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Hiroshi Miki

Publications and source records attributed to Hiroshi Miki.

27 records · Page 2Linked to original sources
arXiv2013

Growth rate distribution of NH_4Cl dendrite and its scaling structure

Scaling structure of the growth rate distribution on the interface of a dendritic pattern is investigated. The distribution is evaluated for an ${\rm NH_4Cl}$ quasi-two-dimensional crystal by numerically solving the Laplace equation with the boundary condition taking account of the surface tension effect. It is found that the distribution has multifractality and the surface tension effect is almost ineffective in the unscreened large growth region. The values of the minimum singular exponent and the fractal dimension are smaller than those for the diffusion-limited aggregation pattern. The Makarov's theorem, the information dimension equals one, and the Turkevich-Scher conjecture between the fractal dimension and the minimum singularity exponent hold.

nlin.PS↗
arXiv2012

A superintegrable finite oscillator in two dimensions with SU(2) symmetry

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is found that the dynamical difference eigenvalue equation can be written in terms of creation and annihilation operators. The wavefunctions of the Hamiltonian are expressed in terms of two known families of bivariate Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials form bases for SU(2) irreducible representations. It is further shown that the pair of eigenvalue equations for each of these families are related to each other by an SU(2) automorphism. A finite model of the anisotropic oscillator that has wavefunctions expressed in terms of the same Rahman polynomials is also introduced. In the continuum limit, when the number of grid points goes to infinity, standard two-dimensional harmonic oscillators are obtained. The analysis provides the $N\rightarrow \infty$ limit of the bivariate Krawtchouk polynomials as a product of one-variable Hermite polynomials.

math-ph↗
arXiv2012

Quantum State Transfer in a Two-dimensional Regular Spin Lattice of Triangular Shape

Quantum state transfer in a triangular domain of a two-dimensional, equally-spaced, spin lat- tice with non-homogeneous nearest-neighbor couplings is analyzed. An exact solution of the one- excitation dynamics is provided in terms of 2-variable Krawtchouk orthogonal polynomials that have been recently defined. The probability amplitude for an excitation to transit from one site to another is given. For some values of the parameters, perfect transfer is shown to take place from the apex of the lattice to the boundary hypotenuse.

math-ph↗
arXiv2012

Discrete Spectral Transformations of Skew Orthogonal Polynomials and Associated Discrete Integrable Systems

Discrete spectral transformations of skew orthogonal polynomials are presented. From these spectral transformations, it is shown that the corresponding discrete integrable systems are derived both in 1+1 dimension and in 2+1 dimension. Especially in the (2+1)-dimensional case, the corresponding system can be extended to 2x2 matrix form. The factorization theorem of the Christoffel kernel for skew orthogonal polynomials in random matrix theory is presented as a by-product of these transformations.

math-ph↗
arXiv2011

Non-Hermitian oscillator Hamiltonians and multiple Charlier polynomials

A set of r non-Hermitian oscillator Hamiltonians in r dimensions is shown to be simultaneously diagonalizable. Their spectra is real and the common eigenstates are expressed in terms of multiple Charlier polynomials. An algebraic interpretation of these polynomials is thus achieved and the model is used to derive some of their properties.

math-ph↗
arXiv2008

Achievement of Alternative Configurations of Vehicles on Multiple Lanes

Heavy traffic congestion daily occurs at merging sections on highway. For releasing this congestion, possibility of alternative configuration of vehicles on multiple-lane road is discussed in this paper. This is the configuration where no vehicles move aside on the other lane. It has a merit in making smooth merging at an intersection or a junction due to so-called the "zipper effect". We show, by developing a cellular automaton model for multiple lanes, that this configuration is achieved by simple local interactions between vehicles neighboring each other. The degree of the alternative configuration in terms of the spatial increase of parallel driving length is studied by using both numerical simulations and mean field theory. We successfully construct a theoretical method for calculating this degree of the alternative configuration by using cluster approximation. It is shown that the theoretical results coincide with those of the simulations very well.

physics.soc-ph↗
arXiv2004

Pump process of the rotatory molecular motor and its energy efficiency

The pump process of the ratchet model inspired by the $F_o$ rotatory motor of ATP synthase is investigated. In this model there are two kinds of characteristic time. One is dynamical, the relaxation time of the system. Others are chemical, the chemical reaction rates at which a proton binds to or dissociates from the motor protein. The inequalities between them affect the behavior of the physical quantities, such as the rotation velocity and the proton pumping rates across the membrane. The energy transduction efficiency is calculated and the condition under which the efficiency can become higher is discussed. The proton pumping rate and the efficiency have a peak where a certain set of inequalities between the chemical reaction rates and the reciprocal of the relaxation time holds. The efficiency also has a peak for a certain value of the load. The best efficiency condition for the pump process is consistent with that for the motor process.

physics.bio-ph↗
arXiv2003

Motion of rotatory molecular motor and chemical reaction rate

We examine the dependence of the physical quantities of the rotatory molecular motor, such as the rotation velocity and the proton translocation rate, on the chemical reaction rate using the model based only on diffusion process. A peculiar behavior of proton translocation is found and the energy transduction efficiency of the motor protein is enhanced by this behavior. We give a natural explanation that this behavior is universal when certain inequalities between chemical reaction rates hold. That may give a clue to examine whether the motion of the molecular motor is dominated by diffusion process or not.

physics.bio-ph↗