arXiv subjects

Kei Matsushima

Publications and source records attributed to Kei Matsushima.

17 recordsLinked to original sources

arXiv2026

Topology optimization of isotropic viscoelastic microstructures based on periodic homogenization

Mitigating low-frequency noise is particularly challenging due to its limited natural attenuation. This study aims to design viscoelastic composite microstructures that achieve both low acoustic reflection and high internal damping by simultaneously enhancing their effective acoustic impedance and attenuation characteristics. Using complex-valued periodic homogenization theory and density-based topology optimization, viscoelastic and impedance-matching materials are designed within a highly symmetric unit cell to manipulate these isotropic properties. Numerical results show that the optimized isotropic design robustly outperforms its constituent materials and simple anisotropic laminate structures, exhibiting performance that is stable across a wide frequency band, independent of orientation, and stable across various structural scales. This demonstrates the potential of microstructural engineering for effective low-frequency noise mitigation.

physics.app-ph↗

arXiv2026

A frequency-stable Nyström method for two-dimensional diffraction by periodic gratings at and near Wood anomalies

We propose and analyze a frequency-stable boundary integral equation method for scalar wave scattering by periodic diffraction gratings in two dimensions. The standard quasi-periodic Green function is singular as a function of the frequency at Wood anomaly frequencies, which prevents a direct frequency-uniform error analysis of conventional integral equation discretizations. Our method is based on a modified quasi-periodic Green function obtained by subtracting the singular Rayleigh modes and introducing a finite-dimensional correction that restores the radiation condition. The resulting combined-field boundary integral equation is shown to be uniquely solvable whenever the underlying diffraction problem is uniquely solvable, and the corresponding scattered field depends continuously on the frequency, including at Wood anomalies. We then construct a fully discrete Nyström scheme using an Ewald representation of the Green function and a quadrature rule adapted to the logarithmic singularity of the kernel. For compact frequency intervals that may contain Wood anomaly frequencies, we prove unique solvability of the discrete system for sufficiently large discretization and truncation parameters and establish a frequency-uniform error estimate and bound on the condition number. Numerical examples illustrate the convergence of the scheme and its stability across Wood anomaly frequencies.

math.NA↗

arXiv2025

Efficient LU factorization exploiting direct-indirect Burton-Miller equation for Helmholtz transmission problems

This paper proposes a direct-indirect mixed Burton-Miller boundary integral equation for solving Helmholtz scattering problems with transmissive scatterers. The proposed formulation has three unknowns, one more than the number of unknowns for the ordinary formulation. However, we can construct efficient numerical solvers based on LU factorization by exploiting the sparse alignment of the boundary integral operators of the proposed formulation. Numerical examples demonstrate that the direct solver based on the proposed formulation is approximately 40% faster than the ordinary formulation when the LU-factorization-based solver is used. In addition, the proposed formulation is applied to a fast direct solver employing LU factorization in its algorithm. In the application to the fast direct solver, the proxy method with a weak admissibility low-rank approximation is developed. The speedup achieved using the proposed formulation is also shown to be effective in finding nonlinear eigenvalues, which are related to the uniqueness of the solution, in boundary value problems. Furthermore, the well-posedness of the proposed boundary integral equation is established for scatterers with boundaries of class $C^2$, using the mapping property of boundary integral operators in Hölder space.

math.NA↗

arXiv2025

Non-Bloch band theory for time-modulated discrete mechanical systems

This study establishes a non-Bloch band theory for time-modulated discrete mechanical systems. We consider simple mass-spring chains whose stiffness is periodically modulated in time. Using the temporal Floquet theory, the system is characterized by linear algebraic equations in terms of Fourier coefficients. This allows us to employ a standard linear eigenvalue analysis. Unlike non-modulated linear systems, the time modulation makes the coefficient matrix non-Hermitian, which gives rise to, for example, parametric resonance, non-reciprocal wave transmission, and non-Hermitian skin effects. In particular, we study finite-length chains consisting of spatially periodic mass-spring units and show that the standard Bloch band theory is not valid for estimating their eigenvalue distribution. To remedy this, we propose a non-Bloch band theory based on a generalized Brillouin zone. The proposed theory is verified by some numerical experiments.

physics.class-ph↗

arXiv2025

Approximation in an optimal design problem governed by the heat equation

This paper studies a two-material optimal design problem for the time-averaged duality pairing between a (possibly time-dependent) heat source and the weak solution of an initial-boundary value problem for the heat equation with a two-material diffusion coefficient, under a volume constraint. In general, such optimal designs are not guaranteed to exist, and geometric constraints such as the perimeter are required. As an approximation of the problem with an additional perimeter constraint, a material representation based on a level set function, together with a perturbation of the Dirichlet energy, is employed. It is then shown that optimal level set functions exist for the perturbation problem, and the corresponding minimum value converges to that of the elliptic case, thereby elucidating the long-time behavior. Furthermore, two-material domains satisfying this property are also constructed via the nonlinear diffusion-based level set method. In particular, the asymptotic behavior with respect to the perturbation parameter is clarified, and the validity of the approximation is established.

math.AP↗

arXiv2025

Exceptional points and defective resonances in an acoustic scattering system with sound-hard obstacles

This paper is concerned with non-Hermitian degeneracy and exceptional points associated with resonances in an acoustic scattering problem with sound-hard obstacles. The aim is to find non-Hermitian degenerate (defective) resonances using numerical methods. To this end, we characterize resonances of the scattering problem as eigenvalues of a holomorphic integral operator-valued function. This allows us to define defective resonances and associated exceptional points based on the geometric and algebraic multiplicities. Based on the theory on holomorphic Fredholm operator-valued functions, we show fractional-order sensitivity of defective resonances with respect to operator perturbation. This property is particularly important in physics and associated with intriguing phenomena, e.g., enhanced sensing and dissipation. A defective resonance is sought based on the perturbation analysis and Nyström discretization of the boundary integral equation. Numerical evidence of the existence of a defective resonance is provided. The numerical results combined with theoretical analysis provide a new insight into novel concepts in non-Hermitian physics.

math-ph↗

arXiv2025

Injectivity of boundary integral operator in direct-indirect mixed Burton-Miller equation for wave scattering problems with transmissive circular inclusion

This study proves that the injectivity condition for the integral operator of the direct-indirect mixed Burton-Miller (BM) boundary integral equation (BIE) for Helmholtz transmission problems is identical to that for the ordinary BM BIE for Helmholtz transmission problems with a transmissive circular inclusion. Although some numerical methods based on the direct-indirect mixed BM BIE can be computed faster than the ordinary BM BIE, its well-posedness has been unclear. This study resolves a part of the well-posedness, namely the injectivity of the integral operator with a transmissive circular inclusion.

math.AP↗

arXiv2024

Observation of exceptional points in a spherical open elastic system

Exceptional points (EPs) are spectral singularities in non-Hermitian systems where eigenvalues and their corresponding eigenstates coalesce simultaneously. In this study, we calculate scattering poles in an open spherical solid and propose a depth-first search-based method to identify EPs. Using the proposed method, we numerically identify multiple EPs in a parameter space and confirm the simultaneous degeneracy of scattering poles through numerical experiments. The proposed method and findings enable the exploration of applications in practical three-dimension models.

physics.class-ph↗

arXiv2024

Optimal design problem with thermal radiation

This paper is concerned with configurations of two-material thermal conductors that minimize the Dirichlet energy for steady-state diffusion equations with nonlinear boundary conditions described mainly by maximal monotone operators. To find such configurations, a homogenization theorem will be proved and applied to an existence theorem for minimizers of a relaxation problem whose minimum value is equivalent to an original design problem. As a typical example of nonlinear boundary conditions, thermal radiation boundary conditions will be the focus, and then the Fréchet derivative of the Dirichlet energy will be derived, which is used to estimate the minimum value. Since optimal configurations of the relaxation problem involve the so-called grayscale domains that do not make sense in general, a perimeter constraint problem via the positive part of the level set function will be introduced as an approximation problem to avoid such domains, and moreover, the existence theorem for minimizers of the perimeter constraint problem will be proved. In particular, it will also be proved that the limit of minimizers for the approximation problem becomes that of the relaxation problem in a specific case, and then candidates for minimizers of the approximation problem will be constructed by employing time-discrete versions of nonlinear diffusion equations. In this paper, it will be shown that optimized configurations deeply depend on force terms as a characteristic of nonlinear problems and will also be applied to real physical problems.

math.AP↗

arXiv2023

Orientation Optimization Based on Topological Derivatives in Cooperation with Multi-Material Topology Optimization Based on Extended Level Set Method

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the sensitivity of an objective function with respect to a topological change of anisotropic materials. The sensitivity is incorporated into a new gradient-based optimization algorithm. This method allows us to avoid local optima and seek a global optimal solution. We provide some numerical examples and verify the effectiveness of the proposed method.

cs.CE↗

arXiv2023

Two-Phase Topology Optimization for Metamaterials with Negative Poisson's Ratio

Although recent developments in 3D printing technology have made it possible to fabricate metamaterials with characteristic mechanical properties, it is not easy to fabricate complex shapes containing cavities. In this study, a composite structure comprising two types of materials without a cavity was optimized. Moreover, a mechanical metamaterial with a negative Poisson's ratio that can be fabricated using an additive manufacturing method was developed. First, a homogenization method that characterizes the properties of composite structures was briefly described. Then, an optimization problem to realize a negative Poisson's ratio was formulated, and a level set-based topology optimization method was proposed to solve the abovementioned problem. Next, three-dimensional numerical examples are presented to confirm the effectiveness of the proposed method, and the deformation behaviors of the optimized designs are numerically examined. Furthermore, a sample containing the optimized design with negative Poisson's ratio for the tensile test was fabricated using a 3D printer. We conducted some experiments to evaluate its mechanical performance.

physics.app-ph↗

arXiv2023

Level set-based multiscale topology optimization for a thermal cloak design problem using the homogenization method

Artificially designed composite materials consist of microstructures, that exhibit various thermal properties depending on their shapes, such as anisotropic thermal conductivity. One of the representative applications of such composite materials for thermal control is the thermal cloak. This study proposed a topology optimization method based on a level set method for a heat conduction problem to optimally design composite materials that achieve a thermal cloak. The homogenization method was introduced to evaluate its effective thermal conductivity coefficient. Then, we formulated a multiscale topology optimization method for the composite materials in the framework of the homogenization method, where the microstructures were optimized to minimize objective functions defined using the macroscopic temperature field. We presented examples of optimal structures in a two-dimensional problem and discussed the validity of the obtained structures.

cs.CE↗

arXiv2023

Exceptional points in cylindrical elastic media with radiation loss

Exceptional points (EPs) are singular points on a parameter space at which some eigenvalues (scattering poles) and their corresponding eigenmodes coalesce. This study shows the existence of second- and third-order EPs in cylindrical elastic systems with radiation loss. We consider multilayered cylindrical solids under the plane-strain condition placed in a background elastic or acoustic medium. Elastic and acoustic waves propagating in the background media are subject to the radiation loss. We optimize the radii and the material constants of the multilayered solids, such that some scattering poles coalesce on the complex frequency plane. Some numerical experiments are performed to confirm that the coalescence originates from EPs. We expect that this study provides a new approach for enhancing mechanical sensors.

physics.class-ph↗

arXiv2022

A topology optimization of open acoustic waveguides based on a scattering matrix method

This study presents a topology optimization scheme for realizing a bound state in the continuum along an open acoustic waveguide comprising a periodic array of elastic materials. First, we formulate the periodic problem as a system of linear algebraic equations using a scattering matrix associated with a single unit structure of the waveguide. The scattering matrix is numerically constructed using the boundary element method. Subsequently, we employ the Sakurai--Sugiura method to determine resonant frequencies and the Floquet wavenumbers by solving a nonlinear eigenvalue problem for the linear system. We design the shape and topology of the unit elastic material such that the periodic structure has a real resonant wavenumber at a given frequency by minimizing the imaginary part of the resonant wavenumber. The proposed topology optimization scheme is based on a level-set method with a novel topological derivative. We demonstrate a numerical example of the proposed topology optimization and show that it realizes a bound state in the continuum through some numerical experiments.

math.NA↗

arXiv2022

A coupled-mode theory for two-dimensional exterior Helmholtz problems based on the Neumann and Dirichlet normal mode expansion

This study proposes a novel coupled-mode theory for two-dimensional exterior Helmholtz problems. The proposed approach is based on the separation of the entire space R2 into a fictitious disk and its exterior. The disk is allocated in such a way that it comprises all the inhomogeneity; therefore, the exterior supports cylindrical waves with a continuous spectrum. For the interior, we expand an unknown wave field using normal modes that satisfy some auxiliary boundary conditions on the surface of the disk. For the interior expansion, we propose combining the Neumann and Dirichlet normal modes. We show that the proposed expansion sacrifices L2 orthogonality but significantly improve the convergence. Finally, we present some numerical verifications of the proposed coupled-mode theory.

math.NA↗

arXiv2019

Magnetic correlations in the pressure-induced superconductor CrAs investigated by $^{75}$As nuclear magnetic resonance

We report $^{75}$As-NMR results for CrAs under pressure, which shows superconductivity adjoining a helimagnetically ordered state. We successfully evaluated the Knight shift from the spectrum, which is strongly affected by the quadrupole interaction. The Knight shift shows the remarkable feature that the uniform spin susceptibility increases toward low temperatures in the paramagnetic state. This is in sharp contrast to CrAs at ambient pressure, and also to cuprates and Fe pnictides, where antiferromagnetic correlations are dominant. Superconductivity emerges in CrAs under unique magnetic correlations, which probably originate in the three-dimensional zigzag structure of its nonsymmorphic symmetry.

cond-mat.supr-con↗

arXiv2016

Using the Quantum Zeno Effect for Suppression of Decoherence

Projective measurements are an essential element of quantum mechanics. In most cases, they cause an irreversible change of the quantum system on which they act. However, measurements can also be used to stabilize quantum states from decay processes, which is known as the quantum Zeno effect (QZE). Here, we demonstrate this effect for the case of a superposition state of a nuclear spin qubit, using an ancilla to perform the measurement. As a result, the quantum state of the qubit is protected against dephasing without relying on an ensemble nature of NMR experiments. We also propose a scheme to protect an arbitrary state by using QZE.

quant-ph↗