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Masato Kimura

Publications and source records attributed to Masato Kimura.

35 records · Page 2Linked to original sources
arXiv2021

Comoving mesh method for certain classes of moving boundary problems

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 the moving boundary can be extended throughout the entire domain of definition of the problem using, for instance, the Laplace operator. Then, the boundary as well as the finite element mesh of the domain are easily updated at every time step by moving the nodal points along this velocity field. The feasibility of the method, highlighting its practicality, is illustrated through various numerical experiments. Also, in order to examine the accuracy of the proposed scheme, the experimental order of convergences between the numerical and manufactured solutions for these examples are also calculated.

math.NA↗
arXiv2021

Development of a high-light-yield liquid argon detector using tetraphenyl butadiene and silicon photomultiplier array

To increase the light yield of a liquid Ar (LAr) detector, we optimized the evaporation technique of tetraphenyl butadiene (TPB) on the detector surface and tested the operability of a silicon photomultiplier (SiPM), namely, the multi-pixel photon counter with through-silicon-via (TSV-MPPC, Hamamatsu Photonics K.K.) at LAr temperature. TPB converts the LAr scintillations (vacuum ultraviolet light) to visible light, which can be detected by high-sensitivity photosensors. Because the light yield depends on the deposition mass of TPB on the inner surface of the detector, we constructed a well-controlled TPB evaporator to ensure reproducibility and measured the TPB deposition mass using a quartz crystal microbalance sensor. After optimizing the deposition mass of TPB (30 $μg/cm^2$ on the photosensor window and 40 $μg/cm^2$ on the detector wall), the light yield was 12.8 $\pm$ 0.3 p.e./keVee using PMTs with a quantum efficiency of approximately 30% for TPB-converted light. We also tested the low-temperature tolerance of TSV-MPPC, which has a high photon-detection efficiency, in the LAr environment. The TSV-MPPC detected the LAr scintillations converted by TPB with a photon-detection efficiency exceeding 50%.

physics.ins-det↗
arXiv2020

Particle dynamics with elastic collision at the boundary: existence and partial uniqueness of solutions

We consider the dynamics of point particles which are confined to a bounded, possibly nonconvex domain $Ω$. 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 paper is to develop a precise solution concept for this particle system, and to prove existence of solutions. In this proof we construct a solution by passing to the limit in an auxiliary problem based on the Yosida approximation. In addition to existence of solutions, we establish a partial uniqueness theorem, and show by means of a counterexample that uniqueness of solutions cannot hold in general.

math.AP↗
arXiv2020

Quantitative estimate of the continuum approximations of interacting particle systems in one dimension

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 approximation theory of functions. While it is well established that the minimisers of such interaction energies converge to a certain particle density profile as the number of particles tends to infinity, any bound on the rate of this convergence is only known in special cases by means of quantitative estimates. The main result of this paper extends these quantitative estimates to a large class of interaction energies by a different proof. The proof relies on one-dimensional features such as the convexity of the interaction potential and the ordering of the particles. The main novelty of the proof is the treatment of the singularity of the interaction potential by means of a carefully chosen renormalisation.

math.AP↗
arXiv2019

Chaos in nanomagnet via feedback current

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 ferromagnet. Transient behavior from chaotic to steady oscillation is also observed in another range of the feedback parameter. An analytical theory is also developed, which indicates the appearance of multiple attractors in a phase space due to the feedback current. An instantaneous imbalance between the spin-transfer torque and damping torque causes a transition between the attractors, and results in the complex dynamics.

cond-mat.mes-hall↗
arXiv2019

Weak solutions for gradient flows under monotonicity constraints

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), uniqueness, power and energy identity, comparison principle and continuous dependence. As a byproduct, we show that the energy identity gives a selection criterion for the (non-unique) evolutions obtained by other notions of solutions. We finally show that, for autonomous energies, the solutions obtained with the monotonicity constraint actually coincide with those obtained with a fixed obstacle, given by the initial datum.

math.AP↗
arXiv2019

Theoretical and numerical studies for energy estimates of the shallow water equations with a transmission boundary condition

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 transmission boundary condition, an inequality for the energy estimate is proved under some assumptions to be satisfied in practical computation. Hence, it is recognized that the transmission boundary condition is reasonable in the sense that the inequality holds true. In the numerical part, based on the theoretical results, the energy estimate of the SWEs with a transmission boundary condition is confirmed numerically by a finite difference method (FDM). The choice of a positive constant c0 used in the transmission boundary condition is investigated additionally. Furthermore, we present numerical results by a Lagrange-Galerkin scheme, which are similar to those by the FDM. From the numerical results, it is found that the transmission boundary condition works well numerically.

math.NA↗
arXiv2019

Deformation problem for glued elastic bodies and an alternative iteration method

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 is nothing but an alternating minimizing method of the total energy. The convergence of a monolithic formulation and the alternating iteration method are numerically studied with the finite element method.

math.NA↗
arXiv2018

Analysis of a projection method for the Stokes problem using an $\varepsilon$-Stokes approach

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 $\varepsilon$-Stokes problem converges to the one for the Stokes problem as $\varepsilon$ tends to 0, and to the one for the pressure-Poisson problem as $\varepsilon$ tends to $\infty$. Here, we extend these results to the Neumann and mixed boundary conditions. We also establish error estimates in suitable norms between the solutions to the $\varepsilon$-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in $\varepsilon$. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the $\varepsilon$-Stokes problem has a nice asymptotic structure.

math.AP↗
arXiv2018

The gradient flow structure of an extended Maxwell viscoelastic model and a structure-preserving finite element scheme

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 is proved. Moreover, a structure-preserving P1/P0 finite element scheme is presented and its stability in the sense of energy is shown by using its discrete gradient flow structure. As typical viscoelastic phenomena, two-dimensional numerical examples by the proposed scheme for a creep deformation and a stress relaxation are shown and the effects of the relaxation parameter are investigated.

math.NA↗
arXiv2016

An energy-consistent model of dislocation dynamics in an elastic body

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 in the elastic body. The obtained model becomes a 3D- 2D bulk-surface system and naturally includes the Peach-Koehler force term and the notion of dislocation core. We also derive a 2D-1D bulk-surface system for a straight screw dislocation and give some numerical examples for it.

math.NA↗
arXiv2015

Unidirectional evolution equations of diffusion type

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 solutions is proved in an L^2-framework by introducing a peculiar discretization of the unidirectional diffusion equation by means of variational inequities of obstacle type and by developing a regularity theory for such variational inequalities. The novel discretization argument will be also applied to prove the comparison principle as well as to investigate the long-time behavior of solutions.

math.AP↗
arXiv2010

Polaronic behavior of photoelectron spectra of Fe3O4 revealed by both hard X-ray and extremely low energy photons

Hard X-ray and extremely low energy bulk-sensitive photoelectron spectroscopy has been performed in the temperature range of 100-330 K for Fe3O4. In the high temperature phase just above the Verwey transition, the intensity at the Fermi level (EF) is still negligible, but it increases gradually with further increasing the temperature (250 K, 330 K) in consistence with the temperature dependence of the conductivity. The spectral behaviors near EF with temperature are well explained by the model, which takes the polaron effect into account.

cond-mat.str-el↗
arXiv2008

Shape derivative of potential energy and energy release rate in fracture mechanics

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 with a parameter. Key tools of our abstract theory are a new parameter variational principle and the classical implicit function theorem in Banach spaces.

math.AP↗
arXiv2008

Analytical and numerical aspects on motion of polygonal curves with constant area speed

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 belonging to the polygonal class.

math.NA↗