Gradient flow approach to an exponential thin film equation: global existence and latent singularity

In this work, we study a fourth order exponential equation, $u_t=\Delta e^{-\Delta u},$ derived from thin film growth on crystal surface in multiple space dimensions. We use the gradient flow method in metric space to characterize the latent singularity in global strong solution, which is intrinsic due to high degeneration. We define a suitable functional, which reveals where the singularity happens, and then prove the variational inequality solution under very weak assumptions for initial data. Moreover, the existence of global strong solution is established with regular initial data.Comment: latent singularity, curve of maximal slope. arXiv admin note: text overlap with arXiv:1711.07405 by other author

Nuclear dependence of azimuthal asymmetry in semi-inclusive deep inelastic scattering

Within the framework of a generalized factorization, semi-inclusive deeply inelastic scattering (SIDIS) cross sections can be expressed as a series of products of collinear hard parts and transverse-momentum-dependent (TMD) parton distributions and correlations. The azimuthal asymmetry $of unpolarized SIDIS in the small transverse momentum region will depend on both twist-2 and 3 TMD quark distributions in target nucleons or nuclei. Nuclear broadening of these twist-2 and 3 quark distributions due to final-state multiple scattering in nuclei is investigated and the nuclear dependence of the azimuthal asymmetry$$ is studied. It is shown that the azimuthal asymmetry is suppressed by multiple parton scattering and the transverse momentum dependence of the suppression depends on the relative shape of the twist-2 and 3 quark distributions in the nucleon. A Gaussian ansatz for TMD twist-2 and 3 quark distributions in nucleon is used to demonstrate the nuclear dependence of the azimuthal asymmetry and to estimate the smearing effect due to fragmentation.Comment: 9 pages in RevTex with 2 figure

Reevaluation of the density dependence of nucleon radius and mass in the global color symmetry model of QCD

With the global color symmetry model (GCM) at finite chemical potential, the density dependence of the bag constant, the total energy and the radius of a nucleon in nuclear matter is investigated. A relation between the nuclear matter density and the chemical potential with the action of QCD being taken into account is obtained. A maximal nuclear matter density for the existence of the bag with three quarks confined within is given. The calculated results indicate that, before the maximal density is reached, the bag constant and the total energy of a nucleon decrease, and the radius of a nucleon increases slowly, with the increasing of the nuclear matter density. As the maximal nuclear matter density is reached, the mass of the nucleon vanishes and the radius becomes infinite suddenly. It manifests that a phase transition from nucleons to quarks takes place.Comment: 18 pages, 3 figure

Quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave order

The quasiparticle states around a nonmagnetic impurity in electron-doped iron-based superconductors with spin-density-wave (SDW) order are investigated as a function of doping and impurity scattering strength. In the undoped sample, where a pure SDW state exists, two impurity-induced resonance peaks are observed around the impurity site and they are shifted to higher (lower) energies as the strength of the positive (negative) scattering potential (SP) is increased. For the doped samples where the SDW order and the superconducting order coexist, the main feature is the existence of sharp in-gap resonance peaks whose positions and intensity depend on the strength of the SP and the doping concentration. In all cases, the local density of states exhibits clear $C_2$ symmetry. We also note that in the doped cases, the impurity will divide the system into two sublattices with distinct values of magnetic order. Here we use the band structure of a two-orbital model, which considers the asymmetry of the As atoms above and below the Fe-Fe plane. This model is suitable to study the properties of the surface layers in the iron-pnictides and should be more appropriate to describe the scanning tunneling microscopy experiments.Comment: 11 pages, 18 figure

After-Tax Asset Allocation

This paper discusses after-tax asset allocation for individual investors, investigates mean-variance optimization models, and applies asset location under the after-tax framework. We demonstrate how the traditional allocation approaches fail to take tax properly into consideration. Based on Reichenstein’s early after-tax asset allocation researches, we improve the adjustment for risks of portfolio, especially for fixed income, by choosing appropriate tax rate. Also we test Reichenstein’s and the adjusted models by changing parameters and inputs to evaluate the new model. We illustrate how taxes and saving vehicles affect mean variance optimization and conclude the individual investors should locate bonds in tax-deferred accounts and stocks in taxable accounts

LMSFC: A Novel Multidimensional Index based on Learned Monotonic Space Filling Curves

The recently proposed learned indexes have attracted much attention as they can adapt to the actual data and query distributions to attain better search efficiency. Based on this technique, several existing works build up indexes for multi-dimensional data and achieve improved query performance. A common paradigm of these works is to (i) map multi-dimensional data points to a one-dimensional space using a fixed space-filling curve (SFC) or its variant and (ii) then apply the learned indexing techniques. We notice that the first step typically uses a fixed SFC method, such as row-major order and z-order. It definitely limits the potential of learned multi-dimensional indexes to adapt variable data distributions via different query workloads. In this paper, we propose a novel idea of learning a space-filling curve that is carefully designed and actively optimized for efficient query processing. We also identify innovative offline and online optimization opportunities common to SFC-based learned indexes and offer optimal and/or heuristic solutions. Experimental results demonstrate that our proposed method, LMSFC, outperforms state-of-the-art non-learned or learned methods across three commonly used real-world datasets and diverse experimental settings.Comment: Extended Version. Accepted by VLDB 202