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Hiroaki Nakamura

Publications and source records attributed to Hiroaki Nakamura.

At least 19 recordsLinked to original sources

Development of a 3D-CNN-based Prediction Model for Migration Barriers in Plasma-Wall Interactions

Understanding the long-term transport of hydrogen isotopes in plasma-facing materials, such as tungsten, is critical for the steady-state operation of magnetic confinement fusion reactors. However, dynamically updating the transition parameters for kinetic Monte Carlo (kMC) simulations as the atomic structure evolves under continuous plasma irradiation remains a severe computational bottleneck. Conventionally, calculating these migration barriers requires the iterative and computationally expensive Nudged Elastic Band (NEB) method. To overcome this limitation, this article presents a highly efficient surrogate model for predicting migration barriers using a three-dimensional Convolutional Neural Network (3D-CNN), establishing the final component necessary to realize on-the-fly molecular dynamics (MD) and kMC hybrid simulations. The proposed deep learning model takes a two-channel volumetric input, the local three-dimensional potential energy distribution and the voxelized spatial coordinates of the initial and final trapping sites, to directly output the migration barrier as a scalar value. Trained on a comprehensive dataset of tungsten-hydrogen configurations evaluated using the Embedded Atom Method (EAM) potential, the model demonstrated robust predictive accuracy, achieving a Mean Absolute Error (MAE) of 0.124 eV and a high coefficient of determination of 0.890. Furthermore, utilizing GPU acceleration, the inference time is reduced to approximately 2.7 milliseconds per barrier, achieving a speed-up ratio of over 23,000 compared to conventional NEB calculations. This extraordinary acceleration effectively resolves the computational barrier of transition rate evaluations, paving the way for large-scale, dynamic modeling of plasma-wall interactions.

physics.plasm-ph

Deep Learning-Accelerated Dynamic Kinetic Monte Carlo Simulation for Hydrogen Transport in Tungsten

In magnetic confinement fusion reactors, hydrogen plasma irradiation causes material saturation and recycling, where hydrogen released from the tungsten wall significantly impacts the peripheral plasma. Kinetic Monte Carlo (kMC) simulations are essential for investigating the dynamic balance between incident and emitted fluxes at the atomic scale. However, standard kMC frameworks are inadequate for handling realistic material complexities, such as polycrystalline structures and dynamic evolution under irradiation, being computationally bottlenecked by continuous transition parameter updates. Conventionally, evaluating migration barriers in disordered systems (e.g., grain boundaries) relies on computationally prohibitive on-the-fly atomistic calculations like the Nudged Elastic Band (NEB) method. Here, we present a deep learning-accelerated Dynamic kMC framework that eliminates this reliance. Our approach integrates a three-stage deep learning pipeline: a pix2pix model for predicting local 3D potential energy distributions, a U-Net for extracting hydrogen trapping sites, and a 3D-CNN for directly evaluating migration barriers. To achieve macroscopic timescales, we implemented a hierarchical spatial index combined with a differential local-update algorithm operating in O(1) complexity. This architecture restricts recalculations to the immediate vicinity of moving atoms, accelerating updates. Demonstrated on a large-scale realistic polycrystalline tungsten model, the framework successfully reproduces preferential hydrogen trapping along grain boundaries, bridging the gap between atomic-scale accuracy and macroscopic timescales for full-scale plasma-wall interaction simulations.

cond-mat.mtrl-sci

FDTD Simulation of O-X Mode Conversion Process in Non-uniform Magnetized Plasma

Electron Bernstein Waves (EBWs) are electrostatic waves than can propagate in overdense plasmas without density cutoff, making them suitable for high density plasma heating. Since EBWs cannot be directly launched from vacuum, mode conversion processes such as O-X-B conversion are required. In this study, the O-X mode conversion process is investigated using the finite difference time-domain (FDTD) method in a magnetized plasma with non-uniform density. In particular, the dependence of mode conversion characteristics on the incident angle of the injected wave is studied. The results show that an optimal incident angle exists at which the wave propagates without significant attenuation and strong electric field enhancement is observed near the upper hybrid resonance (UHR) layer. When the incident angle deviates from this optimal angle, an evanescent region appears, resulting in attenuation of the wave. These results demonstrate that angular optimization is essential for efficient wave propagation toward the UHR region and EBW excitation.

physics.plasm-ph

Scattering analysis of nano-scale chiral structures in optical vortex using Method of Moments

This paper presents a full 3D Method of Moments (MoM) simulation for analysis of scattering from nano-scale chiral ribbon structures under optical vortex illumination to aim to investigate electromagnetic mechanism of circular dichroism (CD) and optical vortex dichroism (VD). Both twist and helical nano-ribbons are modeled as dispersive materials scatterer. CD and VD are evaluated quantitatively by differences in scattering power. Numerical results demonstrate that angular momentum of optical light induces dichroic response effectively.

cond-mat.mtrl-sci

Landen's trilogarithm functional equation and $\ell$-adic Galois multiple polylogarithms

The Galois action on the pro-$\ell$ étale fundamental groupoid of the projective line minus three points with rational base points gives rise to a non-commutative formal power series in two variables with $\ell$-adic coefficients, called the $\ell$-adic Galois associator. In the present paper, we focus on how Landen's functional equation of trilogarithms and its $\ell$-adic Galois analog can be derived algebraically from the $S_3$-symmetry of the projective line minus three points. Twofold proofs of the functional equation will be presented, one is based on Zagier's tensor criterion devised in the framework of graded Lie algebras and the other is based on the chain rule for the associator power series. In the course of the second proof, we are led to investigate $\ell$-adic Galois multiple polylogarithms appearing as regular coefficients of the $\ell$-adic Galois associator. As an application, we show an $\ell$-adic Galois analog of Oi-Ueno's functional equation between $Li_{1,\dots,1,2}(1-z)$ and $Li_k(z)$'s $(k=1,2,...)$ .

math.NT

Consideration on relation between penetrated power and topological charge of millimeter-wave vortex in magnetized plasma

It was demonstrated that the vortex field of a hybrid mode can propagate in the mag-netized plasma region where plane waves are unable to propagate due to the cut-off condition. In this study, the dependence of the penetrated power of injected as millime-ter-wave vortices of the hybrid mode in magnetized plasma is analyzed using the Fi-nite-Difference Time-Domain (FDTD) method. The effect of the radius size of the cor-rugated waveguide on the penetrated power is described, revealing its significant con-tribution to reducing the deviation of topological charge in the hybrid mode. Further-more, it was found that the penetrated power of the vortex field in magnetized plasma strongly depends on the topological charge l and the deviation of topological charge

physics.plasm-ph

On a two-parameter family of tropical Edwards curves

In this paper, a certain two-parameter family of plane-embeddings of Edwards elliptic curve $E_a: x^2+y^2=a^2(1+x^2y^2)$ is introduced to provide explicitly computed tropical curves corresponding to degeneration in $a\to 1$. Applying the theta uniformization of $E_a$ with the method of ultradiscretization by Kajiwara-Kaneko-Nobe-Tsuda, we give a formula for the coordinate functions that traces the cycle part of the tropical elliptic curve. We also illustrate how one can recover the whole part of the tropical curve as a quotient of the Bruhat-Tits tree after Speyer's algebraic approach in smooth cases.

math.AG

Reactive Molecular Dynamics Simulation on DNA Double Strand Breaks Induced by Hydrogen Elimination

We propose a scar model to reproduce how double-strand breaks occur in the telomeric DNA damaged by the effect of the $β$-decay of tritium to helium. In this scar model, the two hydrogens bonded to the 5$^\prime$ carbon connecting the pent saccharides and phosphate are removed. Molecular dynamics simulations using the reactive force field are carried out for 10 cases for the telomeric DNA consisting of 16 base pairs (32 nucleotides). It results in double-strand breaks (DSBs) being observed for structures with more than 24 scars. For 16 scar cases, only single-strand breaks (SSB) are observed. Moreover, in the case of $\left\{16, 0 \right\}$ and $\left\{ 0, 16 \right\},$ where only one of the strands had scars, SSB occurs only in the scarred strand. Secondly, in the $\left\{16, 8 \right\}$ and $\left\{ 8, 16 \right\}$ cases, DSBs occurs. Therefore, we conclude that the following conditions are necessary for DSBs:(i) Scars must occur on both the L and R strands. (ii) A large number of scars (24 or more) must occur in close proximity to each other.

cond-mat.soft

The study of propagation characteristics of millimeter-wave vortex in magnetized plasma by using FDTD Method

It is pointed out that millimeter-wave vortex may contribute an efficient plasma heating since it was found that the millimeter-wave vortex can propagate in magnetized plasma even in which the normal plane wave is in cut-off condition. Then, it was assumed that the vortex field was the Laguerre-Gaussian (L-G) mode which is free-space solution, but the generation and stable propagation of the L-G mode vortex are not easy in the millimeter frequency range. On the other hand, it is known that millimeter-wave hybrid mode of cylindrical corrugated waveguide has also vortex property. In this paper, we investigate propagation characteristics of millimeter-wave vortex of a hybrid mode of cylindrical corrugated waveguide in the magnetized plasma by using three dimensional numerical simulations with finite-difference time-domain (FDTD) method.

physics.plasm-ph

Molecular dynamics simulation for coalescence of vacancies in tungsten crystal

We performed molecular dynamics simulations of coalescence of two vacancies in a tungsten (W) crystal to elucidate the effect of temperature and hydrogen atoms. Simulations were performed for two types of vacancy structures, $\mathrm{V}_9 + \mathrm{W}_1 + \mathrm{V}_9$ and $\mathrm{V}_{10} + \mathrm{W}_4 + \mathrm{V}_{10}$ ($\mathrm{V}_{n}$ means that a vacancy corresponds to the absence of $n$ W atoms, and $\mathrm{W}_{m}$ indicates that there are $m$ W atoms between two vacancies) in various cases of temperature and hydrogen atom concentration. Under the vacancy structure $\mathrm{V}_9 + \mathrm{W}_1 + \mathrm{V}_9$, we observed vacancy coalescence for all the cases of the temperature and the number of hydrogen atoms. Evaluating the potential energy required for removing one of the W atoms between two vacancies, we found that high temperature and existing hydrogen atoms in the vacancies facilitate vacancy coalescence, and that under the structure $\mathrm{V}_{10} + \mathrm{W}_4 + \mathrm{V}_{10}$, hydrogen atoms facilitate vacancy coalescence most strongly when the number is around 45 to 54 in each vacancy.

cond-mat.mtrl-sci

Demi-shuffle duals of Magnus polynomials in a free associative algebra

We study two linear bases of the free associative algebra $\mathbb{Z}\langle X,Y\rangle$: one is formed by the Magnus polynomials of type $(\mathrm{ad}_X^{k_1}Y)\cdots(\mathrm{ad}_X^{k_d}Y) X^k$ and the other is its dual basis (formed by what we call the `demi-shuffle' polynomials) with respect to the standard pairing on the monomials of $\mathbb{Z}\langle X,Y\rangle$. As an application, we show a formula of Le-Murakami, Furusho type that expresses arbitrary coefficients of a group-like series $J\in \mathbb{C}\langle\langle X,Y\rangle\rangle$ by the `regular' coefficients of $J$.

math.NT

Lissajous 3-braids

We classify 3-braids arising from collision-free choreographic motions of 3 bodies on Lissajous plane curves, and present a parametrization in terms of levels and (Christoffel) slopes. Each of these Lissajous 3-braids represents a pseudo-Anosov mapping class whose dilatation increases when the level ascends in the natural numbers or when the slope descends in the Stern-Brocot tree. We also discuss 4-symbol frieze patterns that encode cutting sequences of geodesics along the Farey tessellation in relation to odd continued fractions of quadratic surds for the Lissajous 3-braids.

math.GT

On generalized median triangles and tracing orbits

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.

math.MG

On distribution formulas for complex and $\ell$-adic polylogarithms

We study an $\ell$-adic Galois analogue of the distribution formulas for polylogarithms with special emphasis on path dependency and arithmetic behaviors. As a goal, we obtain a notion of certain universal Kummer-Heisenberg measures that enable interpolating the $\ell$-adic polylogarithmic distribution relations for all degrees.

math.NT

A family of geometric operators on triangles with two complex variables

Given a plane triangle $Δ$, one can construct a new triangle $Δ'$ whose vertices are intersections of two cevian triples of $Δ$. We extend the family of operators $Δ\mapstoΔ'$ by complexifying the defining two cevian parameters and study its rich structure from arithmetic-geometric viewpoints. We also find another useful parametrization of the operator family via finite Fourier analysis and apply it to investigate area-preserving operators on triangles.

math.MG

On adelic Hurwitz zeta measures

In this paper we construct a $\hat\mathbb{Z}$-valued measure on $\hat\mathbb{Z}$ which interpolates $p$-adic Hurwitz zeta functions for all $p$.

math.NT