Quantum Canonical Transformations revisited

A preferred form for the path integral discretization is suggested that allows the implementation of canonical transformations in quantum theory.Comment: 8 pages, LaTe

Light-Cone Quantization of the Liouville Model

We present the quantization of the Liouville model defined in light-cone coordinates in (1,1) signature space. We take advantage of the representation of the Liouville field by the free field of the Backl\"{u}nd transformation and adapt the approch by Braaten, Curtright and Thorn. Quantum operators of the Liouville field $\partial_{+}\phi$, $\partial_{-}\phi$, $e^{g\phi}$, $e^{2g\phi}$ are constructed consistently in terms of the free field. The Liouville model field theory space is found to be restricted to the sector with field momentum $P_{+}=-P_{-}$, $P_{+}> 0$ , which is a closed subspace for the Liouville theory operator algebra.Comment: 16 p, EFI-92-6

A KINEMATIC COMPARISON OF THE RUN-WALK TRANSITION AND ULTRAMARATHONERS

The purpose of this study was to compare four kinematic variables seen as part of the runwalk transition with those same variables measured in runners of a 100km race. The sagittal kinematics of six elite, male, ultra-distance runners were analyzed from an equidistant point throughout the race. Vertical oscillations as measured from the greater trochanter and trunk, thigh and shank segment angles, from horizontal, were all measured and compared to patterns noted in previous literature. When compared it was observed that the 100km runners show significant results on at least one of the variables, meaning that some measured kinematics begin to show the signs of gait transition from a run to a walk

DYANA - FOR 3 DIMENSIONAL ANALYSIS OF HUMAN MOTION

The study of the dynamics of human motion has, until recently, been limited to research in two dimensions. Although three dimensional analyses are more common today, they are generally limited to kinematic evaluations with few studies examining the kinetics of human movement. A complete understanding of the biomechanics of human motion requires an examination of the forces and torques driving the movement. The purpose of this research was to develop a computer program capable of doing a complete dynamic analysis of three dimensional motion of the entire human body while performing aerial skills. A 14 segment, rigid link model, with all joints having three rotational degrees of freedom, was used to represent the human body. Body segment parameters were calculated using methods found in biomechanics literature. Two cameras were used to record the airborne phase of tuck jumps, split jumps and straddle jumps performed by two subjects in a calibrated space. The cinematographical records from the two cameras were digitized and then spatial coordinates of all segment endpoints were calculated using the Direct Linear Transform (DLT) technique. The orientation in space for each segment with respect to the inertial frame was defined by a using the xyz-convention of Euler angles. DyAna, a computer program written in 'C', was developed to do three dimensional dynamic analysis of the different jumps. Linear and angular kinematics were calculated for all segments of the body using central difference and finite difference techniques respectively. An inverse dynamics approach based on the Newton-Euler equations of motion was used to calculate the net forces and torques acting at the joints. The program produced good results for linear and angular kinematics and kinetics for the skills studied. As no similar three dimensional studies were found in the literature, the maximum force and torque values calculated for the tested movements were found to be reasonable when compared with two dimensional studies. In geneml, the computer program DyAna was found to work well for doing dynamic analysis of complete human movement for the airborne motions studied. Its best application in the field of biomechanics would be for the study of human motion outside of the lab setting, such as in sporting events when subject preparation is not possible

THE IDENTIFICATION OF RELEASE ON THE HORIZONTAL BAR

A horizontal bar routine in Men's Artistic Gymnastics is characterized by swinging around the bar and by flight elements such as release-regrasp and dismount skills. The release parameters, for these skills, are the primary inputs into any predictive simulations. Cinematography and videography have been the most extensively used data collection methods for analysis of release skills performed on the horizontal bar. Traditionally the release has been defined as the first instant (frame) in which the gymnast is seen to have broken contact with the bar. Harwood et al. (1991) submitted that an error of even one h e can make a large difference to the measured release parameters and any subsequently movement prediction based on those projectile determinants. Harwood defined release as the first instant when the wrist first started moving away from the bar. Given that the image size is often small, considering that a field of view may be as great as 8 meters, identification of release by any definition is subject to error. The purpose of this study was to identifl the point of release from the horizontal bar through direct measurement and to correlate this occurrence to information derived through the traditional method of analysis using cinematography. A local area gymnast performed 6 different release elements from long hang swings. Direct measurement of release was achieved by instrumenting a hand guard with a metal strip that was connected to an A/D board. Using a 3V DC power supply connected directly to the horizontal bar an electrical potential was registered when the circuit was closed (when the grip was in contact with the bar) and no potential was registered when the circuit was open (when the grip was not in contact with the bar). A traditional filming protocol was utilised with a camera placed perpendicular to the movement plane with an 8m field of view. A second high speed cine camera, electronically locked to the other, was zoomed in on the subject's wrist and hand. Standard film data reduction was conducted on the processed film which was shot at 100 framedsecond. Three measures of release were determined, one based on Harwood's definition, one on the traditional definition and the third determined from the close-up view. The results indicated that the first two methods provided similar results yet inferior to the close-up determination of release when compared to the information provided by the hand guard switch. It appears evident that given the opportunity for an additional view that a better estimate of release can be found using a close-up view of the hands and the bar. References Harwood et a1 (1991) Prm. XZIIInt. Congress Biom., Perth, Australia, 73-74

Scattering Mechanism in Modulation-Doped Shallow Two-Dimensional Electron Gases

We report on a systematic investigation of the dominant scattering mechanism in shallow two-dimensional electron gases (2DEGs) formed in modulation-doped GaAs/Al_{x}Ga_{1-x}As heterostructures. The power-law exponent of the electron mobility versus density, mu \propto n^{alpha}, is extracted as a function of the 2DEG's depth. When shallower than 130 nm from the surface, the power-law exponent of the 2DEG, as well as the mobility, drops from alpha \simeq 1.65 (130 nm deep) to alpha \simeq 1.3 (60 nm deep). Our results for shallow 2DEGs are consistent with theoretical expectations for scattering by remote dopants, in contrast to the mobility-limiting background charged impurities of deeper heterostructures.Comment: 4 pages, 3 figures, modified version as accepted in AP

On the quantum KP hierarchy and its relation to the non-linear Schr\"odinger equation

We establish a relation between the classical non-linear Schr\"odinger equation and the KP hierarchy, and we extend this relation to the quantum case by defining a quantum KP hierarchy. We present evidence that an integrable hierarchy of equations is obtained by quantizing the first Hamiltonian structure of the KdV equation. The connection between infinite-dimensional algebras and integrable models is discussed.Comment: 16 pages, KCL-TH-92-