Structure and modeling of the network of two-Chinese-character compound words in the Japanese language

This paper proposes a numerical model of the network of two-Chinese-character compound words (two-character network, for short). In this network, a Chinese character is a node and a two-Chinese-character compound word links two nodes. The basic framework of the model is that an important character gets many edges. As the importance of a character, we use the frequency of each character appearing in publications. The direction of edge is given according to a random number assigned to nodes. The network generated by the model is small-world and scale-free, and reproduces statistical properties in the actual two-character network quantitatively.Comment: 15 pages, 9 figure

Fractal behind smart shopping

The 'minimal' payment - a payment method which minimizes the number of coins in a purse - is presented. We focus on a time series of change given back to a shopper repeating the minimal payment. The delay plot shows visually that the set of successive change possesses a fine structure similar to the Sierpinski gasket. We also estimate effectivity of the minimal-payment method by means of the average number of coins in a purse, and conclude that the minimal-payment strategy is the best to reduce the number of coins in a purse. Moreover, we compare our results to the rule-60 cellular automaton and the Pascal-Sierpinski gaskets, which are known as generators of the discrete Sierpinski gasket.Comment: 16 page

A solvable model of fracture with power-law distribution of fragment sizes

The present paper describes a stochastic model of fracture, whose fragment size distribution can be calculated analytically as a power-law-like distribution. The model is basically cascade fracture, but incorporates the effect that each fragment in each stage of cascade ceases fracture with a certain probability. When the probability is constant, the exponent of the power-law cumulative distribution lies between -1 and 0, depending not only on the probability but the distribution of fracture points. Whereas, when the probability depends on the size of a fragment, the exponent is less than -1, irrespective of the distribution of fracture points

Statistical properties of position-dependent ball-passing networks in football games

Statistical properties of position-dependent ball-passing networks in real football games are examined. We find that the networks have the small-world property, and their degree distributions are fitted well by a truncated gamma distribution function. In order to reproduce these properties of networks, a model based on a Markov chain is proposed.Comment: 19 page

Phase-field systems for grain boundary motions under isothermal solidifications

Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$\phi$-$\eta$-$\theta$ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as a phase-field model of planar grain boundary motion under isothermal solidification. Although each of the systems has specific characteristics and mathematical difficulties, the proofs of the main theorems are based on the time discretization method by means of a common approximating problem. As a consequence, we provide a uniform solution method for a wide scope of parabolic systems associated with the $\phi$-$\eta$-$\theta$ model.Comment: 48 page

Degree distribution of position-dependent ball-passing networks in football games

We propose a simple stochastic model describing the position-dependent ball-passing network in football games. In this network, a player on a certain area in the divided fields is a node, and a pass between two nodes corresponds to an edge. Our model is characterized by the consecutive choice of a node dependent on its intrinsic fitness. We derive the explicit expression of the degree distribution, and find that the derived distribution reproduces the real data quit well.Comment: 20 pages, 7 figure

Comparison of different source calculations in two-nucleon channel at large quark mass

We investigate a systematic error coming from higher excited state contributions in the energy shift of light nucleus in the two-nucleon channel by comparing two different source calculations with the exponential and wall sources. Since it is hard to obtain a clear signal of the wall source correlation function in a plateau region, we employ a large quark mass as the pion mass is 0.8 GeV in quenched QCD. We discuss the systematic error in the spin-triplet channel of the two-nucleon system, and the volume dependence of the energy shift.Comment: 8 pages, 7 figures, Proceedings of the 35th International Symposium on Lattice Field Theory (Lattice 2017), June 19-24, 2017, Granada, Spai

Study of quark mass dependence of binding energy for light nuclei in 2+1 flavor lattice QCD

We investigate the formation of light nuclei with the nuclear mass number less than or equal to four in 2+1 flavor QCD using a non-perturbative improved Wilson quark and Iwasaki gauge actions. The quark mass is decreased from our previous work to the one corresponding to the pion mass of 0.30 GeV. In each multi-nucleon channel, the energy shift of the ground state relative to the assembly of free nucleons is calculated on two volumes, whose spatial extents are 4.3 fm and 5.8 fm. From the volume dependence of the energy shift, we distinguish a bound state of multi nucleons from an attractive scattering state. We find that all the ground states measured in this calculation are bound states. As in the previous studies at larger $m_\pi$, our result indicates that at $m_\pi = 0.30$ GeV the effective interaction between nucleons in the light nuclei is relatively stronger than the one in nature, since the results for the binding energies are larger than the experimental values and a bound state appears in the dineutron channel, which is not observed in experiment. Possible sources of systematic error in this calculation are discussed.Comment: 30 pages, 18 figures. Systematic errors are reestimated, and four figures are adde

Bound states of multi-nucleon channels in N_f=2+1 lattice QCD

We calculate the energies for multi-nucleon ground states with the nuclear mass number less than or equal to 4 in 2+1 flavor QCD at the lattice spacing of a = 0.09 fm employing a relatively heavy quark mass corresponding to m_pi = 0.51 GeV. We investigate the volume dependence of the energy shift of the ground state and the state of free nucleons to distinguish a bound state from attractive scattering states. From the investigation we conclude that ^4He, ^3He, deuteron and dineutron are bound at m_pi = 0.51 GeV. We compare their binding energies with those in our quenched studies and also with some recent investigations.Comment: 7 pages, 4 figures. Proceedings of the 30th International Symposium on Lattice Field Theory, June 24 - 29, 2012, Cairns, Australi