arXiv subjects

Hirokazu Maruoka

Publications and source records attributed to Hirokazu Maruoka.

10 recordsLinked to original sources

arXiv2026

Why dimensional analysis works: general classification of self-similarity based on scale-invariance

In this work, we formulate self-similarity from the perspective of scale invariance, where a self-similar form is understood as the transformation of a function into a form invariant under scale transformations. By applying this formulation to physical parameters, which consist of numerical values and units, it is demonstrated that dimensional analysis works for physical problems because scale invariance is partially shared between units and physical parameters. This naturally leads to the distinction between similarity of the first kind and similarity of the second kind according to whether the scale functions induced by units and those associated with physical parameters are equivalent or not. Self-similar solutions of the second kind can be further classified according to whether the power exponents of the similarity parameters include functions of dimensionless numbers. This leads to the conclusion that there are three kinds of self-similar solutions. The present work provides a unified framework for understanding dimensional analysis and a universal classification of self-similarity in physical problems.

cond-mat.stat-mech↗

arXiv2025

Prigogine's temporalization of physics: two agnostic attitudes of physicists

In this paper, I aim to clarify the unconscious ideologies and attitudes held by physicists through Prigogine's work. Prigogine was an outstanding chemist and physicist who made significant contributions to the development of non-equilibrium thermodynamics. At the same time, he extended his ideas beyond physics into the humanities, engaging in an interdisciplinary exploration of scientific and philosophical thought. Due to his unique career, Prigogine's reception has been deeply divided. This study highlights his intellectual endeavors to formulate two distinct agnostic attitudes -- one held by dynamicists and the other by Prigogine himself. Building on this formulation, I examine how physics has been spatialized, drawing on the philosophy of Bergson. Finally, I explore an alternative path that Prigogine might have envisioned -- the temporalization of physics -- in a broader context to extend and revitalize his philosophy.

physics.hist-ph↗

arXiv2025

Early-stage impact dynamics in dense suspensions of millimeter-sized particles

This study investigates the phenomenon of the early-stage dynamics of impact-induced hardening in dense suspensions, where materials undergo solidification upon impact. While Stokes flow theory traditionally applies to suspensions with micrometer-sized particles due to their low Reynolds numbers, suspensions containing larger particles defy such idealizations. Our work focuses on the early-stage impact-induced hardening of suspensions containing millimeter-sized particles through dynamic impact experiments. We are particularly interested in the maximum drag force $F_\mathrm{max}$ acting on the projectile as a function of the impact speed $u_0$. We successfully conducted experiments using these suspensions and confirmed the relation $F_\mathrm{max}\sim u_0^{3/2}$ for relatively large $u_0$ as observed in the previous studies suspensions of micrometer-sized particles. Our findings reveal that the early-stage behaviors of millimeter-sized particle suspensions align well with predictions from the floating model, typically applicable under Stokes flow conditions. This research sheds light on the complex dynamics of impact-induced hardening in dense suspensions, particularly with larger particles, advancing our understanding beyond conventional micrometer-sized systems.

cond-mat.soft↗

arXiv2025

Droplet impact on elastic substrates: force scaling crossover

Droplet impacts are fundamental to fluid-structure interactions, shaping processes from erosion to bioprinting. While previous scaling laws have provided insights into droplet dynamics, force scaling laws remain insufficiently understood, particularly for soft substrates where both the droplet and substrate deform significantly. Here, we show that droplet impacts on elastic substrates exhibit a scaling crossover in maximum impact force, transitioning from inertial force scaling, typical for rigid substrates under high inertia, to Hertzian impact scaling, characteristic of rigid spheres on elastic substrates. Using high-speed photoelastic tomography, we captured high-resolution dynamic stress fields and identified a similarity parameter governing the interplay between droplet inertia, substrate elasticity, and deformation time scales. Our findings redefine how substrate properties influence impact forces, demonstrating that droplets under high inertia -- long thought to follow inertial force scaling -- can instead follow Hertzian impact scaling on soft substrates. This framework provides practical insights for designing soft, impact-resistant materials.

cond-mat.soft↗

arXiv2025

Data-driven discovery of self-similarity using neural networks

Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this paper, we present a novel neural network-based approach that discovers self-similarity directly from observed data, without presupposing any models. The presence of self-similar solutions in a physical problem signals that the governing law contains a function whose arguments are given by power-law monomials of physical parameters, which are characterized by power-law exponents. The basic idea is to enforce such particular forms structurally in a neural network in a parametrized way. We train the neural network model using the observed data, and when the training is successful, we can extract the power exponents that characterize scale-transformation symmetries of the physical problem. We demonstrate the effectiveness of our method with both synthetic and experimental data, validating its potential as a robust, model-independent tool for exploring self-similarity in complex systems.

cond-mat.soft↗

arXiv2023

The Relational Interpretations on soft matter as intermediate asymptoitcs

In this paper, it is demonstrated that there is a parallelism between the relational interpretation of Rovelli and the interpretation of soft matter based on intermediate asymptotics. The general interpretation of physics strongly assumes the duality of the observer and the world, and the uniqueness of the world though the relational interpretation suggested different conclusions: {\ it no properties, no interaction}, and {\ it facts are relative}. These conclusions are seemingly counterintuitive, though this work shows that similar conclusions are found in the interpretation of soft matter based on the concept of intermediate asymptotics. The interpretation of soft matter based on intermediate asymptotics also concludes that the properties are not determined without the scale. This is due to the conclusion of intermediate asymptotics that any formalization and its interpretation are localized by the scale. It is demonstrated that the similarity between the two interpretations originated from its monism of relations. This logical structure is also compared with the works in other disciplines. This work reports the insight that the relational interpretation can be a general and fundamental concept, not the one applicable to special cases.

physics.hist-ph↗

arXiv2023

A framework for crossover of scaling law as a self-similar solution : dynamical impact of viscoelastic board

In this paper, a new framework for crossover of scaling law is proposed: a crossover of scaling law can be described by a self-similar solution. A crossover emerges as a result of the interference from similarity parameters of the higher class of the self-similarity. This framework was verified for the dynamical impact of solid sphere onto a viscoelastic board. All the physical factors including the size of spheres and the impact of velocity are successfully summarized using primal dimensionless numbers which construct a self-similar solution of the second kind, which represents the balance between dynamical elements involved in the problem. The self-similar solution gives two different scaling laws by the perturbation method describing the crossover. These theoretical predictions are compared with experimental results to show good agreement. It was suggested that a hierarchical structure of similarity plays a fundamental role on crossover, which offers a fundamental insight to self-similarity in general.

cond-mat.soft↗

arXiv2019

Intermediate asymptotics on dynamical impact of solid sphere on mili-textured surface

Complex phenomena incorporating several physical properties are abundant while they are occasionally revealing the variation of power-law behavior depending on the scale. In this present work, the global scaling-behavior of dynamical impact of solid sphere onto elastic surface is described. Its fundamental dimensionless function was successfully obtained by applying the dimensional analysis combined with the solution by energy conservation complementally. It demonstrates that its power-law behavior is given by the competition between two power-law relations representing inertial and elastic property respectively which is strengthened by scale size of sphere. These factors are successfully summarized by the newly defined dimensionless parameters which gives two intermediate asymptotics in different scale range. These power-law behaviors given by the theoretical model were compared with experimental results, showing good agreement. This study supplies the insights to dimensional analysis and self-similarity in general.

cond-mat.soft↗

arXiv2018

Dynamics of a dry-rebounding drop: observations, simulations, and modeling

Dynamics of a dry-rebounding drop was studied experimentally, numerically, and theoretically. Experimental results were reproduced by our computational fluid dynamics simulations, from which time series of kinetic energy, potential energy, and surface energy were obtained. The time series of these energies quantitatively clarified the energy conversion and loss during the dry-rebound. These results were interpreted by using an imaginary spring model and a spherical harmonic analysis. The spring model explained the vertical deformation of the drop, however, could not completely explain the energy loss, the timings of the energy loss did not match. From a viewpoint of the spherical harmonic deformation of a drop, the deformation of the drop after the impact was found to be a combination of two vibrational motions. One of the two vibrational motions is an inertial motion derived from the free-fall and the another is a pressure-induced motion derived from a pressure surge due to the sudden stop of the bottom part of the drop at the impact. The existence of the pressure surge at the impact was confirmed in the simulated results. The pressure-induced motion resists the inertial motion and consequently dumps the kinetic energy of the drop.

physics.flu-dyn↗

arXiv2017

Shannon entropy analysis of the stretched exponential process : application to various shear induced multilamellar vesicles system

The stretched exponential function, $\exp[-(t/τ_{K})^β]$, describes various relaxation processes while it has been suggested that the power exponent, $β$ is derived from the non-uniformity of the process. In this paper, we attempted to estimate this non-uniformity by introducing Shannon entropy. Shannon entropy evaluates the average information contents of the distribution function, which reflects statistical homogeneity. We investigated the relaxation process of shear induced multilamellar system, which is described with the stretched exponential function. Three types of shear (constant, square, sine) at different frequencies are attempted in order to determine their effects on the relaxation process. We found that the Shannon entropy to which the first moment was introduced is maximized at $β~=~1$ : a single exponential. The Shannon entropy of sine shear experiments exhibited the frequency dependence. Thus it is interpreted that the increase of the intensity of shearing and the thermodynamic entropy are reflected on the Shannon entropy. We discussed the meaning of the maximum Shannon entropy in terms of various points of view, it was found that it corresponds to the diffusion process free from the restriction such as geometrical constraints. The constraints and the non-uniformity of process were successfully estimated by Shannon entropy. This study gives a new insight of entropy in general.

cond-mat.soft↗