Is there a Jordan geometry underlying quantum physics?

There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such approaches: there is a ``Jordan geometry'' belonging to the Jordan part of the algebra of observables, in the same way as Lie groups belong to the Lie part. Both the Lie geometry and the Jordan geometry are well-adapted to describe certain features of quantum theory. We concentrate here on the mathematical description of the Jordan geometry and raise some questions concerning possible relations with foundational issues of quantum theory.Comment: 30 page

Residue Formulas for the Large k Asymptotics of Witten's Invariants of Seifert Manifolds. The Case of SU(2)

We derive the large k asymptotics of the surgery formula for SU(2) Witten's invariants of general Seifert manifolds. The contributions of connected components of the moduli space of flat connections are identified. The contributions of irreducible connections are presented in a residue form. This form is similar to the one used by A. Szenes, L. Jeffrey and F. Kirwan. This similarity allows us to express the contributions of irreducible connections in terms of intersection numbers on their moduli spaces.Comment: 39 pages, no figures, LaTe

Defect healing at room temperature in pentacene thin films and improved transistor performance

We report on a healing of defects at room temperature in the organic semiconductor pentacene. This peculiar effect is a direct consequence of the weak intermolecular interaction which is characteristic of organic semiconductors. Pentacene thin-film transistors were fabricated and characterized by in situ gated four-terminal measurements. Under high vacuum conditions (base pressure of order 10E-8 mbar), the device performance is found to improve with time. The effective field-effect mobility increases by as much as a factor of two and mobilities up to 0.45 cm2/Vs were achieved. In addition, the contact resistance decreases by more than an order of magnitude and there is a significant reduction in current hysteresis. Oxygen/nitrogen exposure and annealing experiments show the improvement of the electronic parameters to be driven by a thermally promoted process and not by chemical doping. In order to extract the spectral density of trap states from the transistor characteristics, we have implemented a powerful scheme which allows for a calculation of the trap densities with high accuracy in a straightforward fashion. We show the performance improvement to be due to a reduction in the density of shallow traps <0.15 eV from the valence band edge, while the energetically deeper traps are essentially unaffected. This work contributes to an understanding of the shallow traps in organic semiconductors and identifies structural point defects within the grains of the polycrystalline thin films as a major cause.Comment: 13 pages, 13 figures, to be published in Phys. Rev.

Competitively coupled orientation selective cellular neural networks

We extend previous work in orientation selective cellular neural networks to include competitive couplings between different layers tuned to different orientations and spatial frequencies. The presence of these interactions sharpens the spatial frequency tuning of the filters in two ways, when compared to a similar architecture proposed previously which lacks these interactions. The first is the introduction of nulls in the frequency response. The second is the introduction of constraints on the passbands of the coupled layers. Based on an understanding of these two effects, we propose a method for choosing spatial frequency tunings of the individual layers to enhance orientation selectivity in the coupled system

Oxygen-related traps in pentacene thin films: Energetic position and implications for transistor performance

We studied the influence of oxygen on the electronic trap states in a pentacene thin film. This was done by carrying out gated four-terminal measurements on thin-film transistors as a function of temperature and without ever exposing the samples to ambient air. Photooxidation of pentacene is shown to lead to a peak of trap states centered at 0.28 eV from the mobility edge, with trap densities of the order of 10(18) cm(-3). These trap states need to be occupied at first and cause a reduction in the number of free carriers, i.e. a consistent shift of the density of free holes as a function of gate voltage. Moreover, the exposure to oxygen reduces the mobility of the charge carriers above the mobility edge. We correlate the change of these transport parameters with the change of the essential device parameters, i.e. subthreshold performance and effective field-effect mobility. This study supports the assumption of a mobility edge for charge transport, and contributes to a detailed understanding of an important degradation mechanism of organic field-effect transistors. Deep traps in an organic field-effect transistor reduce the effective field-effect mobility by reducing the number of free carriers and their mobility above the mobility edge.Comment: 13 pages, 14 figures, to be published in Phys. Rev.

\u27Mini-interval gait\u27 switching: Understanding the positive implications of a novel training regime

The neuromechanical reorganization required to change gaits imposes an energetic cost 75% greater than either a walking or running step at the same speed. By combining walking and running with the requisite gait switching transition steps, an exercise protocol can be generated with virtually any desired metabolic output even at relatively slow treadmill speed. Gait switching increases metabolic demand through discrete events, which can be tolerated more easily by individuals recovering from health problems, just as interval training allows greater work production for healthy individuals. In addition to cardio-respiratory benefits, ‘mini-intervals’ with frequent gait switching also provides positive effects and attributes such as distributing muscle group activation, re-training neural coordination, and avoiding repetitive joint overloading. It has the added benefit of developing stability during transitions while a safety hand rail is present which can lead to greater stability in more complex natural environments. Finally, increased mental focus may help avoid the monotony of usual treadmill workouts, aiding adherence to an exercise program. We review evidence for the cost increase of the gait transition step and explain the mechanisms involved. We also discuss literature supporting the range of benefits for mini-interval gait switching as a training and rehabilitation tool

Affordance Boundaries Are Defined by Dynamic Capabilities of Parkour Athletes in Dropping from Various Heights

Available behaviors are determined by the fit between features of the individual and reciprocal features of the environment. Beyond some critical boundary certain behaviors become impossible causing sudden transitions from one movement pattern to another. Parkour athletes have developed multiple movement patterns to deal with their momentum during landing. We were interested in whether drop distance would cause a sudden transition between a two-footed (precision) landing and a load-distributing roll and whether the transition height could be predicted by dynamic and geometric characteristics of individual subjects. Kinematics and ground reaction forces were measured as Parkour athletes stepped off a box from heights that were incrementally increased or decreased from 0.6 to 2.3 m. Individuals were more likely to roll from higher drops; those with greater body mass and less explosive leg power, were more likely to transition to a roll landing at a lower height. At some height a two-footed landing is no longer feasible but for some athletes this height was well within the maximum drop height used in this study. During low drops the primary task constraint of managing momentum could be achieved with either a precision landing or a roll. This meant that participants were free to select their preferred landing strategy, which was only partially influenced by the physical demands of the task. However, athletes with greater leg power appeared capable of managing impulse absorption through a leg mediated strategy up to a greater drop height

Mechanical Behavior of Mushy Zone in DC casting using a Viscoplastic Material Model

Direct Chill (DC) casting is a semi-continuous metal manufacturing process for producing non-ferrous alloys such as aluminum and magnesium. During the solidification of the alloy, there exists a semi-solid state of material known as mushy zone which is more prone to hot tearing. Precise modeling of hot tearing is the most challenging task due to the interaction of many physical fields. The deformation of the partially coherent solid strongly influences the hot cracking. This work focuses on the material behavior of the mushy zone which is the prerequisite for the development of hot tearing criteria. The rate-dependent nature plays a crucial role at higher temperatures. Therefore, the viscoplastic material models with temperature-dependent coefficients are implemented for the characterization of the mushy zone. The numerical integration of the constitute equations are explained in detail. The liquid flow is neglected, and the momentum and energy equations are solved for the mushy and solid phases. With the help of a viscoplastic material models, the stress and strain evolution in the mushy zone is captured. It is found that the state of stress in mushy region is tensile in nature which is a favorable situation for the hot cracks. The influence of the casting speed and secondary cooling on the mushy stress state are analyzed in detail

Self-organized cortical map formation by guiding connections

We describe an algorithm for self-organizing connections from a source array to a target array of neurons that is inspired by neural growth cone guidance. Each source neuron projects a Gaussian pattern of connections to the target layer. Learning modifies the pattern center location. The small number of parameters required to specify connectivity has enabled this algorithm\u27s implementation in a neuromorphic silicon system. We demonstrate that this algorithm can lead to topographic feature maps similar to those observed in the visual cortex, and characterize its operation as function maximization, which connects this approach with other models of cortical map formation