Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Infinite propagation speed of the Camassa-Holm equation

We use the inverse scattering transform to show that a solution of the Camassa-Holm equation is identically zero whenever it vanishes on two horizontal half-lines in the x-t space. In particular, a solution that has compact support at two different times vanishes everywhere, proving that the Camassa-Holm equation has infinite propagation speed.     

Exact Controllability and Asymptotic Analysis for Shallow Shells

The authors consider the exact controllability of the vibrations of a thin shallow shell, of thickness 2εwith controls imposed on the lateral surface and at the top and bottom of the shell. Apart from proving the existence of exact controls, it is shown that the solutions of the three dimensional exact controllability problems converge, as the thickness of the shell goes to zero, to the solution of an exact controllability problem in two dimensions.     

A Singular Limit Problem for Conservation Laws Related to the Camassa–Holm Shallow Water Equation

We consider a shallow water equation of the Camassa–Holm type, which contains nonlinear dispersive effects as well as fourth order dissipative effects. We prove that as the diffusion and dispersion parameters tend to zero, with a condition on the relative balance between these two parameters, smooth solutions of the shallow water equation converge to discontinuous weak solutions of a scalar conservation law. The proof relies on deriving suitable a priori estimates together with an application of the compensated compactness method in the L ^p setting.     

浅海波导界面对点源振速方向的影响

采用“虚源法”分析计算了浅海波导环境中接收点处点源总振速方向与水平面夹角,侧重讨论确定性界面反射对总振速方向的影响。研究结果表明：总振速方向和接收点与声源的水平距离、两者深度,海底、海面特性以及声速剖面等有关。在等声速均匀浅海波导中,由于确定性界面反射的影响,当直达声掠射角为1°～50°时,合成总振速方向偏离直达声方向达1.5°～10.5°,声速剖面呈负梯度时,偏离程度更甚.     

A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.     

A practical approach to the preparative purification of peptides using analytical instrumentation with analytical and semipreparative columns

Summary We have examined the effect of particle size of silica-based reversed-phase packings and column packing techniques on the reversed-phase analytical separation of a peptide mixture. A C₁₈ packing of 15–20 μm average particle size produced satisfactory peptide resolution, allowing a relatively inexpensive scale up to the preparative purification of peptides. A shallow gradient (0.1% acetonitrile/min) elution procedure was developed for the preparative purification of closely related decapeptides (differing by one methyl group) on analytical (250×4.1 mm I.D.) and semipreparative (250×10 mm I.D.) columns. Up to 30 mg and 225 mg of the two-peptide mixture was efficiently resolved, with high yields of homogeneous peptides, on analytical and semipreparative columns, respectively, containing the 15–20 μm packing. We have also demonstrated the potential of our purification procedure for resolving more complex multicomponent mixtures by efficiently separating a total of 22 mg of three closely-related peptides on analytical columns containing 7 μm or 15–20 μm particle size reversed-phase packings. The use of the inexpensive 15–20 μm packing, coupled with the ability to pack efficient columns with analytical HPLC instrumentation, offers great cost saving potential.     

Effect of hydrogen doping in ZnO thin films by pulsed DC magnetron sputtering

This study examined the role of hydrogen impurities in highly oriented ZnO thin films. Hydrogen intentionally incorporated was found to play an important role as a donor in n-type conduction, improving the free carrier concentration. The increase in the conductivity of ZnO thin films was attributed to the two centers assigned to isolated hydrogen atoms in the anti-bonding sites as well as bond-centered interstitial hydrogen located between the Zn–O bonds and Zn vacancy passivated by one or two hydrogen atoms. Micro Raman spectroscopy showed two additional modes at approximately 501 and 573 cm⁻¹. These two peaks were attributed to damage to the crystal lattice, which could be explained by the optical-phonon branch at the zone boundary and host lattice defects, such as vacancy clusters, respectively.     

Meshing Requirements for Tidal Modeling in the Western North Atlantic

This paper presents an a posteriori approach to unstructured mesh generation via a localized truncation error analysis and applies it to the Western North Atlantic Tidal (WNAT) model domain. The WNAT model domain encompasses the Gulf of Mexico, the Caribbean Sea, and the North Atlantic Ocean east to the 60°W Meridian. Herein, we pay particular attention to the area surrounding the Bahamas.

A bathymetric data set with fine resolution is employed in seven separate linear, harmonic simulations of shallow water tidal flow for seven different tidal-forcing constituents. Each set of simulation results is used to perform a truncation error analysis of a linear, harmonic form of the depth-averaged momentum equations for each of the seven different tidal-forcing frequencies. Truncation error is then driven to a more uniform, domain-wide value by solving for local node spacing requirements. The process is built upon successful research aiming to produce unstructured grids for large-scale domains that can be used in the accurate and efficient modeling of shallow water flow. The methodology described herein can also be transferred to other modeling applications.     

A simple finite volume method for the shallow water equations

We present a new finite volume method for the numerical solution of shallow water equations for either flat or non-flat topography. The method is simple, accurate and avoids the solution of Riemann problems during the time integration process. The proposed approach consists of a predictor stage and a corrector stage. The predictor stage uses the method of characteristics to reconstruct the numerical fluxes, whereas the corrector stage recovers the conservation equations. The proposed finite volume method is well balanced, conservative, non-oscillatory and suitable for shallow water equations for which Riemann problems are difficult to solve. The proposed finite volume method is verified against several benchmark tests and shows good agreement with analytical solutions.