arXiv subjects

Ken Yamamoto

Publications and source records attributed to Ken Yamamoto.

At least 19 recordsLinked to original sources

arXiv2026

Analysis of pairs in a generalized deck of playing cards

In this study, we analyze the number of pairs (i.e., two cards of the same rank) in a set of cards randomly selected from a deck of playing cards. While the standard deck of playing cards comprises 52 cards excluding the joker with 4 suits and 13 ranks, our analysis considers a generalized deck where the numbers of suits and ranks can be set arbitrarily. We derive the exact formulas for the mean and variance of the number of pairs in a given number of cards randomly selected from this generalized deck, expressed using the Gauss hypergeometric function. Moreover, we derive the asymptotic behavior of the mean and variance as the number of ranks tends to infinity.

math.GM↗

arXiv2026

Theoretical analysis of the maximum range of a projectile released from a pendulum

The motion of a projectile released from a simple pendulum is analyzed, with particular emphasis on investigating the optimal release angle that maximizes the horizontal range and the corresponding maximum range. This system serves as a simplified model of the Tarzan jump problem. Using simple analytical methods, the optimal release angle is shown to be characterized by a cubic equation and to increase with the initial velocity. In addition, asymptotic expressions for both the optimal angle and maximum range are derived in the limits of low and high initial velocity.

math-ph↗

arXiv2026

Quantifying defensive pressure on the ball carrier in soccer based on minimum arrival time

Defensive pressure on the ball carrier is a fundamental component of soccer tactics. Existing pressure measures often involve additional modeling assumptions, which may reduce interpretability. In this study, we quantify defensive pressure as the opponent minimum arrival time to the ball-carrier location, computed from a physics-based motion model. Using synchronized event and tracking data from all 306 matches in the top division of the Japan Professional Football League during the 2023 season, we analyze the statistical characteristics and temporal evolution of this quantity during ball-possession intervals. The results show that the opponent minimum arrival time tends to decrease during possession and to increase again at the start of the next possession after ball release. We also find that possessions starting under stronger defensive pressure tend to yield smaller ball progression, and that, for intentional open-play passes, possessions ending under stronger pressure are more likely to be lost. These findings indicate that minimum arrival time provides an interpretable and physically grounded measure of immediate defensive pressure on the ball carrier. The proposed framework provides a simple and interpretable baseline for quantifying pressing dynamics from tracking data.

physics.soc-ph↗

arXiv2025

P\'olya urn model for analysis of football passes

This study analyzes pass networks in football (soccer) using a stochastic model known as the P\'olya urn. By focusing on preferential selection, it theoretically demonstrates that the time evolution of networks can be characterized by a single parameter. Building on this result, a data analysis method is proposed and applied to a large-scale public dataset of professional football matches. The statistical properties of the preferential-selection parameter are examined, demonstrating its correlation with pass accuracy and with mean pass difficulty. This method is applicable to various evolving networks.

physics.soc-ph↗

arXiv2025

Geometric Brownian motion with random observation time as generalization of the double Pareto distribution

We study the probability distribution of the value of geometric Brownian motion at the stochastic observation time. It is known that the exponentially distributed observation time yields the distribution called the double Pareto distribution, and this study aims to generalize this distribution. First, we provide a calculation formula for the moment of the observed value of geometric Brownian motion using the moment-generating function of the observation time distribution. Next, the probability density of the observed value of geometric Brownian motion is exactly derived under the observation time following the generalized inverse Gaussian distribution. This result includes cases where the observation time follows the gamma, inverse gamma, and inverse Gaussian distributions, and can be regarded as a generalization of the double Pareto distribution.

math.PR↗

arXiv2024

On exceptionality of dimension three in terms of lattice angles

In this study, we investigate the lattice angle, which is defined as the angle between two vectors whose components are integers. We focus on the set of angles between a fixed integer vector and other integer vectors. For non-three-dimensional lattices, we proved that this set contains all lattice angles, irrespective of the fixed vector choice. In contrast, for the three-dimensional lattice, we proved that this set of angles cannot cover all lattice angles, for any fixed vector. Thus, only the three-dimensional lattice is an exception. We further provide the condition for a given three-dimensional integer vector to intersect another integer vector at a given angle, which involves a number-theoretic property of the squared norm of the given vector and the squared tangent of the given angle.

math.NT↗

arXiv2024

Complete corrected formula for generating functions of the hypergeometric distribution

The hypergeometric distribution is a popular distribution, whose properties have been extensively investigated. Generating functions of this distribution, such as the probability-generating function, the moment-generating function, and the characteristic function, are known to involve the Gauss hypergeometric function. We elucidate that the existing formula of generating functions is incomplete and provide the corrected formula. In view of the utility and applicability of the hypergeometric distribution, the exact and correct foundation is crucially important.

math.PR↗

arXiv2024

Exact solution of the propagation of ON-OFF signals by dispersive waves

The propagation of ON-OFF signals with dispersive waves is examined in this study. An integral-form exact solution for a simple ON-OFF switching event is derived, which holds for any dispersion relation. The integral can be exactly calculated for two types of dispersion relations. Further, the analysis of these solutions shows that the ON-OFF signal propagates with the group velocity and that the boundary thickness of the signal increases with time, typically at a rate proportional to the square root of time, owing to dispersion. Additionally, an approximate solution for a general dispersion relation is derived, and a for a higher-complexity ON-OFF switching pattern is constructed.

math-ph↗

arXiv2024

Drop impact on wet granular beds: water-content effects on the cratering

Drop impact events on wet granular bed show rich variety by changing the substrate composition. We observe the drop impact onto dry/wet granular substrates with different grain size (50-400 μm) and water content (0-22 vol %). Although the impactor condition is fixed (impact velocity: 4.0 m/s, water drop radius: 1.8 mm), the experiment reveals that the post-impact behaviors of both impactor and target are strongly affected by the substrate composition. We sort these behaviors into several phases regarding liquid splashing and crater shapes left after the event. As these phases show relevance each other, we measure the mechanical characteristics of the substrates and find that the onset of splashing and particle ejection are explained by a fracture of the substrate. Furthermore, we discuss several timescales of the event to understand more detailed phase separations. Consequently, we find that the splashing phase and the crater shape are determined by a competition of the timescales of impact, penetration, and contact.

cond-mat.soft↗

arXiv2024

Deformation of power law in the double Pareto distribution using uniformly distributed observation time

The double Pareto distribution is a heavy-tailed distribution with a power-law tail, that is generated via geometric Brownian motion with an exponentially distributed observation time. In this study, we examine a modified model wherein the exponential distribution of the observation time is replaced with a continuous uniform distribution. The probability density, complementary cumulative distribution, and moments of this model are exactly calculated. Furthermore, the validity of the analytical calculations is discussed in comparison with numerical simulations of stochastic processes.

cond-mat.stat-mech↗

arXiv2023

Energy dissipation of a sphere rolling up a granular slope: slip and deformation of granular surface

We experimentally investigate the dynamics of a sphere rolling up a granular slope. During the rolling-up motion, the sphere experiences slipping and penetration (groove formation) on the surface of the granular layer. The former relates to the stuck motion of the rolling sphere, and the latter causes energy dissipation due to the deformation of the granular surface. To characterize these phenomena, we measured the motion of a sphere rolling up a granular slope of angle $α$. The initial velocity $v_0$, initial angular velocity $ω_0$, angle of slope $α$, and density of the sphere $ρ_s$ were varied. As a result, the penetration depth can be scaled solely by the density ratio between the sphere and granular layer. By considering the rotational equation of motion, we estimate the friction due to the slips. Besides, by considering energy conservation, we define and estimate the friction due to groove formation. Moreover, the translational friction is proportional to the penetration depth. Using these results, we can quantitatively predict the sphere's motion including stuck behavior.

cond-mat.soft↗

arXiv2023

Theory and data analysis of player and team ball possession time in football

In this study, the stochastic properties of player and team ball possession times in professional football matches are examined. Data analysis shows that player possession time follows a gamma distribution and the player count of a team possession event follows a mixture of two geometric distributions. We propose a formula for expressing team possession time in terms of player possession time and player count in a team's possession, verifying its validity through data analysis. Furthermore, we calculate an approximate form of the distribution of team possession time, and study its asymptotic property.

physics.soc-ph↗

arXiv2023

Analysis of size distributions of fictional characters: from Pokémon to Godzilla

In this letter, the size (height and weight) of fictional characters in animations, superhero series, movies, and other media is studied. We find that the distributions of character height and weight approximately follow lognormal distributions in common to five selected works. We propose a mechanism governing this lognormal behavior based on the principle of maximum entropy and the Weber-Fechner law. Moreover, we provide a comparison to the size distributions of real animals. Although the size distributions of fictional characters and real animals are both lognormal, the distributions are essentially different, particularly in the scaling between height and weight.

physics.soc-ph↗

arXiv2023

Azimuthal rotation induced by the Marangoni force makes small Leidenfrost droplets move in random zig-zag directions

We observed the zig-zag motion of small Leidenfrost water droplets (radii less than 0.6 mm) on a hot, flat substrate. To understand this motion, we conducted an experiment using a glass capillary to fix a droplet at its edge and control the droplet height. Thermographic and interferometric observations reveal that the droplets rotated both vertically and azimuthally. Based on the characteristic frequency of the azimuthal rotation depending on the substrate temperature and droplet height, we developed a semi-empirical model considering unsteady Marangoni convection and its relaxation. We confirmed that our model can predict the characteristic time of the zig-zag motion of unfixed Leidenfrost droplets.

physics.flu-dyn↗

arXiv2022

Lubrication effects on droplet manipulation by electrowetting-on-dielectric (EWOD)

Electrowetting has a potential to realize stand-alone point-of-care (POC) devices. Here we report droplet-migration characteristics on oil-infused electrowetting-on-dielectric (EWOD) substrates. We prepare sparse micropillars to retain the oil layer in order to exploit the layer as a lubricating film. A physical model of the droplet velocity is developed, and effects of the lubrication, the oil viscosity, the droplet volume, and the thickness of solid and liquid dielectric layers are discussed. It is found that the droplet velocity is scaled as square of E, which differs from a relationship of cube of E for droplets sliding down on liquid-infused surfaces by gravity. Furthermore, our device achieves droplet velocity of 1 mm/s at the applied voltage of 15 V. The velocity is approximately tenfold as high as the same condition (applied voltage and oil viscosity) on porous-structure-based liquid-infused surfaces. The achieved high velocity is explained by a lubrication-flow effect.

physics.flu-dyn↗

arXiv2022

Analysis and application of multiplicative stochastic process with a sample-dependent lower bound

A multiplicative stochastic process with the lower bound lognormally distributed is investigated. For the process, the model is constructed, and its distribution function (involving four parameters) and the related statistical properties are derived. By adjusting the parameters, it is confirmed that the theoretical distribution is consistent with empirical distributions of some real data.

physics.data-an↗

arXiv2019

Large deviation theorem for branches of the random binary tree in the Horton-Strahler analysis

The Horton-Strahler analysis is a graph-theoretic method to measure the bifurcation complexity of branching patterns, by defining a number called the order to each branch. The main result of this paper is a large deviation theorem for the number of branches of each order in a random binary tree. The rate function associated with a large deviation cannot be derived in a closed form; instead, asymptotic forms of the rate function are given.

math.PR↗

arXiv2018

Concentration-adjustable micromixer using droplet injection into a microchannel

A novel micromixing technique that exploit a thrust of droplets into the mixing interface is developed. The technique enhances the mixing by injecting immiscible droplets in a mixing channel and the methodology enables a control of the mixing level simply by changing the droplet injection frequency. We experimentally characterize the mixing performance with various droplet injection frequencies, channel geometries, and diffusion coefficients. Consequently, it is revealed that the mixing level increases with the injection frequency, the droplet-diameter-to-channel-width ratio, and the diffusion coefficient. Moreover, the mixing level is found to be a linear function of the droplet volume fraction in the mixing section. The results suggest that the developed technique can produce a large amount of sample solution whose concentration is arbitrary and precisely controllable with a simple and stable operation.

physics.flu-dyn↗