arXiv subjects

Ken Yamamoto

Publications and source records attributed to Ken Yamamoto.

35 records · Page 2Linked to original sources

arXiv2017

Initiation of the Worthington jet on the droplet impact

Deformation of liquid droplets by impingement induces Worthington jet in certain range of the impact velocity. Although the growth of the jet as well as its tip velocity is predicted from similar cases to the droplet impact, the mechanism of the jet generation is yet to be understood. In this study, high-speed visualization of the droplet impact on a superhydrophobic surface was conducted to understand the initiation of the jet generated by a collapse of an air cavity. Water droplets whose diameter are 2.0 mm and 3.0 mm were generated and the Weber number of the droplet was varied in a range of 2 to 20. The jet velocity was measured from the captured images and it was found that it has a peak at the Weber number equals to approximately seven. The resulting jet velocity at the peak was approximately 15 folds higher than the impact velocity. Moreover, we observed that surface waves were generated by a collision of the droplet on the solid and the waves induced an oscillation of the droplet cap as they propagate from the solid-liquid contact line to the top portion of the droplet. Furthermore, we found the phase of the oscillation is related to the Weber number and it influences the jet velocity significantly, as it determines the initial condition of the jet generation.

physics.flu-dyn↗

arXiv2017

Central limit theorem for the Horton-Strahler bifurcation ratio of general branch order

The Horton-Strahler ordering method, originating in hydrology, formulates the hierarchical structure of branching patterns using a quantity called the bifurcation ratio. The main result of this paper is the central limit theorem for bifurcation ratio of general branch order. This is a generalized form of the central limit theorem for the lowest bifurcation ratio, which was previously proved. Some useful relations are also derived in the proofs of the main theorems.

math.PR↗

arXiv2016

Analysis of a stochastic model for bacterial growth and the lognormality of the cell-size distribution

This paper theoretically analyzes a phenomenological stochastic model for bacterial growth. This model comprises cell division and the linear growth of cells, where growth rates and cell cycles are drawn from lognormal distributions. We find that the cell size is expressed as a sum of independent lognormal variables. We show numerically that the quality of the lognormal approximation greatly depends on the distributions of the growth rate and cell cycle. Furthermore, we show that actual parameters of the growth rate and cell cycle take values that give a good lognormal approximation; thus, the experimental cell-size distribution is in good agreement with a lognormal distribution.

physics.bio-ph↗

arXiv2015

Phase Diagram of Collective Motion of Bacterial Cells in a Shallow Circular Pool

The collective motion of bacterial cells in a shallow circular pool is systematically studied using the bacterial species $Bacillus$ $subtilis$. The ratio of cell length to pool diameter (i.e., the reduced cell length) ranges from 0.06 to 0.43 in our experiments. Bacterial cells in a circular pool show various types of collective motion depending on the cell density in the pool and the reduced cell length. The motion is classified into six types, which we call random motion, turbulent motion, one-way rotational motion, two-way rotational motion, random oscillatory motion, and ordered oscillatory motion. Two critical values of reduced cell lengths are evaluated, at which drastic changes in collective motion are induced. A phase diagram is proposed in which the six phases are arranged.

physics.bio-ph↗

arXiv2015

A non-intrusive measurement technique applying CARS for concentration measurement in a gas mixing flow

Coherent anti-Stokes Raman scattering (CARS) microscope system was built and applied to a non-intrusive gas concentration measurement of a mixing flow in a millimeter-scale channel. Carbon dioxide and nitrogen were chosen as test fluids and CARS signals from the fluids were generated by adjusting the wavelengths of the Pump and the Stokes beams. The generated CARS signals, whose wavelengths are different from those of the Pump and the Stokes beams, were captured by an EM-CCD camera after filtering out the excitation beams. A calibration experiment was performed in order to confirm the applicability of the built-up CARS system by measuring the intensity of the CARS signal from known concentrations of the samples. After confirming that the measured CARS intensity was proportional to the second power of the concentrations as was theoretically predicted, the CARS intensities in the gas mixing flow channel were measured. Ten different measurement points were set and concentrations of both carbon dioxide and nitrogen at each point were obtained. Consequently, it was observed that the mixing of two fluids progressed as the measurement point moved downstream. The results show the applicability of CARS to the non-intrusive concentration measurement of gas flows without any preprocess such as gas absorption into liquid or solid.

physics.flu-dyn↗

arXiv2015

Obtaining superhydrophobicity using commercial razor blades

Because the superhydrophobic characteristic appears by forming a composite surface consisting of solid and air underneath the droplets, a large number of rough surfaces that can trap air have been fabricated. Recently, the air trapping on materials whose equilibrium contact angles are less than 90 degrees was achieved by fabricating proper structures that lead energetic stability at the condition. Whereas these methods were proposed under the assumption of the static and equilibrium conditions, we take a dynamic and non-equilibrium approach in this study through droplet deposition and droplet impact experiments. By employing test surfaces that consist of commercially available stainless steel razor blades, we show the pinning effect brings the apparent water contact angle of approximately 160 degrees on a "hydrophilic" substrate. We call this state the "non-equilibrium Cassie state" and give theoretical explanations. Furthermore, the dynamic characteristics of the droplet impact on these surfaces are discussed in a range of moderate Weber numbers.

physics.flu-dyn↗

arXiv2015

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.

physics.soc-ph↗

arXiv2014

A simple view of the heavy-tailed sales distributions and application to the box-office grosses of U.S. movies

This letter treats of the power-law distribution of the sales of items. We propose a simple stochastic model which expresses a selling process of an item. This model produces a stationary power-law distribution, whose power-law exponent is analytically derived. Next we compare the model with an actual data set of movie income. We focus on the return on investment (ROI), defined as the gross income divided by the production budget. We confirm that the power-law exponent of ROI distribution can be estimated from the ratios of income between two adjoining weeks, as predicted by the model analysis. Moreover, exponential decay of weekly income is observed both in the model and actual income. Therefore, the proposed model is simple enough, but it can quantitatively describe the power-law sales distribution.

physics.soc-ph↗

arXiv2014

Fractal patterns related to dividing coins

The present paper formulates and solves a problem of dividing coins. The basic form of the problem seeks the set of the possible ways of dividing coins of face values 1,2,4,8,... between three people. We show that this set possesses a nested structure like the Sierpinski-gasket fractal. For a set of coins with face values power of r, the number of layer of the gasket becomes r. A higher-dimensional Sierpinski gasket is obtained if the number of people is more than three. In addition to Sierpinski-type fractals, the Cantor set is also obtained in dividing an incomplete coin set between two people.

math.CO↗

arXiv2014

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.

physics.soc-ph↗

arXiv2014

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.

physics.data-an↗

arXiv2013

Hypergeometric solution to a gambler's ruin problem with a nonzero halting probability

This paper treats of a kind of a gambler's ruin problem, which seeks the probability that a random walker first hits the origin at a certain time. In addition to a usual random walk which hops either rightwards or leftwards, the present paper introduces the `halt' that the walker does not hop with a certain probability. The solution to the problem can be obtained exactly using a Gauss hypergeometric function. The moment generating function of the duration is also calculated, and a calculation technique of the moments is developed. The author derives the long-time behavior of the ruin probability, which exhibits power-law behavior if the walker hops to the right and left with equal probability.

math-ph↗

arXiv2011

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.

cond-mat.stat-mech↗

arXiv2011

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.

cs.DM↗

arXiv2009

Topological self-similarity on the random binary-tree model

Asymptotic analysis on some statistical properties of the random binary-tree model is developed. We quantify a hierarchical structure of branching patterns based on the Horton-Strahler analysis. We introduce a transformation of a binary tree, and derive a recursive equation about branch orders. As an application of the analysis, topological self-similarity and its generalization is proved in an asymptotic sense. Also, some important examples are presented.

math-ph↗

arXiv2009

Numerical Approach to Central Limit Theorem for Bifurcation Ratio of Random Binary Tree

A central limit theorem for binary tree is numerically examined. Two types of central limit theorem for higher-order branches are formulated. A topological structure of a binary tree is expressed by a binary sequence, and the Horton-Strahler indices are calculated by using the sequence. By fitting the Gaussian distribution function to our numerical data, the values of variances are determined and written in simple forms.

physics.data-an↗

arXiv2009

Network of two-Chinese-character compound words in Japanese language

Some statistical properties of a network of two-Chinese-character compound words in Japanese language are reported. In this network, a node represents a Chinese character and an edge represents a two-Chinese-character compound word. It is found that this network has properties of "small-world" and "scale-free." A network formed by only Chinese characters for common use ({\it joyo-kanji} in Japanese), which is regarded as a subclass of the original network, also has small-world property. However, a degree distribution of the network exhibits no clear power law. In order to reproduce disappearance of the power-law property, a model for a selecting process of the Chinese characters for common use is proposed.

cs.CL↗