Unsteady RANS simulation of the ship forward speed diffraction problem

The forward speed diffraction problem for a surface ship is analyzed numerically, using a RANS approach with a single-phase level set method to compute the free surface and a blended k-ε/k-ω model for the turbulent viscosity. Simulations were run for a DTMB 5512 model under head incident waves at two speeds and two wavelengths with the same wave amplitude (a = 0.006L, with L the ship length). The medium speed case (Fr = 0.28) with long wavelength incident waves (λ = 1.5L) behaves linearly and has been extensively compared against available experimental data for resistance and heave forces and pitching moment, unsteady free surface elevations, and unsteady velocity fields at the nominal wake plane (x/L = 0.935). Quantitative verification and validation was performed for this case by running three grids and three time steps with refinement ratio of and the flow field analyzed in detail. The behavior of the boundary layer is analyzed to explain the origin of large first harmonic amplitudes on the axial velocity observed both experimentally and numerically. The high speed case (Fr = 0.41) with short wavelength incident waves (λ = 0.5L) exhibits non-linear behavior on the forces and moment with a strong second harmonic component and an unsteady breaking bow wave. The second harmonic has been reproduced by the CFD computations and the breaking wave predicted. Analysis of the flow indicates that the breaking wave could be responsible for the non-linear behavior on the forces and moment.     

Ship motions using single-phase level set with dynamic overset grids

The problem of surface ships free to pitch and heave in regular head waves is analyzed numerically with an unsteady Reynolds averaged Navier Stokes (URANS) approach. The unsteady single-phase level set method previously developed by the authors was extended to include six degrees of freedom (6DOF) motions. The method uses rigid overset grids that move with relative motion during the computation, and the interpolation coefficients between the grids are recomputed dynamically every time the grids move. The motions in each time step are integrated implicitly using a predictor-corrector approach. An earth-based reference system is used for the solution of the fluid flow, while a ship-based reference system is used to compute the rigid-body equations of motion. Predicted results for sinkage and trim and resistance at two Froude numbers (medium, Fr = 0.28 and large, Fr = 0.41) were compared against experimental data, showing good agreement. Pitch and heave motions were computed for near-resonant cases at Fr = 0.28 and 0.41, with regular linear head waves with slope ak = 0.025 and wavelength λ = 1.5L, with L the ship length. The predicted motions compare favorably with existing experimental data. A solution for a large amplitude head wave case (ak = 0.075) was also obtained, in which the transom wave breaks and extreme motions are observed. The medium Froude number case was subject to a verification and validation analysis. A problem with two ships pitching and heaving one behind the other is demonstrated.     

Study of CFD variation on transport configurations from the second drag-prediction workshop

This paper describes and analyzes a series of nearly 90 CFD test cases performed as a contribution to the second Drag Prediction Workshop, held in Orlando, Florida in June 2003. Two configurations are included: DLR-F6 wing-body and wing-body-nacelle-pylon. The ability of CFD to predict the drag, lift, and pitching moment from experiment--including the “delta” arising from the addition of the nacelle and pylon--is assessed. In general, at a fixed angle of attack CFD overpredicts lift, but predicts the ΔC_L reasonably well. At low lift levels (C_L < 0.3), ΔC_D is 20-30 drag counts (30-45%) high. At the target lift coefficient of C_L  =  0.5, ΔC_D is overpredicted by between 11 and 16 counts. However, the primary contribution of this paper is not so much the assessment of CFD against experiment, but rather a detailed assessment and analysis of CFD variation. The series of test cases are designed to determine the sensitivity/variability of CFD to a variety of factors, including grid, turbulence model, transition, code, and viscous model. Using medium-level grids (6-11 million points) at the target lift coefficient, the maximum variation in drag due to different grids is 5-11 drag counts, due to code is 5-10 counts, due to turbulence model is 7-15 counts, due to transition is 10-11 counts, and due to viscous model is 4-5 counts. Other specific variations are described in the paper.     

Load-sharing system model and its application to the real data set

This study deals with the classical and Bayesian estimation of the parameters of a k-components load-sharing parallel system model in which each component's lifetime follows Lindley distribution. Initially, the failure rate of each of the k components in the system is h(t,θ₁) until the first component failure. However, upon the first failure within the system, the failure rates of the remaining (k − 1) surviving components change to h(t,θ₂) and remain the same until next failure. After second failure, the failure rates of (k − 2) surviving components change to h(t,θ₃) and finally when the (k − 1)th component fails, the failure rate of the last surviving component becomes h(t,θ_k). In classical set up, the maximum likelihood estimates of the load share parameters, system reliability and hazard rate functions along with their standard errors are computed. 100 × (1 − γ)% confidence intervals and two bootstrap confidence intervals for the parameters have also been constructed. Further, by assuming Jeffrey's invariant and gamma priors of the unknown parameters, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals of the parameters are obtained. Markov Chain Monte Carlo technique such as Metropolis–Hastings algorithm has been utilized to generate draws from the posterior densities of the parameters.     

An acoustic wave sensor for the hydrophilic fluoride

A new acoustic wave sensor to detect and quantify fluoride, one of the most hydrophilic anions, is proposed. Meso-octamethylcalix[4]pyrrole (OMCP) and seven of its derivatives were evaluated as piezoelectric quartz crystal coatings. Some of these sensors experienced appreciable coating leaching under a water flow, while others did show a very small sensitivity to fluoride. As the OMCP-naphthoquinone sensor was very sensitive to fluoride and did not lose a significant amount (α = 0.05) of coating during eight weeks, it was selected among all the others. A piezoelectric crystal coated with an amount of OMCP-naphthoquinone that produced a frequency decrease of 22 kHz showed a linear calibration range that extended up to 80 mg L⁻¹, within which sensitivity to fluoride was 0.45 Hz L mg⁻¹_, and was able to detect fluoride at the concentration of 3.66 mg L⁻¹. This sensor was used to determine fluoride in commercial fluoride tablets, and the result found was not statistically different (α = 0.05) from the value provided by the manufacturer.     

Convergence of a two-layer scheme for equations of gas dynamics in Eulerian variables with geo-physical applications

This paper deals with the convergence of a completely conservative, two-layer difference scheme for equations of gas dynamics in Eulerian variables. The convergence of the difference solution to the smooth solution of the original periodic Cauchy problem of order τ²+h ² at layer-by-layer norm L ₂ is proved, provided that the mesh step sizes are sufficiently small and that τ=h ^1+? (?=constant>0). Several modifications of the proposed method were used for the numerical solution of a one-dimensional mathematical model (on the basis of the shallow water theory), which describes crash events produced by dam collapse.     

Quantitative analysis of salt-affected soil reflectance spectra: A comparison of two adaptive methods (PLSR and ANN)

In this paper the possibility of predicting salt concentrations in soils from measured reflectance spectra is studied using partial least squares regression (PLSR) and artificial neural network (ANN). Performance of these two adaptive methods has been compared in order to examine linear and non-linear relationship between soil reflectance and salt concentration.Experiment-, field- and image-scale data sets were prepared consisting of soil EC measurements (dependent variable) and their corresponding reflectance spectra (independent variables). For each data set, PLSR and ANN predictive models of soil salinity were developed based on soil reflectance data. The predictive accuracies of PLSR and ANN models were assessed against independent validation data sets not included in the calibration or training phase.The results of PLSR analyses suggest that an accurate to good prediction of EC can be made based on models developed from experiment-scale data (R² > 0.81 and RPD (ratio of prediction to deviation) > 2.1) for soil samples salinized by bischofite and epsomite minerals. For field-scale data sets, the PLSR predictive models provided approximate quantitative EC estimations (R² = 0.8 and RPD = 2.2) for grids 1 and 6 and poor estimations for grids 2, 3, 4 and 5. The salinity predictions from image-scale data sets by PLSR models were very reliable to good (R² between 0.86 and 0.94 and RPD values between 2.6 and 4.1) except for sub-image 2 (R² = 0.61 and RPD = 1.2).The ANN models from experiment-scale data set revealed similar network performances for training, validation and test data sets indicating a good network generalization for samples salinized by bischofite and epsomite minerals. The RPD and the R² between reference measurements and ANN outputs of theses models suggest an accurate to good prediction of soil salinity (R² > 0.92 and RPD > 2.3). For the field-scale data set, prediction accuracy is relatively poor (0.69 > R² > 0.42). The ANN predictive models estimating soil salinity from image-scale data sets indicate a good prediction (R² > 0.86 and RPD > 2.5) except for sub-image 2 (R² = 0.6 and RPD = 1.2).The results of this study show that both methods have a great potential for estimating and mapping soil salinity. Performance indexes from both methods suggest large similarity between the two approaches with PLSR advantages. This indicates that the relation between soil salinity and soil reflectance can be approximated by a linear function.     

Large-scale DES computations of the forward speed diffraction and pitch and heave problems for a surface combatant

This paper aims at presenting the most resolved solutions to date for the ship forward speed diffraction and pitch and heave problems, and discuss the method that enables these computations. Large-scale DES computations (60-115 million grid points, 276-500 processors) of ship hydrodynamics problems are presented for the DTMB model 5512 surface combatant. The forward speed diffraction problem is studied at Fr = 0.28 with waves of amplitude a = 0.006 and wavelength λ=1.5, with the ship static allowing the overset assembly to be a pre-processing step. In the pitch and heave problem the ship faces head waves at Fr = 0.41 with waves of amplitude a = 0.006 and wavelength λ=1.5, with the ship is allowed to pitch and heave, thus requiring dynamic overset grid processing. The code CFDShip-Iowa version 4 and the overset assembly code Suggar were modified to carry out some large scale simulations of free surface ship hydrodynamics. These modifications were focused on reducing the memory requirement and optimizing the per-processor and parallel performance at the implementation and algorithmic levels, plus the addition of a lagged mode for the overset domain connectivity computation. The simulation results show very significant improvements in the local flow and free surface results, but minor in forces and moments when compared with previous URANS computations performed with grids with about three million points.     

Theoretical analysis of a remotely measurable soil evaporation transfer coefficient

Reducing soil evaporation (E) is an important way to increase water use efficiency for agriculture and sustainable water use. To achieve this goal, an accurate estimate of soil evaporation at the macro-scale level is necessary. By including the surface temperature of dry soil, the three temperatures model (3T model) was proposed as an estimate of E, and its temperature term was defined as the soil evaporation transfer coefficient (h_a). Although it has been primarily shown that h_a determines the boundaries of E, further studies of its properties are necessary because h_a has the application potential for remote sensing. The objectives of this study are to (1) investigate the relationships between h_a and those parameters that are important for E estimation but are not able to be remotely measured (aerodynamic resistance, soil surface resistance (r_s), and cumulative evaporation (E_c)); and (2) discuss the possibility for remote sensing application. Two experiments were carried out for these purposes: one in an open field and the other one in a closed growth chamber at constant temperature, humidity, and radiation. The following results were obtained: (1) Given the boundaries of 0 ≤ h_a ≤ 1, E was determined between its maximum value (potential evaporation rate) and minimum value (zero); (2) During the period when evaporation is controlled by r_s, a linear relation between h_a and log (r_s) is observed with a coefficient of determination r² = 0.76. Because h_a and r_s are independent variables with significant differences in properties and magnitudes, these results indicate that h_a and r_s are well related to each other; (3) During stage 1 of evaporation, cumulative evaporation (E_c) increased with time while h_a remained constant. Afterwards, h_a linearly increased with E_c. The relationships among h_a, E_c, r_a, and r_s would be useful for estimation of evapotranspiration by remote sensing.     

An efficient parity detection technique using the two-moduli set {2 − 1, 2 + 1}

Lu and Chiang used both the table lookup and fractional number approaches to discover the parity of an RNS number. To eliminate the need for table space and time for computing fractions, a two-moduli set {2^h − 1, 2^h + 1} is used to speed up the technique proposed by Lu and Chiang. Based on this modified two-moduli set, it is found that the parity of an RNS number X = (x₁, x₂) is if x₁ ? x₂. On the contrary, if x₁ < x₂, the parity of X is .     

Stability and absolute stability of a three-point difference scheme

Consider a three-point difference scheme −h⁻²Δ⁽²⁾y_n + q_n(h)y_n = f_n(h), n ϵ Z = {0, ±1, ±2, …}, where h ϵ (0, h₀], h₀ is a given positive number, Δ⁽²⁾y_n = y_n+1 + y_n−1, f(h) = {f_n(h)}_{n ϵ Z} ϵ L_∞(h), L_∞(h) = {f(h) : ∥f(h)∥_L∞(h) < ∞}, ∥f(h)∥_L∞(h) = sup_nϵZ ∥f_n(h)∥.We assume a unique a priori requirement 0 <- q_n(h) < ∞ for any n ϵ Z and h ϵ (0, h₀]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L_∞(h).     

Convergence conditions for iterative methods seeking multi-component solitary waves with prescribed quadratic conserved quantities

We obtain linearized (i.e., non-global) convergence conditions for iterative methods that seek solitary waves with prescribed values of quadratic conserved quantities of multi-component Hamiltonian nonlinear wave equations. These conditions extend the ones found for single-component solitary waves in a recent publication by Yang and the present author. We also show that, and why, these convergence conditions coincide with dynamical stability conditions for ground-state solitary waves.Notably, our analysis applies regardless of whether the number of quadratic conserved quantities, s, equals or is less than the number of equations, S. To illustrate the situation when s < S, we use one of our iterative methods to find ground-state solitary waves in spin-1 Bose-Einstein condensates in a magnetic field (s = 2, S = 3).     

Comments on “Generalised finite Radon transform for N × N images”

In Kingston and Svalbe [1], a generalized finite Radon transform (FRT) that applied to square arrays of arbitrary size N × N was defined and the Fourier slice theorem was established for the FRT. Kingston and Svalbe asserted that “the original definition by Matúš and Flusser was restricted to apply only to square arrays of prime size,” and “Hsung, Lun and Siu developed an FRT that also applied to dyadic square arrays,” and “Kingston further extended this to define an FRT that applies to prime-adic arrays”. It should be said that the presented generalized FRT together with the above FRT definitions repeated the known concept of tensor representation, or tensor transform of images of size N × N which was published earlier by Artyom Grigoryan in 1984-1991 in the USSR. The above mentioned “Fourier slice theorem” repeated the known tensor transform-based algorithm of 2-D DFT [5-11], which was developed for any order N₁ × N₂ of the transformation, including the cases of N × N, when N = 2^r, (r > 1), and N = L^r, (r ≥ 1), where L is an odd prime. The problem of “over-representation” of the two-dimensional discrete Fourier transform in tensor representation was also solved by means of the paired representation in Grigoryan [6-9].     

Geometric pattern matching for point sets in the plane under similarity transformations

We consider the following geometric pattern matching problem: Given two sets of points in the plane, P and Q, and some (arbitrary) δ>0, find a similarity transformation T (translation, rotation and scale) such that h(T(P),Q)<δ, where h(⋅,⋅) is the directional Hausdorff distance with L_∞ as the underlying metric; or report that none exists. We are only interested in the decision problem, not in minimizing the Hausdorff distance, since in the real world, where our applications come from, δ is determined by the practical uncertainty in the position of the points (pixels). Similarity transformations have not been dealt with in the context of the Hausdorff distance and we fill the gap here. We present efficient algorithms for this problem imposing a reasonable separation restriction on the points in the set Q. If the L_∞ distance between every pair of points in Q is at least 8δ, then the problem can be solved in O(mn²logn) time, where m and n are the numbers of points in P and Q respectively. If the L_∞ distance between every pair of points in Q is at least cδ, for some c, 0<c<1, we present a randomized approximate solution with expected runtime O(n²c−4ε−8log⁴mn), where ε>0 controls the approximation. Our approximation is on the size of the subset, B⊆P, such that h(T(B),Q)<δ and |B|>(1−ε)|P| with high probability.     

Simulating the impact of discrete-return lidar system and survey characteristics over young conifer and broadleaf forests

We present a model-based investigation of the effect of discrete-return lidar system and survey characteristics on the signal recorded over young forest environments. A Monte Carlo ray tracing (MCRT) model of canopy scattering was used to examine the sensitivity of model estimates of lidar-derived canopy height, h_lidar to signal triggering method, canopy structure, footprint size, sampling density and scanning angle, for broadleaf and conifer canopies of varying density. Detailed 3D models of Scots pine (Pinus sylvestris) and Downy birch (Betula pubescens) were used to simulate lidar response, with minimal assumptions about canopy structure. Use of such models allowed the impact of lidar parameters on canopy height retrieval to be tested under a range of conditions typically not possible in practice. Retrieved h_lidar was generally found to be an underestimate of ‘true’ canopy height, h_canopy, but with exceptions. Choice of signal triggering method caused h_lidar to underestimate h_canopy by ∼ 4% for birch and ∼ 7% for pine (up to 66% in extreme cases). Variations in canopy structure resulted on average in underestimation of h_canopy by 13% for birch and between 29 and 48% for pine depending on age, but with over-estimates in some cases of up to 10%. Increasing footprint diameter from 0.1 to 1 m increased retrieved h_lidar from significant underestimates of h_canopy to values indistinguishable from h_canopy. Increased sampling density led to slightly increased values of h_lidar to close to h_canopy, but not significantly. Increasing scan angle increased h_lidar by up to 8% for birch, and 19% for pine at a scan angle of 30°. The impact of scan angle was greater for conifers as a result of large variation in crown height. Results showed that interactions between physically modelled (hypothetical) within canopy returns are similar to findings made in other studies using actual lidar systems, and that these modelled returns can depend strongly on the type of canopy and the lidar acquisition characteristics, as well as interactions between these properties. Physical models of laser pulse/canopy interactions may provide additional information on pulse interactions within the canopy, but require validation and testing before they are applied to actual survey planning and logistics.     

An electrochemical sensor for trace uranium determination based on 6-O-palmitoyl-l-ascorbic acid-modified graphite electrodes

The development of a preconcentrating sensor based on 6-O-palmitoyl-l-ascorbic acid (PAA)-modified graphite (GRA) electrodes for the determination of uranium is described. PAA, a water insoluble compound of ascorbic acid, was immobilized onto the surface of the GRA electrodes through physical adsorption from acetone solutions. Uranium was accumulated by heterogeneous complexation (10 min, in 0.1 M H₃BO₃, pH 4.3) and then, it was reduced by means of a differential pulse voltammetric scan in 0.1 M H₃BO₃, pH 3.4. Alternatively, the performance of both preconcentration and voltammetric steps in a single run, at 0.1 M H₃BO₃, pH 3.65, was also examined; however, in this case the observed current signals were lower by 30%. The experimental variables were investigated and under the selected conditions, a linear calibration curve in the range 2.7-67.5 μg L⁻¹ U(VI) was constructed (r² = 0.9981). The 3σ limit of detection and the relative standard deviation of the method were 1.8 μg L⁻¹ U(VI) and 8% (n = 5, 20 μg L⁻¹ U(VI), preconcentration time 10 min), respectively. By increasing the preconcentration time to 30 min, a limit of detection as low as 0.26 μg L⁻¹ U(VI) can be achieved. The effect of potential interferences was also examined. The accuracy of the method was established by recovery studies in inoculated tap and lake water samples. A simple and fast procedure based on filtering of the sample through a C-18 microcolumn was successfully used to remove the organic matter from the lake water samples.     

An assessment of chlorophyll-a algorithms available for SeaWiFS in coastal and open areas of the Bay of Bengal and Arabian Sea

Three ocean colour algorithms, OC4v6, Carder and OC5 were tested for retrieving Chlorophyll-a (Chla) in coastal areas of the Bay of Bengal and open ocean areas of the Arabian Sea. Firstly, the algorithms were run using ~ 80 in situ Remote Sensing Reflectance, (R_rs(λ)) data collected from coastal areas during eight cruises from January 2000 to March 2002 and the output was compared to in situ Chla. Secondly, the algorithms were run with ~ 20 SeaWiFS R_rs(λ) and the results were compared with coincident in situ Chla. In both cases, OC5 exhibited the lowest log₁₀-RMS, bias, had a slope close to 1 and this algorithm appears to be the most accurate for both coastal and open ocean areas. Thirdly the error in the algorithms was regressed against Total Suspended Material (TSM) and Coloured Dissolved Organic Material (CDOM) data to assess the co-variance with these parameters. The OC5 error did not co-vary with TSM and CDOM. OC4v6 tended to over-estimate Chla > 2 mg m⁻³ and the error in OC4v6 co-varied with TSM. OC4v6 was more accurate than the Carder algorithm, which over-estimated Chla at concentrations > 1 mg m⁻³ and under-estimated Chla at values < 0.5 mg m⁻³. The error in Carder Chla also co-varied with TSM. The algorithms were inter-compared using > 5500 SeaWiFS R_rs(λ) data from coastal to offshore transects in the Northern Bay of Bengal. There was good agreement between OC4v6 and OC5 in open ocean waters and in coastal areas up to 2 mg m⁻³. There was a strong divergence between Carder and OC5 in open ocean and coastal waters. OC4v6 and Carder tended to over-estimate Chla in coastal areas by a factor of 2 to 3 when TSM > 25 g m⁻³. We strongly recommend the use of OC5 for coastal and open ocean waters of the Bay of Bengal and Arabian Sea. A Chla time series was generated using OC5 from 2000 to 2003, which showed that concentrations at the mouths of the Ganges reach a maxima (~ 5 mg m⁻³) in October and November and were 0.08 mg m⁻³ further offshore increasing to 0.2 mg m⁻³ during December. Similarly in early spring from February to March, Chla was 0.08 to 0.2 mg m⁻³ on the east coast of the Bay.     

Solitary wave simulations of Complex Modified Korteweg-de Vries Equation using differential quadrature method

Complex Modified Korteweg-deVries Equation is solved numerically using differential quadrature method based on cosine expansion. Three test problems, motion of single solitary wave, interaction of solitary waves and wave generation, are simulated. The accuracy of the method is measured via the discrete root mean square error norm L₂, maximum error norm L_∞ for the motion of single solitary wave since it has an analytical solution. A rate of convergency analysis for motion of single solitary wave containing both real and imaginary parts is also given. Lowest three conserved quantities are computed for all test problems. A comparison with some earlier works is given.     

An Inverse Homomorphic Characterization of Full Principal AFL

The main result of this paper is: Let L be a full principal AFL closed under context-free substitution. Then there is a fixed language l₀ in L such that for each L in L there exist a weak coding h and a homomorphism g such that L = hg^?1(L₀). As a corollary, it immediately follows that there is a fixed ETOL language L₀ such that for each ETOL language L there exist a weak coding h and a homomorphism g such that L = hg^?1(L₀).     

Asymptotic behavior and blow up of solutions for semilinear parabolic equations at critical energy level

In this paper we study the initial boundary value problem of semilinear parabolic equations with semilinear term f(u). By using the family of potential wells method we prove that if f(u) satisfies some conditions, J(u₀) ≤ d and I(u₀) > 0, then the solution decays to zero exponentially as t → ∞. On the other hand, if J(u₀) ≤ d, I(u₀) < 0, then the solution blows up in finite time.