Energies of knot diagrams

We introduce and begin the study of new knot energies defined on knot diagrams. Physically, they model the internal energy of thin metallic solid tori squeezed between two parallel planes. Thus the knots considered can perform the second and third Reidemeister moves, but not the first one. The energy functionals considered are the sum of two terms, the uniformization term (which tends to make the curvature of the knot uniform) and the resistance term (which, in particular, forbids crossing changes). We define an infinite family of uniformization functionals, depending on an arbitrary smooth function $f$ and study the simplest nontrivial case $f(x)=x^2$, obtaining neat normal forms (corresponding to minima of the functional) by making use of the Gauss representation of immersed curves, of the phase space of the pendulum, and of elliptic functions

A Chandra Study of the Effects of a Major Merger on the Structure of Abell 2319

We present an analysis of a Chandra observation of the massive, nearby galaxy cluster Abell 2319. A sharp surface brightness discontinuity--suggested by previous, lower angular resolution X-ray imaging--is clearly visible in the ACIS image. This roughly 300kpc feature suggests that a major merger is taking place with a significant velocity component perpendicular to the line of sight. The cluster emission-weighted mean temperature is 11.8+/-0.6kev, somewhat higher than previous temperature measurements. The Chandra temperature map of A2319 reveals substructure resembling that anticipated based on hydrodynamic simulations of cluster mergers. The merger feature shows a pressure change across the surface brightness discontinuity by a factor of <=2.5. The higher density side of the front has a lower temperature, suggesting the presence of a cold front similar to those in many other merging clusters. The velocity of the front is roughly sonic. We compare bulk properties of the ICM and galaxies in A2319 to the same properties in a large sample of clusters as a way of gauging the effects of the major merger. Interestingly, by comparing A2319 to a sample of 44 clusters studied with the ROSAT PSPC we find that the X-ray luminosity, isophotal size, and ICM mass are consistent with the expected values for a cluster of its temperature; in addition, the K-band galaxy light is consistent with the light--temperature scaling relation derived from a sample of about 100 clusters studied with 2MASS. Together, these results indicate either that the merger in A2319 has not been effective at altering the bulk properties of the cluster, or that there are large but correlated displacements in these quantities.Comment: 11 pages, 8 figures, ApJ Submitte

Cooper pairing and single particle properties of trapped Fermi gases

We calculate the elementary excitations and pairing of a trapped atomic Fermi gas in the superfluid phase. The level spectra and pairing gaps undergo several transitions as the strength of the interactions between and the number of atoms are varied. For weak interactions, the Cooper pairs are formed between particles residing in the same harmonic oscillator shell. In this regime, the nature of the paired state is shown to depend critically on the position of the chemical potential relative to the harmonic oscillator shells and on the size of the mean field. For stronger interactions, we find a region where pairing occur between time-reversed harmonic oscillator states in different shells also.Comment: Slightly revised version: Mistakes in equation references in figures corrected. Accepted for Phys. Rev.

Efficient and robust initialization of a qubit register with fermionic atoms

We show that fermionic atoms have crucial advantages over bosonic atoms in terms of loading in optical lattices for use as a possible quantum computation device. After analyzing the change in the level structure of a non-uniform confining potential as a periodic potential is superimposed to it, we show how this structure combined with the Pauli principle and fermion degeneracy can be exploited to create unit occupancy of the lattice sites with very high efficiency.Comment: 4 pages, 3 figure

Measurement of the Zero Crossing in a Feshbach Resonance of Fermionic 6-Li

We measure a zero crossing in the scattering length of a mixture of the two lowest hyperfine states of 6-Li. To locate the zero crossing, we monitor the decrease in temperature and atom number arising from evaporation in a CO2 laser trap as a function of magnetic field B. The temperature decrease and atom loss are minimized for B=528(4) G, consistent with no evaporation. We also present preliminary calculations using potentials that have been constrained by the measured zero crossing and locate a broad Feshbach resonance at approximately 860 G, in agreement with previous theoretical predictions. In addition, our theoretical model predicts a second and much narrower Feshbach resonance near 550 G.Comment: Five pages, four figure

Collective excitations in a fermion-fermion mixture with different Fermi surfaces

In this paper, collective excitations in a homogeneous fermion-fermion mixture with different Fermi surfaces are studied. In the Fermi liquid phase, the zero-sound velocity is found to be larger than the largest Fermi velocity. With attractive interactions, the superfluid phase appears below a critical temperature, and the phase mode is the low-energy collective excitation. The velocity of the phase mode is proportional to the geometric mean of the two Fermi velocities. The difference between the two velocities may serve as a tool to detect the superfluid phase.Comment: 4 pages. To be published in Phys. Rev.

Boson induced s-wave pairing in dilute boson-fermion mixtures

We show that in dilute boson-fermion mixtures with fermions in two internal states, even when the bare fermion-fermion interaction is repulsive, the exchange of density fluctuations of the Bose condensate may lead to an effective fermion-fermion attraction, and thus to a Cooper instability in the s-wave channel. We give an analytical method to derive the associated $T_c$ in the limit where the phonon branch of the Bogoliubov excitation spectrum of the bosons is important. We find a $T_c$ of the same order as for a pure Fermi gas with bare attraction.Comment: 12 pages, no figure

3D modelling of upwelling around a headland

Hydrodynamic

CONVERTING THEORY AND WAR DOCTRINE TO REALISTIC TRAINING FOR ENSURING THE SUCCESS OF MILITARY CAMPAIGN PLANNING

Military campaigns in the 21st Century are extremely complex multi-dimensional undertakings. In today’s globalized reality, influence of wars will go beyond the theatre of operations into issues of international economy, human migration, airspace and sea lanes, thus adding new dimensions to campaign planning.  Converting theory and doctrine to practice is never easy.  Realistic training may be the best bridge to ensure that classroom knowledge is correctly applied to the real battlefield.  This paper looks at this challenge through the combined experience of six foreign exchange students who graduated from Indonesia’s Air Command and Staff College, 2018.  The purpose of this paper is to highlight some of the challenges to campaign planning, especially in light of multinational influences, extract lessons learned from recent military campaigns and then provide feedback for Indonesia’s wargaming training methodology as practiced in the air command and staff college.  The foundation to Indonesia’s wargaming exercises is the 14-step Military Decision Making Process (MDMP).  MDMP in its general form is part of the campaign planning processes for the authors’ respective countries too, varying only in the sequence and emphasis on steps and tasks within the process and strategies for exercising the process.  This paper will conclude that even the most theoretically sound campaign planning process would lead to operational failure, unless critical thinking &amp; planning abilities are developed in upcoming military leaders through a sound understanding of theory, realistic wargaming, and deep analysis. This requires realistic training in an open learning environment, and a willingness to analyse one’s own country-specific mistakes and successes

Six-year body composition change in male elite senior rugby league players

This study investigated the change in body composition and bone mineral content (BMC) of senior rugby league (RL) players between 2008 and 2014. Twelve male professional RL players (age, 24.6 ± 4.0 years; stature, 183.4 ± 8.4 cm) received a dual-energy X-ray absorptiometry scan during preseason in 2008 and 2014. Between 2008 and 2014, very likely increases in leg lean mass (LM), total trunk and leg BMC, and a likely increase in arm BMC and possible increases in body mass (BM), total and trunk fat mass (FM), and total, trunk and arm LM were observed. Unlikely decreases and unclear changes in leg and arm FM were also found. Large negative correlations were observed between age and BM (r = −0.72), LM (r = −0.70), FM (r = −0.61) and BMC (r = −0.84) change. Three participants (19.1 ± 1.6 years) increased LM by 7.0–9.3 kg. Younger players had the largest increases in LM during this period, although an older player (30-year old) still increased LM. Differences in body composition change were also observed for participants of the same age, thus contextual factors should be considered. This study demonstrates the individuality of body composition changes in senior professional rugby players, while considering the potential change in young athletes