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Taehun Lee

Publications and source records attributed to Taehun Lee.

At least 19 recordsLinked to original sources

The $C^{p'}$-regularity conjecture near $p=2$

We prove the $C^{p'}$-regularity conjecture in every dimension when $p>2$ is sufficiently close to $2$. To this end, we establish improved H\"older estimates for the gradients of $p$-harmonic functions. These estimates also determine the first-order asymptotics of the optimal gradient H\"older exponent in every dimension. The proof combines compactness, harmonic rigidity of the limiting profiles, and a sharp uniform gap estimate for the first variation of the gradient excess.

math.AP

Spectral element lattice Boltzmann method for non-ideal gases with partial wetting boundary condition

We present a spectral element lattice Boltzmann method (LBM) for partial wetting on curved geometries. A non-ideal gas phase-field model is incorporated into the LBM framework to enable phase separation with a constant interface thickness and the potential form of surface tension force is used. We adopt the force-splitting approach, yielding significantly improved stability and accuracy. Complex boundaries are naturally handled using a flux bounce-back scheme, which resolves inconsistencies in normal vectors across adjacent elements. Additionally, a general wetting boundary condition is implemented to capture static contact line in a thermodynamically consistent manner. The method is validated through simulations of droplets on flat surfaces, 2/3-dimensional curved surfaces, and equilibrium droplets without boundaries. Results demonstrate that parasitic currents are significantly reduced on unstructured meshes with complex geometries, reaching residual kinetic energy levels on the order of $10^{-24}$ for wetting configurations and $10^{-30}$ for isolated droplets.

physics.flu-dyn

Liouville theorems for nonlocal Lane--Emden inequalities with degenerate kernels

We establish a Liouville-type theorem for the inequality $\mathcal{L}_K u \ge |u|^q$ in $\mathbb{R}^n$, where $\mathcal{L}_K$ is a translation-invariant, degenerate elliptic integro-differential operator whose kernel is even and satisfies $0\le K(z)\le \Lambda|z|^{-n-2s}$. No lower ellipticity bound is imposed on the kernel, and no sign condition is imposed on the solution. We prove that every such solution is trivial when $1 \le q \le \frac{n}{n-2s}$ if $n > 2s$, and for every $q \ge 1$ if $n \le 2s$. The proof combines a test function method with a dyadic decomposition of the nonlocal tail and uses neither the maximum principle nor a fundamental solution.

math.AP

Nodal set comparison for Allen--Cahn solutions with conical asymptotics

We establish a comparison principle for entire solutions of the Allen--Cahn equation whose nodal sets, possibly singular, are asymptotic to a regular minimizing hypercone. We show that inclusion of the positive phases enforces a global ordering of the solutions. As a consequence, the positive phase uniquely determines the solution, and strict phase inclusion implies that the corresponding nodal sets are disjoint. Our analysis relies on a maximum principle for the linearized operator on unbounded domains that are not necessarily smooth, and yields an Allen--Cahn analogue of the strong maximum principle for minimal hypersurfaces.

math.AP

Fine-Tuning Bulk-oriented Universal Interatomic Potentials for Surfaces: Accuracy, Efficiency, and Forgetting Control

Accurate prediction of surface energies and stabilities is essential for materials design, yet first-principles calculations remain computationally expensive and most existing interatomic potentials are trained only on bulk systems. Here, we demonstrate that fine-tuning foundation machine learning potentials (MLPs) significantly improves both computational efficiency and predictive accuracy for surface modeling. While existing universal interatomic potentials (UIPs) have been solely trained and validated on bulk datasets, we extend their applicability to complex and scientifically significant unary, binary, and ternary surface systems. We systematically compare models trained from scratch, zero-shot inference, conventional fine-tuning, and multi-head fine-tuning approach that enhances transferability and mitigates catastrophic forgetting. Fine-tuning consistently reduces prediction errors with orders-of-magnitude fewer training configurations, and multi-head fine-tuning delivers robust and generalizable predictions even for materials beyond the initial training domain. These findings offer practical guidance for leveraging pre-trained MLPs to accelerate surface modeling and highlight a scalable path toward data-efficient, next-generation atomic-scale simulations in computational materials science.

cond-mat.mtrl-sci

A flux bounce-back scheme for the filtered Spectral Element Lattice Boltzmann Method

We develop a spectral element lattice Boltzmann method (SELBM) with the flux bounce-back (FBB) scheme, to enable accurate simulations of single-phase fluid dynamics in unstructured mesh. We adopt an Eulerian description of the streaming process in place of the perfect shift in the regular LBM. The spectral element method is used to spatially discretize the convective term, while the strong stability-preserving Runge-Kutta (SSPRK) method is used for time integration. To increase stability, we investigate the use of an explicit filter, particularly in the context of the sensitive double shear layer problem. The results indicate that by using the high-order polynomial, we can effectively eliminate the small vortices around the neck region. We introduce the flux bounce-back scheme to enable the current scheme to handle complex boundaries. The proposed scheme and flux boundary method are validated through benchmark simulations, including the unsteady Couette flow and the planar Poiseuille flow. Further validation is provided through the Taylor-Green vortex problem, demonstrating the accuracy and convergence of the scheme for isotropic turbulence. Finally, we consider a fully developed turbulent flow within a cylindrical pipe and correctly predict the turbulent boundary layer profile.

physics.flu-dyn

Machine-Learning-Accelerated Surface Exploration of Reconstructed BiVO$_{4}$(010) and Characterization of Their Aqueous Interfaces

Understanding the semiconductor-electrolyte interface in photoelectrochemical (PEC) systems is crucial for optimizing stability and reactivity. Despite the challenges in establishing reliable surface structure models during PEC cycles, this study explores the complex surface reconstructions of BiVO$_{4}$(010) by employing a computational workflow integrated with a state-of-the-art active learning protocol for a machine-learning interatomic potential and global optimization techniques. Within this workflow, we identified 494 unique reconstructed surface structures that surpass conventional chemical intuition-driven, bulk-truncated models. After constructing the surface Pourbaix diagram under Bi- and V-rich electrolyte conditions using density functional theory and hybrid functional calculations, we proposed structural models for the experimentally observed Bi-rich BiVO$_{4}$ surfaces. By performing hybrid functional molecular dynamics simulations with explicit treatment of water molecules on selected reconstructed BiVO$_{4}$(010) surfaces, we observed spontaneous water dissociation, marking the first theoretical report of this phenomenon. Our findings demonstrate significant water dissociation on reconstructed Bi-rich surfaces, highlighting the critical role of bare and under-coordinated Bi sites (only observable in reconstructed surfaces) in driving hydration processes. Our work establishes a foundation for understanding the role of complex, reconstructed Bi surfaces in surface hydration and reactivity. Additionally, our theoretical framework for exploring surface structures and predicting reactivity in multicomponent oxides offers a precise approach to describing complex surface and interface processes in PEC systems.

cond-mat.mtrl-sci

A difference-free conservative phase-field lattice Boltzmann method

We propose an innovative difference-free scheme that combines the one-fluid lattice Boltzmann method (lBM) with the conservative phase-field (CPF) lBM to effectively solve large-scale two-phase fluid flow problems. The difference-free scheme enables the derivation of the derivative of the order parameter and the normal vector through the moments of the particle distribution function (PDF). We further incorporate the surface tension force in a continuous surface stress form into the momentum equations by modifying the equilibrium PDF to eliminate the divergence operator. Consequently, the entire computation process, executed without any inter-grid finite difference formulation, demonstrates improved efficiency, making it an ideal choice for high-performance computing applications. We conduct simulations of a single static droplet to evaluate the intensity of spurious currents and assess the accuracy of the scheme. We then introduce the density or viscosity ratio and apply an external body force to model the Rayleigh-Taylor instability and the behavior of a single rising bubble, respectively. Finally, we employ our method to study the phenomenon of a single bubble breaking up in a Taylor-Green vortex. The comparison between the difference-free scheme and the finite difference method demonstrates the scheme's capability to yield accurate results. Furthermore, based on the performance evaluation, the current scheme exhibits an impressive $47\% $ increase in efficiency compared to the previous method.

physics.flu-dyn

Ancient mean curvature flows with finite total curvature

We construct an $I$-family of ancient graphical mean curvature flows over a minimal hypersurface in $\mathbb{R}^{n+1}$ of finite total curvature with the Morse index $I$ by establishing exponentially fast convergence in terms of $|x|^2-t$. As a corollary, we show that these ancient flows have finite total curvature and finite mass drop. Moreover, one family of these flows is mean convex by a pointwise estimate.

math.DG

Spreading and engulfment of a viscoelastic film onto a Newtonian droplet

We use the conservative phase-field lattice Boltzmann method to investigate the dynamics when a Newtonian droplet comes in contact with an immiscible viscoelastic liquid film. The dynamics of the three liquid phases are explored through numerical simulations, with a focus on illustrating the contact line dynamics and the viscoelastic effects described by the Oldroyd-B model. The droplet dynamics are contrasted with the case of a Newtonian fluid film. The simulations demonstrate that when the film is viscoelastic, the droplet dynamics become insensitive to the film thickness when the polymer viscosity and relaxation time are large. A viscoelastic ridge forms at the moving contact line, which evolves with a power-law dependence on time. By rescaling the interface profile of the ridge using its height and width, it appears to collapse onto a similar shape. Our findings reveal a strong correlation between the viscoelastic stress and the interface shape near the contact line.

physics.flu-dyn

Gauss curvature flow with shrinking obstacle

We consider a flow by powers of Gauss curvature under the obstruction that the flow cannot penetrate a prescribed region, so called an obstacle. For all dimensions and positive powers, we prove the optimal curvature bounds of solutions and all time existence with its long time behavior. We also prove the $C^1$ regularity of free boundaries under a uniform thickness assumption.

math.DG

An eigenvalue problem for prescribed curvature equations

We study an eigenvalue problem for prescribed $σ_k$-curvature equations of star-shaped, $k$-convex, closed hypersurfaces. We establish the existence of a unique eigenvalue and its associated hypersurface, which is also unique, provided that the given data is even. Moreover, we show that the hypersurface must be strictly convex. A crucial aspect of our proof involves deriving uniform estimates in $p$ for $L_p$-type prescribed curvature equations.

math.DG

On the uniqueness of energy-minimizing curves in constrained spaces

In this paper, we investigate energy-minimizing curves with fixed endpoints $p$ and $q$ in a constrained space. We prove that when one of the endpoints, say $p$, is fixed, the set of points $q$ for which the energy-minimizing curve is not unique has no interior points.

math.DG

Curvature bound for $L_p$ Minkowski problem

We establish curvature estimates for anisotropic Gauss curvature flows. By using this, we show that given a measure $\mu$ with a positive smooth density $f$, any solution to the $L_p$ Minkowski problem in $\mathbb{R}^{n+1}$ with $p \le -n+2$ is a hypersurface of class $C^{1,1}$. This is a sharp result because for each $p\in [-n+2,1)$ there exists a convex hypersurface of class $C^{1,\frac{1}{n+p-1}}$ which is a solution to the $L_p$ Minkowski problem for a positive smooth density $f$. In particular, the $C^{1,1}$ regularity is optimal in the case $p=-n+2$ which includes the logarithmic Minkowski problem in $\mathbb{R}^3$.

math.DG

Interaction between a Rising Bubble and a Stationary Droplet Immersed in a Liquid Pool using Ternary Conservative Phase-Field Lattice Boltzmann Method

When a stationary bubble and a stationary droplet immersed in a liquid pool are brought in contact with each other, they form a bubble-droplet aggregate. Its equilibrium morphology and stability largely depend on the combination of different components' surface tensions, known as spreading factor. In this study, we look at the interaction between a rising bubble and a stationary droplet to better understand the dynamics of coalescence and rising as well as morphological changes for the bubble-droplet aggregate. A systematic study is conducted on the interaction processes with various bubble sizes and spreading factors. The current simulation framework consists of the ternary conservative phase-field Lattice Boltzmann method (LBM) for interface tracking and the velocity-pressure LBM for hydrodynamics, which is validated for the benchmark cases such as liquid lens and parasitic currents around a static droplet with several popular surface tension formulations. We further test our LBM for the morphology changes of two droplets initially in contact with various spreading factors and depict the final morphologies in a phase diagram. The separated, partially engulfed and completely engulfed morphologies can be replicated by systematically altering the sign of the spreading factors. The rising bubble and stationary droplet interaction is simulated based on the final morphologies obtained under stationary conditions by imposing an imaginary buoyancy force on the rising bubble. The results indicate that the bubble-droplet aggregate with double emulsion morphology can minimize the distotion of the bubble-droplet aggregate and achieve a greater terminal velocity than the aggregate with partially engulfed morphology.

physics.flu-dyn

Engulfment of a drop on solids coated by thin and thick fluid films

When an aqueous drop contacts an immiscible oil film, it displays complex interfacial dynamics. Upon contact the oil spreads onto the drop's liquid-air interface, first forming a curvature that drives an apparent drop spreading motion and later fully engulfing the drop. We study this flow using both 3-phase Lattice-Boltzmann simulations based on the conservative phase field model and experiments. Inertially and viscously limited dynamics are explored using the Ohnesorge number $Oh$ as a function of $R/H$, the ratio between the initial drop radius $R$ and the film height $H$. Both regimes show that the apparent spreading radius $r$ is fairly independent of the film height, and scales with time $T$ as $r\sim T^{1/2}$ for $Oh\ll 1$ and for $Oh\gg 1$ as $r\sim T^{2/5}$. For $Oh\gg 1$ we show experimentally that this immiscible apparent spreading motion is analogous with the miscible drop-film coalescence case. Contrary to the apparent spreading, however, we find that the late time engulfment dynamics and final interface profiles are significantly affected by the ratio of $H/R$.

physics.flu-dyn

Diameter estimate for planar $L_p$ dual Minkowski problem

In this paper, given a prescribed measure on $\mathbb{S}^1$ whose density is bounded and positive, we establish a uniform diameter estimate for solutions to the planar $L_p$ dual Minkowski problem when $0<p<1$ and $q\ge 2$. We also prove the uniqueness and positivity of solutions to the $L_p$ Minkowski problem when the density of the measure is sufficiently close to a constant in $C^\alpha$.

math.DG

IMEXLBM 1.0: A Proxy Application based on the Lattice Boltzmann Method for solving Computational Fluid Dynamic problems on GPUs

The US Department of Energy launched the Exascale Computing Project (ECP) in 2016 as part of a coordinated effort to achieve the next generation of high-performance computing (HPC) and to accelerate scientific discovery. The Exascale Proxy Applications Project began within the ECP to: (1) improve the quality of proxies created by the ECP (2) provide small, simplified codes which share important features of large applications and (3) capture programming methods and styles that drive requirements for compilers and other elements of the tool chain. This article describes one Proxy Application (or "proxy app") suite called IMEXLBM which is an open-source, self-contained code unit, with minimal dependencies, that is capable of running on heterogeneous platforms like those with graphic processing units (GPU) for accelerating the calculation. In particular, we demonstrate functionality by solving a benchmark problem in computational fluid dynamics (CFD) on the ThetaGPU machine at the Argonne Leadership Computing Facility (ALCF). Our method makes use of a domain-decomposition technique in conjunction with the message-passing interface (MPI) standard for distributed memory systems. The OpenMP application programming interface (API) is employed for shared-memory multi-processing and offloading critical kernels to the device (i.e. GPU). We also verify our effort by comparing data generated via CPU-only calculations with data generated with CPU+GPU calculations. While we demonstrate efficacy for single-phase fluid problems, the code-unit is designed to be versatile and enable new physical models that can capture complex phenomena such as two-phase flow with interface capture.

cs.CE