arXiv subjects

Jae Hun Kim

Publications and source records attributed to Jae Hun Kim.

6 recordsLinked to original sources

arXiv2025

Stochastic Partial Differential Equations Associated with Pseudo-Differential Operators and Hilbert Space-Valued Gaussian Processes

In this paper, we prove the unique existence and investigate the $L^{p}$-regularity of solutions to stochastic partial differential equations in Hilbert spaces associated with pseudo-differential operators, driven by Hilbert space-valued Gaussian processes that satisfy certain regularity conditions for the covariance kernels of the Gaussian processes. For our purposes, we develop an $L^{p}$-regularity framework for the solutions to the stochastic partial differential equations associated with pseudo-differential operators. As the main tools, we establish the $p$-th moment maximal inequality for stochastic integrals with respect to a Hilbert space-valued Gaussian process and a Littlewood-Paley type inequality for Banach space-valued functions. Additionally, during our study, we improved the sufficient conditions for Fourier multipliers and examined the covariance kernels for Gaussian processes.

math.AP↗

arXiv2025

A Generalization of Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo Differential Operators

In this paper, we first prove that the Littlewood-Paley $g$-function, related to the convolution corresponding to the composition of pseudo-differential operator and evolution system associated with pseudo-differential operators, is a bounded operator from $L^{q}((a,b)\times \mathbb{R}^{d};V)$ with a Hilbert space $V$ into $L^{q}((a,b)\times \mathbb{R}^{d})$. Secondly, we prove that the sharp function of the Littlewood-Paley $g$-function is bounded by some maximal function. Finally, by applying Fefferman-Stein theorem and Hardy-Littlewood maximal theorem, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators.

math.AP↗

arXiv2025

Littlewood-Paley Type Inequality for Evolution Systems Associated with Pseudo-Differential Operators

In this paper, we first prove that the kernel of convolution operator, corresponding the composition of pseudo-differential operator and evolution system associated with the symbol depending on time, satisfies the H\"ormander's condition. Secondly, we prove that the convolution operator is a bounded linear operator from the Besov space on $\mathbb{R}^{d}$ into $L^{q}(\mathbb{R}^{d};V)$ for a Banach space $V$. Finally, by applying the Calder\'{o}n-Zygmund theorem for vector-valued functions, we prove the Littlewood-Paley type inequality for evolution systems associated with pseudo-differential operators.

math.AP↗

arXiv2023

Orientation disparity in GaN/graphene/$m$-sapphire: control-based re-examination of thru-hole epitaxy

The crystallographic orientation of films grown on 2D-masked substrates is often used to infer the pathway among remote, van der Waals, and thru-hole (pinhole-seeded) epitaxy. However, attribution of a specific growth mechanism based on orientation can be ambiguous unless mask continuity and substrate pre-treatment are evaluated within a single process window. We compare GaN grown under identical conditions on four m-plane sapphire templates: (i) bare, (ii) "graphene-grown" (high-temperature Ar/H2 with CH4 on), (iii) "anneal-only" (high-temperature Ar/H2 with CH4 off), and (iv) graphene oxide spin-coated and reduced on pristine sapphire. GaN selects (103) on graphene-grown and anneal-only m-plane sapphire, selects (100) on bare m-plane sapphire, and is predominantly (100) with a minority (103) on graphene oxide spin-coated and reduced/pristine m-plane sapphire. High-resolution TEM shows that, on partly graphene-covered samples, nucleation occurs on exposed sapphire (thru-hole), not on graphene, providing mechanism evidence independent of orientation. Within this window, the substrate surface state set by high-temperature Ar/H2 pre-treatment (rather than mask continuity) primarily governs orientation, while open-area effects can play a secondary role. Thus, preferred orientation alone may not determine the growth mechanism; mask continuity and substrate pre-treatment must be explicitly controlled when using orientation as evidence for mechanism assignment.

cond-mat.mtrl-sci↗

arXiv2015

Anomalous Lattice Dynamics of Mono-, Bi-, and Tri-layer WTe2

Tungsten ditelluride (WTe2) is a layered material that exhibits excellent magnetoresistance and thermoelectric behaviors, which are deeply related with its distorted orthorhombic phase that may critically affect the lattice dynamics. Here, for the first time, we present comprehensive characterization of the Raman spectroscopic behavior of WTe2 from bulk to monolayer using experimental and computational methods. We discover that mono and bi-layer WTe2 can be easily identified by Raman spectroscopy since double or single Raman modes that are observed in higher-layer WTe2 are substantially suppressed in the monolayer and bilayer WTe2, respectively. In addition, different from hexagonal metal dichalcogenides, the frequency of in-plane mode of WTe2 remains almost constant as the layer number decreases, while the other Raman modes consistently blueshift. First-principles calculation validates the experiments and reveals that the negligible shift of the mode is attributed to the lattice vibration along the tungsten chains that make WTe2 structurally one-dimensional.

cond-mat.mes-hall↗

arXiv2015

Highly sensitive and selective sugar detection by terahertz nano-antennas

Molecular recognition and discrimination of carbohydrates are important because carbohydrates perform essential roles in most living organisms for energy metabolism and cell-to-cell communication. Nevertheless, it is difficult to identify or distinguish various carbohydrate molecules owing to the lack of a significant distinction in the physical or chemical characteristics. Although there has been considerable effort to develop a sensing platform for individual carbohydrates selectively using chemical receptors or an ensemble array, their detection and discrimination limits have been as high in the millimolar concentration range. Here we show a highly sensitive and selective detection method for the discrimination of carbohydrate molecules using nano-slot-antenna array-based sensing chips which operate in the terahertz frequency range. This THz metamaterial sensing tool recognizes various types of carbohydrate molecules over a wide range of molecular concentrations. Strongly localized and enhanced terahertz transmission by nano-antennas can effectively increase the molecular absorption cross sections, thereby enabling the detection of these molecules even at low concentrations. We verified the performance of nano-antenna sensing chip by both THz spectra and images of transmittance. Screening and identification of various carbohydrates can be applied to test even real market beverages with a high sensitivity and selectivity.

physics.optics↗