Proton sea quark flavour asymmetry and Roper resonance

We study the proton and the Roper resonance together with the meson cloud model, by constructing a Hamiltonian matrix and solving the eigenvalue equation. The proton sea quark flavour asymmetry and some properties of the Roper resonance are thus reproduced in one scheme.     

Roper resonance—Its static and dynamic properties from single- and double-pion production

In most investigations the Roper resonance is sensed only very indirectly via complex partial wave analyses. We find indications for its excitation in the pp→npπ⁺ reaction, where some resonance-like structure is observed in the invariant nπ⁺ mass spectrum at with a width of 150 MeV. The values fit very favorably to the most recent phase shift results as well as to the observations at BES. In near-threshold two-pion production pp→ppπ⁰π⁰ the Roper excitation and its subsequent decay into Nππ is the only dominant process. There we find its decay into the Nσ channel as the dominating decay process — in favor of a monopole nature of the Roper excitation.     

A hierarchical fracture model for the iterative multiscale finite volume method

An iterative multiscale finite volume (i-MSFV) method is devised for the simulation of multiphase flow in fractured porous media in the context of a hierarchical fracture modeling framework. Motivated by the small pressure change inside highly conductive fractures, the fully coupled system is split into smaller systems, which are then sequentially solved. This splitting technique results in only one additional degree of freedom for each connected fracture network appearing in the matrix system. It can be interpreted as an agglomeration of highly connected cells; similar as in algebraic multigrid methods. For the solution of the resulting algebraic system, an i-MSFV method is introduced. In addition to the local basis and correction functions, which were previously developed in this framework, local fracture functions are introduced to accurately capture the fractures at the coarse scale. In this multiscale approach there exists one fracture function per network and local domain, and in the coarse scale problem there appears only one additional degree of freedom per connected fracture network. Numerical results are presented for validation and verification of this new iterative multiscale approach for fractured porous media, and to investigate its computational efficiency. Finally, it is demonstrated that the new method is an effective multiscale approach for simulations of realistic multiphase flows in fractured heterogeneous porous media.     

Towards finite density QCD with Taylor expansions

Convergence properties of Taylor expansions of observables, which are also used in lattice QCD calculations at non-zero chemical potential, are analyzed in an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model. A recently developed algorithmic technique allows the calculation of higher-order Taylor expansion coefficients in functional approaches. This novel technique is for the first time applied to an effective Nf=2+1$N_f=2+1$ flavor Polyakov quark–meson model and the findings are compared with the full model solution at finite densities. The results are used to discuss prospects for locating the QCD phase boundary and a possible critical endpoint in the phase diagram.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Nearly conformal gauge theories in finite volume

We report new results on nearly conformal gauge theories with fermions in the fundamental representation of the SU(3)$\mathit{SU}(3)$ color gauge group as the number of fermion flavors is varied in the Nf=4–16$N_f=4\text{–}16$ range. To unambiguously identify the chirally broken phase below the conformal window we apply a comprehensive lattice tool set in finite volumes which includes the test of Goldstone pion dynamics, the spectrum of the fermion Dirac operator, and eigenvalue distributions of random matrix theory. We also discuss the theory inside the conformal window and present our first results on the running of the renormalized gauge coupling and the renormalization group beta function. The importance of understanding finite volume zero momentum gauge field dynamics inside the conformal window is illustrated. Staggered lattice fermions are used throughout the calculations.     

Compact third-order limiter functions for finite volume methods

We consider finite volume methods for the numerical solution of conservation laws. In order to achieve high-order accurate numerical approximation to non-linear smooth functions, we introduce a new class of limiter functions for the spatial reconstruction of hyperbolic equations. We therefore employ and generalize the idea of double-logarithmic reconstruction of Artebrant and Schroll [R. Artebrant, H.J. Schroll, Limiter-free third order logarithmic reconstruction, SIAM J. Sci. Comput. 28 (2006) 359-381].     

谐振管内非线性驻波的有限体积数值算法

为了扩展谐振管内非线性驻波在工程中的应用, 以及克服现有数值计算方法仅局限于求解直圆柱形和指数形谐振管内非线性驻波的问题. 根据变截面的非稳态可压缩热黏性流体Navier-Stokes方程和空间守恒方程, 并基于求解压力速度耦合方程的半隐式算法和交错网格技术, 构建一种能够计算任意形状轴对称谐振管受活塞驱动时内部非线性驻波的有限体积算法. 分别对圆柱形、指数形和圆锥形谐振管内的非线性驻波进行仿真计算. 通过与现有试验结果以及数值仿真结果的对比, 验证了该方法的正确性.并获得除驻波声压之外的另外一些新的物理结果, 包括速度、密度、温度的瞬时变化.在直圆柱形谐振管内产生冲击声压波, 速度波形中出现钉状结构.而在指数形和圆锥形谐振管内产生高声压幅值的驻波, 没有出现冲击波, 速度波形中均未发现钉状结构. 计算结果表明谐振管内非线性驻波的物理属性与谐振管形状之间有密切关系.     

美式回望期权定价问题的有限体积法

随着金融市场的不断发展, 期权作为一种能够规避风险的金融衍生产品越来越引起投资者的青睐, 成交量呈逐年上升的趋势, 期权定价问题已经成为金融数学领域中一个重要的研究课题. 本文主要研究Black-Scholes模型下美式回望期权定价问题的数值解法. 美式回望期权定价问题是一个二维非线性抛物问题, 难以直接应用数值方法进行求解. 通过分析该问题的求解难点, 本文给出解决该困难的有效方法. 首先利用计价单位变换将定价问题转换为一维自由边值问题, 并采用Landau's变换将求解区域规范化; 而后针对问题的非线性特点,利用有限体积法和Newton法交替迭代求解期权价格和最佳实施边界, 并对数值解的非负性进行了分析. 最后, 通过与二叉树方法进行比较, 验证了本文方法的正确性和有效性, 为实际应用提供了理论基础.     

The numerical prediction of planar viscoelastic contraction flows using the pom–pom model and higher-order finite volume schemes

This study investigates the numerical solution of viscoelastic flows using two contrasting high-order finite volume schemes. We extend our earlier work for Poiseuille flow in a planar channel and the single equation form of the extended pom–pom (SXPP) model [M. Aboubacar, J.P. Aguayo, P.M. Phillips, T.N. Phillips, H.R. Tamaddon-Jahromi, B.A. Snigerev, M.F. Webster, Modelling pom–pom type models with high-order finite volume schemes, J. Non-Newtonian Fluid Mech. 126 (2005) 207–220], to determine steady-state solutions for planar 4:1 sharp contraction flows. The numerical techniques employed are time-stepping algorithms: one of hybrid finite element/volume type, the other of pure finite volume form. The pure finite volume scheme is a staggered-grid cell-centred scheme based on area-weighting and a semi-Lagrangian formulation. This may be implemented on structured or unstructured rectangular grids, utilising backtracking along the solution characteristics in time. For the hybrid scheme, we solve the momentum-continuity equations by a fractional-staged Taylor–Galerkin pressure-correction procedure and invoke a cell-vertex finite volume scheme for the constitutive law. A comparison of the two finite volume approaches is presented, concentrating upon the new features posed by the pom–pom class of models in this context of non-smooth flows. Here, the dominant feature of larger shear and extension in the entry zone influences both stress and stretch, so that larger stretch develops around the re-entrant corner zone as Weissenberg number increases, whilst correspondingly stress levels decline.     

Finite volume effects on the QCD chiral phase transition in the finite size de-pendent Nambu-Jona-Lasinio model

The effective Lagrangian of a finite volume system should, in principle, depend on the system size. In the framework of the Nambu-Jona-Lasinio(NJL) model, by considering the influence of quark feedback on the effective coupling, we obtain a modified NJL model so that its Lagrangian depends on the volume. Based on the modified NJL model, we study the influence of finite volume on the chiral phase transition at finite temperature, and find that the pseudo-critical temperature of crossover is much lower than that obtained in the normal NJL model. This clearly shows that the volume dependent effective Lagrangian plays an important role in the chiral phase transitions at finite temperature.     

Recent advances in lattice gauge theories

Recent progress in the field of lattice gauge theories is briefly reviewed for a nonspecialist audience. While the emphasis is on the latest and more definitive results that have emerged prior to this symposium, an effort has been made to provide them with minimal technicalities.     

Extraction of the resonance parameters at finite times

In this paper we propose a model-independent method to extract the resonance parameters on the lattice directly from the Euclidean 2-point correlation functions of the field operators at finite times. The method is tested in case of the two-point function of the Δ-resonance, calculated at one loop in Small Scale Expansion. Further, the method is applied to a 1+1$1+1$-dimensional model with two coupled Ising spins and the results are compared with earlier ones obtained by using Lüscher's approach.     

Strong interaction at finite temperature

We review two methods discussed in the literature to determine the effective parameters of strongly interacting particles as they move through a heat bath. The first one is the general method of chiral perturbation theory, which may be readily applied to this problem. The other is the method of thermal QCD sum rules. We show that, when the spectral sides of the sum rules are calculated correctly, they do not lead to any new results, but reproduce those of the vacuum sum rules.     

激光熔蚀金属平板的三维有限体积法数值分析

为了研究气流条件下强激光对金属靶的熔蚀效应,采用有限体积方法建立了数值模型,并开发了三维Fortran计算程序。综合考虑强激光与材料耦合规律、光束能量空间分布、材料高温热物理性能以及熔蚀界面移动等关键影响因素,模拟了激光辐照下金属靶板升温、熔化和剥蚀的复杂物理过程。最后,将计算结果与试验数据进行了比较,验证了计算模型和程序的有效性。结果表明,计算模型能够反映强激光熔蚀金属平板的基本规律,熔蚀深度和后表面温度计算值与试验吻合较好,并且自编计算程序简单高效。     

The swelling of nucleons in nuclei and the Roper resonance

Conditions where some swelling of the nucleon occurs, and, in particular the relation of this effect with the attractive character of the force acting on it, are studied. It is found that short range repulsive correlations can turn the swelling into a shrinking, in spite of a globally attractive interaction, whereas repulsive velocity dependent forces can lead to some swelling. The role of the Roper resonance in this nucleon change of size is considered in some detail.