Lewis P. Fulcher

Fermions and bosons interacting with arbitrarily strong external fields

Abstract The question, “What happens to the electron orbitals as the charge of the nucleus is increased without bounds?” has inspired much of the interest in the description of particles bound strongly by external fields. Interest in this problem and in the related Klein paradox extends back nearly to the beginnings of relativistic quantum mechanics. However, the correct interpretation of the theory for overcritical potentials, where the parts of the complete set of single particle solutions associated with particles and antiparticles are no longer distinct, was given only recently. The understanding of the spectrum of the Dirac and Klein-Gordon equations is essential in order to obtain an appropriate physical description with quantum field theory. The strong binding by more than twice the rest mass of the particles in overcritical external potentials leads to qualitatively new effects. In the case of fermions we find spontaneous positron emission accompanied by creation of a charged lowest energy state, i.e. a charged vacuum. The number of positrons produced spontaneously is limited by the Pauli exclusion principle. For bosons we find that depending on the character of the external potential, either neutral or charged Bose condensates develop. While the questions associated with the meson fields seem academic at the moment, the effects attributed to the fermion field stand a good chance of being tested in an experiment in the near future. It is expected that in heavy ion collisions such as uranium on uranium near the Coulomb barrier overcritical electromagnetic fields will be created.

Phenomenological predictions of the properties of the

We present a comprehensive calculation of the energies, splittings and electromagnetic decay rates of the bottom charmed meson system. Our calculated result for the ground state lifetime is 0.38 \pm 0.03 ps, in good agreement with the recent CDF measurement. In order to incorporate running coupling constant effects, we choose Richardsons potential for the central potential and take the spin-dependent potentials from the radiative one-loop expressions of Pantaleone, Tye and Ng. The effects of a nonperturbative spin-orbit potential are also included. Our parameters are determined from the low-lying levels of the upsilon system (avg. dev. of 4.3 MeV) and charmonium (avg. dev. of 19.9 MeV). We carry out detailed comparison with the earlier work of Eichten and Quigg and lattice calculations. Our predicted result for the ground state energy is 6286_{-6}^{+15} MeV. Our results are generally in agreement with the earlier calculations. However, we find the two lowest 1^{+} states to be very close to the j-j limit, in agreement with the NRQCD lattice calculations, but at odds with many of the earlier phenomenological calculations. The implications of this finding for the photon spectra of the 1P and 2S states are discussed in some detail. Some strategies for the observation of these states are discussed, and a table of their cascades to the ground state are presented.

B_c

An effective one-mass model of phonation is developed. It borrows the salient features of the classic two-mass model of human speech developed by Ishizaka, Matsudaira, and Flanagan. Their model is based on the idea that the oscillating vocal folds maintain their motion by deriving energy from the flow of air through the glottis. We argue that the essence of the action of the aerodynamic forces on the vocal folds is captured by negative Coulomb damping, which acts on the oscillator to energize it. A viscous force is added to include the effects of tissue damping. The solutions to this single oscillator model show that when it is excited by negative Coulomb damping, it will reach a limit cycle. Displacements, phase portraits, and energy histories are presented for two underdamped linear oscillators. A nonlinear force is added so that the variations of the fundamental frequency and the open quotient with lung pressure are comparable to the behavior of the two-mass model.

system

Pressure distributions for the uniform glottis were obtained with a static physical model (M5). Glottal diameters of d=0.005, 0.0075, 0.01, 0.02, 0.04, 0.08, 0.16, and 0.32 cm were used with a range of phonatory transglottal pressures. At each pressure and diameter, entrance loss and exit coefficients were determined. In general, both coefficients decreased in value as the transglottal pressure or the diameter increased. Entrance loss coefficients ranged from 0.69 to 17.6. Use of these coefficients with the measured flow rates in straightforward equations accurately reproduced the pressure distributions within the glottis and along the inferior vocal fold surface.

Negative Coulomb damping, limit cycles, and self-oscillation of the vocal folds

In an important paper on the physics of small amplitude oscillations, Titze showed that the essence of the vertical phase difference, which allows energy to be transferred from the flowing air to the motion of the vocal folds, could be captured in a surface wave model, and he derived a formula for the phonation threshold pressure with an explicit dependence on the geometrical and biomechanical properties of the vocal folds. The formula inspired a series of experiments [e.g., R. Chan and I. Titze, J. Acoust. Soc. Am 119, 2351-2362 (2006)]. Although the experiments support many aspects of Titzes formula, including a linear dependence on the glottal half-width, the behavior of the experiments at the smallest values of this parameter is not consistent with the formula. It is shown that a key element for removing this discrepancy lies in a careful examination of the properties of the entrance loss coefficient. In particular, measurements of the entrance loss coefficient at small widths done with a physical model of the glottis (M5) show that this coefficient varies inversely with the glottal width. A numerical solution of the time-dependent equations of the surface wave model shows that adding a supraglottal vocal tract lowers the phonation threshold pressure by an amount approximately consistent with Chan and Titzes experiments.

Pressure distributions in a static physical model of the uniform glottis: Entrance and exit coefficients

Ishizaka and Flanagans classic two-mass model of vocal fold motion is applied to small oscillations where the equations become linear and the aerodynamic driving force is described by an effective stiffness. The solution of these equations includes an analytic formula for the two eigenfrequencies; this shows that conjugate imaginary parts of the frequencies emerge beyond eigenvalue synchronization and that one of the imaginary parts becomes zero at a pressure signaling the instability associated with the onset of threshold. Using recent measurements by Fulcher et al. of intraglottal pressure distributions [J. Acoust. Soc. Am. 129, 1548-1553 (2011).] to inform the behavior of the entrance loss coefficients, an analytic formula for threshold pressure is derived. It fits most of the measurements Chan and Titze reported for their 2006 physical model of the vocal fold mucosa. Two sectors of the mass-stiffness parameter space are used to produce these fits. One is based on a rescaling of the typical glottal parameters of the original Ishizaka and Flanagan work. The second requires setting two of the spring constants equal and should be closer to the experimental conditions. In both cases, values of the elastic shear modulus are calculated from the spring constants.

Phonation threshold pressure: Comparison of calculations and measurements taken with physical models of the vocal fold mucosa

Pressure distributions were obtained for 5°, 10°, and 20° convergent angles with a static physical model (M5) of the glottis. Measurements were made for minimal glottal diameters from d = 0.005-0.32 cm with a range of transglottal pressures of interest for phonation. Entrance loss coefficients were calculated at the glottal entrance for each minimal diameter and transglottal pressure to measure how far the flows in this region deviate from Bernoulli flow. Exit coefficients were also calculated to determine the presence and magnitude of pressure recovery near the glottal exit. The entrance loss coefficients for the three convergent angles vary from values near 2.3-3.4 for d = 0.005 cm to values near 0.6 for d = 0.32 cm. These coefficients extend the tables of entrance loss and exit coefficients obtained for the uniform glottis according to Fulcher, Scherer, and Powell [J. Acoust. Soc. Am. 129, 1548-1553 (2011)].

Phonation threshold pressure and the elastic shear modulus: Comparison of two-mass model calculations with experiments

Pressure distributions for the uniform glottis were taken with a static physical model (M5) for the diameters d=0.005, 0.0075, 0.01, 0.02, 0.04, 0.08, 0.16, and 0.32 cm for a number of transglottal pressures of interest for phonation. At each pressure and diameter, entrance loss and exit coefficients are calculated. The pressure dependence and the diameter dependence of these coefficients are catalogued and compared with some standard values from the earlier literature. The accuracy with which tabulations of these coefficients reproduce the M5 pressure distributions is examined. To an excellent approximation, the intraglottal pressures at smaller diameters decrease linearly with the axial distance, and remnants of this behavior are seen at d=0.08 cm and 0.16 cm. It is shown that the intraglottal pressure gradients are linear functions of the glottal flow rates. Thus, dividing the pressure gradients by the flow rates allows one to isolate the geometric dependence of viscous effects. It is shown that an inv...

Entrance loss coefficients and exit coefficients for a physical model of the glottis with convergent angles

A mathematical model was developed to investigate possible causes of jitter and shimmer. The model builds on the classic, lumped element model of Ishizaka and Flanagan and allows for asymmetric motions of the vocal folds and aerodynamic imbalances. The intraglottal pressures were derived from empirical pressure data obtained from a static physical model of the larynx (M5). The mathematical model is based on ten, second‐order, nonlinear, coupled, ordinary differential equations that were solved simultaneously using the software Mathematica. The solutions were analyzed graphically and numerically to identify perturbations in the fundamental frequency and amplitude of the glottal airflow. Jitter and shimmer were quantified using the jitter factor and the amplitude variability index. The results indicate that only time‐dependent variations in biomechanical and aerodynamic parameters result in jitter and shimmer. The magnitudes of jitter and shimmer tend to be less than those observed in the natural sounding voice, even when the asymmetries are large. Although time‐independent asymmetries may cause the vocal folds to oscillate out of phase or with different amplitudes, they tend to entrain and vibrate at a common frequency. [Work supported by NIH R01DC03577.]

Intraglottal pressures in a static physical model of the uniform glottis: Entrance loss coefficients and viscous effects

The classic work on laryngeal flow resistance by van den Berg et al. [J. Acoust. Soc. Am. 29, 626-631 (1957)] is revisited. These authors used a formula to summarize their measurements, and thus they separated the effects of entrance loss and pressure recovery from those of viscosity within the glottis. Analysis of intraglottal pressure distributions obtained from the physical model M5 [R. Scherer et al., J. Acoust. Soc. Am. 109, 1616-1630 (2001)] reveals substantial regions within the glottis where the pressure gradient is almost constant for glottal diameters from 0.005 to 0.16 cm, as expected when viscous effects dominate the flow resistance of a narrow channel. For this set of glottal diameters, the part of the pressure gradient that has a linear dependence on the glottal volume velocity is isolated. The inverse cube diameter of the Poiseuille expression for glottal flows is examined with the data set provided by the M5 intraglottal pressure distributions. The Poiseuille effect is found to give a reasonable account of viscous effects in the diameter interval from 0.0075 to 0.02 cm, but an inverse 2.59 power law gives a closer fit across all diameters.