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Yoritaka Iwata

Publications and source records attributed to Yoritaka Iwata.

At least 19 recordsLinked to original sources

Machine Learning Insights into Discrepancies Between Theoretical and Experimental Fission Barrier Heights

Accurate determination of nuclear fission barrier heights is essential for understanding nuclear stability, fission dynamics, and nucleosynthesis. However, theoretical models such as the Extended Thomas-Fermi plus Strutinsky Integral (ETFSI) approach and the macroscopic-microscopic calculations of Möller et al. exhibit systematic deviations from experiment, especially in regions of strong deformation and pronounced shell effects. In this work, machine learning is used as a diagnostic tool to analyze these discrepancies. Using the Extreme Gradient Boosting (XGBoost) algorithm within a residual-learning framework, the model learns corrections to ETFSI predictions from physically motivated nuclear features, including proton and neutron numbers, binding energies, separation energies, and pairing-related quantities. The model reproduces experimental barrier heights with root-mean-squared errors of about 0.3-1.2 MeV across training, test, and cross-validation datasets. Feature-importance analysis shows that inner barriers depend on binding-energy trends, mass and neutron-number effects, and pairing contributions, whereas outer barriers are governed more strongly by macroscopic quantities, particularly proton number, consistent with the dominant role of Coulomb repulsion and fissility at large deformation. These results show that machine learning can improve predictive accuracy while providing physically interpretable insight into the limitations of theoretical nuclear models.

nucl-th

Fractional Powers of Operators: Characterization via $δ$-Regularized Logarithmic Representation

For the fractional powers of operators, the classical formulation by V. Balakrishnan inherently requires positivity or specific sectorial conditions of the generator (i.e., the generation of analytic semigroups). To overcome these limitations, this paper presents a novel approach to constructing fractional powers of operators $D^k$ through the $δ$-regularized logarithmic representation of infinitesimal generators $D$, based on the framework of $C^0$-semigroup theory for abstract evolution equations in Banach spaces. The proposed method bypasses the conventional geometric constraints by employing an algebraic $δ$-regularization for bounded operators. Specifically, by applying a complex-analytic logarithmic representation to a family of bounded operators derived from the resolvent of the semigroup, we mathematically prove that, under the minimal algebraic assumption of invertibility, the fractional powers for generators of more general $C^0$-semigroups are uniquely and rigorously well-defined, independent of the choice of the regularization parameter $δ$. The theoretical framework established in this study offers extensive potential for applications, including regularity estimates for non-analytic semigroups and non-autonomous systems where the infinitesimal generators depend explicitly on the time variable.

math.FA

A Locally Deployed RAG-Based Academic Advising System for Course Selection

The correct sequence of courses in the curriculum based on prerequisites between courses is of great importance for students to develop their knowledge and skills holistically. However, students crafting this sequence in isolation frequently struggle with recognition limitations and information overload that leads to confusion. Simultaneously, education institutions encounter difficulties in providing adequate academic advice for the correct sequence due to limited education resources. To address these challenges, we propose a locally deployed RAG-based academic advising system grounded in syllabus information. By combining large language models with retrieval from structured syllabus data, the system is designed to support course selection, prerequisite understanding, and personalized study planning in a privacy-preserving manner.

cs.CL

Dynamical symmetry breaking described by cubic nonlinear Klein-Gordon equations

The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for clarifying the dynamical symmetry breaking, it is necessary to use a sufficiently high-precision scheme in the time-dependent framework. Second, the error of numerical calculations is generally more easily accumulated for calculating hyperbolic equations rather than parabolic equations. Third, numerical calculations become easily unstable for nonlinear cases. Our strategy for the high-precision and stable scheme is to implement the implicit Runge-Kutta method for time, and the Fourier spectral decomposition for space. %%% In this paper, focusing on the breather solutions, the relationship between the velocity, mass, and the amplitude of the perturbation is clarified. As a result, the conditions for transitioning from one state to another are clarified.

math.NA

Low-energy neutrino responses for 71Ga by electron capture rates, charge exchange reactions and shell model calculations

Weak Gamow-Teller (GT) responses for low-lying states in ${}^{71}\mathrm{Ga}$ are crucial for studying low-energy solar neutrinos and the Ga anomaly, i.e., the possible transition to the sterile state. The responses for the ground state, the first excited state, and the second excited state are evaluated for the first time using the experimental electron capture rates, the experimental charge exchange reaction (CER) rates corrected for the tensor-interaction effect and the theoretical interacting shell model (ISM) calculations. The contributions from the two excited states to the solar and ${}^{51}\mathrm{Cr}$ neutrinos are found to be $4.2 \pm 1.2\%$ of that for the ground state. This is slightly larger than the ISM values but little smaller than the CER values without corrections for the tensor interaction effect. The Ga anomaly is far beyond the uncertainty of the obtained nuclear responses.

nucl-th

Recurrence formula for some higher order evolution equations

Riccati's differential equation is formulated as abstract equation in finite or infinite dimensional Banach spaces. Since the Riccati's differential equation with the Cole-Hopf transform shows a relation between the first order evolution equations and the second order evolution equations, its generalization suggests the existence of recurrence formula leading to a sequence of differential equations with different order. %%% In conclusion, by means of the logarithmic representation of operators, a transform between the first order evolution equations and the higher order evolution equation is presented. Several classes of evolution equations with different orders are given, and some of them are shown as examples.

math.FA

Time-dependent finite-dimensional dynamical system representation of breather solutions

A concept of finite-dimensional dynamical system representation is introduced. Since the solution trajectory of partial differential equations are usually represented within infinite-dimensional dynamical systems, the proposed finite-dimensional representation provides decomposed snapshots of time evolution. Here we focus on analyzing the breather solutions of nonlinear Klein-Gordon equations, and such a solution is shown to form a geometrical object within finite-dimensional dynamical systems. In this paper, based on high-precision numerical scheme, we represent the breather solutions of the nonlinear Klein-Gordon equation as the time evolving trajectory on a finite-dimensional dynamical system. Consequently, with respect to the evolution of finite-dimensional dynamical systems, we confirm that the rotational motion around multiple fixed points plays a role in realizing the breather solutions. Also, such a specific feature of breather solution provides us to understand mathematical mechanism of realizing the coexistence of positive and negative parts in nonlinear systems.

math.FA

Unbounded generalization of logarithmic representation of infinitesimal generators

The logarithmic representation of infinitesimal generators is generalized to the cases when the evolution operator is unbounded. The generalized result is applicable to the representation of infinitesimal generators of unbounded evolution operators, where unboundedness of evolution operator is an essential ingredient of nonlinear analysis. In conclusion a general framework for the identification between the infinitesimal generators with evolution operators is established. A mathematical framework for such an identification is indispensable to the rigorous treatment of nonlinear transforms: e.g., transforms appearing in the theory of integrable systems.

math.FA

Static analysis for coupled nonlinear Klein-Gordon equations with asymmetric parameter settings

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For a system of nonlinear Klein-Gordon equations, a systematic analysis of the time evolution for their spatially uniform solutions has been performed \cite{21takei}. In the study, the parameters (mass, wave propagation speed, and the force parameters) are chosen to be symmetric between the two single equations. Symmetric parameter settings are equivalent to assume the interacting two same particles. In this paper, for a system of nonlinear Klein-Gordon equations with asymmetric parameter settings, the time evolution for their spatially uniform solutions are studied. This is equivalent to assume the interacting two different particles. As a result, based on the high precision numerical scheme \cite{22takei}, the existence of divergent and bounded solutions that depend on parameter settings is revealed. The competition, coherence, and decoherence of different waves are shown to appear depending on the choice of asymmetrically-implemented parameter values.

math-ph

Unbounded generalization of the Baker-Campbell-Hausdorff formulae

Based on the operator representation on the module over Banach algebra $B(X)$, the Campbell-Baker-Hausdorff formula is generalized to the unbounded situations. In conclusion, by means of the logarithmic representation of generally-unbounded operators, the Campbell-Baker-Hausdorff formula is generalized to be applicable to the unbounded operators.

math.FA

Inertial energy dissipation in nuclear dynamics

We present the TDDFT+Langevin model that incorporates microscopic time-dependent density function theory (TDDFT) with macroscopic Langevin model. By extracting the energy-dependent dissipation effect from the TDDFT dynamics, quantum effects are introduced to the Langevin-type stochastic fission analysis. In this paper, by means of Skyrme nuclear effective interactions, the energy-dependent friction coefficients to be used in Langevin calculations are provided individually for 25 fission nuclei chosen from uranium, plutonium, curium, californium, and fermium isotopes. The validity of the energy-dependent friction coefficients are confirmed by comparing to the existing experimental fission fragment yields. In conclusion, depending on the energy, the transition of energy dissipation mechanism from conventional viscous energy dissipation to inertial energy dissipation is shown.

nucl-th

Spinodal Instability at the Onset of Collective Expansion in Nuclear Collisions

Using transport theory to model central Au + Au collisions in the energy region of 20 - 110 MeV/u, at impact parameters b <= 5 fm, we predict a measurable impact of spinoidal instability as the collective expansion sets in with energy. Two transport models are employed, the pBUU model, solving a Boltzmann-Uehling-Uhlenbeck equation, and the Brownian Motion (BM) model, solving a set of Langevin equations to describe the motion of individual nucleons in a noisy nuclear medium. We find without ambiguity, for the first time, that a combination of delayed equilibration, onset of collective expansion and the spinodal instability produces a pair of transient ring structures, made of the projectile and target remnants, with spectator nucleons predicted to end in the entities reminiscent of stones in jewelry, on the rings. The ring structures, calculated in the configuration space and mapped onto the velocity space, could be detected in experimental collective flow data.

nucl-th

Abstract formulation of the Miura transform

Miura transform is known as the transformation between Korteweg de-Vries equation and modified Korteweg de-Vries equation. Its formal similarity to the Cole-Hopf transform has been noticed. This fact sheds light on the logarithmic type transformations as an origin of certain kind of nonlinearity in the soliton equations. In this article, based on the logarithmic representation of operators in infinite-dimensional Banach spaces, a structure common to both Miura and Cole-Hopf transforms is discussed. In conclusion, the Miura transform is generalized as the transform in abstract Banach spaces, and it is applied to the higher order abstract evolution equations.

math.AP

Theory of $B(X)$-module -Algebraic module structure of generally-unbounded infinitesimal generators-

The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally-unbounded infinitesimal generators. In conclusion the concept of module over a Banach algebra is proposed as the generalization of Banach algebra. As an application to mathematical physics, the rigorous formulation of rotation group, which consists of unbounded operators being written by differential operators, is provided using the module over a Banach algebra.

math.FA

Space-time breather solution for nonlinear Klein-Gordon equations

Klein-Gordon equations describe the dynamics of waves/particles in sub-atomic scales. For nonlinear Klein-Gordon equations, their breather solutions are usually known as time periodic solutions with the vanishing spatial-boundary condition. The existence of breather solution is known for the Sine-Gordon equations, while the Sine-Gordon equations are also known as the soliton equation. The breather solutions is a certain kind of time periodic solutions that are not only play an essential role in the bridging path to the chaotic dynamics, but provide multi-dimensional closed loops inside phase space. In this paper, based on the high-precision numerical scheme, the appearance of breather mode is studied for nonlinear Klein-Gordon equations with periodic boundary condition. The spatial periodic boundary condition is imposed, so that the breathing-type solution in our scope is periodic with respect both to time and space. In conclusion, the existence condition of space-time periodic solution is presented, and the compact manifolds inside the infinite-dimensional dynamical system is shown. The space-time breather solutions of Klein-Gordon equations can be a fundamental building block for the sub-atomic nonlinear dynamics.

nlin.PS

Numerical scheme based on the spectral method for calculating nonlinear hyperbolic evolution equations

High-precision numerical scheme for nonlinear hyperbolic evolution equations is proposed based on the spectral method. The detail discretization processes are discussed in case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with the order of total calculation cost $O(N \log 2N)$ is proposed. As benchmark results, the relation between the numerical precision and the discretization unit size are demonstrated.

math.NA

Solitons in nuclear time-dependent density functional theory

The soliton existence in sub-atomic many-nucleon systems is discussed. In many nucleon dynamics represented by the nuclear time-dependent density functional formalism, much attention is paid to energy and mass dependence of the soliton existence. In conclusion, the existence of nuclear soliton is clarified if the temperature of nuclear system is from 10 to 30 MeV. With respect to the mass dependence $^{4}$He and $^{16}$O are suggested to be the candidates for the self-bound states exhibiting the property of nuclear soliton.

nucl-th

Operator topology for logarithmic infinitesimal generators

Generally-unbounded infinitesimal generators are studied in the context of operator topology. Beginning with the definition of seminorm, the concept of locally convex topological vector space is introduced as well as the concept of Fr{é}chet space. These are the basic concepts for defining an operator topology. Consequently, by associating the topological concepts with the convergence of sequence, a suitable mathematical framework for obtaining the logarithmic representation of infinitesimal generators is presented.

math.FA