arXiv subjects

Jaeyong Shin

Publications and source records attributed to Jaeyong Shin.

12 recordsLinked to original sources

arXiv2026

Eventual regularity and asymptotic behavior of Leray-Hopf weak solutions for the Hall-MHD system

In this paper, we study the incompressible, viscous and resistive Hall-magnetohydrodynamic (Hall-MHD) system. We first prove that every two-dimensional Leray-Hopf weak solution becomes smooth after a finite time. In three dimensions, where eventual smoothness for arbitrary Leray-Hopf weak solutions is not known, we construct Leray-Hopf weak solutions for which the magneto-vorticity field $B+\nabla\times u$ eventually gains additional regularity. Finally, under suitable low-frequency pseudomeasure assumptions on initial data, we establish decoupled algebraic decay rates for the velocity and magnetic fields by combining a generalized Fourier splitting method with the eventual smoothness in two dimensions and strong regularity in three dimensions.

math.AP↗

arXiv2026

Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection

This paper proposes a novel alternative to existing sim-to-real methods for training control policies with simulated experiences. Unlike prior methods that typically rely on domain randomization over a fixed finite set of parameters, the proposed approach injects state-dependent perturbations into the input joint torque during forward simulation. These perturbations are designed to simulate a broader spectrum of reality gaps than standard parameter randomization without requiring additional training. By using neural networks as flexible perturbation generators, the proposed method can represent complex, state-dependent uncertainties, such as nonlinear actuator dynamics and contact compliance, that parametric randomization cannot capture. Experimental results demonstrate that the proposed approach enables humanoid locomotion policies to achieve superior robustness against complex, unseen reality gaps in both simulation and real-world deployment.

cs.RO↗

arXiv2025

Local well-posedness and asymptotic analysis of a nonlocal incompressible Navier--Stokes--Korteweg system

We consider a relaxed formulation of the inhomogeneous incompressible Navier--Stokes--Korteweg system, where the classical third-order capillarity term is replaced by a nonlocal approximation. We first establish the local-in-time well-posedness of the relaxed system, under standard regularity and positivity assumptions on the initial data. The existence time is uniform with respect to both the capillarity coefficient and the relaxation parameter. We then study two asymptotic limits of the system: the nonlocal-to-local limit as the relaxation parameter tends to infinity, and the vanishing capillarity limit. In each case, we prove convergence of the solution to that of the corresponding target system. Our analysis provides a rigorous justification for the use of nonlocal relaxation models in approximating capillarity-driven incompressible fluid flows.

math.AP↗

arXiv2025

Spectral Normalization for Lipschitz-Constrained Policies on Learning Humanoid Locomotion

Reinforcement learning (RL) has shown great potential in training agile and adaptable controllers for legged robots, enabling them to learn complex locomotion behaviors directly from experience. However, policies trained in simulation often fail to transfer to real-world robots due to unrealistic assumptions such as infinite actuator bandwidth and the absence of torque limits. These conditions allow policies to rely on abrupt, high-frequency torque changes, which are infeasible for real actuators with finite bandwidth. Traditional methods address this issue by penalizing aggressive motions through regularization rewards, such as joint velocities, accelerations, and energy consumption, but they require extensive hyperparameter tuning. Alternatively, Lipschitz-Constrained Policies (LCP) enforce finite bandwidth action control by penalizing policy gradients, but their reliance on gradient calculations introduces significant GPU memory overhead. To overcome this limitation, this work proposes Spectral Normalization (SN) as an efficient replacement for enforcing Lipschitz continuity. By constraining the spectral norm of network weights, SN effectively limits high-frequency policy fluctuations while significantly reducing GPU memory usage. Experimental evaluations in both simulation and real-world humanoid robot show that SN achieves performance comparable to gradient penalty methods while enabling more efficient parallel training.

cs.RO↗

arXiv2025

On the double Beltrami states in Hall magnetohydrodynamics

In this paper, we investigate double Beltrami states in the Hall magnetohydrodynamic (Hall MHD) equations. Initially, we examine the double Beltrami states as a special class of steady solutions to the ideal Hall MHD equations, which are closely related to Beltrami flows in incompressible fluid dynamics. Specifically, we classify the double Beltrami states and show that they can be derived by using the variational method as energy minimizers, subject to the conservation of two helicities. We then extend our analysis to time-dependent double Beltrami states in the viscous and resistive Hall MHD equations, exploring their exact form and stability properties.

math.AP↗

arXiv2025

Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection

This paper proposes a novel alternative to existing sim-to-real methods for training control policies with simulated experiences. Prior sim-to-real methods for legged robots mostly rely on the domain randomization approach, where a fixed finite set of simulation parameters is randomized during training. Instead, our method adds state-dependent perturbations to the input joint torque used for forward simulation during the training phase. These state-dependent perturbations are designed to simulate a broader range of reality gaps than those captured by randomizing a fixed set of simulation parameters. Experimental results show that our method enables humanoid locomotion policies that achieve greater robustness against complex reality gaps unseen in the training domain.

cs.RO↗

arXiv2024

Hidden dormant phase mediating the glass transition in disordered matter

Metallic glass is a frozen liquid with structural disorder that retains degenerate free energy without spontaneous symmetry breaking to become a solid. For over half a century, this puzzling structure has raised fundamental questions about how structural disorder impacts glass-liquid phase transition kinetics, which remain elusive without direct evidence. In this study, through single-pulse, time-resolved imaging using X-ray free-electron lasers, we visualized the glass-to-liquid transition, revealing a previously hidden dormant phase that does not involve any macroscopic volume change within the crossover regime between the two phases. Although macroscopically inactive, nanoscale redistribution occurs, forming channeld low-density bands within this dormant phase that drives the glass transition. By providing direct microscopic evidence, this work presents a new perspective on the phase transition process in disordered materials, which can be extended to various liquid and solid phases in other complex systems.

cond-mat.dis-nn↗

arXiv2024

Photoinduced surface plasmon control of ultrafast melting modes in Au nanorods

Photoinduced ultrafast phenomena in materials exhibiting nonequilibrium behavior can lead to the emergence of exotic phases beyond the limits of thermodynamics, presenting opportunities for femtosecond photoexcitation. Despite extensive research, the ability to actively control quantum materials remains elusive owing to the lack of clear evidence demonstrating the explicit control of phase-changing kinetics through light-matter interactions. To address this drawback, we leveraged single-pulse time-resolved X-ray imaging of Au nanorods undergoing photoinduced melting to showcase control over the solid-to-liquid transition process through the use of localized surface plasmons. Our study uncovers transverse or longitudinal melting processes accompanied by characteristic oscillatory distortions at different laser intensities. Numerical simulations confirm that the localized surface plasmons, excited by polarized laser fields, dictate the melting modes through anharmonic lattice deformations. These results provide direct evidence of photoinduced surface plasmon-mediated ultrafast control of matter, establishing a foundation for the customization of material kinetics using femtosecond laser fields.

cond-mat.mes-hall↗

arXiv2024

On the regularity of magneto-vorticity field and the global existence for the Hall magnetohydrodynamic equations

In this paper, we investigate the incompressible viscous and resistive Hall magnetohydrodynamic equations (Hall MHD in short). We first study the regularity of the magneto-vorticity field $B+\omega$. In three dimensions, we derive some bounds of $B+\omega$ under a condition of the velocity field $u$. Moreover, if we consider the Hall MHD with 2D variables, the uniform-in-time bounds of $B+\omega$ come from the three dimensional case. The regularity of $B+\omega$ gives us a crucial clue of blow-up scenario and provides conditions of the existence of global-in-time solutions. In particular, we prove the global well-posedness of the Hall MHD (also the electron MHD) with 2D variables when the third component of the initial current density $J_0=\nabla\times B_0$ is sufficiently small. We also derive temporal decay rate of $B+\omega$.

math.AP↗

arXiv2024

On the temporal estimates for the incompressible Navier-Stokes equations and the Hall-magnetohydrodynamic equations

In this paper, we derive decay rates for solutions to the incompressible Navier-Stokes equations and Hall-magnetohydrodynamic equations. We first improve the decay rate of weak solutions to these equations by refining the Fourier splitting method with initial data in the space of pseudo-measures. Additionally, we investigate these equations with initial data in the Lei-Lin spaces and establish decay rates for those solutions.

math.AP↗

arXiv2024

Global existence and long time behavior of solutions to some Oldroyd type models in hybrid Besov spaces

In this paper, we deal with some Oldroyd type models, which describe incompressible viscoelastic fluids. There are 3 parameters in these models: the viscous coefficient of fluid $\nu_{1}$, the viscous coefficient of the elastic part of the stress tensor $\nu_{2}$, and the damping coefficient of the elastic part of the stress tensor $\alpha$. In this paper, we assume at least one of the parameters is zero: $(\nu_{1}, \nu_{2},\alpha)=(+,0,+), (+,0,0), (0,+,+), (0,+,0), (0,0,+)$ and prove the global existence of unique solutions to all these 5 cases in the framework of hybrid Besov spaces. We also derive decay rates of the solutions except for the case $(\nu_{1}, \nu_{2},\alpha)=(+,0,0)$. To the best of our knowledge, decay rates in this paper are the first results in this framework, and can improve some previous works.

math.AP↗

arXiv2023

Global solutions to Stokes-Magneto equations with fractional dissipations

In this paper, we investigate a Stokes-Magneto system with fractional diffusions. We first deal with the non-resistive case in $\mathbb{T}^{d}$ and establish the local and global well-posedness with initial magnetic field $\mathbf{b}_0\in H^{s}(\mathbb{T}^d)$. We also show the existence of a unique mild solution of the resistive case with initial data $\mathbf{b}_0$ in the critical $L^{p}(\mathbb{R}^d)$ space. Moreover, we show that $\|\mathbf{b}(t)\|_{L^{p}}$ converges to zero as $t\rightarrow\infty$ when the initial data is sufficiently small.

math.AP↗