arXiv subjects

Satoshi Takada

Publications and source records attributed to Satoshi Takada.

At least 19 recordsLinked to original sources

arXiv2026

Revisiting Stress Analysis in a Three-Dimensional Elastic Hollow Sphere under Uniaxial Compression via the Inverse Laplace Transform Expressions within an Elastodynamic Framework

The stress analysis of a three-dimensional elastic hollow sphere subjected to uniaxial compression is revisited, employing an elastodynamic framework. Through the application of the Laplace transform, the scalar and vector potentials of displacement are expanded, facilitating a detailed exploration of the system's mechanical behavior. The static solutions for displacement and stress distributions are derived in the long-time limit, which reveal key insights into the response of the elastic hollow sphere. Notably, on the inner surface, certain quantities exhibit a peak at the point where the angle between the compressive force and the point on the surface becomes perpendicular, indicating localized stress concentration. These findings provide a robust analytical approach for understanding and predicting the behavior of elastic hollow spheres under uniaxial loading, with implications for material science and structural engineering.

physics.class-ph↗

arXiv2026

Quantum tunneling Mpemba effect

The quantum tunneling Mpemba effect is investigated within a continuous one-dimensional symmetric double-well potential open to external environmental sinks at the boundaries ($x=\pm L$). Using a non-Hermitian spectral decomposition of the effective Hamiltonian, we characterize the open-system relaxation dynamics without relying on abstract state-space quenches. We mathematically prove that the non-monotonic behavior of the first non-trivial even-parity spectral coefficient, $a_{2}(T_{i})$, with respect to the initial preparation temperature $T_{i}$ is a universal topological property born from quantum statistical mechanics. Crucially, we demonstrate that this intermediate thermal peak is governed by the Sturm-Liouville oscillation theorem and remains completely invariant with respect to the global system size $L$, contrasting sharply with the boundary-driven classical Mpemba effect. This universal peak arises from the geometric and nodal alignment between highly localized unperturbed states and extended non-Hermitian decay channels. Furthermore, we clarify that while this mechanism is robust, the actual observation of anomalous crossings in the total survival probability trace $S(t,T_{i})$ and the trace distance $\mathcal{D}(t,T_i)$ demand a strict separation of timescales, requiring the over-barrier escape rate to vastly exceed the decay rate of the deep-well tunneling doublet ($\Gamma_{2}\gg \Gamma_{0}$ and $\Gamma_2\gg \Gamma_1$). Our continuous formulation successfully bridges real-space classical boundary-driven dissipation with open quantum dynamics, providing novel insights for engineering non-equilibrium states via tailored boundary loss.

cond-mat.stat-mech↗

arXiv2026

Mpemba effect in a sheared granular gas with velocity-dependent restitution

We investigate the Mpemba effect in a dilute sheared granular gas with a velocity-dependent restitution coefficient. Using kinetic theory based on Grad's moment method, we analyze the relaxation dynamics following a sudden change in the shear rate. We show that, despite having a higher initial temperature, a system starting from an isotropic state can relax faster than a system prepared in a sheared steady state, demonstrating a clear Mpemba effect in the temperature evolution. We further demonstrate the emergence of a viscosity Mpemba effect, characterized by crossings in the relaxation curves of the shear viscosity. Remarkably, multiple crossings arise due to an additional intrinsic timescale introduced by the velocity dependence of the restitution coefficient, providing a minimal kinetic mechanism for multiple Mpemba effects in driven granular gases.

cond-mat.soft↗

arXiv2026

Revisiting the Stress Field Inside an Elastic Sphere Subjected to a Concentrated Load

We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional linearized elastodynamic equations, the displacement and stress fields are derived using scalar and vector potential representations combined with spherical harmonic expansions. All expansion coefficients are determined explicitly by enforcing the traction boundary conditions. The static elastic solution is obtained rigorously as the long-time limit of the dynamical formulation. Closed-form expressions for all components of the stress tensor are provided, enabling direct evaluation of the principal stresses and their differences throughout the interior of the sphere. The analytical solution is further generalized to arbitrary loading positions by means of rotational transformations, allowing systematic treatment of multiple concentrated loads through superposition.

physics.class-ph↗

arXiv2026

Mpemba effect in a two-dimensional bistable potential

We present an exactly solvable model of the Mpemba effect in an overdamped Langevin system confined to a two-dimensional, radially symmetric bistable potential. The potential is constructed as a piecewise quadratic-logarithmic function that is continuous and differentiable at the matching radii, enabling an exact mapping of the corresponding Fokker-Planck operator to a Schr\"{o}dinger-type eigenvalue problem. The relaxation spectrum and eigenmodes are obtained analytically in each region in terms of confluent hypergeometric functions, with eigenvalues determined from matching conditions. % Focusing on isotropic equilibrium initial states at inverse temperature $\beta_{\rm ini}$ quenched to a bath at inverse temperature $\beta$, we derive explicit expressions for the mode amplitudes governing long-time relaxation. We demonstrate that the coefficient of the slowest mode exhibits a non-monotonic dependence on $\beta_{\rm ini}$ and identify a sufficient crossing condition for the Kullback-Leibler divergence in terms of the two slowest modes, if the global minimum of the potential is located far away from the origin and the second minimum exists near the origin. For corresponding parameters, we demonstrate that the Mpemba effect can be realized. % Our results provide a rare example of an analytically tractable two-dimensional model exhibiting anomalous relaxation without any confining walls, extending previous one-dimensional constructions with a hard wall and clarifying the role of radial geometry in nonequilibrium relaxation phenomena.

cond-mat.stat-mech↗

arXiv2026

Discontinuous change of viscosity in a sheared granular gas with velocity-dependent restitution

We investigate the rheology of a sheared granular gas composed of hard spheres with a velocity-dependent restitution coefficient. Using kinetic theory, we derive the shear viscosity and show that it exhibits an S-shaped dependence on the shear rate when the restitution coefficient switches between two values depending on the collision velocity. As a result, a discontinuous change of viscosity emerges between low- and high-shear regimes, both characterized by Bagnold-type scaling. While the phenomenology resembles the Wyart-Cates scenario for dense suspensions, the present transition arises purely from kinetic effects without frictional contacts or jamming.

cond-mat.soft↗

arXiv2026

Inverse Reconstruction of Moving Contact Loads on an Elastic Half-Space Using Prescribed Surface Displacement

This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the displacement and stress fields generated by a point load traveling at a constant velocity along the surface, explicitly incorporating elastodynamic effects through Mach number dependence. These moving-load solutions serve as building blocks for constructing more general loading scenarios via linear superposition. Based on Green's functions, an inverse problem is formulated to reconstruct the unknown surface traction responsible for a given surface displacement. The inverse analysis is performed through a Fourier-domain inversion with regularization, which enables a direct and computationally efficient determination of the contact pressure without iterative forward simulations. This framework is applied to a rigid wheel-ground contact problem, where the imposed displacement is dictated by the wheel geometry. The reconstructed surface traction exhibits a smooth, symmetric distribution within the contact region, while the resulting subsurface stress fields are obtained in closed analytical form and involve dilogarithm functions. The principal stress difference reveals characteristic spatial patterns similar to photoelastic fringes, and their asymmetry increases with the Mach number, reflecting the dynamic nature of the moving contact.

physics.class-ph↗

arXiv2026

Kinetic theory of dilute weakly charged granular gases with hard-core and inverse power-law interactions under uniform shear flow

We develop a kinetic-theory framework to investigate the steady rheology of a dilute gas interacting via a repulsive potential under uniform shear flow. Starting from the Boltzmann equation with a restitution coefficient that depends on the impact velocity and potential strength, we derive evolution equations for the stress tensor based on Grad's moment expansion. The resulting expressions for the collisional rates and transport coefficients are fitted with simple analytical functions that capture their temperature dependence over a wide range of shear rates. Comparison with direct simulation Monte Carlo (DSMC) results shows excellent quantitative agreement for the shear stress, temperature anisotropy, and shear viscosity. We also analyze the velocity distribution functions, revealing that the system remains nearly Maxwellian even under strong shear.

cond-mat.soft↗

arXiv2025

Stress Analysis of a Square Elastic Body Under Biaxial Loading Using Airy Stress Functions

This study presents an analytical investigation of stress distributions in square-shaped elastic bodies subjected to concentrated compressive loads under uniaxial and biaxial conditions. By employing the Airy stress function method, we derive closed-form solutions that satisfy the governing biharmonic equation and the prescribed boundary conditions along the edges of the square domain. The stress components are expressed as series expansions, with coefficients determined to enforce boundary constraints. In the uniaxial compression case, the resulting stress fields exhibit strong agreement with photoelastic fringe patterns previously observed in experimental studies. For biaxial loading, the solution represents a superposition of two orthogonal compression scenarios, producing spatial variations in the principal stress difference depending on the location within the domain.

physics.class-ph↗

arXiv2025

Proposal for fast computational method for Hertzian contact theory

Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with good accuracy in a small number of iterations is reported. This method is also shown to be applicable from the case of a near perfect circle to the case where the major diameter is sufficiently long compared to the minor diameter.

physics.class-ph↗

arXiv2025

Stress distribution in elastic disks with a hole under uniaxial compression

This paper investigates the stress and displacement distribution in a two-dimensional elastic hollow disk subjected to distributed diametric loading, extending our previous analysis of concentrated loading [Okamura et al. Strength Mater. 57, 102-114 (2025)]. The study provides deeper insights into the mechanical behavior of materials such as concrete and rock by examining the effects of load distribution on stress localization and displacement patterns. Using elastodynamic theory, we derive the static stress distributions and identify key differences from the concentrated loading case, particularly in the locations and magnitudes of stress extrema. This work contributes to a more comprehensive understanding of stress behavior in elastic disks under realistic loading conditions.

cond-mat.soft↗

arXiv2025

Displacement and Stress Analysis of an Elastic Hollow Disk: Comparison with Strength of Materials' Prediction

This paper analyzes the stress distribution in a two-dimensional elastic disk under diametric loading, with a focus on enhancing the understanding of concrete and rock materials' mechanical behavior. The study revisits the Brazilian test and addresses its high shear stress issue near loading points by exploring the ring test, which introduces a central hole in the disk. Using dynamic elasticity theory, we derive stress distributions over time and extend the analysis to static conditions. This approach distinguishes between longitudinal and transverse wave effects, providing a detailed stress field analysis. By drawing parallels with curved beam theories, we demonstrate the applicability of dynamic elasticity theory to complex stress problems, offering improved insights into the stress behavior in elastic disks.

cond-mat.soft↗

arXiv2025

Rheology of dilute granular gases with hard-core and inverse power-law potentials

The kinetic theory of dilute granular gases with hard-core and inverse power-law potentials is developed. The scattering process is studied theoretically, which yields the relative speed and the impact parameter dependence of the scattering angle. The viscosity is derived from the Boltzmann equation and its temperature dependence is plotted. We also perform the direct simulation Monte Carlo to check the validity of the theory.

cond-mat.soft↗

arXiv2024

Fermion Casimir effect and magnetic Larkin-Ovchinnikov phases

This paper explores how magnetic fields affect the Casimir effect within the context of a simple quasi-1D interacting fermionic system. A novel phenomenon emerges, resulting from the interaction between external magnetic fields and boundary conditions, which alters the ground state in complex ways and leads to first-order phase transitions among various ground states, specifically inhomogeneous solutions with differing node counts. We calculate the Casimir force, which exhibits discontinuities (jumps) at the transition points between the different ground states.

hep-th↗

arXiv2024

Kinetic theory of dilute granular gases having an inverse power law potential

The kinetic theory of dilute granular gases having an inverse power law repulsive potential is studied. We derive the time evolution of the temperature and the transport coefficients from the Boltzmann equation. We also investigate the linear stability analysis of the hydrodynamics, and study the softness dependence of the thresholds for the shear and heat modes against the restitution coefficient.

cond-mat.soft↗

arXiv2023

Revisiting stress propagation in a two-dimensional elastic circular disk under diametric loading

In this paper, we present a comprehensive investigation of stress propagation in a two-dimensional elastic circular disk. To accurately describe the displacements and stress fields within the disk, we employ a scalar and vector potential approach, representing them as sums of Bessel functions. The determination of the coefficients for these expansions is accomplished in the Laplace space, where we compare the boundary conditions. By converting the inverse Laplace transforms into complex integrals using residue calculus, we successfully derive explicit expressions for the displacements and stress fields. Notably, these expressions encompass primary, secondary, and surface waves, providing a thorough characterization of the stress propagation phenomena within the disk. Our findings contribute to the understanding of mechanical behavior in disk-shaped components and can be valuable in the design and optimization of such structures across various engineering disciplines.

cond-mat.soft↗

arXiv2023

Multiple quantum Mpemba effect: exceptional points and oscillations

We explore the role of exceptional points and complex eigenvalues on the occurrence of the quantum Mpemba effect. To this end, we study a two-level driven dissipative system subjected to an oscillatory electric field and dissipative coupling with the environment. We find that both exceptional points and complex eigenvalues can lead to $multiple$ quantum Mpemba effect. It occurs in an observable when time evolved copies corresponding to two different initial conditions, one initially having higher observable value compared to the other and both relaxing towards the same steady state, intersect each other more than once during their relaxation process. Each of the intersections denotes a quantum Mpemba effect and marks the reversal of identities between the two copies i.e. the copy with higher observable value before the intersection becomes the lower valued copy (and vice versa) after the intersection. Such multiple intersections originate from additional algebraic time dependence at the exceptional points and due to oscillatory relaxation in the case of complex eigenvalues. We provide analytical results for quantum Mpemba effect in the density matrix in presence of coherence. Depending on the control parameters (drive and dissipation), observables such as energy, von Neumann entropy, temperature etc. exhibit either single or multiple quantum Mpemba effect. However, the distance from steady state measured in terms of the Kullback-Leibler divergence shows only single quantum Mpemba effect although the corresponding speed gives rise to either single or multiple quantum Mpemba effect.

quant-ph↗

arXiv2023

Quantum Mpemba effect in a quantum dot with reservoirs

We demonstrate the quantum Mpemba effect in a quantum dot coupled to two reservoirs, described by the Anderson model. We show that the system temperatures starting from two different initial values (hot and cold), cross each other at finite time (and thereby reverse their identities i.e. hot becomes cold and vice versa) to generate thermal quantam Mpemba effect. The slowest relaxation mode believed to play the dominating role in Mpemba effect in Markovian systems, does not contribute to such anomalous relaxation in the present model. In this connection, our analytical result provides necessary condition for producing quantum Mpemba effect in the density matrix elements of the quantum dot, as a combined effect of the remaining relaxation modes.

cond-mat.stat-mech↗