Quarkonia measurements with STAR

We report results on quarkonium production from the STAR experiment at the Relativistic Heavy-Ion Collider (RHIC). J/ψ spectra in p+p and Cu+Cu collisions at  GeV with transverse momenta in the range of 0.5–14 GeV/c and 5–8 GeV/c, respectively, are presented. We find that for p _T >5 GeV/c yields in p+p collisions are consistent with those in minimum-bias Cu+Cu collisions scaled with the respective number of binary nucleon-nucleon collisions. In this range the nuclear modification factor, R _AA , is measured to be 0.9±0.2 (stat). For the first time at RHIC, high-p _T J/ψ-hadron correlations were studied in p+p collisions. Implications from our measurements on J/ψ production mechanisms, constraints on open bottom yields, and J/ψ dissociation mechanisms at high-p _T are discussed. In addition, we give a brief status of measurements of ϒ production in p+p and Au+Au collisions and present projections of future quarkonia measurements based on an upgrades to the STAR detector and increased luminosity achieved through stochastic cooling of RHIC.     

Quarkonia in a Gluonic Background Field

We give a systematic treatment of relativistic corrections to a Coulomb system of heavy quarks in a colour background field with a finite correlation time. The relativistic corrections turn out to be significant. Comparison with experiment favors a correlation time of 0.2−0.5 fm. We predict the ³S₁ − ¹S₀ and ³P₁ − ¹P₁ hyperfine splitting.     

Rayleigh-Ritz variational method with suitable asymptotic behaviour

This paper considers the Rayleigh-Ritz variational calculations with non-orthogonal basis sets that exhibit the correct asymptotic behaviour. This approach is illustrated by constructing suitable basis sets for one-dimensional models such as the two double-well oscillators recently considered by other authors. The rate of convergence of the variational method proves to be considerably greater than the one exhibited by the recently developed orthogonal polynomial projection quantization.     

An improved variational method

In order to improve the unitarity of the S-matrix, an improved variational formulism is derived by proposing new generating functionals and adopting proper asymptotic boundary conditions for trial relative wave functions. The formulas with the weighted line-column balance for the single-channel and multi-channel scatterings, where the non-central interaction is implicitly considered, are presented. A numerical check is performed with a soluble model in a four coupled channel scattering problem. The result shows that the high accuracy and the unitarity of the S-matrix are reached.     

An improved variational method

In order to improve the unitarity of the S-matrix, an improved variational formulism is derived by proposing new generating functionals and adopting proper asymptotic boundary conditions for trial relative wave functions. The formulas with the weighted line-column balance for the single-channel and multi-channel scatterings, where the non-central interaction is implicitly considered, are presented. A numerical check is performed with a soluble model in a four coupled channel scattering problem. The result shows that the high accuracy and the unitarity of the S-matrix are reached.     

Modified variational iteration method

In this Letter, we introduce a modified variational iteration method by inserting some unknown parameters into the correctional functional. The main advantage of this method is that one can avoid the uncontrollability problems, of the nonzero endpoint conditions, encountered in the traditional variational iteration method. Moreover, the method is applied to some nonlinear equations and the numerical solutions reveal that the modified method is accurate and efficient to solve a large class of nonlinear differential equations. Furthermore, the method does not share the drawbacks of the conventional variational iteration method, namely the restriction of the order of the nonlinearity term or even the form of the boundary conditions.     

基于变分方法的混沌系统参数估计

提出一种基于变分原理的估计混沌系统未知参数的方法,对以x= F(x,θ) 为控制方程的所有混沌系统具有普适性.首先将混沌系统方程引入到目标泛函中;接着利用变分原理导出了混沌系统的伴随方程和待辨识参数泛函梯度的通用公式;然后设计了估计混沌系统未知参数的算法;最后对典型的Lorenz混沌系统和超混沌Chen系统的未知参数进行了估计.数值仿真结果表明该方法是一种非常有效的估计混沌系统未知参数的方法. 关键词： 混沌系统 参数估计 变分方法 伴随方程     

Quarkonia and heavy flavors at the LHC

Perspectives for measurements of quarkonia and heavy flavors in heavy ion collisions at the LHC are reviewed. Arrival of the final proofs: 20 April 2005     

Quarkonia from charmonium and renormalization group equations

A prediction of the upsilon and strangeonium spectra is made from the charmonium spectrum by solving the Salpeter equation using an identical potential to that used in charmonium. Effective quark masses and coupling parameters α_s are functions of the inter-quark distance according to the renormalization group equations. The use of the Fermi-Breit-Hamiltonian for obtaining the charmonium hyperfine splitting is criticized.     

D=1+2 phase diagram forZ N with a variational method

Trial ground state are constructed which forZ _N gauge theories inD=1+2 dimensions lead to phase diagrams which are in agreement both with theoretical expectations and Monte Carlo results. The nature of the phase transition is correctly predicted for eachN.     

A new many-particle variational method

The results of calculation of the properties of three- and four-particle systems within the framework of the recently suggested stochastic variational method (SVM) are presented. The 3N, 4N and 3α model systems with two-particle S-wave central forces have been investigated. The results of all calculations are compared with similar results of other workers, and a higher efficiency of the method proposed as compared with other methods is demonstrated.     

厄尔尼诺和南方涛动海气耦合模型中参数估计的变分方法

提出一种基于变分原理估计厄尔尼诺和南方涛动海气耦合模型中未知参数的方法. 首先将所研究的非线性海气耦合动力方程引入到目标泛函中; 接着利用变分方法导出伴随方程和待辨识参数泛函梯度的公式; 然后设计了估计未知参数的算法.数值试验结果表明变分方法是一 种能有效估计海气耦合非线性系统未知参数的方法.     

Research on the discrete variational method for a Birkhoffian system

In this paper, we present a new integration algorithm based on the discrete Pfaff-Birkhoff principle for Birkhoffian systems. It is proved that the new algorithm can preserve the general symplectic geometric structures of Birkhoffian systems. A numerical experiment for a damping oscillator system is conducted. The result shows that the new algorithm can better simulate the energy dissipation than the R-K method, which illustrates that we can numerically solve the dynamical equations by the discrete variational method in a Birkhoffian framework for the systems with a general symplectic structure. Furthermore, it is demonstrated that the results of the numerical experiments are determined not by the constructing methods of Birkhoffian functions but by whether the numerical method can preserve the inherent nature of the dynamical system.     

非线性映射参数辨识的离散变分方法

提出一种辨识非线性映射系统中未知参数的离散变分方法, 对以x_k+1 = F(x_k,θ)为状态控制方程的所有映射混沌系统具有通用性. 对典型的Logistic映射和Henón映射中的未知参数进行了估计, 仿真结果表明了该方法的有效性.     

A variational Bayesian method to inverse problems with impulsive noise

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback–Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm.     

The variational method in atomic scattering

This paper reviews the application of the variational method to the scattering (both elastic and inelastic) of electrons and positrons by atoms. The coupled equations of scattering theory are formulated using a pseudostate expansion. The Kohn variational procedure for multichannel scattering is derived. Many variants are considered, including the inverse Kohn procedure, the “optimized minimum norm”, the “optimized anomaly free”, and the “variational least squares”. Applications to both model and realistic problems are described. Results obtained for scattering by hydrogen, and by complex atoms are discussed.