The dynamics and tuning of orchestral crotales

Crotales are center-weighted, tuned cymbals that are found in the percussion section of most orchestras. They are arranged like a keyboard in octave sets and are commercially available in two octaves, from C6 to C8. Little information about the physics of crotales has been reported in the literature, despite their having the interesting property of producing a particularly pleasing sound. In this study, the acoustic and vibrational properties of crotales from C6 to C8 are theoretically and experimentally investigated. Interferograms of typical vibrational modes are presented, and the frequencies of the acoustically important modes of crotales are identified and reported. The acoustic spectra of the crotales are compared to theoretical predictions for thin circular plates and annular plates clamped at the center. These models are found to be insufficient for predicting the normal modes of the crotales. An accurate model is developed using finite element analysis, and this model is used to investigate the effects of subtle changes in the magnitude and size of the center mass on the acoustic spectrum. This investigation serves as a basis for suggestions for improvement of the crotales by modifying the center mass. Finally, the physical parameters for a set of clamped annular plates are derived such that the set has similar acoustic properties to a set of crotales, but with more accurate tuning. The validity of these parameters is confirmed using finite element analysis

Non-degenerate normal-mode doublets in vibrating flat circular plates

The vibrations of flat circular plates have been studied for hundreds of years, and they are well understood by the scientific community. Unfortunately, when vibrating circular plates are discussed in textbooks, the relationship between pairs of spatially orthogonal vibrational patterns that occur at each of the normal-mode frequencies is often ignored. Usually these orthogonal solutions are presented to the student as being degenerate in frequency; however, in practice the degeneracy of the doublet is often broken and the two spatially orthogonal solutions are separated in frequency. We show theoretically and experimentally that the degeneracy can be broken by a small asymmetry in the plate, and we derive a formula for predicting the magnitude of the frequency-splitting. We have used electronic speckle pattern interferometry to investigate the phenomena of doublet splitting and have confirmed the validity of the theory

Photonic band gaps and defect states induced by excitations of Bose-Einstein condensates in optical lattices

We study the interaction of a Bose-Einstein condensate, which is confined in an optical lattice, with a largely detuned light field propagating through the condensate. If the condensate is in its ground state it acts as a periodic dielectric and gives rise to photonic band gaps at optical frequencies. The band structure of the combined system of condensed lattice-atoms and photons is studied by using the concept of polaritons. If elementary excitations of the condensate are present, they will produce defect states inside the photonic band gaps. The frequency of localized defect states is calculated using the Koster-Slater model.Comment: 10 pages, 1 figure, RevTe

Resolved-sideband Raman cooling to the ground state of an optical lattice

We trap neutral Cs atoms in a two-dimensional optical lattice and cool them close to the zero-point of motion by resolved-sideband Raman cooling. Sideband cooling occurs via transitions between the vibrational manifolds associated with a pair of magnetic sublevels and the required Raman coupling is provided by the lattice potential itself. We obtain mean vibrational excitations \bar{n}_x \approx \bar{n}_y \approx 0.01, corresponding to a population \sim 98% in the vibrational ground state. Atoms in the ground state of an optical lattice provide a new system in which to explore quantum state control and subrecoil laser coolingComment: PDF file, 13 pages including 3 figure

The Explication Defence of Arguments from Reference

In a number of influential papers, Machery, Mallon, Nichols and Stich have presented a powerful critique of so-called arguments from reference, arguments that assume that a particular theory of reference is correct in order to establish a substantive conclusion. The critique is that, due to cross-cultural variation in semantic intuitions supposedly undermining the standard methodology for theorising about reference, the assumption that a theory of reference is correct is unjustified. I argue that the many extant responses to Machery et al.’s critique do little for the proponent of an argument from reference, as they do not show how to justify the problematic assumption. I then argue that it can in principle be justified by an appeal to Carnapian explication. I show how to apply the explication defence to arguments from reference given by Andreasen (for the biological reality of race) and by Churchland (against the existence of beliefs and desires)

Quantum computing in optical microtraps based on the motional states of neutral atoms

We investigate quantum computation with neutral atoms in optical microtraps where the qubit is implemented in the motional states of the atoms, i.e., in the two lowest vibrational states of each trap. The quantum gate operation is performed by adiabatically approaching two traps and allowing tunneling and cold collisions to take place. We demonstrate the capability of this scheme to realize a square-root of swap gate, and address the problem of double occupation and excitation to other unwanted states. We expand the two-particle wavefunction in an orthonormal basis and analyze quantum correlations throughout the whole gate process. Fidelity of the gate operation is evaluated as a function of the degree of adiabaticity in moving the traps. Simulations are based on rubidium atoms in state-of-the-art optical microtraps with quantum gate realizations in the few tens of milliseconds duration range.Comment: 11 pages, 7 figures, for animations of the gate operation, see http://www.itp.uni-hannover.de/~eckert/na/index.htm

Superfluidity of Bose-Einstein Condensate in An Optical Lattice: Landau-Zener Tunneling and Dynamical Instability

Superflow of Bose-Einstein condensate in an optical lattice is represented by a Bloch wave, a plane wave with periodic modulation of the amplitude. We review the theoretical results on the interaction effects in the energy dispersion of the Bloch waves and in the linear stability of such waves. For sufficiently strong repulsion between the atoms, the lowest Bloch band develops a loop at the edge of the Brillouin zone, with the dramatic consequence of a finite probability of Landau-Zener tunneling even in the limit of a vanishing external force. Superfluidity can exist in the central region of the Brillouin zone in the presence of a repulsive interaction, beyond which Landau instability takes place where the system can lower its energy by making transition into states with smaller Bloch wavenumbers. In the outer part of the region of Landau instability, the Bloch waves are also dynamically unstable in the sense that a small initial deviation grows exponentially in time. In the inner region of Landau instability, a Bloch wave is dynamically stable in the absence of persistent external perturbations. Experimental implications of our findings will be discussed.Comment: A new section on tight-binding approximation is added with a new figur

The movement and physiological demands of international and regional men’s touch rugby matches

This study compared the internal and external match demands imposed on international and regional standard male touch rugby players. The study adopted a cohort design with independent groups. Twelve international players (mean age 27.8 ± 6.2 y, body mass 72.8 ± 3.7 kg, stature 174.5 ± 5.4 cm) and nine regional players (mean age 25.5 ± 5.5 y, body mass 74.2 ± 7 kg, stature 174.1 ± 7 cm) were analysed during nine competitive matches from the 2013 season. Movement demands were measured using a 5 Hz global positioning system (GPS), alongside heart rate and session rating of perceived exertion (s-RPE) to quantify internal load. Total distance covered by international players was lower than regional players (2265.8 ± 562.3 cf. 2970 ± 558.9 m, p14 km·h) was not different between groups (p>0.05), but relative high speed running (39.3 ± 12.0 cf. 26.0 ± 13.6 m·min) was higher for international players. Regional players performed more absolute low speed activity (≤14 km·h) than international players (p0.05). Very high speed running (>20 km·h) distance, bout number and frequency, peak and average speed were all greater in international players (p<0.05). Higher average heart rate, summated heart rate and s-RPE (p<0.05) indicated higher internal loads during matches for regional players. These data indicate that performance in men's touch rugby is characterised by more relative high speed running and better repeated sprint capacities in higher standard players

Cold bosonic atoms in optical lattices

The dynamics of an ultracold dilute gas of bosonic atoms in an optical lattice can be described by a Bose-Hubbard model where the system parameters are controlled by laser light. We study the continuous (zero temperature) quantum phase transition from the superfluid to the Mott insulator phase induced by varying the depth of the optical potential, where the Mott insulator phase corresponds to a commensurate filling of the lattice (``optical crystal''). Examples for formation of Mott structures in optical lattices with a superimposed harmonic trap, and in optical superlattices are presented.Comment: 4 pages 4 figures New: added references; Postscript version available at: http://th-physics.uibk.ac.at/zoller/Publications/PZListOfPublications.htm