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Anh Tuan Duong

Publications and source records attributed to Anh Tuan Duong.

12 recordsLinked to original sources
arXiv2026

The weighted $L^2$-Caffarelli-Kohn-Nirenberg inequalities for the curl-free vector fields and second order derivatives: The sharp constants and stability estimates

In this paper, we study the weighted $L^2$-Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields and second order derivatives. Firstly, we prove a family of the sharp weighted second order $L^2$-Caffarelli-Kohn-Nirenberg inequalities that complements the results in [{\it C. Cazacu, J. Flynn and N. Lam, Calc. Var. Partial Differential Equations 62 (2023), no. 4, Paper No. 118, 26 pp.}] and [{\it A. T. Duong and V. H. Nguyen, On the sharp second order Caffarelli-Kohn-Nirenberg inequality. Ann. Fenn. Math., 50(1):275--286, 2025}]. Secondly, we establish a stability version of the sharp weighted $L^2$-Caffarelli-Kohn-Nirenberg inequalities for curl-free vector fields proved by Cazacu, Flynn and Lam. Finally, we prove a stability estimate for the sharp weighted second order $L^2$-Caffarelli-Kohn-Nirenberg inequalities established in this paper. Our approach is based on the spherical harmonic decomposition method, the one dimensional integral inequalities and their improvements.

math.AP↗
arXiv2026

Liouville Type Results for Quasilinear Elliptic Inequalities Involving Gradient Terms on Weighted Graphs

In this paper, we study the following quasi-linear elliptic inequality $Δ_m u +u^p |\nabla u|^q \leqslant 0$ on weighted graphs, where $(m,p,q)\in (1,\infty)\times\mathbb{R}\times\mathbb{R}$. According to the ranges of parameters $(m, p, q)$, we establish the non-existence of nontrivial positive solutions under the corresponding sharp volume growth conditions. Our results can be viewed as a discrete generalization of their counterparts on Riemannian manifolds established by [Sun, Yuhua; Xiao, Jie; Xu, Fanheng, Math. Ann. 384 (2022), no. 3-4, 1309--1341.]. However, this generalization is far from trivial, many results exhibit significant differences from the manifold setting, highlighting the distinct behaviors and challenges that arise in the discrete weighted graph framework.

math.AP↗
arXiv2026

Non-existence results for a system of wave inequalities on locally finite graphs

Let $V$ be a locally finite, connected and weighted graph. We study non-existence results of non-trivial, non-negative solutions of the system $$ \begin{cases} u_{t t}-Δu \geq h_1|v|^p & \text { in } V \times(0, \infty), v_{t t}-Δv \geq h_2|u|^q & \text { in } V \times(0, \infty), u=u_0;\;v=v_0 & \text { in } V \times\{0\}, u_t=u_1;\;v_t=v_1 & \text { in } V \times\{0\}, \end{cases}$$ where $p,q>1$, $h_1, h_2$ are positive potentials. Under some volume growth condition of a ball, we prove that the system has no non-trivial non-negative solutions. In particular, our result is a natural extension of that in [\textit{D.~D.~Monticelli, F.~Punzo, and J.~Somaglia. Nonexistence results for the semilinear wave equation on graphs. arXiv.2506.08697, 2025.}] from a single inequality to a system.

math.AP↗
arXiv2025

Blow up results and lifespan estimates for nonlinear damped wave equations on weighted graphs

In this article, we are interested in studying the Cauchy problems for nonlinear damped wave equations and their systems on a weighted graph. Our main purpose is two-fold, namely, under certain conditions for volume growth of a ball and the initial data we would like to not only prove nonexistence of global (in time) weak solutions but also indicate lifespan estimates for local (in time) weak solutions when a blow-up phenomenon in finite time occurs. Throughout the present paper, we will partially give a positive answer for the optimality of our results by an application to the $n$-dimensional integer lattice graph $\Z^n$ to recover the well-known results in the Euclidean setting.

math.AP↗
arXiv2024

The Discovery of Giant Positive Magnetoresistance in Proximity to Helimagnetic Order in Manganese Phosphide Nanostructured Films

The study of magnetoresistance (MR) phenomena has been pivotal in advancing magnetic sensors and spintronic devices. Helimagnets present an intriguing avenue for spintronics research. Theoretical predictions suggest that MR magnitude in the helimagnetic (HM) regime surpasses that in the ferromagnetic (FM) regime by over an order of magnitude. However, in metallic helimagnets like manganese phosphide, MR in the HM phase remains modest (10%), limiting its application in MR devices. Here, a groundbreaking approach is presented to achieve a giant low field MR effect in nanostructured manganese phosphide films by leveraging confinement and strain effects along with spin helicity. Unlike the modest MR observed in bulk manganese phosphide single crystals and large grain polycrystalline films, which exhibit a small negative MR in the FM region (2%) increasing to 8% in the HM region across 10-300 K, a grain size-dependent giant positive MR (90%) is discovered near FM to HM transition temperature (110 K), followed by a rapid decline to a negative MR below 55 K in manganese phosphide nanocrystalline films. These findings illuminate a novel strain-mediated spin helicity phenomenon in nanostructured helimagnets, presenting a promising pathway for the development of high-performance MR sensors and spintronic devices through the strategic utilization of confinement and strain effects.

physics.app-ph↗
arXiv2022

The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle

In this paper we prove a class of second order Caffarelli-Kohn-Nirenberg inequalities which contains the sharp second order uncertainty principle recently established by Cazacu, Flynn and Lam \cite{CFL2020} as a special case. We also show the sharpness of our inequalities for several classes of parameters. Finally, we prove two stability versions of the sharp second order uncertainty principle of Cazacu, Flynn and Lam by showing that the difference of both sides of the inequality controls the distance to the set of extremal functions in $L^2$ norm of gradient of functions.

math.FA↗
arXiv2022

Spin Seebeck effect in iron oxide thin films: Effects of phase transition, phase coexistence, and surface magnetism

Understanding impacts of phase transition, phase coexistence, and surface magnetism on the longitudinal spin Seebeck effect (LSSE) in a magnetic system is essential to manipulate the spin to charge current conversion efficiency for spincaloritronic applications. We aim to elucidate these effects by performing a comprehensive study of the temperature dependence of LSSE in biphase iron oxide (BPIO = alpha-Fe2O3 + Fe3O4) thin films grown on Si (100) and Al2O3 (111) substrates. A combination of temperature-dependent anomalous Nernst effect (ANE) and electrical resistivity measurements show that the contribution of ANE from the BPIO layer is negligible compared to the intrinsic LSSE in the Si/BPIO/Pt heterostructure even at room temperature. Below the Verwey transition of the Fe3O4 phase, the total signal across BPIO/Pt is dominated by the LSSE. Noticeable changes in the intrinsic LSSE signal for both Si/BPIO/Pt and Al2O3/BPIO/Pt heterostructures around the Verwey transition of the Fe3O4 phase and the antiferromagnetic (AFM) Morin transition of the alpha-Fe2O3 phase are observed. The LSSE signal for Si/BPIO/Pt is found to be almost two times greater than that for Al2O3/BPIO/Pt, an opposite trend is observed for the saturation magnetization though. Magnetic force microscopy reveals the higher density of surface magnetic moments of the Si/BPIO film compared to the Al2O3/BPIO film, which underscores a dominant role of interfacial magnetism on the LSSE signal and thereby explains the larger LSSE for Si/BPIO/Pt.

cond-mat.mtrl-sci↗
arXiv2021

Strain-modulated helimagnetism and emergent magnetic phase diagrams in highly crystalline MnP nanorod films

We explore strain-modulated helimagnetism in highly crystalline MnP nanorod films grown on Si(100) substrates using molecular beam epitaxy. The strained MnP film exhibits a paramagnetic to ferromagnetic (PM-FM) phase transition at TC ~ 279 K, and the FM to helical phase transition at TN ~ 110 K. The value of TN is greater than TN ~ 47 K for the MnP single crystal, indicating strong strain-modulated helimagnetic states in the MnP nanorod film. The presence of significant thermal hysteresis in the helical phase indicates coexistence of competing magnetic interactions, leading to the first-order metamagnetic transition. Similar to its single crystal counterpart, an anisotropic magnetic effect is observed in the MnP film, which is independently confirmed by magnetic hysteresis loop and radio-frequency transverse susceptibility (TS) measurements. The evolution of screw (SCR) to CONE and FAN phase is precisely tracked from magnetization versus magnetic field/temperature measurements. The temperature dependence of the anisotropy fields, extracted from the TS spectra, yields further insight into the competing nature of the magnetic phases. Unfolding of the different helical phases at T < 120 K (~TN) is analyzed by the temperature- and field-dependent magnetic entropy change. Based on these findings, the comprehensive magnetic phase diagrams of the MnP nanorod film are constructed for the first time for both the in-plane and out-of-plane magnetic field directions, revealing emergent strain/dimensionality-driven helical magnetic features that are absent in the magnetic phase diagram of the MnP single crystal.

cond-mat.mtrl-sci↗
arXiv2020

A plausible method of preparing the ideal p-n junction interface of a thermoelectric material by surface doping

Recent advances in two-dimensional (2D) crystals make it possible to realize an ideal interface structure that is required for device applications. Specifically, a p-n junction made of 2D crystals is predicted to exhibit an atomically well-defined interface that will lead to high device performance. Using angle-resolved photoemission spectroscopy, a simple surface treatment was shown to allow the possible formation of such an interface. Ta adsorption on the surface of a p-doped SnSe shifts the valence band maximum towards higher binding energy due to the charge transfer from Ta to SnSe that is highly localized at the surface due to the layered structure of SnSe. As a result, the charge carriers of the surface are changed from holes of its bulk characteristics to electrons, while the bulk remains as a p-type semiconductor. This observation suggests that the well-defined interface of a p-n junction with an atomically thin {\it n}-region is formed between Ta-adsorbed surface and bulk.

cond-mat.mtrl-sci↗
arXiv2020

Liouville type theorems for fractional elliptic problems

In this paper, we establish Liouville type theorems for stable solutions on the whole space $\mathbb R^N$ to the fractional elliptic equation $$(-Δ)^su=f(u)$$ where the nonlinearity is nondecreasing and convex. We also obtain a classification of stable solutions to the fractional Lane-Emden system $$\begin{cases} (-Δ)^s u = v^p \mbox{ in }\mathbb R^N (-Δ)^s v = u^q \mbox{ in }\mathbb R^N \end{cases}$$ with $p>1$ and $ q>1$. In our knowledge, this is the first classification result for stable solutions of the fractional Lane-Emden system in literature.

math.AP↗
arXiv2013

Trace asymptotics formula for the Schrödinger operators with constant magnetic fields

In this paper, we consider the 2D- Schrödinger operator with constant magnetic field $H(V)=(D_x-By)^2+D_y^2+V_h(x,y)$, where $V$ tends to zero at infinity and $h$ is a small positive parameter. We will be concerned with two cases: the semi-classical limit regime $V_h(x,y)=V(h x,h y)$, and the large coupling constant limit case $V_h(x,y)=h^{-δ} V(x,y)$. We obtain a complete asymptotic expansion in powers of $h^2$ of ${\rm tr}(Φ(H(V),h))$, where $Φ(\cdot,h)\in C^\infty_0(\mathbb R;\mathbb R)$. We also give a Weyl type asymptotics formula with optimal remainder estimate of the counting function of eigenvalues of $H(V)$.

math-ph↗