Jet Methods in Time-Dependent Lagrangian Biomechanics

In this paper we propose the time-dependent generalization of an `ordinary' autonomous human biomechanics, in which total mechanical + biochemical energy is not conserved. We introduce a general framework for time-dependent biomechanics in terms of jet manifolds associated to the extended musculo-skeletal configuration manifold, called the configuration bundle. We start with an ordinary configuration manifold of human body motion, given as a set of its all active degrees of freedom (DOF) for a particular movement. This is a Riemannian manifold with a material metric tensor given by the total mass-inertia matrix of the human body segments. This is the base manifold for standard autonomous biomechanics. To make its time-dependent generalization, we need to extend it with a real time axis. By this extension, using techniques from fibre bundles, we defined the biomechanical configuration bundle. On the biomechanical bundle we define vector-fields, differential forms and affine connections, as well as the associated jet manifolds. Using the formalism of jet manifolds of velocities and accelerations, we develop the time-dependent Lagrangian biomechanics. Its underlying geometric evolution is given by the Ricci flow equation. Keywords: Human time-dependent biomechanics, configuration bundle, jet spaces, Ricci flowComment: 13 pages, 3 figure

Densities of states of the Falicov-Kimball model off half filling in infinite dimensions

An approximate analytical scheme of the dynamical mean field theory (DMFT) is developed for the description of the electron (ion) lattice systems with Hubbard correlations within the asymmetric Hubbard model where the chemical potentials and electron transfer parameters depend on an electron spin (a sort of ions). Considering a complexity of the problem we test the approximation in the limiting case of the infinite-$U$ spinless Falicov-Kimball model. Despite the fact that the Falicov-Kimball model can be solved exactly within DMFT, the densities of states of localized particles have not been completely investigated off half filling. We use the approximation to obtain the spectra of localized particles for various particle concentrations (chemical potentials) and temperatures. The effect of a phase separation phenomenon on the spectral function is considered.Comment: 9 pages, 11 figures, submitted to Phys. Rev.

Microwave-resonance-induced magnetooscillations and vanishing resistance states in multisubband two-dimensional electron systems

The dc magnetoconductivity of the multisubband two-dimensional electron system formed on the liquid helium surface in the presence of resonant microwave irradiation is described, and a new mechanism of the negative linear response conductivity is studied using the self-consistent Born approximation. Two kinds of scatterers (vapor atoms and capillary wave quanta) are considered. Besides a conductivity modulation expected near the points, where the excitation frequency for inter-subband transitions is commensurate with the cyclotron frequency, a sign-changing correction to the linear conductivity is shown to appear for usual quasi-elastic inter-subband scattering, if the collision broadening of Landau levels is much smaller than thermal energy. The decay heating of the electron system near the commensurability points leads to magnetooscillations of electron temperature, which are shown to increase the importance of the sign-changing correction. The line shape of magnetoconductivity oscillations calculated for wide ranges of temperature and magnetic field is in a good accordance with experimental observations.Comment: 13 pages, 8 figure

The fine structure of microwave-induced magneto-oscillations in photoconductivity of the two-dimensional electron system formed on a liquid-helium surface

The influence of the inelastic nature of electron scattering by surface excitations of liquid helium (ripplons) on the shape of magnetoconductivity oscillations induced by resonance microwave (MW) excitation is theoretically studied. The MW field provides a substantial filling of the first excited surface subband which sparks off inter-subband electron scattering by ripplons. This scattering is the origin of magneto-oscillations in the momentum relaxation rate. The inelastic effect becomes important when the energy of a ripplon involved compares with the collision broadening of Landau levels. Usually, such a condition is realized only at sufficiently high magnetic fields. On the contrary, the inelastic nature of inter-subband scattering is shown to be more important in a lower magnetic field range because of the new enhancement factor: the ratio of the inter-subband transition frequency to the cyclotron frequency. This inelastic effect affects strongly the shape of conductivity oscillations which acquires an additional wavy feature (a mixture of splitting and inversion) in the vicinity of the level-matching points where the above noted ratio is close to an integer.Comment: 10 pages 6 figure

The spontaneous generation of magnetic fields at high temperature in a supersymmetric theory

The spontaneous generation of magnetic and chromomagnetic fields at high temperature in the minimal supersymmetric standard model (MSSM) is investigated. The consistent effective potential including the one-loop and the daisy diagrams of all bosons and fermions is calculated and the magnetization of the vacuum is observed. The mixing of the generated fields due to the quark and s-quark loop diagrams and the role of superpartners are studied in detail. It is found that the contribution of these diagrams increases the magnetic and chromomagnetic field strengths as compared with the case of a separate generation of fields. The magnetized vacuum state is found to be stable due to the magnetic masses of gauge fields included in the daisy diagrams. Applications of the results obtained are discussed. A comparison with the standard model case is done.Comment: 14 pages, 2 figures, 3 table