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Wave Approximation (wave + approximation)
Selected AbstractsLattice-Registered Two-Photon Polymerized Features within Colloidal Photonic Crystals and Their Optical Properties,ADVANCED FUNCTIONAL MATERIALS, Issue 13 2008Erik C. Nelson Abstract In this work we demonstrate a significant advance in the introduction of embedded defects in 3D photonic crystals by means of two-photon polymerization. We have developed the ability to precisely position embedded defects with respect to the lattice of 3D photonic crystals by imaging the structure concurrently with two-photon writing. Defects are written with near-perfect lattice registration and at specifically defined depths within the crystal. The effect of precise defect position on the optical response is investigated for embedded planar cavities written in a photonic crystal. The experimental data are compared to spectra calculated using the Scalar Wave Approximation (SWA). [source] Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange includedHYDROLOGICAL PROCESSES, Issue 9 2005V. P. Singh Abstract Error equations for kinematic wave and diffusion wave approximations were derived for time-independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF , 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF , 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd. [source] Validation of a vegetated filter strip model (VFSMOD)HYDROLOGICAL PROCESSES, Issue 5 2001Dr Majed Abu-Zreig Abstract Vegetated filter strips (VFS) are designed to reduce sediment load and other pollutants into water bodies. However, adaptation of VFS in the field has been limited owing to lack of data about their efficiency and performance under natural field conditions. A number of models are available that simulate sediment transport and trapping in VFS, but there is a general lack of confidence in VFS models owing to limited validation studies and model limitations that prevent correct application of these models under field conditions. The objective of this study is to test and validate a process-based model (VFSMOD) that simulates sediment trapping in VFS. This model links three submodels: modified Green,Ampt's infiltration, Quadratic overland flow submodel based on kinematic wave approximation and University of Kentucky sediment filtration model. A total of 20 VFS, 2, 5, 10 and 15 m long and with various vegetation covers, were tested under simulated sediment and runoff conditions. The results of these field experiments were used to validate the VFS model. The model requires 25 input parameters distributed over five input files. All input parameters were either measured or calculated using experimental data. The observed sediment trapping efficiencies varied from 65% in the 2-m long VFS to 92% in the 10-m long filters. No increase in sediment removal efficiency was observed at higher VFS length. Application of the VFS model to experimental data was satisfactory under the condition that actual flow widths are used in the model instead of the total filter width. Predicted and observed sediment trapping efficiencies and infiltration volume fitted very well, with a coefficient of determination (R2) of 0·9 and 0·95, respectively. Regression analyses revealed that the slope and intercept of the regression lines between predicted versus observed infiltration volume and trapping efficiency were not significantly different than the line of perfect agreement with a slope of 1·0 and intercept of 0·0. Copyright © 2001 John Wiley & Sons, Ltd. [source] THE TWO-DIMENSIONAL UPLAND EROSION MODEL CASC2D-SED,JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION, Issue 1 2000Billy E. Johnson ABSTRACT: The two-dimensional soil erosion model CASC2D-SED simulates the dynamics of upland erosion during single rainstorms. The model is based on the raster-based surface runoff calculations from CASC2D. Rainfall precipitation is distributed in time and space. Infiltration is calculated from the Green-Ampt equations. Surface runoff is calculated from the diffusive wave approximation to the Saint-Venant equations in two-dimensions. Watershed data bases in raster Geographical Information System (GIS) provide information on the soil type, size fractions, soil erodibility, cropping management, and conservation practice factors for soil erosion calculations. Upland sediment transport is calculated for the size fractions (sand, silt, and clay), and the model displays the sediment flux, the amount of suspended sediment, and the net erosion and deposition using color graphics. The model has been tested on Goodwin Creek, Mississippi. The peak discharge and time to peak are within ± 20 percent and sediment transport rates within ,50 percent to 200 percent. [source] Four-sublattice ferrimagnetic systems: I. Quantum fluctuations of spins at zero temperaturePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2004Rong-ke Qiu Abstract Within the framework of the linear spin wave approximation, the quantum fluctuations of spins at zero temperature in four-sublattice ferrimagnetic systems are studied by employing retard Green's functions. The effects of exchange constants on the quantum fluctuations of spins are discussed for three different spin-configurations. The magnetic properties of these spin configurations are related to their magnetically structural symmetry. When the parameters of the exchange couplings are adjusted, the crossover of the spin configurations results in the strong quantum fluctuations, owing to the behaviors of the non-three-dimensional magnetically system. When two of the four exchange-constants in the present four-sublattice bulk systems are set to be zero, the system behaves as a non-three-dimensionally magnetic system, although the structure of the system is still three-dimensional. All the exchange couplings involve in the quantum competition of the systems, but the effects of antiferromagnetic and ferromagnetic exchange couplings are different evidently. The antiferromagnetic exchange couplings play an important role in a balance of the quantum competition. (© 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Probing of Thin Slipping Films by Persistent External DisturbancesTHE CANADIAN JOURNAL OF CHEMICAL ENGINEERING, Issue 5 2007N. Alleborn Abstract This paper investigates the propagation of thickness disturbances on the free surface of a thin viscous liquid film on a solid substrate. On the free surface of the film the disturbances are induced by moving local external pressure perturbations acting on the surface. The analysis is performed by the Fourier-Laplace transform applied to the linearized perturbation equations for small amplitudes. The amplitude of the interface deflection caused by the disturbance, is reconstructed by the inverse Fourier-Laplace transform and numerically evaluated in the long time limit in long wave approximation. The proposed technique appears promising for probing the slip length of a thin film by recording its free surface response to a moving perturbation. On étudie dans cet article la propagation des perturbations d'épaisseur à la surface libre d'un film liquide visqueux sur un substrat solide. Sur la surface libre du film, les perturbations sont provoquées en déplaçant des perturbations de pression externes locales agissant sur la surface. L'analyse est effectuée par l'application de la transformée de Fourier-Laplace aux équations de perturbation linéarisées pour des petites amplitudes. L'amplitude de la déviation de surface causée par la perturbation est reconstruite par la transformée de Fourier-Laplace inverse et évaluée numériquement pour un temps très long par l'approximation des ondes longues. La technique proposée apparaît prometteuse pour sonder la longueur de glissement d'un film mince en enregistrant la réponse de sa surface libre à une perturbation mobile. [source] Rapid simulated hydrologic response within the variably saturated near surfaceHYDROLOGICAL PROCESSES, Issue 3 2008Brian A. Ebel Abstract Column and field experiments have shown that the hydrologic response to increases in rainfall rates can be more rapid than expected from simple estimates. Physics-based hydrologic response simulation, with the Integrated Hydrology Model (InHM), is used here to investigate rapid hydrologic response, within the variably saturated near surface, to temporal variations in applied flux at the surface boundary. The factors controlling the speed of wetting front propagation are discussed within the Darcy,Buckingham conceptual framework, including kinematic wave approximations. The Coos Bay boundary-value problem is employed to examine simulated discharge, pressure head, and saturation responses to a large increase in applied surface flux. The results presented here suggest that physics-based simulations are capable of representing rapid hydrologic response within the variably saturated near surface. The new InHM simulations indicate that the temporal discretization and measurement precision needed to capture the rapid subsurface response to a spike increase in surface flux, necessary for both data-based analyses and evaluation of physics-based models, are smaller than the capabilities of the instrumentation deployed at the Coos Bay experimental catchment. Copyright © 2007 John Wiley & Sons, Ltd. [source] Errors of kinematic wave and diffusion wave approximations for time-independent flows with infiltration and momentum exchange includedHYDROLOGICAL PROCESSES, Issue 9 2005V. P. Singh Abstract Error equations for kinematic wave and diffusion wave approximations were derived for time-independent flows on infiltrating planes and channels under one upstream boundary and two downstream boundary conditions: zero flow at the upstream boundary, and critical flow depth and zero depth gradient at the downstream boundary. These equations specify error in the flow hydrograph as a function of space. The diffusion wave approximation was found to be in excellent agreement with the dynamic wave approximation, with errors below 2% for values of KF (e.g. KF , 7·5), where K is the kinematic wave number and F is the Froude number. Even for small values of KF (e.g. KF = 2·5), the errors were typically less than 3%. The accuracy of the diffusive approximation was greatly influenced by the downstream boundary condition. For critical flow depth downstream boundary condition, the error of the kinematic wave approximation was found to be less than 10% for KF , 7·5 and greater than 20% for smaller values of KF. This error increased with strong downstream boundary control. The analytical solution of the diffusion wave approximation is adequate only for small values of K. Copyright © 2005 John Wiley & Sons, Ltd. [source] | ||||||||||