Toshiaki Itoh

Hamiltonian-conserving discrete canonical equations based on variational difference quotients

Abstract New discrete mechanics based on the assumption of the discrete time is proposed. The discrete mechanics does not contain any continuous differentiation, but contains only difference quotients. Resulting discrete Hamiltonians canonical equations are single time-step difference equations and exactly conserve the Hamiltonian. The canonical equations give the numerical results more accurately than the Heun scheme and the 4th-order Runge-Kutta scheme.

Particle simulation of the kinetic Kelvin–Helmholtz instability in a magnetoplasma

The kinetic Kelvin–Helmholtz instability in a collisionless magnetoplasma is simulated numerically in cases where the ion gyroradius is comparable with or larger than the spatial scale of the cross‐field shear. The approach consists of starting the simulation from a state close to equilibrium, then observing the linear growth of instabilities and their ultimate saturation. The initial quasiequilibrium state is set up by a newly developed particle loading method; the instabilities are excited by numerical noise. The simulation is performed in two dimensions, in the plane perpendicular to the magnetic field, using an electrostatic particle code. The results for the kinetic Kelvin–Helmholtz instability are similar to those predicted by a hydromagnetic model, except that they depend slightly on the sign of the shear. Other instabilities are observed also: when the ion gyroradius is small on the scale of the shear, there is an unidentified short‐wavelength instability characterized by k Δx≥1, where k is the wa...

Discrete Lagrange's equations and canonical equations based on the principle of least action

By assuming that time is discrete, discrete Lagranges equations and discrete canonical equations are derived on the basis of the principle of least action. The discrete mechanics contains no differentiation and integration, but contains difference quotients and summations. The time interval is not required to be infinitesimal. The discrete canonical equations conserve the Hamiltonian exactly.

Fractal dimension and convergence property of recursively generated symplectic integrators

Abstract Recursive constructions of symplectic integrators for the Hamiltonian dynamical system are discussed in a general form. Moreover, using the fractal dimensions, we introduce the classification procedure of the symplectic integrators. We also show that the obtained fractal dimensions are related to the convergence and stability of the symplectic integrators.

Advancement in singing ability using The YUBA Method in patients with cochlear implants

Conclusion. Although overall improvement was not so dramatic due to a lack of retention, session by session advancement of matching pitch for targeted MIDI (Musical Instrument Digital Interface) sound was predominantly obvious. It was proved that The YUBA Method worked to improve singing ability for patients with cochlear implants. Objectives. This study sought to verify whether or not the Yuba theory and method improved the singing ability of patients with cochlear implants. Subjects and methods. Based on diagnosis, the instructor experimented to improve matching pitch of singing for three patients with cochlear implants using The YUBA Method. The mean fundamental frequencies and standard deviation of singing were then compared with before and after instructions to patients. The instruction was given for over 40 days at the University of Tokyo Hospital. Results. For each patient, the mean fundamental frequencies of their singing approached the mean MIDI specified frequencies as references for tests done in all three songs. Overall, the SD between fundamental frequencies of their singing and reference MIDI sounds became smaller.

FRACTAL IMAGE COMPRESSION USING LOCALLY REFINED PARTITIONS

In the present report, we show a practical fractal image compression method using locally refined partition which is generated automatically and controlled by the values of gradients in images, The method is similar to the ones by Barnsley and Hurd. In our method, using the quad-tree scheme, before the compression processes of the image, we locally refine the domain regions recursively until the size of the regions become smaller than the scale lengths of the gradients in the image or until the predefined minimum refinement size is reached. Based on our method, it is possible to assess the optimum-like set of domain regions for the desired file size.

Verification of RRA and CMC in OpenSim

OpenSim is the free software that can handle various analysis and simulation of skeletal muscle dynamics with PC. This study treated RRA and CMC tools in OpenSim. It is remarkable that we can simulate human motion with respect to nerve signal of muscles using these tools. However, these tools seem to still in developmental stages. In order to verify applicability of these tools, we analyze bending and stretching motion data which are obtained from motion capture device using these tools. In this study, we checked the consistency between real muscle behavior and numerical results from these tools.

Algebraic Construction of Exact Difference Equations from Symmetry of Equations

Difference equations or exact numerical integration scheme, which have general solutions, are treated algebraically. Eliminating the symmetry in mixed functions, we can construct numerical integration schemes correspond to some ordinary differential equations that have same mixed functions. When arbitrary functions are given, whether we can construct numerical integration schemes that have solution functions equal to given function or not are treated.

Symplectic integrable mappings and discrete Painlevé equations

Abstract The symplectic integrable mappings found by Suris are transformed into the discrete nonlinear equations which were found by Quispel et al. The transformed discrete equations contain the discrete Painleve equations which were found by Ramani et al. and the discrete time generalized Toda lattice equation.