Constantin and Iyer's representation formula for the Navier--Stokes equations on manifolds

The purpose of this paper is to establish a probabilistic representation formula for the Navier--Stokes equations on compact Riemannian manifolds. Such a formula has been provided by Constantin and Iyer in the flat case of $\mathbb R^n$ or of $\mathbb T^n$. On a Riemannian manifold, however, there are several different choices of Laplacian operators acting on vector fields. In this paper, we shall use the de Rham--Hodge Laplacian operator which seems more relevant to the probabilistic setting, and adopt Elworthy--Le Jan--Li's idea to decompose it as a sum of the square of Lie derivatives.Comment: 26 pages. We add Section 4 discussing the Killing vector fields on Riemannian symmetric spaces which satisfy the conditions in Section

Method for Extracting the Glueball Wave Function

We describe a nonperturbative method for calculating the QCD vacuum and glueball wave functions, based on an eigenvalue equation approach to Hamiltonian lattice gauge theory. Therefore, one can obtain more physical information than the conventional simulation methods. For simplicity, we take the 2+1 dimensional U(1) model as an example. The generalization of this method to 3+1 dimensional QCD is straightforward.Comment: 3 pages, Latex. Presented at Lattice 97: 15th International Symposium on Lattice Field Theory, Edinburgh, Scotland, 22-26 Jul 1997, to appear in Nucl. Phys. B(Proc. Suppl.

QCD at Finite temperature and density with staggered and Wilson quarks

One of the most challenging issues in particle physics is to study QCD in extreme conditions. Precise determination of the QCD phase diagram on temperature $T$ and chemical potential $\mu$ plane will provide valuable information for quark-gluon plasma (QGP) and neutron star physics. We present results for phase structure on the $(\mu, T)$ plane for lattice QCD with Wilson fermions from strong coupling Hamiltonian analysis and Kogut-Susskind Fermions from Lagrangian Monte Carlo simulations at intermediate coupling.Comment: Lattice 2004 (nonzero

The Effects of Outdoor Air Pollutants on the Costs of Stroke Hospitalizations in China

Stroke, the most frequent cause of severe disability and the second cause of death among adults in the world, brings tremendous mental and economic burden to patients and their families. Emerging evidence indicates that the air pollution mixture contributes to strokes. Knowing the relationship between the air pollution and the hospital costs of stroke can help us predict the costs due to air pollution, provide grounds for the allocation of medical insurance funds, and provide better working arrangements for CDC. However, few studies have examined this connection. We used time series analysis with a generalized additive model to estimate the associations between ambient air pollutions and hospital costs between the period of 2015–2017. We were surprised to find that although same-day air pollutions were positively associated with stroke mortality hospital costs were found to have a negatively association. Suggestive evidence of an association between fine particles and the costs of stroke were found: more serious air pollution increases the risk of stroke, but has a dampening effect on hospital costs. This study is the first step in optimizing medical resources, which is essential for policy making, service planning, and cost-effectiveness analysis of new therapeutic strategies

Hamiltonian lattice quantum chromodynamics at finite density with Wilson fermions

Quantum chromodynamics (QCD) at sufficiently high density is expected to undergo a chiral phase transition. Understanding such a transition is of particular importance for neutron star or quark star physics. In Lagrangian SU(3) lattice gauge theory, the standard approach breaks down at large chemical potential $\mu$, due to the complex action problem. The Hamiltonian formulation of lattice QCD doesn't encounter such a problem. In a previous work, we developed a Hamiltonian approach at finite chemical potential $\mu$ and obtained reasonable results in the strong coupling regime. In this paper, we extend the previous work to Wilson fermions. We study the chiral behavior and calculate the vacuum energy, chiral condensate and quark number density, as well as the masses of light hadrons. There is a first order chiral phase transition at zero temperature.Comment: 23 pages. Version accepted for publication in Physical Review