Masato Kimura

Masato Kimura
Kanazawa University | Kindai · Faculty of Mathematics and Physics, Institute of Science and Engineering,

About

82
Publications
7,618
Reads
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358
Citations
Additional affiliations
April 2011 - March 2013
Kyushu University
Position
  • Professor (Associate)
April 2007 - March 2008
Czech Technical University in Prague
Position
  • Researcher
November 2001 - March 2011
Kyushu University
Position
  • Professor (Associate)

Publications

Publications (82)
Article
Full-text available
The authors were not aware of typographical errors made in the writing phase, and, hence, wish to make the following corrections to the original paper [...]
Article
Full-text available
It is often observed that thermal stress enhances crack propagation in materials, and, conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot and study its energy dissipation property. The Biot thermoelasticity model takes into account the f...
Article
Full-text available
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraints. First, we provide a notion of weak solution, inspired by the theory of curves of maximal slope, and then we prove existence (employing time-discrete schemes with different implementations of the constraint), uniqueness, power and energy identity, comp...
Preprint
Full-text available
It is often observed that thermal stress enhances crack propagation in materials, and conversely, crack propagation can contribute to temperature shifts in materials. In this study, we first consider the thermoelasticity model proposed by M. A. Biot (1956) and study its energy dissipation property. The Biot thermoelasticity model takes into account...
Article
Full-text available
Three new industrial applications of irreversible phase field models for crack growth are presented in this study. The phase field model for irreversible crack growth in an elastic material is derived as a unidirectional gradient flow of the Francfort–Marigo energy with the Ambrosio–Tortorelli regularization, which is known to be consistent with cl...
Article
Full-text available
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain \(\Omega \). Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics into a coupled system of second order ODEs with discontinuous right-hand side. The main contribution of this...
Preprint
Full-text available
A Lagrangian-type numerical scheme called the "comoving mesh method" or CMM is developed for numerically solving certain classes of moving boundary problems which include, for example, the classical Hele-Shaw flow problem and the well-known mean curvature flow problem. This finite element scheme exploits the idea that the normal velocity field of t...
Preprint
Full-text available
We prove a universal approximation property (UAP) for a class of ODENet and a class of ResNet, which are used in many deep learning algorithms. 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 width $n+m$ with any non-polynomial continuous activation function...
Preprint
We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $\Omega$. Collisions with the boundary are described as purely elastic collisions. This turns the description of the particle dynamics into a coupled system of second order ODEs with discontinuous right-hand side. The main contribution of this pap...
Chapter
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it...
Preprint
We consider a large class of interacting particle systems in 1D described by an energy whose interaction potential is singular and non-local. This class covers Riesz gases (in particular, log gases) and applications to plasticity and numerical integration. While it is well established that the minimisers of such interaction energies converge to a c...
Book
This book focuses on mathematical theory and numerical simulation related to various areas of continuum mechanics, such as fracture mechanics, (visco)elasticity, optimal shape design, modelling of earthquakes and Tsunami waves, material structure, interface dynamics and complex systems. Written by leading researchers from the fields of applied math...
Article
Nonlinear magnetization dynamics excited by spin-transfer effect with feedback current is studied both numerically and analytically. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates the positive Lyapunov exponent for a certain range of the feedback rate, which identifies the existence of chaos in a nanostructured ferromagn...
Preprint
Nonlinear magnetization dynamics excited by spin-transfer effect with feedback current is studied both numerically and analytically. The numerical simulation of the Landau-Lifshitz-Gilbert equation indicates the positive Lyapunov exponent for a certain range of the feedback rate, which identifies the existence of chaos in a nanostructured ferromagn...
Preprint
In this paper, we shall prove a LS-inequality (Lewy-Stampacchia type inequality) for the fractional Laplacian on a bounded domain $\Omega$ in $\mathbb{R}^{n}$. In \cite{SV13}, Servadei and Valdinoci also proved a version of LS-inequality for regional fractional Laplacian $(-\Delta)_{R}^{s}$, that is, the restriction of $\mathbb{R}^{n}$-fractional L...
Article
This article aims to contribute to the understanding of the curvature flow of curves in a higher-dimensional space. Evolution of curves in R^m by their curvature is compared to the motion of hypersurfaces with constrained normal velocity. The special case of shrinking hyperspheres is further analyzed both theoretically and numerically by means of a...
Preprint
Full-text available
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and then existence (employing time-discrete schemes with different "implementations" of the constraint), uniquenes...
Preprint
Full-text available
We consider the gradient flow of a quadratic non-autonomous energy under monotonicity constraint in time and natural regularity assumptions. We provide first a notion of weak solution, inspired by the theory of curves of maximal slope, and then existence (employing time-discrete schemes with different "implementations" of the constraint), uniquenes...
Article
Full-text available
We introduce a new Lagrange–Galerkin scheme for computing fluid flow through porous media. The method of volume averaging of the velocity and pressure deviation in the pore is employed to derive the macroscopic mass and momentum conservation in the porous medium in which this technique was established by Hsu and Cheng. We derive the Lagrange–Galerk...
Article
We generalize pressure boundary conditions of an \(\varepsilon \)-Stokes problem. Our \(\varepsilon \)-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter \(\varepsilon >0\). For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191, 2...
Article
We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and random matrix theory. Our main result shows that both...
Article
Full-text available
An extended Maxwell viscoelastic model with a relaxation parameter is studied from mathematical and numerical points of view. It is shown that the model has a gradient flow property with respect to a viscoelastic energy. Based on the gradient flow structure, a structure-preserving time-discrete model is proposed and existence of a unique solution i...
Preprint
Full-text available
Energy estimates of the shallow water equations (SWEs) with a transmission boundary condition are studied theoretically and numerically. In the theoretical part, using a suitable energy, we begin with deriving an equality which implies an energy estimate of the SWEs with the Dirich-let and the slip boundary conditions. For the SWEs with a transmiss...
Preprint
Full-text available
Energy estimates of the shallow water equations (SWEs) with a transmission boundary condition are studied theoretically and numerically. In the theoretical part, using a suitable energy, we begin with deriving an equality which implies an energy estimate of the SWEs with the Dirichlet and the slip boundary conditions. For the SWEs with a transmissi...
Preprint
Full-text available
We study a mathematical model for deformation of glued elastic bodies in 2D or 3D, which is a linear elasticity system with adhesive force on the glued surface. We reveal a variational structure of the model and prove the unique existence of a weak solution based on it. Furthermore, we also consider an alternating iteration method and show that it...
Preprint
Full-text available
We generalize pressure boundary conditions of an $\varepsilon$-Stokes problem. Our $\varepsilon$-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter $\varepsilon>0$. For the Dirichlet boundary condition, it is proven in K. Matsui and A. Muntean (2018) that the solution for the $\v...
Preprint
Full-text available
We consider the dynamics of particle systems where the particles are confined by impenetrable barriers to a bounded, possibly non-convex domain $\Omega$. When particles hit the boundary, we consider an instant change in velocity, which turns the systems describing the particle dynamics into an ODE with discontinuous right-hand side. Other than the...
Presentation
Evaluation of improvement in press control machine
Conference Paper
Full-text available
In engineering area, investigation of shape effect in elastic materials was very important. It can lead changing elasticity and surface energy, and also increase of crack propagation in the material. A two-dimensional mathematical model was developed to investigation of elasticity and surface energy in elastic material by Adaptive Finite Element Me...
Book
As the sequel to the proceedings of the International Conference of Continuum Mechanics Focusing on Singularities (CoMFoS15), the proceedings of CoMFoS16 present further advances and new topics in mathematical theory and numerical simulations related to various aspects of continuum mechanics. These include fracture mechanics, shape optimization, mo...
Chapter
Full-text available
The importance of the optimal shape design has been increasing in the present industrial design due to the request to make their production more efficient.
Article
We consider both the minimisation of a class of nonlocal interaction energies over non-negative measures with unit mass and a class of singular integral equations of the first kind of Fredholm type. Our setting covers applications to dislocation pile-ups, contact problems, fracture mechanics and 1D log gases. Our main result shows that both the min...
Book
This book focuses on mathematical theory and numerical simulation related to various aspects of continuum mechanics, such as fracture mechanics, elasticity, plasticity, pattern dynamics, inverse problems, optimal shape design, material design, and disaster estimation related to earthquakes. Because these problems have become more important in engin...
Article
Two examples of extention of crack growth model with phase field approach are derived. A crack growth model for visco-elastic material is introduced from exctended free energy which add effect of Maxwell fluid. Another model with effect of H-embrittlement is introduced by adding some equations. Ability of phase field model which can describe crack...
Poster
Full-text available
Changing temperature drastically can be destructive electronic devices. This poster research has objective such as: modeling crack propagation in thermal effect
Chapter
We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as a gradient flow for the sum of a regularized Allen-Cahn type energy in the slip plane and an elastic energy i...
Article
We consider a threshold-type algorithm for curvature-dependent motions of hypersurfaces. This algorithm was numerically studied by [27], [9] and [35], where they used the signed distance function. It is also regarded as a variant of the Bence-Merriman-Osher algorithm for the mean curvature flow ( [4]). In this paper we prove the convergence of our...
Article
Full-text available
We simulate straight crack propagation using idea from the classical Grith theory and Francfort-Marigo energy. According to the energy-theoretic model proposed by Francfort and Marigo, propagation of a straight crack is described by means of sum of elastic and surface energies. We modify the Francfort-Marigo model by replacing the global minimum by...
Article
Full-text available
We take a shape optimization approach to solve a free boundary problem of the Poisson equation numerically. A numerical method called traction method invented by one of the authors are applied. We begin by changing the free boundary problem to a shape optimization problem and define a least square functional as a cost function. Then shape derivativ...
Article
Full-text available
This paper is concerned with the uniqueness, existence, comparison principle and long-time behavior of solutions to the initial-boundary value problem for a unidirectional diffusion equation. The unidirectional evolution often appears in Damage Mechanics due to the strong irreversibility of crack propagation or damage evolution. The existence of so...
Article
We study spring-block systems which are equivalent to the P1-finite element methods for the linear elliptic partial differential equation of second order and for the equations of linear elasticity. Each derived spring-block system is consistent with the original partial differential equation, since it is discretized by P1-FEM. Symmetry and positive...
Chapter
We consider a phase field model for crack propagation in an elastic body. The model is derived as an irreversible gradient flow of the Francfort-Marigo energy with the Ambrosio-Tortorelli regularization and is consistent to the classical Griffith theory. Some numerical examples computed by adaptive mesh finite element method are presented.
Article
We study a polygonal analogue of the Hele-Shaw moving boundary problem 1 with surface tension based on a framework of polygonal motion proposed by Beneš et al. [5]. A key idea is to introduce a polygonal Dirichlet-to-Neumann map. We study variational properties of the polygonal Dirichlet to-Neumann map and show that our polygonal Hele-Shaw problem...
Article
The differentiability of a potential energy with respect to variable domains in a nonlinear problem is shown as the differentiability of a functional with respect to a parameter using convex analysis in Banach spaces, where the parameter stands for mappings from a reference domain. We apply the abstract result to the differentiability of the p-Lapl...
Article
Full-text available
The paper presents the results of numerical solution of the Allen-Cahn equation with a non-local term. This equation originally mentioned by J. Rubinstein and P. Sternberg [IMA J. Appl. Math. 48, No. 3, 249–264 (1992; Zbl 0763.35051)] is related to the mean-curvature flow with the constraint of constant volume enclosed by the evolving curve. We stu...
Article
We consider a discrete version of phase field model based on the spring-mass system, and show some relation to the DEM type crack propagation model. We also briefly introduce our phase field model with two or three dimensional linear elasticity that is based on the Francfort-Marigo type energy8) with the Ambrosio-Tortorelli regularization1). We sho...
Article
Full-text available
A phase field model for anti-plane shear crack growth in two dimensional isotropic elastic material is proposed. We introduce a phase field to represent the shape of the crack with a regulaxization parameter epsilon > 0 and we approximate the Francfort-Marigo type energy using the idea of Ambrosio and Tortorelli. The phase field model is derived as...
Chapter
Full-text available
The text provides an elementary introduction to mathematical foundation of shape derivative of potential energy and provides several ap- plications of the theory to some elliptic problems. Among many important applications the text focus on the energy release rate in fracture mechanics.
Chapter
Full-text available
The text provides a record of an intensive lecture course on the moving boundary problems. Keeping the applications to moving boundary problems in R^2 or R^3 in mind, the text systematically constructs the math- ematical foundations of hypersurfaces and moving hypersurfaces in R^m for m ≥ 2. Main basic concepts treated in the text are differential...
Article
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We study general mathematical framework for variation of potential energy with respect to domain deformation. It enables rigorous derivation of the integral formulas for the energy release rate in crack problems. Applying a technique of the shape sensitivity analysis, we formulate the shape derivative of potential energy as a variational problem wi...
Article
Full-text available
We study polygonal analogues of several moving boundary problems and their time discretization which preserves the constant area speed property. We establish various polygonal analogues of geometric formulas for moving boundaries and make use of the geometric formulas for our numerical scheme and its analysis of general constant area speed motion o...
Article
Full-text available
General area-preserving motion of polygonal curves is formulated as a system of ODEs. Solution polygonal curves belong to a prescribed polygonal class, which is similar to the admissible class used in the crystalline curvature flow. The ODEs are discretized implicitly in time keeping a given constant area speed while solution polygonal curves keep...
Article
Full-text available
We study an asymptotic behaviour of the principal eigenvalue for an elliptic operator with large advection which is given by a gradient of a potential function. It is shown that the principal eigenvalue decays exponentially under the velocity potential well condition as the parameter tends to infinity. We reveal that the depth of the potential well...
Article
Full-text available
This article deals with flow of plane curves driven by the curvature and external force. We make use of such a geometric flow for the purpose of image segmentation. A parametric model for evolving curves with uniform and curvature adjusted redistribution of grid points will be described and compared.
Article
The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance c...
Article
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This study is concerned with the asymptotic behaviour of the first eiginvalue of a Sturm-Liouville problem with a large drifting term. The magnitude of the drift is controled by a parameter p. Under a suitable condition, it is known that the first eigenvalue λ(p) > 0 tends to zero exponentially if p → ∞. We prove a precise behaviour of such exponen...
Article
In this paper, we shall discuss about the large-time behavior of solutions of an Allen–Cahn type equation generated by the total variation functional with constraints. In the one-dimensional case, the large time behavior of solutions has been studied in (Nonlinear Anal. 46 (2001) 435; Funkcial. Ekvac. 44 (2001) 119; J. Math. Anal. 47 (2001) 3195)....
Article
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A level set method based on the piecewise linear finite element approximation of the signed distance function is proposed for several moving boundary problems. As a prototype of our level set method, we consider a level set discretization of the mean curvature flow problem and give an effective algorithm guaranteed by the maximum principle. Two-pha...
Article
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We consider a geometric minimizing problem which arises in time discretization of the Mullins-Sekerka problem. Some new geometric estimate for the shape of the global minimizer is presented. We also show that such a geometric estimate is useful to improve standard norm estimates. 1 Geometric variational problem We suppose thatOmega is a bounded Lip...
Article
A moving boundary problem for one phase Hele-Shaw flow with surface tension is considered. The fluid domain is unbounded and its boundary has an infinite length, and a finite number of suction (or injection) points are given. This is a mathematical model of the ‘fingering phenomenon’. We prove the existence of a unique solution locally in time.
Article
A new numerical scheme of the boundary tracking method for moving boundary problems is proposed. A key point of the scheme is to avoid concentration of tracking points on the moving boundary, and a convergence theorem is proved for the curve shortening problem. Some numerical examples for the curve shortening problem and the Hele-Shaw problem by th...
Article
We apply the boundary element methods (BEM) to the interior Dirichlet problem of the two dimensional Laplace equation, and its discretization is carried out with the collocation method using piecewise linear elements. In this paper, some precise asymptotic estimations for the discretization matrix (where denotes the division number) are investigate...
Article
An accurate finite difference scheme for the flow by curvature in 2 is presented, and its convergence theorem is stated. The numerical scheme has a correction term which is effective in locating points uniformly and the effect prevents the computation from breaking down.
Chapter
Recently, various types of numerical computation for crack problems are carried out by using the finite element methods (e.g. [1]) and the boundary element methods (e.g. [2]). According to linear elastic fracture mechanics, the displacement and the stress up to a crack tip have singularities of O(r 1/2) and O(r −1/2) respectively, where r denotes t...
Article
Full-text available
A quantitative study of the validity of an adaptive mesh finite element method is presented for pattern dynamics in several reaction-diffusion systems. As numerical tests, we consider an activator-inhibitor system and a resource-consumer system (the Gray-Scott model) in 2D and 3D. They produces several types of patterns. In order to make clear the...
Article
An abstract framework of autonomous moving boundary value problems is considered using the concept of surface operators. We introduce shape derivatives of surface operators to describe their natural linearization. A systematic study of the shape derivative is made and several applications of this new technique are discussed.
Article
Full-text available
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality 九州大学21世紀COEプログラム「機能数理学の構築と展開」 We study the effectivity of an adaptive mesh algorithm with triangular finite elements for two or three dimensional pattern dynamics appearing in several reactiondiffusion systems. The aim of this paper is to investiga...
Article
Kyushu University 21st Century COE Program Development of Dynamic Mathematics with High Functionality 九州大学21世紀COEプログラム「機能数理学の構築と展開」 We study general mathematical framework for rigorous derivation of the energy release rate which plays an important role in the theory of fracture mechanics. Applying a technique of the shape sensitivity analysis, we f...