arXiv subjects

Masato Kimura

Publications and source records attributed to Masato Kimura.

At least 19 recordsLinked to original sources

arXiv2026

Muon acceleration at J-PARC

Muon acceleration is a key technology for producing low-emittance muon beams over a wide energy range. Various acceleration schemes have been proposed for applications ranging from low-energy $\mu$SR and precision particle-physics measurements to neutrino factories and muon colliders. Experimental demonstrations of muon acceleration, however, have so far been limited. At J-PARC, a positive-muon accelerator based on the production and acceleration of ultraslow muons is being developed, and in 2024 the first RF acceleration of positive muons was demonstrated. In this review, we provide a brief overview of muon-acceleration methods and related experiments, and then review the acceleration method, current status, and future prospects at J-PARC.

physics.acc-ph↗

arXiv2026

Existence and regularity of minimizers for a variational problem of species population density

We study a variational problem motivated by models of species population density in a nonhomogeneous environment. We first analyze local minimizers and the structure of the saturated region (where the population attains its maximal density) from a free boundary perspective. By comparing the original problem with a radially symmetric minimization problem and studying its properties, we then establish the existence and structure of a global solution. Analytic examples of radially symmetric solutions and numerical simulations illustrate the theoretical results and provide insight into spatial saturation patterns in population models. We further highlight an unresolved question regarding the quasiconcavity of minimizers.

math.AP↗

arXiv2025

Mathematical and numerical study of symmetry and positivity of the tensor-valued spring constant defined from P1-FEM for two- and three-dimensional linear elasticity

In this study, we consider a spring-block system that approximates a $d$-dimensional linear elastic body, where $d=2$ or $d=3$. We derive a $d\times d$ matrix as the spring constant using the P1 finite element method with a triangular mesh for the linear elasticity equations. We mathematically analyze the symmetry and positive-definiteness of the spring constant. Even if we assume full symmetry of the elasticity tensor, the symmetry of the matrix obtained as the spring constant is not trivial. However, we have succeeded in proving this in a unified manner for both 2D and 3D cases. This is an alternative proof for the 2D case in Notsu-Kimura (2014) and is a new result for the 3D case. We provide a necessary and sufficient condition for the spring constant to be positive-definite in the case of an isotropic elasticity tensor, along with a sufficient condition in terms of mesh regularity and the Poisson ratio. These theoretical results are supported by several numerical experiments. The positive-definiteness of the spring constant derived from the finite element method plays a vital role in fracture simulations of elastic bodies using the spring-block system.

math.NA↗

arXiv2025

Threshold dynamics in time-delay systems: polynomial $\beta$-control in a pressing process and connections to blow-up

This paper addresses a press control problem in straightening machines with small time delays due to system communication. To handle this, we propose a generalized $\beta$-control method, which replaces conventional linear velocity control with a polynomial of degree $\beta \ge 1$. The resulting model is a delay differential equation (DDE), for which we derive basic properties through nondimensionalization and analysis. Numerical experiments suggest the existence of a threshold initial velocity separating overshoot and non-overshoot dynamics, which we formulate as a conjecture. Based on this, we design a control algorithm under velocity constraints and confirm its effectiveness. We also highlight a connection between threshold behavior and finite-time blow-up in DDEs. This study provides a practical control strategy and contributes new insights into threshold dynamics and blow-up phenomena in delay systems.

math.OC↗

arXiv2025

Energy-consistent dynamic fracture phase field models: unilateral constraints and finite element simulations

Phase field models have emerged as a powerful and flexible framework for simulating complex interface-driven phenomena across a wide range of scientific and engineering applications. In fracture mechanics, the phase field approach--formulated as a gradient flow of the Griffith fracture energy with Ambrosio-Tortorelli regularization--has gained significant attention for its ability to capture complex crack topologies. In this study, we propose a dynamic fracture phase field model (DF-PFM) based on the elastodynamic wave equation. We further extend this framework by incorporating a unilateral contact condition, yielding a refined model suitable for simulating fault rupture under high pressure. For both models, we formally derive energy dissipation identities under mixed boundary conditions, providing insights into the energetic structure of the formulations. To validate the proposed approach, we conduct numerical experiments using linear implicit time discretization and finite element methods. Our simulations demonstrate that the unilateral contact condition is essential for accurately capturing shear-dominated crack propagation and preventing non-physical interpenetration, especially under high-compression loading scenarios relevant to seismic faulting.

math.NA↗

arXiv2025

Mass conservation and gelation for the Smoluchowski coagulation equation: a generalized moment approach

The Smoluchowski coagulation equation (SCE) is a population balance model that describes the time evolution of cluster size distributions resulting from particle aggregation. Although it is formally a mass-conserving system, solutions may exhibit a gelation phenomenon-a sudden loss of mass-when the coagulation kernel grows superlinearly. In this paper, we rigorously analyze mass conservation and gelation for weak solutions to the SCE with inhomogeneous coagulation kernels. By introducing a generalized moment framework, we derive sharp sufficient conditions for both mass conservation and gelation, expressed in terms of the initial data and the properties of the coagulation kernel.

math.AP↗

arXiv2024

Universal approximation property of ODENet and ResNet with a single activation function

We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We consider dynamical systems with vector fields given by a single composition of the activation function and an affine mapping, which is the most common choice of the ODENet or ResNet vector field in actual machine learning systems. We show that such an ODENet and ResNet with a restricted vector field can uniformly approximate ODENet with a general vector field.

cs.LG↗

arXiv2024

On the well-posedness of a Hele-Shaw-like system resulting from an inverse geometry problem formulated through a shape optimization setting

The purpose of this study is twofold. First, we revisit a shape optimization reformulation of a prototypical shape inverse problem and briefly propose a simple yet efficient numerical approach for solving the corresponding minimization problem. Second, we examine the existence, uniqueness, and continuous dependence of a classical solution to a Hele-Shaw-like system, which is derived from the continuous setting of a numerical discretization of the shape optimization reformulation for the shape inverse problem. The analysis is based on the methods developed by G. I. Bizhanova and V. A. Solonnikov in ``On Free Boundary Problems for Second Order Parabolic Equations" (Algebra Anal. 12 (6) (2000) 98-139), and by V. A. Solonnikov in ``Lectures on Evolution Free Boundary Problems: Classical Solutions" (Lect. Notes Math., Springer, 2003, pp. 123-175).

math.AP↗

arXiv2024

Anisotropic extended Burgers model, its relaxation tensor and properties of the associated Boltzmann viscoelastic system

We provide a new method for constructing the anisotropic relaxation tensor and proving its exponential decay property for the extended Burgers model (abbreviated by EBM). The EBM is an important viscoelasticity model in rheology, and used in Earth and planetary sciences. Upon having this tensor, the EBM can be converted to a Boltzmann-type viscoelastic system of equations (abbreviated by BVS). Historically, the relaxation tensor for the EBM is derived by solving the constitutive equation using the Laplace transform. (We refer to this approach by the L-method.) Since inverting the inverse Laplace transform needs a partial fractions expansion, the L-method needs to assume that the EBM elasticity tensors satisfy a commutivity condition. The new method not only avoids this condition but also enables obtaining several important properties of the relaxation tensor, including its positivity, smoothness with respect to the time variable, its exponential decay property together with its derivative, and its causality. Furthermore, we show that the BVS converted from the EBM has the exponential decay property. That is, any solution for its initial boundary value problem with homogeneous boundary data and source decays exponentially as time tends to infinity.

math.AP↗

arXiv2024

Two-step minimization approach to an $L^\infty$-constrained variational problem with a generalized potential

We study a variational problem on $H^1({\mathbb R})$ under an $L^\infty$-constraint related to Sobolev-type inequalities for a class of generalized potentials, including $L^p$-potentials, non-positive potentials, and signed Radon measures. We establish various essential tools for this variational problem, including the decomposition principle, the comparison principle, and the perturbation theorem, which are the basis of the two-step minimization method. As for their applications, we present precise results for minimizers of minimization problems, such as the study of potentials of Dirac's delta measure type and the analysis of trapped modes in potential wells.

math.AP↗

arXiv2024

Two-step minimization approach to Sobolev-type inequality with bounded potential in 1D

We present a new method to determine the best constant of the Sobolev-type embedding in one dimension with a norm including a bounded inhomogeneous potential term. This problem is closely connected to the Green function of the Schrödinger operator with inhomogeneous potential. A minimization problem of a Rayleigh-type quotient in a Sobolev space gives the best constant of the Sobolev embedding. We decompose the minimization problem into two sub-minimization problems and show that the Green function provides the minimizer of the first minimization problem. Then, it enables us to derive a new precise estimate of the best constant and function for inhomogeneous bounded potential cases. As applications, we give some examples of the inhomogeneous potential whose best constant and function of the Sobolev-type embedding are explicitly determined.

math.AP↗

arXiv2023

What is the physical origin of the gradient flow structure of variational fracture models?

We investigate a physical characterization of the gradient flow structure of variational fracture models for brittle materials: a Griffith-type fracture model and an irreversible fracture phase field model. We derive the Griffith-type fracture model by assuming that the fracture energy in Griffith's theory is an increasing function of the crack tip velocity. Such a velocity dependence of the fracture energy is typically observed in polymers. We also prove an energy dissipation identity of the Griffith-type fracture model, in other words, its gradient flow structure. On the other hand, the irreversible fracture phase field model is derived as a unidirectional gradient flow of a regularized total energy with a small time relaxation parameter based on the variational fracture theory by Francfort and Marigo (1998) and a mathematical space regularization proposed by Ambrosio and Tortorelli (1992). We have considered the time relaxation parameter a mathematical approximation parameter, which we should choose as small as possible. In this research, however, we reveal the physical origin of the gradient flow structure of the fracture phase field model and show that the small time relaxation parameter is characterized as the rate of velocity dependence of the fracture energy. It is verified by comparing the energy dissipation properties of those two models and by analyzing a traveling wave solution of the irreversible fracture phase field model.

math.AP↗

arXiv2023

Resolvent Estimates for Viscoelastic Systems of Extended Maxwell Type and their Applications

In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent estimates for the system of equations for the anisotropic, extended Maxwell model, abbreviated as the EMM, and its marginal realization which includes an inertia term; special attention is paid to the introduction of augmented variables. This leads to the augmented system that will also be referred to as the "original" system. A reduced system is then formed which encodes essentially the EMM; it is a closed system with respect to the particle velocity and the difference between the elastic and viscous strains. Based on resolvent estimates, it is shown that the original and reduced systems generate $C_0$-groups and the reduced system generates a $C_0$-semigroup of contraction. Naturally, the EMM can be written in integrodifferential form leading explicitly to relaxation and a viscoelastic integro-differential system. However, there is a difference between the original and integrodifferential systems, in general, with consequences for whether their solutions generate semigroups or not. Finally, an energy estimate is obtained for the reduced system, and it is proven that its solutions decay exponentially as time tends to infinity. The limiting amplitude principle follows readily from these two results.

math.AP↗

arXiv2023

Universal Approximation Properties for an ODENet and a ResNet: Mathematical Analysis and Numerical Experiments

We prove a universal approximation property (UAP) for a class of ODENet and a class of ResNet, which are simplified mathematical models for deep learning systems with skip connections. The UAP can be stated as follows. Let $n$ and $m$ be the dimension of input and output data, and assume $m\leq n$. Then we show that ODENet of width $n+m$ with any non-polynomial continuous activation function can approximate any continuous function on a compact subset on $\mathbb{R}^n$. We also show that ResNet has the same property as the depth tends to infinity. Furthermore, we derive the gradient of a loss function explicitly with respect to a certain tuning variable. We use this to construct a learning algorithm for ODENet. To demonstrate the usefulness of this algorithm, we apply it to a regression problem, a binary classification, and a multinomial classification in MNIST.

cs.LG↗

arXiv2023

A two-step Lagrange-Galerkin scheme for the shallow water equations with a transmission boundary condition and its application to the Bay of Bengal region. Part I: Flat bottom topography

This study presents a two-step Lagrange-Galerkin scheme for the shallow water equations with a transmission boundary condition (TBC). Firstly, the experimental order of convergence of the scheme is shown to see the second-order accuracy in time. Secondly, the effect of the TBC on a simple domain is discussed; the artificial reflections are kept from the Dirichlet boundaries and removed significantly from the transmission boundaries. Thirdly, the scheme is applied to a complex practical domain, i.e., the Bay of Bengal region, which is non-convex and includes islands. The effect of the TBC is discussed again for the complex domain; the artificial reflections are removed significantly from transmission boundaries, which are set on open sea boundaries. Based on the numerical results, it is revealed that the scheme has the following properties; (i) the same advantages of Lagrange-Galerkin methods (the CFL-free robustness for convection-dominated problems and the symmetry of the matrices for the system of linear equations); (ii) second-order accuracy in time; (iii) mass preservation of the function for the water level from the reference height (until the contact with the transmission boundaries of the wave); and (iv) no significant artificial reflection from the transmission boundaries. The numerical results by the scheme are presented in this paper for the flat bottom topography of the domain. In the next part of this work, Part II, the scheme will be applied to rapidly varying bottom surfaces and a real bottom topography of the Bay of Bengal region.

math.NA↗

arXiv2022

Reconstruction of multiple Compton scattering events in MeV gamma-ray Compton telescopes towards GRAMS: the physics-based probabilistic model

Aimed at progress in mega-electron volt (MeV) gamma-ray astronomy, which has not yet been well-explored, Compton telescope missions with a variety of detector concepts have been proposed so far. One of the key techniques for these future missions is an event reconstruction algorithm that is able to determine the scattering orders of multiple Compton scattering events and to identify events in which gamma rays escape from the detectors before they deposit all of their energies. We revisit previous event reconstruction methods and propose a modified algorithm based on a probabilistic method. First, we present a general formalism of the probabilistic model of Compton scattering describing physical interactions inside the detector and measurement processes. Then, we also introduce several approximations in the calculation of the probability functions for efficient computation. For validation, the developed algorithm has been applied to simulation data of a Compton telescope using a liquid argon time projection chamber, which is a new type of Compton telescope proposed for the GRAMS project. We have confirmed that it works successfully for up to 8-hit events, including correction of incoming gamma-ray energies for escape events. The proposed algorithm can be used for next-generation MeV gamma-ray missions featured by large-volume detectors, e.g., GRAMS.

astro-ph.IM↗

arXiv2021

Measurement of emission spectrum for gaseous argon electroluminescence in visible light region from 300 to 600 nm

A double-phase Ar detector can efficiently identify particles and reconstruct their positions. However, the properties of electroluminescence (EL) for secondary light emission in the gas phase are not fully understood. Earlier studies have explained the EL process using an ordinary EL mechanism because of an Ar excimer; however, this mechanism does not predict the emission of visible light (VL). Recent measurements have demonstrated VL components in Ar gas EL, to explain which a new mechanism called neutral bremsstrahlung (NBrS) was proposed. In this study, we investigated gaseous Ar EL in the VL region from 300 to 600 nm at room temperature and normal pressure using a gaseous time projection chamber (TPC). The secondary emission light from the TPC luminescence region was dispersed using a spectrometer. The observed spectrum was interpreted using the ordinary EL and NBrS models, and the effect of nitrogen impurities is discussed herein.

physics.ins-det↗

arXiv2021

The Lewy-Stampacchia Inequality for the Fractional Laplacian and Its Application to Anomalous Unidirectional Diffusion Equations

In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posedness of fractional-type anomalous unidirectional diffusion equations. This study is an extension of the work by Akagi-Kimura (2019) for the standard Laplacian. However, there exist several difficulties due to the nonlocal feature of the fractional Laplacian. We overcome those difficulties employing the Caffarelli-Silvestre extension of the fractional Laplacian.

math.AP↗