus on bulk FeSe and the effects of physical pressure and chemical substitutions as tuning parameters. The experimental results are discussed in the context of the well-studied iron-pnictide superconductors and interpretations from theoretical approaches are presented.Comment: Topical Review submitted to Journal of Physics: Condensed Matte

Surface Plasmons and Topological Insulators

We study surface plasmons localized on interfaces between topologically trivial and topologically non-trivial time reversal invariant materials in three dimensions. For the interface between a metal and a topological insulator the magnetic polarization of the surface plasmon is rotated out of the plane of the interface; this effect should be experimentally observable by exciting the surface plasmon with polarized light. More interestingly, we argue that the same effect also is realized on the interface between vacuum and a doped topological insulator with non-vanishing bulk carrier density.Comment: 6 pages, 1 figure; v2: typo in eq. (27) correcte

Metrics and isospectral partners for the most generic cubic PT-symmetric non-Hermitian Hamiltonian

We investigate properties of the most general PT-symmetric non-Hermitian Hamiltonian of cubic order in the annihilation and creation operators as a ten parameter family. For various choices of the parameters we systematically construct an exact expression for a metric operator and an isospectral Hermitian counterpart in the same similarity class by exploiting the isomorphism between operator and Moyal products. We elaborate on the subtleties of this approach. For special choices of the ten parameters the Hamiltonian reduces to various models previously studied, such as to the complex cubic potential, the so-called Swanson Hamiltonian or the transformed version of the from below unbounded quartic -x^4-potential. In addition, it also reduces to various models not considered in the present context, namely the single site lattice Reggeon model and a transformed version of the massive sextic x^6-potential, which plays an important role as a toy modelto identify theories with vanishing cosmological constant.Comment: 21 page