arXiv subjects

Jun Hu

Publications and source records attributed to Jun Hu.

At least 253 records · Page 14Linked to original sources

arXiv2016

Quiver Schur algebras for linear quivers

We define a graded quasi-hereditary covering for the cyclotomic quiver Hecke algebras $\mathcal{R}^Λ_n$ of type $A$ when $e=0$ (the linear quiver) or $e\ge n$. We show that these algebras are quasi-hereditary graded cellular algebras by giving explicit homogeneous bases for them. When $e=0$ we show that the KLR grading on the quiver Hecke algebras is compatible with the gradings on parabolic category $\mathcal{O}$ previously introduced in the works of Beilinson, Ginzburg and Soergel and Backelin. As a consequence, we show that when $e=0$ our graded Schur algebras are Koszul over field of characteristic zero. Finally, we give an LLT-like algorithm for computing the graded decomposition numbers of the quiver Schur algebras in characteristic zero when $e=0$.

math.RT↗

arXiv2016

A unified analysis of quasi-optimal convergence for adaptive mixed finite element methods

In this paper, we present a unified analysis of both convergence and optimality of adaptive mixed finite element methods for a class of problems when the finite element spaces and corresponding a posteriori error estimates under consideration satisfy five hypotheses. We prove that these five conditions are sufficient for convergence and optimality of the adaptive algorithms under consideration. The main ingredient for the analysis is a new method to analyze both discrete reliability and quasi-orthogonality. This new method arises from an appropriate and natural choice of the norms for both the discrete displacement and stress spaces, namely, a mesh-dependent discrete $H^1$ norm for the former and a $L^2$ norm for the latter, and a newly defined projection operator from the discrete stress space on the coarser mesh onto the discrete divergence free space on the finer mesh. As applications, we prove these five hypotheses for the Raviart--Thomas and Brezzi--Douglas--Marini elements of the Poisson and Stokes problems in both 2D and 3D.

math.NA↗

arXiv2015

Neutrino Physics with JUNO

The Jiangmen Underground Neutrino Observatory (JUNO), a 20 kton multi-purpose underground liquid scintillator detector, was proposed with the determination of the neutrino mass hierarchy as a primary physics goal. It is also capable of observing neutrinos from terrestrial and extra-terrestrial sources, including supernova burst neutrinos, diffuse supernova neutrino background, geoneutrinos, atmospheric neutrinos, solar neutrinos, as well as exotic searches such as nucleon decays, dark matter, sterile neutrinos, etc. We present the physics motivations and the anticipated performance of the JUNO detector for various proposed measurements. By detecting reactor antineutrinos from two power plants at 53-km distance, JUNO will determine the neutrino mass hierarchy at a 3-4 sigma significance with six years of running. The measurement of antineutrino spectrum will also lead to the precise determination of three out of the six oscillation parameters to an accuracy of better than 1\%. Neutrino burst from a typical core-collapse supernova at 10 kpc would lead to ~5000 inverse-beta-decay events and ~2000 all-flavor neutrino-proton elastic scattering events in JUNO. Detection of DSNB would provide valuable information on the cosmic star-formation rate and the average core-collapsed neutrino energy spectrum. Geo-neutrinos can be detected in JUNO with a rate of ~400 events per year, significantly improving the statistics of existing geoneutrino samples. The JUNO detector is sensitive to several exotic searches, e.g. proton decay via the $p\to K^++\barν$ decay channel. The JUNO detector will provide a unique facility to address many outstanding crucial questions in particle and astrophysics. It holds the great potential for further advancing our quest to understanding the fundamental properties of neutrinos, one of the building blocks of our Universe.

physics.ins-det↗

arXiv2015

Phosphorene: Synthesis, Scale-up, and Quantitative Optical Spectroscopy

Phosphorene, a two-dimensional (2D) monolayer of black phosphorus, has attracted considerable theoretical interest, although the experimental realization of monolayer, bilayer, and few-layer flakes has been a significant challenge. Here we systematically survey conditions for liquid exfoliation to achieve the first large-scale production of monolayer, bilayer, and few-layer phosphorus, with exfoliation demonstrated at the 10-gram scale. We describe a rapid approach for quantifying the thickness of 2D phosphorus and show that monolayer and few-layer flakes produced by our approach are crystalline and unoxidized, while air exposure leads to rapid oxidation and the production of acid. With large quantities of 2D phosphorus now available, we perform the first quantitative measurements of the material's absorption edge-which is nearly identical to the material's band gap under our experimental conditions-as a function of flake thickness. Our interpretation of the absorbance spectrum relies on an analytical method introduced in this work, allowing the accurate determination of the absorption edge in polydisperse samples of quantum-confined semiconductors. Using this method, we found that the band gap of black phosphorus increased from 0.33 +/- 0.02 eV in bulk to 1.88 +/- 0.24 eV in bilayers, a range that is larger than any other 2D material. In addition, we quantified a higher-energy optical transition (VB-1 to CB), which changes from 2.0 eV in bulk to 3.23 eV in bilayers. This work describes several methods for producing and analyzing 2D phosphorus while also yielding a class of 2D materials with unprecedented optoelectronic properties.

cond-mat.mtrl-sci↗

arXiv2015

On involutions in symmetric groups and a conjecture of Lusztig

Let $(W, S)$ be a Coxeter system equipped with a fixed automorphism $\ast$ of order $\leq 2$ which preserves $S$. Lusztig (and with Vogan in some special cases) have shown that the space spanned by set of "twisted" involutions was naturally endowed with a module structure of the Hecke algebra of $(W, S)$. Lusztig has conjectured that this module is isomorphic to the right ideal of the Hecke algebra (with Hecke parameter $u^2$) associated to $(W,S)$ generated by the element $X_{\emptyset}:=\sum_{w^\ast=w}u^{-\ell(w)}T_w$. In this paper we prove this conjecture in the case when $\ast=\text{id}$ and $W$ is the symmetric group on $n$ letters.

math.RT↗

arXiv2015

Capacity of the Adini element for biharmonic equations

This paper is devoted to the convergence analysis of the Adini element scheme for the fourth order problem in arbitrary dimension. We prove that, the Adini element scheme is $\mathcal{O}(h^2)$ order convergent in energy norm provided the exact solution is in $H^4$, and the convergence rate in $L^2$ norm can not be nontrivially higher than $\mathcal{O}(h^2)$ order. Numerical verifications are presented.

math.NA↗

arXiv2015

Locally Non-rigid Registration for Mobile HDR Photography

Image registration for stack-based HDR photography is challenging. If not properly accounted for, camera motion and scene changes result in artifacts in the composite image. Unfortunately, existing methods to address this problem are either accurate, but too slow for mobile devices, or fast, but prone to failing. We propose a method that fills this void: our approach is extremely fast---under 700ms on a commercial tablet for a pair of 5MP images---and prevents the artifacts that arise from insufficient registration quality.

cs.CV↗

arXiv2015

Candidate source of flux noise in SQUIDs: adsorbed oxygen molecules

A major obstacle to using SQUIDs as qubits is flux noise. We propose that the heretofore mysterious spins producing flux noise could be $O_2$ molecules adsorbed on the surface. Using density functional theory calculations, we find that an $O_2$ molecule adsorbed on an α-alumina surface has a magnetic moment of ~1.8 μB. When the spin is oriented perpendicular to the axis of the O-O bond, the barrier to spin rotations is about 10 mK. Monte Carlo simulations of ferromagnetically coupled, anisotropic XY spins on a square lattice find 1/f magnetization noise, consistent with flux noise in Al SQUIDs.

cond-mat.supr-con↗

arXiv2015

Finite element approximations of symmetric tensors on simplicial grids in Rn: the high order case

The design of mixed finite element methods in linear elasticity with symmetric stress approximations has been a longstanding open problem until Arnold and Winther designed the first family of mixed finite elements where the discrete stress space is the space of $H(\d,Ω; \mathbb {S})$---$P_{k+1}$ tensors whose divergence is a $P_{k-1}$ polynomial on each triangle for $k\geq 2$.Such a two dimensional family was extended, by Arnold, Awanou and Winther, to a three dimensional family of mixed elements where the discrete stress space is the space of $H(\d,Ω; \mathbb {S})$---$P_{k+2}$ tensors, whose divergence is a $P_{k-1}$ polynomial on each tetrahedron for $k\geq 2$. In this paper, we are able to construct, in a unified fashion, mixed finite element methods with symmetric stress approximations on an arbitrary simplex in $\mathbb{R}^n$ for any space dimension. On the contrary, the discrete stress space here is the space of $H(\d,Ω;\mathbb {S})$---$P_k$ tensors, and the discrete displacement space here is the space of $L^2(Ω; \mathbb{R}^n)$---$P_{k-1}$ vectors for $k\geq n+1$. These finite element spaces are defined with respect to an arbitrary simplicial triangulation of the domain, and can be regarded as extensions to any dimension of those in two and three dimensions by Hu and Zhang.

math.NA↗

arXiv2015

Finite element approximations of symmetric tensors on simplicial grids in Rn: the lower order case

In this paper, we construct, in a unified fashion, lower order finite element subspaces of spaces of symmetric tensors with square-integrable divergence on a domain in any dimension. These subspaces are essentially the symmetric H(div)-Pk (1=<k<=n) tensor spaces, enriched, for each n-1 dimensional simplex, by (n+1)n/2 H(div)-Pn+1 bubble functions when 1=< k<= n-1, and by (n-1)n/2 H(div)-P n+1 bubble functions when k= n. These spaces can be used to approximate the symmetric matrix field in a mixed formulation problem where the other variable is approximated by discontinuous piecewise Pk-1 polynomials. This in particular leads to first order mixed elements on simplicial grids with total degrees of freedom per element $18$ plus $3$ in 2D, 48 plus 6 in 3D. The previous record of the degrees of freedom of first order mixed elements is, 21 plus 3 in 2D, and 156 plus 6 in 3D, on simplicial grids. We also derive, in a unified way and without using any tools like differential forms, a family of auxiliary mixed finite elements in any dimension. One example in this family is the Raviart-Thomas elements in one dimension, the second example is the mixed finite elements for linear elasticity in two dimensions due to Arnold and Winther, the third example is the mixed finite elements for linear elasticity in three dimensions due to Arnold, Awanou and Winther.

math.NA↗

arXiv2015

Chern Half Metals: A New Class of Topological Materials to Realize the Quantum Anomalous Hall Effect

The search of new topological insulators that demonstrate the quantum anomalous Hall effect (QAHE) is a cutting-edge research topic in condensed matter physics and materials science. So far, the QAHE has been observed only in Cr-doped (Bi,Sb)2Te3 at extremely low temperature. Therefore, it is important to find new materials with large topological band gap and high thermal stability for the realization of the QAHE. Based on first-principles and tight-binding model calculations, we discovered a new class of topological phase$-$Chern half metal which manifests the QAHE in one spin channel while is metallic in the other spin channel$-$in Co or Rh deposited graphene. Meanwhile, these systems have large perpendicular magnetic anisotropy energies of 5.3 and 11.5 meV, necessary for the observation of the QAHE at reasonably high temperature.

cond-mat.mtrl-sci↗

arXiv2015

Magnetic anisotropy of FePt nanoparticles

We carry out a systematic theoretical investigation of Magneto Crystalline Anisotropy (MCA) of L10 FePt clusters with alternating Fe and Pt planes along the (001) direction. We calculate the structural relaxation and magnetic moment of each cluster by using ab initio spin-polarized density functional theory (DFT), and the MCA with both spin-polarized DFT (including spin-orbit coupling self-consistently) and the torque method. We find that the MCA of any composite structure of a given size is enhanced with respect to that of the same-sized pure Pt or pure Fe cluster as well as to that of any pair of Fe and Pt atoms in bulk L10 FePt. This enhancement results from the hybridization we observe between the 3d orbital of the Fe atoms and the 5d orbital of their Pt neighbors. This hybridization, however, affects the electronic properties of the component atoms in significantly different ways. While it somewhat increases the spin moment of the Fe atoms, it has little effect on their orbital moment; at the same time, it greatly increases both the spin and orbital moment of the Pt atoms. Given the fact that the spin-orbit coupling (SOC) constant of Pt is about 7 times greater than that of Fe, this Fe-induced jump in the orbital moment of the Pt atoms produces the increase in MCA of the composite structures over that of their pure counterparts. That any composite structure exhibits higher MCA than bulk L10 FePt results from the lower coordination of Pt atoms in the cluster, whether Fe or Pt predominates within it. We also find that bipyramidal clusters whose central layer is Pt have higher MCA than their same-sized counterparts whose central layer is Fe. This results from the fact that Pt atoms in such configurations are coordinated with more Fe atoms than in the latter. By thus participating in more instances of hybridization, they contribute higher orbital moments to the overall MCA of the unit.

cond-mat.mes-hall↗

arXiv2015

A new family of efficient conforming mixed finite elements on both rectangular and cuboid meshes for linear elasticity in the symmetric formulation

A new family of mixed finite elements is proposed for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. For two dimensions, the normal stress of the matrix-valued stress field is approximated by an enriched Brezzi-Douglas-Fortin-Marini element of order $k$, and the shear stress by the serendipity element of order $k$, the displacement field by an enriched discontinuous vector-valued $P_{k-1}$ element. The degrees of freedom on each element of the lowest order element, which is of first order, is $10$ plus $4$. For three dimensions, the normal stress is approximated by an enriched Raviart-Thomas element of order $k$, and each component of the shear stress by a product space of the serendipity element space of two variables and the space of polynomials of degree $\leq k-1$ with respect to the rest variable, the displacement field by an enriched discontinuous vector-valued $Q_{k-1}$ element. The degrees of freedom on each element of the lowest order element, which is of first order, is $21$ plus $6$. A family of reduced elements is also proposed by dropping some interior bubble functions of the stress and employing the discontinuous vector-valued $P_{k-1}$ (resp. $Q_{k-1}$) element for the displacement field on each element. As a result the lowest order elements have $8$ plus $2$ and $18$ plus $3$ degrees of freedom on each element for two and three dimensions, respectively. The well-posedness condition and the optimal a priori error estimate are proved for this family of finite elements. Numerical tests are presented to confirm the theoretical results.

math.NA↗

arXiv2015

A family of conforming mixed finite elements for linear elasticity on triangular grids

This paper presents a family of mixed finite elements on triangular grids for solving the classical Hellinger-Reissner mixed problem of the elasticity equations. In these elements, the matrix-valued stress field is approximated by the full $C^0$-$P_k$ space enriched by $(k-1)$ $H(\d)$ edge bubble functions on each internal edge, while the displacement field by the full discontinuous $P_{k-1}$ vector-valued space, for the polynomial degree $k\ge 3$. The main challenge is to find the correct stress finite element space matching the full $C^{-1}$-$P_{k-1}$ displacement space. The discrete stability analysis for the inf-sup condition does not rely on the usual Fortin operator, which is difficult to construct. It is done by characterizing the divergence of local stress space which covers the $P_{k-1}$ space of displacement orthogonal to the local rigid-motion. The well-posedness condition and the optimal a priori error estimate are proved for this family of finite elements. Numerical tests are presented to confirm the theoretical results.

math.NA↗

arXiv2015

Superconvergence of both two and three dimensional rectangular Morley elements for biharmonic equations

In the present paper, superconvergence of second order, after an appropriate postprocessing, is achieved for both the two and three dimensional first order rectangular Morley elements of biharmonic equations. The analysis is dependent on superconvergence of second order for the consistency error and a corrected canonical interpolation operator, which help to establish supercloseness of second order for the corrected canonical interpolation. Then the final superconvergence follows a standard postprocessing. For first order nonconforming finite element methods of both two and three dimensional fourth order elliptic problems, it is the first time that full superconvergence of second order is obtained without an extra boundary condition imposed on exact solutions. It is also the first time that superconvergence is established for nonconforming finite element methods of three dimensional fourth order elliptic problems. Numerical results are presented to demonstrate the theoretical results.

math.NA↗

arXiv2014

Lower bounds of eigenvalues of the biharmonic operators by the rectangular Morley element methods

In this paper, we analyze the lower bound property of the discrete eigenvalues by the rectangular Morley elements of the biharmonic operators in both two and three dimensions. The analysis relies on an identity for the errors of eigenvalues. We explore a refined property of the canonical interpolation operators and use it to analyze the key term in this identity. In particular, we show that such a term is of higher order for two dimensions, and is negative and of second order for three dimensions, which causes a main difficulty. To overcome it, we propose a novel decomposition of the first term in the aforementioned identity. Finally, we establish a saturation condition to show that the discrete eigenvalues are smaller than the exact ones. We present some numerical results to demonstrate the theoretical results.

math.NA↗

arXiv2014

Seminormal forms and cyclotomic quiver Hecke algebras of type $A$

This paper shows that the cyclotomic quiver Hecke algebras of type $A$, and the gradings on these algebras, are intimately related to the classical seminormal forms. We start by classifying all seminormal bases and then give an explicit "integral" closed formula for the Gram determinants of the Specht modules in terms of the combinatorics which utilizes the KLR gradings. We then use seminormal forms to give a deformation of the KLR algebras of type $A$. This makes it possible to study the cyclotomic quiver Hecke algebras in terms of the semisimple representation theory and seminormal forms. As an application we construct a new distinguished graded cellular basis of the cyclotomic KLR algebras of type $A$.

math.RT↗

arXiv2014

Molecular-Scale Hydrophilicity Induced by Solute: Molecular-thick Charged Pancakes of Aqueous Salt Solution on Hydrophobic Carbon-based Surfaces

We directly observed molecular-thick aqueous salt-solution pancakes on a hydrophobic graphite surface under ambient conditions employing atomic force microscopy. This observation indicates the unexpected molecular-scale hydrophilicity of the salt solution on graphite surfaces, which is different from the macroscopic wetting property of a droplet standing on the graphite surface. Interestingly, the pancakes spontaneously displayed strong positively charged behavior. Theoretical studies showed that the formation of such positively charged pancakes is attributed to cation-π interactions between Na+ ions in the aqueous solution and aromatic rings on the graphite surface, promoting the adsorption of water molecules together with cations onto the graphite surface; i.e., Na+ ions as a medium adsorbed to the graphite surface through cation-π interactions on one side while at the same time bonding to water molecules through hydration interaction on the other side at a molecular scale. These findings suggest that actual interactions regarding carbon-based graphitic surfaces including those of graphene, carbon nanotubes, and biochar may be significantly different from existing theory and they provide new insight into the control of surface wettability, interactions and related physical, chemical and biological processes.

cond-mat.soft↗