COMPARISON OF INSIDE CONTACT PHASE AND OUTSIDE CONTACT PHASE IN CURVED SPRINTING

One of differences of running between in straight path and in bent path is the body lean inward. When athletes run in the bent path, athletes are influenced by centrifugal force. Athletes produce the medio-lateral component of ground reaction force (GRF) with inclining the body inward, to balance the centrifugal force. The centripetal force can be estimated by F=mv2 where F is the centripetal force, m is the mass of the body, v is the running velocity, and r is the radius of track. We can see from this equation, the influence of the running velocity on centripetal force is strong. So we can’t ignore the centripetal force in sprint race (i.e. 200m dash). The body lean angle increase, as the running velocity increase. Athletes must change the running direction along the bent path. One step of running consist of the flight phase and the contact phase. It is impossible to change running direction during the flight phase. Therefore it is expected to change running direction during the contact phase. It was said the functions of inside and outside legs were asymmetrical (Stoner and Ben-Sira, 1979, Hamill et al, 1987). But there are no study to compare the inside foot contact phase with the outside foot contact phase with in relation to the centripetal force and the body lean angle. The purpose of this study is to compare the inside (left) foot contact phase with the outside (right) foot contact phase with in relation to the centripetal force and the body lean angle. Then we would obtain new knowlege about curved sprinting

Spin dynamics of a one-dimensional spin-1/2 fully anisotropic Ising-like antiferromagnet in a transverse magnetic field

We consider the one-dimensional Ising-like fully anisotropic S=1/2 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of transverse magnetic field $h_x$. We obtain dynamical spin correlation functions along the magnetic field $S^{xx}(q,\omega)$ and perpendicular to it $S^{yy}(q,\omega)$. It is shown that the line shapes of $S^{xx}(q,\omega)$ and $S^{yy}(q,\omega)$ are purely symmetric at the zone-boundary. It is observed in $S^{yy}(q,\omega)$ for $\pi/2<q<\pi$ that the spectral weight moves toward low energy side with the increase of $h_x$. This model is applicable to study the spin dynamics of CsCoCl$_3$ in the presence of weak interchain interactions.Comment: 19 pages, LaTeX, 12 eps figure

Guardians Ad Litem as Surrogate Parents: Implication for Role Definition and Confidentiality

SALMON (Scalable Ab-initio Light–Mattersimulator for Optics and Nanoscience, http://salmon-tddft.jp) is a software package for the simulation of electron dynamics and optical properties of molecules, nanostructures, and crystalline solids based on first-principles time-dependent density functional theory. The core part of the software is the real-time, real-space calculation of the electron dynamics induced in molecules and solids by an external electric field solving the time-dependent Kohn–Sham equation. Using a weak instantaneous perturbing field, linear response properties such as polarizabilities and photoabsorptions in isolated systems and dielectric functions in periodic systems are determined. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear in the field strength is investigated in time domain. The propagation of the laser pulse in bulk solids and thin films can also be included in the simulation via coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic fields. The code is efficiently parallelized so that it may describe the electron dynamics in large systems including up to a few thousand atoms. The present paper provides an overview of the capabilities of the software package showing several sample calculations. Program summary Program Title: SALMON: Scalable Ab-initio Light–Matter simulator for Optics and Nanoscience Program Files doi:http://dx.doi.org/10.17632/8pm5znxtsb.1 Licensing provisions: Apache-2.0 Programming language: Fortran 2003 Nature of problem: Electron dynamics in molecules, nanostructures, and crystalline solids induced by an external electric field is calculated based on first-principles time-dependent density functional theory. Using a weak impulsive field, linear optical properties such as polarizabilities, photoabsorptions, and dielectric functions are extracted. Using an optical laser pulse, the ultrafast electronic response that may be highly nonlinear with respect to the exciting field strength is described as well. The propagation of the laser pulse in bulk solids and thin films is considered by coupling the electron dynamics in many microscopic unit cells using Maxwell’s equations describing the time evolution of the electromagnetic field. Solution method: Electron dynamics is calculated by solving the time-dependent Kohn–Sham equation in real time and real space. For this, the electronic orbitals are discretized on a uniform Cartesian grid in three dimensions. Norm-conserving pseudopotentials are used to account for the interactions between the valence electrons and the ionic cores. Grid spacings in real space and time, typically 0.02 nm and 1 as respectively, determine the spatial and temporal resolutions of the simulation results. In most calculations, the ground state is first calculated by solving the static Kohn–Sham equation, in order to prepare the initial conditions. The orbitals are evolved in time with an explicit integration algorithm such as a truncated Taylor expansion of the evolution operator, together with a predictor–corrector step when necessary. For the propagation of the laser pulse in a bulk solid, Maxwell’s equations are solved using a finite-difference scheme. By this, the electric field of the laser pulse and the electron dynamics in many microscopic unit cells of the crystalline solid are coupled in a multiscale framework

Dynamical Structure Factors of the S=1/2 Bond-Alternating Spin Chain with a Next-Nearest-Neighbor Interaction in Magnetic Fields

The dynamical structure factor of the S=1/2 bond-alternating spin chain with a next-nearest-neighbor interaction in magnetic field is investigated using the continued fraction method based on the Lanczos algorithm. When the plateau exists on the magnetization curve, the longitudinal dynamical structure factor shows a large intensity with a periodic dispersion relation, while the transverse one shows a large intensity with an almost dispersionless mode. The periodicity and the amplitude of the dispersion relation in the longitudinal dynamical structure factor are sensitive to the coupling constants. The dynamical structure factor of the S=1/2 two-leg ladder in magnetic field is also calculated in the strong interchain-coupling regime. The dynamical structure factor shows gapless or gapful behavior depending on the wave vector along the rung.Comment: 8 pages, 4 figures, to appear in Journal of the Physical Society of Japan, vol. 69, no. 10, (2000

Ground states of a one-dimensional lattice-gas model with an infinite range nonconvex interaction. A numerical study

We consider a lattice-gas model with an infinite range pairwise noncovex interaction. It might be relevant, for example, for adsorption of alkaline elements on W(112) and Mo(112). We study a competition between the effective dipole-dipole and indirect interactions. The resulting ground state phase diagrams are analysed (numerically) in detail. We have found that for some model parameters the phase diagrams contain a region dominated by several phases only with periods up to nine lattice constants. The remaining phase diagrams reveal a complex structure of usually long periodic phases. We also discuss a possible role of surace states in phase transitions.Comment: 16 pages, 5 Postscript figures; Physical Review B15 (15 August 1996), in pres

Spin Wave Response in the Dilute Quasi-one Dimensional Ising-like Antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3

Inelastic neutron scattering profiles of spin waves in the dilute quasi-one-dimensional Ising-like antiferromagnet CsCo_{0.83}Mg_{0.17}Br_3 have been investigated. Calculations of S^{xx}(Q,omega), based on an effective spin Hamiltonian, accurately describe the experimental spin wave spectrum of the 2J mode. The Q dependence of the energy of this spin wave mode follows the analytical prediction omega_{xx}(Q)=(2J)(1-5epsilon^{2}cos^{2}Qa+2epsilon^{2})^{1/2}, calculated by Ishimura and Shiba using perturbation theory.Comment: 13 pages, 4 figure

Fractional S^z excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain

We present the microscopic view for the excitations around the 1/3 plateau state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations around the plateau with the degenerating perturbation theory from the Ising limit, combined with the Bethe-form wave function. We then find that the domain-wall particles carrying $S^z=\pm 1/3$ and its bound state of $S^z=\pm 2/3$ describe well the low-energy excitations around the 1/3 plateau state. The formation of the bound state of the domain-walls clearly provides the microscopic mechanism of the cusp singularities and the even-odd behavior in the magnetization curve.Comment: 13 pages, 15 figure

Nonlinear Parabolic Equations arising in Mathematical Finance

This survey paper is focused on qualitative and numerical analyses of fully nonlinear partial differential equations of parabolic type arising in financial mathematics. The main purpose is to review various non-linear extensions of the classical Black-Scholes theory for pricing financial instruments, as well as models of stochastic dynamic portfolio optimization leading to the Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both problems can be represented by solutions to nonlinear parabolic equations. Qualitative analysis will be focused on issues concerning the existence and uniqueness of solutions. In the numerical part we discuss a stable finite-volume and finite difference schemes for solving fully nonlinear parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387

Motion of Bound Domain Walls in a Spin Ladder

The elementary excitation spectrum of the spin-$\frac{1}{2}$ antiferromagnetic (AFM) Heisenberg chain is described in terms of a pair of freely propagating spinons. In the case of the Ising-like Heisenberg Hamiltonian spinons can be interpreted as domain walls (DWs) separating degenerate ground states. In dimension $d>1$, the issue of spinons as elementary excitations is still unsettled. In this paper, we study two spin-$\frac{1}{2}$ AFM ladder models in which the individual chains are described by the Ising-like Heisenberg Hamiltonian. The rung exchange interactions are assumed to be pure Ising-type in one case and Ising-like Heisenberg in the other. Using the low-energy effective Hamiltonian approach in a perturbative formulation, we show that the spinons are coupled in bound pairs. In the first model, the bound pairs are delocalized due to a four-spin ring exchange term in the effective Hamiltonian. The appropriate dynamic structure factor is calculated and the associated lineshape is found to be almost symmetric in contrast to the 1d case. In the case of the second model, the bound pair of spinons lowers its kinetic energy by propagating between chains. The results obtained are consistent with recent theoretical studies and experimental observations on ladder-like materials.Comment: 12 pages, 7 figure