A low communication and large time step explicit finite-volume solver for non-hydrostatic atmospheric dynamics

An explicit finite-volume solver is proposed for numerical simulation of non-hydrostatic atmospheric dynamics with promise for efficiency on massively parallel machines via low communication needs and large time steps. Solving the governing equations with a single stage lowers communication, and using the method of characteristics to follow information as it propagates enables large time steps. Using a non-oscillatory interpolant, the method is stable without post-hoc filtering. Characteristic variables (built from interface flux vectors) are integrated upstream from interfaces along their trajectories to compute time-averaged fluxes over a time step. Thus we call this method a Flux-Based Characteristic Semi-Lagrangian (FBCSL) method. Multidimensionality is achieved via a second-order accurate Strang operator splitting. Spatial accuracy is achieved via the third- to fifth-order accurate Weighted Essentially Non-Oscillatory (WENO) interpolant.We implement the theory to form a 2-D non-hydrostatic compressible (Euler system) atmospheric model in which standard test cases confirm accuracy and stability. We maintain stability with time steps larger than CFL = 1 (CFL number determined by the acoustic wave speed, not advection) but note that accuracy degrades unacceptably for most cases with CFL > 2. For the smoothest test case, we ran out to CFL = 7 to investigate the error associated with simulation at large CFL number time steps. Analysis suggests improvement of trajectory computations will improve error for large CFL numbers.     

Weak solutions for partial differential equations with source terms: Application to the shallow water equations

Weak solutions of problems with m equations with source terms are proposed using an augmented Riemann solver defined by m + 1 states instead of increasing the number of involved equations. These weak solutions use propagating jump discontinuities connecting the m + 1 states to approximate the Riemann solution. The average of the propagated waves in the computational cell leads to a reinterpretation of the Roe’s approach and in the upwind treatment of the source term of Vázquez-Cendón. It is derived that the numerical scheme can not be formulated evaluating the physical flux function at the position of the initial discontinuities, as usually done in the homogeneous case. Positivity requirements over the values of the intermediate states are the only way to control the global stability of the method. Also it is shown that the definition of well-balanced equilibrium in trivial cases is not sufficient to provide correct results: it is necessary to provide discrete evaluations of the source term that ensure energy dissipating solutions when demanded. The one and two dimensional shallow water equations with source terms due to the bottom topography and friction are presented as case study. The stability region is shown to differ from the one defined for the case without source terms, and it can be derived that the appearance of negative values of the thickness of the water layer in the proximity of the wet/dry front is a particular case, of the wet/wet fronts. The consequence is a severe reduction in the magnitude of the allowable time step size if compared with the one obtained for the homogeneous case. Starting from this result, 1D and 2D numerical schemes are developed for both quadrilateral and triangular grids, enforcing conservation and positivity over the solution, allowing computationally efficient simulations by means of a reconstruction technique for the inner states of the weak solution that allows a recovery of the time step size.     

A spectral element semi-Lagrangian (SESL) method for the spherical shallow water equations

A spectral element semi-Lagrangian (SESL) method for the shallow water equations on the sphere is presented. The sphere is discretized using a hexahedral grid although any grid imaginable can be used as long as it is comprised of quadrilaterals. The equations are written in Cartesian coordinates to eliminate the pole singularity which plagues the equations in spherical coordinates. In a previous paper [Int. J. Numer. Methods Fluids 35 (2001) 869] we showed how to construct an explicit Eulerian spectral element (SE) model on the sphere; we now extend this work to a semi-Lagrangian formulation. The novelty of the Lagrangian formulation presented is that the high order SE basis functions are used as the interpolation functions for evaluating the values at the Lagrangian departure points. This makes the method not only high order accurate but quite general and thus applicable to unstructured grids and portable to distributed memory computers. The equations are discretized fully implicitly in time in order to avoid having to interpolate derivatives at departure points. By incorporating the Coriolis terms into the Lagrangian derivative, the block LU decomposition of the equations results in a symmetric positive-definite pseudo-Helmholtz operator which we solve using the generalized minimum residual method (GMRES) with a fast projection method [Comput. Methods Appl. Mech. Eng. 163 (1998) 193]. Results for eight test cases are presented to confirm the accuracy and stability of the method. These results show that SESL yields the same accuracy as an Eulerian spectral element semi-implicit (SESI) while allowing for time-steps 10 times as large and being up to 70% more efficient.     

Application of recurrent radon precursors for forecasting large earthquakes (Mw > 6.0) near Antung,Taiwan

Radon anomalies in groundwater were recorded prior to three major earthquakes – (1) 2003 M_w = 6.8 Chengkung, (2) 2006 M_w = 6.1 Taitung, and (3) 2008 M_w = 5.4 Antung. The epicenters were located 24 km, 52 km, and 13 km, respectively, from the Antung radon-monitoring station. Prior to the three major earthquakes, radon decreased from background levels of 29.3 ± 1.7, 28.2 ± 2.1, and 27.2 ± 1.8 Bq dm^?3 to minima of 12.1 ± 0.3, 13.7 ± 0.3, and 17.8 ± 1.6 Bq dm^?3, respectively. Based on the radon precursory data, this paper correlates the observed radon minima with earthquake magnitude and precursory time. The correlations provide a possible means for forecasting local disastrous earthquakes in the southern segment of coastal range and longitudinal valley of eastern Taiwan.     

High-order discontinuous Galerkin schemes on general 2D manifolds applied to the shallow water equations

An innovating approach is proposed to solve vectorial conservation laws on curved manifolds using the discontinuous Galerkin method. This new approach combines the advantages of the usual approaches described in the literature. The vectorial fields are expressed in a unit non-orthogonal local tangent basis derived from the polynomial mapping of curvilinear triangle elements, while the convective flux functions are written is the usual 3D Cartesian coordinate system. The number of vectorial components is therefore minimum and the tangency constraint is naturally ensured, while the method remains robust and general since not relying on a particular parametrization of the manifold. The discontinuous Galerkin method is particularly well suited for this approach since there is no continuity requirement between elements for the tangent basis definition. The possible discontinuities of this basis are then taken into account in the Riemann solver on inter-element interfaces.     

能量加权时间特征用于浅海声源深度类型判别

针对浅海水面与水下低频宽带脉冲声源深度类型判别问题,提出了一种水平线列阵接收时利用能量加权到达时间特征判别声源深度类型的方法,并给出了工作频段选择的方法。该方法在脉冲宽度内以能量作为权值,对到达时间加权平均,将时间加权平均值与脉冲到达接收阵初始时间值的差值作为评判量,定义合适的水面与水下声源深度界限后,将评判量与拷贝声场中深度界限对应阈值比较,实现声源深度类型判别。经仿真数据验证,方法在等声速、负梯度、温跃层水文环境下的近距离声场均可实现。分析了声源距离、声源方位、海深、水平阵接收深度及阵列孔径等参数对方法性能的影响,进一步分析了声源距离失配、海底纵波声速失配、海深失配时方法的鲁棒性。除海底纵波声速失配时的影响较大外,方法具有较好的鲁棒性。     

An explicit one-soliton solution of the (2+1)-dimensional generalized sine-gordon equations

The (n+1)-dimensional differential geometric generalization of the sine-Gordon equation (SGE) given by Tenenblat and Terng is solved explicitly in the casen=2 to obtain a one-soliton solution. The solution yields the soliton solution of the (1+1)-dimensional SGE in the limit as one of the three independent variables approaches infinity. However, more than one variable plays the role of time in these limits.     

Constructing discrete Painlevé equations: from E8(1) to A1(1) and back

The ‘restoration method’ is a novel method we recently introduced for systematically deriving discrete Painlevé equations. In this method we start from a given Painlevé equation, typically with symmetry, obtain its autonomous limit and construct all possible QRT-canonical forms of mappings that are equivalent to it by homographic transformations. Discrete Painlevé equations are then obtained by deautonomising the various mappings thus obtained. We apply the restoration method to two challenging examples, one of which does not lead to a QRT mapping at the autonomous limit but we verify that even in that case our method is indeed still applicable. For one of the equations we derive we also show how, starting from a form where the independent variable advances one step at a time, we can obtain versions that correspond to multiple-step evolutions.     

Fully nonlinear (2+1)-dimensional displacement shallow water wave equation

Recently, a new(2+1)-dimensional displacement shallow water wave equation(2DDSWWE) was constructed by applying the variational principle of analytic mechanics in the Lagrange coordinates. However, the simplification of the nonlinear term related to the incompressibility of the shallow water in the 2DDSWWE is a disadvantage of this approach.Applying the theory of nonlinear continuum mechanics, we add some new nonlinear terms to the 2DDSWWE and construct a new fully nonlinear(2+1)-dimensional displacement shallow water wave equation(FN2DDSWWE). The presented FN2DDSWWE contains all nonlinear terms related to the incompressibility of shallow water. The exact travelling-wave solution of the proposed FN2DDSWWE is also obtained, and the solitary-wave solution can be deduced from the presented travelling-wave solution under a special selection of integral constants.     

Usage of pattern recognition scheme in kinetic Monte Carlo simulations: Application to cluster diffusion on Cu(1 1 1)

We have invoked a simple pattern recognition scheme in kinetic Monte Carlo simulations of post-deposition evolution of two dimensional islands on fcc(1 1 1) surfaces. On application of the technique to the diffusion of small Cu clusters (8-100 atoms) on Cu(1 1 1) we find that, at room temperature, clusters with certain magic numbers show stick-slip type of motion with striking patterns rather than the random paths followed by the others. At higher temperatures all clusters display random motion. The calculated diffusion coefficients show dependence on size and temperature with an effective barrier ranging between 0.62 eV and 0.84 eV. Small asymmetries in diffusion barriers lead to a large difference in the frequencies of adatom diffusion along the two types of micro-facetted steps on Cu(1 1 1) leading to consequences in their shape evolution. The pattern recognition scheme revealed 49 basic periphery single atom diffusion processes whose activation energy barriers were calculated using the nudged elastic band technique and interatomic potentials from the embedded atom method.     

Kac-moody lie algebras and soliton equations: II. Lax equations associated with A1(1)

The soliton equations associated with sl(2) eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment; they are shown to be generated by a single family of commuting Hamiltonians on a subalgebra of the loop algebra of sl(2). The conserved densities and fluxes of the usual ANKS hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems. The Hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment.     

Kac-moody lie algebras and soliton equations: III. Stationary equations associated with A1(1)

The Hamiltonian structure of stationary soliton equations associated with the AKNS eigenvalue problem is derived in two ways. First, it is shown to arise from the Kostant-Kirillov symplectic structure on a coadjoint orbit in an infinite-dimensional Lie algebra. Second, it is obtained as the restriction to a finite-dimensional manifold of the infinite-dimensional Hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter.     

A mass,energy, vorticity,and potential enstrophy conserving lateral boundary scheme for the shallow water equations using piecewise linear boundary approximations

A numerical scheme for treating fluid–land boundaries in inviscid shallow water flows is derived that approximates boundary profiles with piecewise linear segments (shaved cells) while conserving the domain-summed mass, energy, vorticity, and potential enstrophy. The new scheme is a generalization of a previous scheme that also conserves these quantities but uses stairsteps to approximate boundary profiles. Numerical simulations are carried out demonstrating the conservation properties and accuracy of the piecewise linear boundary scheme (the PLS) for inviscid flows and comparing its performance with that of the stairstep scheme (the STS). It is found that while both schemes conserve all four domain-summed quantities, the PLS generates depth and velocity fields that are one-half to one order more accurate than those generated by the STS, and it generates vorticity and potential vorticity fields that are at least as accurate as those generated by the STS and often more accurate. The higher accuracy of the PLS is due to its ability to generate smoother flow fields near boundaries of arbitrary shape.     

Using high haze (> 90%) light-trapping film to enhance the efficiency of a-Si:H solar cells

The high haze light-trapping (LT) film offers enhanced scattering of light and is applied to a-Si:H solar cells. UV glue was spin coated on glass, and then the LT pattern was imprinted. Finally, a UV lamp was used to cure the UV glue on the glass. The LT film effectively increased the Haze ratio of glass and decreased the reflectance of a-Si:H solar cells. Therefore, the photon path length was increased to obtain maximum absorption by the absorber layer. High Haze LT film is able to enhance short circuit current density and efficiency of the device, as partial composite film generates broader scattering light, thereby causing shorter wave length light to be absorbed by the P layer so that the short circuit current density decreases. In case of lab-made a-Si:H thin film solar cells with v-shaped LT films, superior optoelectronic performances have been found (V_oc = 0.74 V, J_sc = 15.62 mA/cm², F.F. = 70%, and η = 8.09%). We observed ~ 35% enhancement of the short-circuit current density and ~ 31% enhancement of the conversion efficiency.     

Exact solutions of a(2+1)-dimensional extended shallow water wave equation

We give the bilinear form and n-soliton solutions of a(2+1)-dimensional [(2+1)-D] extended shallow water wave(eSWW) equation associated with two functions v and r by using Hirota bilinear method. We provide solitons, breathers,and hybrid solutions of them. Four cases of a crucial φ(y), which is an arbitrary real continuous function appeared in f of bilinear form, are selected by using Jacobi elliptic functions, which yield a periodic solution and three kinds of doubly localized dormion-type solution. The first order Jacobi-type solution travels parallelly along the x axis with the velocity(3k_1~2+ α, 0) on(x, y)-plane. If φ(y) = sn(y, 3/10), it is a periodic solution. If φ(y) = cn(y, 1), it is a dormion-type-Ⅰ solutions which has a maximum(3/4)k_1p_1 and a minimum-(3/4)k_1p_1. The width of the contour line is ln■. If φ(y) = sn(y, 1), we get a dormion-type-Ⅱ solution(26) which has only one extreme value-(3/2)k_1p_1. The width of the contour line is ln■. If φ(y) = sn(y, 1/2)/(1 + y~2), we get a dormion-type-Ⅲ solution(21) which shows very strong doubly localized feature on(x, y) plane. Moreover, several interesting patterns of the mixture of periodic and localized solutions are also given in graphic way.     

A novel approach to measure the step line tension and the step dipole moment on vicinal Au(0 0 1) electrodes

In this paper we introduce a new experimental approach to determine the potential dependence of the step line tension on metal electrodes in contact with an electrolyte: (0 0 1) and (1 1 n) surfaces of single crystal gold electrodes were investigated by impedance spectroscopy in solutions containing weakly adsorbing anions, such as , F⁻ and . Within the limits of error the shift in the potential of zero charge is proportional to the step density of the vicinal surfaces indicative of a well-defined dipole moment per step length. The dipole moments per step atom are 6.8 ± 0.8, 5.2 ± 0.4, 5.8 ± 0.5 × 10⁻³ eÅ for , , and F⁻ containing electrolytes, respectively. Using the values for the pzc and the potential dependence of the capacitance curves, the potential dependence of the surface tension of the vicinal surfaces is determined. The line tension of the steps is then calculated from the difference between the surface tension of the stepped and the step free surface. Our results represent the first experimental confirmation of a recent theoretical model proposing that in absence of specifically adsorbed ions the step line tension should decrease (roughly linear) with potential.     

Study of the 1D lattice Boltzmann shallow water equation and its coupling to build a canal network

The D1Q3 lattice Boltzmann (LB) shallow water equation is analyzed in detail and compared with other numerical schemes. Analytical results are derived and used to discuss the accuracy and stability of the model. We show how such D1Q3 LB models for canal reaches may be easily coupled with various hydraulic interconnection structures to build models of complex irrigation networks.     

AnO(3, 1) approach to Maxwell's equations

Using the principal series representations of the Lorentz group, a method parallel to that of Gelfand and Yaglom is suggested to obtain Maxwell's equations, which dispenses with the arbitrary introduction of a degenerate transformation with respect to which the photon equations are invariant. The method also gives subsidiary conditions which, in conjunction with the masslessness of the particle, yield the Lorentz condition and the correct values of photon polarization.     

Kinetic length and step permeability on the Si(1 1 1) (1 × 1) surface

Information on the kinetic regime of step motion and step permeability on the Si(1 1 1) (1 × 1) surface has been obtained from observations of island decay that were made with low energy electron microscopy. Island area during decay exhibits the expected power law dependence on time, with exponent, α, that is a qualitative indicator of the kinetic regime. A new method is presented for determining the kinetic length quantitatively from measurements of the decay exponent in the symmetric island decay geometry on top of a larger concentric circular island. Using this approach, we determine the kinetic length on the Si(1 1 1) (1 × 1) surface at 1163 K to be d ∼ 75a, where a is the lattice constant. It is shown that this result locates step motion firmly in the diffusion limited regime. Mass conservation of decaying island stacks is also observed at this temperature, which indicates that steps are effectively impermeable in the context of diffusion limited step kinetics.