On relationship between curve numbers and phi indices

The curve number and phi(4)-index models each provide a simple one-parameter relationship between storm-event rainfall and runoff. It is shown that the curve number and 4-index models can both be used to segregate the rainfall hyetograph into initial abstraction, retention, and runoff amounts. However, the principal advantages of the 4-index model are that both rainfall distribution and duration can be explicitly taken into account in calculating runoff, and the 4 index is more physically based than the curve number. The quantitative relationship between the curve number and the 4 index is presented and validated with field measurements. Knowing the relationship between the curve number and the 4 index is useful in that it facilitates using the extensive database of curve numbers in the more realistic 4-index model in calculating a runoff hydrograph from a given rainfall hyetograph. It is demonstrated that conventional adjustments to curve numbers can be largely explained by variations in storm duration, which suggests that variable rainfall duration can possibly be an essential factor in accounting for deviations from the median curve number of a catchment.

Elliptic Curve Point Multiplication by Generalized Mersenne Numbers

Montgomery modular multiplication in the residue number system （RNS） can be applied for elliptic curve cryptography. In this work, unified modular multipliers over generalized Mersenne numbers are proposed for RNS Montgomery modular multiplication, which enables efficient elliptic curve point multiplication （ECPM）. Meanwhile, the elliptic curve arithmetic with ECPM is performed by mixed coordinates and adjusted for hardware implementation. In addition, the conversion between RNS and the binary number system is also discussed. Compared with the results in the literature, our hardware architecture for ECPM demonstrates high performance. A 256-bit ECPM in Xilinx XC2VP100 field programmable gate array device （FPGA） can be performed in 1.44 ms, costing 22147 slices, 45 dedicated multipliers, and 8.25K bits of random access memories （RAMs）.

Improving Curve Number Runoff Estimates Using Dual Hydrologic Soil Classification and Potential Contributing Source Areas Delineation Methods

Runoff models such as the Curve Number (CN) model are dependent upon land use and soil type within the watershed or contributing area. In regions with internal drainage (e.g. wetlands) watershed delineation methods that fill sinks can result in inaccurate contributing areas and estimations of runoff from models such as the CN model. Two methods to account for this inaccuracy have been 1) to adjust the initial abstraction value within the CN model;or 2) to improve the watershed delineation in order to better account for internal drainage. We used a combined approach of examining the watershed delineation, and refining the CN model by the incorporating of dual hydrologic soil classifications. For eighteen watersheds within Wisconsin, we compared the CN model results of three watershed delineation methods to USGS gaged values. We found that for large precipitation events (>100 mm) the CN model estimations are closer to observed values for watershed delineations that identify the directly connected watershed and use the undrained hydrologic soil classification.

Comparison of Three Delineation Methods Using the Curve Number Method to Model Runoff

Digital Elevation Models (DEMs) are spatial grids which are used to automate watershed boundary determination. Sinks are present within most DEMs. In order to easily process the watershed boundary, the sinks are reassigned to elevation equivalent to an adjacent cell. The derived DEM is called a “filled” DEM. Due to its relative simplicity, the use of the “filled” DEM is one of the most widely used methods to delineate watershed boundaries and works well in about 70 percent of the watersheds in the US. In landscapes with internal drainage, sinks may accurately represent these depressions. In this study, we compare two delineation methods that do not fill in sinks to another method that does fill in sinks. We examined ten gaged watersheds in Wisconsin and Minnesota. We found the spatial extent of the watersheds from the three methods were significantly different. To evaluate the delineation methods, we modeled ten runoff events using the Curve Number (CN) method and compared them to USGS gage discharge for each watershed. For small storms we found that there were no significant differences in the modeled runoff for three delineation methods. For large storms, we found the no-fill methods had a smaller error, but overall the difference was insignificant. This research suggests that capturing internal drainage by the delineation does not have much of an impact on the widely used CN model.

Probabilistic Properties of a Curve Number:A Case Study for Small Polish and Slovak Carpathian Basins

The proper determination of the curve number （CN） in the SCS-CN method reduces errors in predicting runoff volume. In this paper the variability of CN was studied for 5 Slovak and S Polish Carpathian catchments. Empirical curve numbers were applied to the distribution fitting. Next, theoretical characteristics of CN were estimated. For loo-CN the Generalized Extreme Value （GEV） distribution was identified as the best fit in most of the catchments. An assessment of the differences between the characteristics estimated from theoretical distributions and the tabulated values of CN was performed. The comparison between the antecedent runoff conditions （ARC） of Hawkins and Hjelmfelt was also completed. The analysis was done for various magnitudes of rainfall. Confidence intervals （CI） were helpful in this evaluation. The studies revealed discordances between the tabulated and estimated CNs. The tabulated CNs were usually lower than estimated values; therefore, an application of the median value and the probabilistic ARC of Hjelmfelt for wet runoff conditions is advisable. For dry conditions the ARC of Hjelmfelt usually better estimated CN than ARC of Hawkins did, but in several catchments neither the ARC of Hawkins nor Hjelmfelt sufficiently depicted the variability in CN.

Impact of Monthly Curve Number on Daily Runoff Estimation for Ozat Catchment in India

The Soil Conservation Service Curve Number (SCS-CN) is a well-established loss-rate model to estimate runoff. It combines watershed parameters and climatic factors in one entity curve number (CN). The CN exhibits an inherent seasonality beyond its spatial variability, which cannot be accounted for by the conventional methods. In the present study, an attempt has been made to determine the CN for different months of monsoon season with an objective to evaluate the impact of monthly CN on runoff estimation for Ozat catchment (Gujarat State, India). The standard CN and month wise CN were determined by three procedures, viz, the median, geometric mean and standard asymptotic fit using gauged rainfall and runoff. This study shows that the predictive capability of CN determination methods can be improved by using monthly CN. Refined Willmott’s index (dr) and mean absolute error (MAE) were used to assess and validate the performance of each method. The asymptotic fit CN method with monthly CN resulting dr from 0.46 to 0.49 and MAE from 1.13 mm to 1.18 mm was judged to be more consistent with the existing commonly used CN methods in terms of runoff estimation for the study area.

Using modified Soil Conservation Service curve number method to simulate the role of forest in flood control in the upper reach of the Tingjiang River in China

To improve flood control efficiency and increase urban resilience to flooding,the impacts of forest type change on flood control in the upper reach of the Tingjiang River(URTR) were evaluated by a modified model based on the Soil Conservation Service curve number(SCS-CN) method. Parameters of the model were selected and determined according to the comprehensive analysis of model evaluation indexes. The first simulation of forest reconstruction scenario,namely a coniferous forest covering 59.35km^2 is replaced by a broad-leaved forest showed no significant impact on the flood reduction in the URTR. The second simulation was added with 61.75km^2 bamboo forest replaced by broad-leaved forest,the reduction of flood peak discharge and flood volume could be improved significantly. Specifically,flood peak discharge of 10-year return period event was reduced to 7-year event,and the reduction rate of small flood was 21%-28%. Moreover,the flood volume was reduced by 9%-14% and 18%-35% for moderate floods and small floods,respectively. The resultssuggest that the bamboo forest reconstruction is an effective control solution for small to moderate flood in the URTR,the effect of forest conversion on flood volume is increasingly reduced as the rainfall amount increases to more extreme magnitude. Using a hydrological model with scenarios analysis is an effective simulation approach in investigating the relationship between forest type change and flood control. This method would provide reliable support for flood control and disaster mitigation in mountainous cities.

On Elliptic Curves with Everywhere Good Reduction over Certain Number Fields

We prove the existence and nonexistence of elliptic curves having good reduction everywhere over certain real quadratic fields Q(m) for m≤200. These results of computations give best-possible data including structures of Mordell-Weil groups over some real quadratic fields via two-descent. We also prove similar results for the case of certain cubic fields. Especially, we give the first example of elliptic curve having everywhere good reduction over a pure cubic field using our method.

Integral Points on a Class of Elliptic Curve

We prove all integral points of the elliptic curve y^2=x^2-30x＋133 are （x,y） = （-7,0）,（-3,±14）,（2, ±9）,（6,±13）, （5143326,±11664498677）, by using the method of algebraic number theory and p-adic analysis. Furthermore, we develop a computation method to find all integral points on a class of elliptic curve y^2= （x＋α）（x^2-α）（x^2-αx＋b） ,α ,b∈Z,α^2〈4b and find all integer solutions of hyperelliptic Diophantine equation Dy^2=Ax^4 ＋ Bx^2 ＋C,B^2〈4AC.

Effects of aspect ratio on unsteady solutions through curved duct flow

The effects of the aspect ratio on unsteady solutions through the curved duct flow are studied numerically by a spectral based computational procedure with a temperature gradient between the vertical sidewalls for the Grashof number 100 ≤ Gr ≤ 2 000. The outer wall of the duct is heated while the inner wall is cooled and the top and bottom walls are adiabatic. In this paper, unsteady solutions are calculated by the time history analysis of the Nusselt number for the Dean numbers Dn = 100 and Dn = 500 and the aspect ratios 1≤γ≤ 3. Water is taken as a working fluid （Pr =7.0）. It is found that at Dn = 100, there appears a steady-state solution for small or large Gr. For moderate Gr, however, the steady-state solution turns into the periodic solution if γ is increased. For Dn = 500, on the other hand, it is analyzed that the steady-state solution turns into the chaotic solution for small and large Gr for any γ lying in the range. For moderate Gr at Dn = 500, however, the steady-state flow turns into the chaotic flow through the periodic oscillating flow if the aspect ratio is increased.

A CALCULATION METHOD FOR FULLY DEVELOPED FLOWS IN CURVED RECTANGULAR TUBES

In this paper, A method, consisted of perturbation method, Garlerkin method and finite-difference method, is designed to calculate fully developed flows in curved tubes of rectangular cross-section. It costs less computation than that of direct solving N-S equations, and prevents from building high-order difference equations and extra dealing with the boundary conditions. Numerical results in the situation of small curvature and low Dean number is in accordance with former's numerical and experimental results in quality, and it shows the feasibility of this paper's method.

Combined Effects of Centrifugal and Coriolis Instability of the Flow through a Rotating Curved Duct with Rectangular Cross Section

Combined effects of centrifugal and coriolis instability of the flow through a rotating curved duct with rectangular cross section have been studied numerically by using a spectral method, and covering a wide range of the Taylor number ?for a constant Dean number. The rotation of the duct about the center of curvature is imposed in the positive direction, and the effects of rotation (Coriolis force) on the flow characteristics are investigated. As a result, multiple branches of asymmetric steady solutions with two-, three-and multi-vortex solutions are obtained. To investigate the non-linear behavior of the unsteady solutions, time evolution calculations as well as power spectrum of the unsteady solutions are performed, and it is found that the unsteady flow undergoes through various flow instabilities in the scenario “chaotic?→ multi-periodic?→ periodic?→ steady-state”, if Tr is increased in the positive direction. The present results show the characteristics of both the secondary flow and axial flow distribution in the flow.

Text Encryption Using Pell Sequence and Elliptic Curves with Provable Security

The demand for data security schemes has increased with the significant advancement in the field of computation and communication networks.We propose a novel three-step text encryption scheme that has provable security against computation attacks such as key attack and statistical attack.The proposed scheme is based on the Pell sequence and elliptic curves,where at the first step the plain text is diffused to get a meaningless plain text by applying a cyclic shift on the symbol set.In the second step,we hide the elements of the diffused plain text from the attackers.For this purpose,we use the Pell sequence,a weight function,and a binary sequence to encode each element of the diffused plain text into real numbers.The encoded diffused plain text is then confused by generating permutations over elliptic curves in the third step.We show that the proposed scheme has provable security against key sensitivity attack and statistical attacks.Furthermore,the proposed scheme is secure against key spacing attack,ciphertext only attack,and known-plaintext attack.Compared to some of the existing text encryption schemes,the proposed scheme is highly secure against modern cryptanalysis.

Concept Paper： Developing Pavement Structural Deterioration Curves

A SN （structural number） can be calculated for a road pavement from the properties and thicknesses of the surface, basecourse, sub-base and subgrade. Historically, the cost of collecting structural data has been very high. Data was initially collected using Benkelman Beams and now by FWD （falling weight deflectometer）. The structural strength of pavements weakens over time due to environmental and traffic loading factors but due to a lack of data, no structural deterioration curve for pavements has been implemented in a PMS （pavement management system）. IRI （international roughness index） is a measure of the road longitudinal profile and has been used as a proxy for a pavement’s structural integrity. This paper offers two conceptual methods to develop PSDC （pavement structural deterioration curves）. Firstly, structural data are grouped in sets by design ESA （equivalent standard axles）. An ISN （“initial” SN）, SNI （intermediate SN） and a TSN （terminal SN）, are used to develop the curves. Using FWD data, the ISN is the SN after the pavement is rehabilitated （Financial Accounting “Modern Equivalent”）. Intermediate SNIs, are SNs other than the ISN and TSN. The TSN was defined as the SN of the pavement when it was approved for pavement rehabilitation. The second method is to use TSD （traffic speed deflectometer） data. The road network already divided into road blocks, is grouped by traffic loading. For each traffic loading group, road blocks that have had a recent pavement rehabilitation, are used to calculate the ISN and those planned for pavement rehabilitation to calculate the TSN. The remaining SNs are used to complete the age-based or if available, historical traffic loading-based SNIs.

Comparative Thermal Performance in SiO_(2)–H_(2)O and (MoS_(2)–SiO_(2))–H_(2)O Over a Curved Stretching Semi-Infinite Region: A Numerical Investigation

The investigation of Thermal performance in nanofluids and hybrid nanofluids over a curved stretching infinite region strengthens its roots in engineering and industry.Therefore,the comparative thermal analysis in SiO_(2)–H_(2)O and(MoS_(2)–SiO_(2))–H_(2)O is conducted over curved stretching surface.The model is reduced in the dimensional version via similarity transformation and then treated numerically.The velocity and thermal behavior for both the fluids is decorated against the preeminent parameters.From the analysis,it is examined that the motion of under consideration fluids declines against Fr and
.The thermal performance enhances for higher volumetric fraction and
.Further,it is noticed that thermal performance prevailed in(MoS_(2)–SiO_(2))–H_(2)O throughout the analysis.Therefore,(MoS_(2)–SiO_(2))–H_(2)O is better for industrial and engineering uses where high heat transfer is required to accomplished different processes of production.

基于可靠性的疲劳试验数据处理方法

本文基于疲劳可靠性的基本原理,在疲劳寿命对数正态分布的假设下,根据t分布理论,结合船舶及海洋工程一般构件具有95%置信度和97.72%可靠度下的P-S-N曲线的基本要求,推算出了具有95%置信度和误差限度5%内的疲劳试件个数与允许的最大变异系数数值对应关系,以此作为成组法疲劳试验的最少试件个数的判据开展典型节点的疲劳试验,得到具有95%置信度的百位估计值Np;并通过线性相关系数r判断对数疲劳应力Y=log S与X=log Np之间线性相关的程度,采用最小二乘法对对数疲劳寿命lg Np和对数疲劳应力lg S线性拟合,得到具有95%置信度的P-S-N曲线,并与IIW规范中相应的曲线进行对比分析,验证了本文试验方法的可行性和可靠性。

成组法疲劳试件个数选取方法研究

目的 在成组法疲劳试验过程中,确定最少疲劳试件个数判据,获取有效可靠的疲劳试验结果。方法基于疲劳可靠性的基本原理,在疲劳寿命对数正态分布的假设下,根据t分布理论,结合船舶及海洋工程一般构件具有95%置信度和可靠度p=97.72%下的P-S-N曲线的基本要求,推算出相应置信度和可靠度下5%误差限度内的疲劳试件个数与允许的最大变异系数数值的对应关系,以此作为成组法疲劳试验最少试件个数的判据,开展典型节点的疲劳试验。结果 得到了具有95%置信度的百位估计值Np,并通过线性相关系数r,判断对数疲劳应力Y=lg S与X=lg Np之间线性相关的程度,采用最小二乘法对对数疲劳寿命lg Np和对数疲劳应力lg S进行线性拟合,得到了具有95%置信度的P-S-N曲线,与IIW规范中相应的曲线一致。结论 文中给出的成组法疲劳试验个数确定方法是合理、可靠的,为船舶与海洋工程结构物典型焊接接头成组法疲劳试验个数的确定提供了依据。

基于精细化数据的广州市番禺区内涝淹没风险研究

[目的]利用精细化测绘调查数据开展城市降雨径流过程模拟,旨在盘活国土资源数据资产和促进城市内涝风险精准管控。[方法]以广东省广州市番禺区为研究区,基于高精度的地形和建筑数据,采用SCS-CN径流模型和GIS技术,模拟不同强度暴雨情境下的城市内涝淹没深度,定量分析研究区内涝淹没风险空间分布特征,同时结合承灾体灾损经验模型,对洪灾损失风险进行评估,识别高发易损规划管理单元。[结果]①番禺区内涝淹没风险区空间上呈现河涌与城市低洼地区聚集状态,临近市桥—沙湾水道、三枝香—大石水道的街镇存在着较高的淹没风险。②随着暴雨强度增加,农业用地和建设用地将受到最严重的影响。③在100a一遇暴雨情形下,番禺区4个规划管理单元处于高损失风险,损失主要来自住宅建筑,而处于中等损失风险的单元主要面临农业耕地淹没损失。[结论]通过精细化的测绘数据建模,从地块级别成功识别了番禺区潜在易淹没高损失区域,与实际情况较为符合,提高了风险研判的精细度,能够为城市内涝治理和海绵城市规划建设高质量发展提供技术支持。

眼镜镜片尖边轮廓的五轴数控加工

为了改善和优化眼镜镜片的加工流程,避免镜片尖边加工过程中刀轴矢量变化剧烈、影响工件表面的加工质量,提出了一种基于UG NX的五轴数控加工路径。利用智能镜框扫描仪对镜框边缘进行扫描,获得镜框凹槽点云数据文件,编写相应程序对符合眼镜片加工标准的OMA文件中的球坐标数据进行坐标及格式转换等处理。基于NURBS曲线拟合算法,实现刀路轨迹的连续性并保证拟合曲线的精度。设计和建立一种控制刀轴矢量平滑变化的刀轴驱动约束方法,依靠曲线驱动刀轴及镜片曲面法向量约束刀轴使刀头平滑进给,并将刀轨文件经过后处理转换为NC文件。最后,对加工后的镜片进行误差测量,结果表明,通过点云数据拟合刀路曲线的方法提高了加工面的精确度和光滑性,有效缩减了加工流程,提高了加工效率。

径流曲线数模型在湖南省山区小流域的优化与应用

径流曲线数模型(Soil Conservation Service Curve Number Model,简称SCS-CN模型)可以利用降雨资料估算径流,对水资源合理配置和山洪灾害预警具有重要意义,因为其方便计算、参数简单,而被广泛应用。目前标准SCS-CN模型在山区小流域的适用性欠佳,因此需要对模型参数进行优化以提高预测精度。本文以湖南省螺岭桥流域为例,根据实测降雨径流资料优化径流曲线数CN(Curve Number)查算表,并利用步长优化参数算法研究初损率对模型精度的影响,将优化模型的方法应用于湖南省凤凰小流域,验证该优化方法的可靠性。结果分析表明:与标准SCS-CN模型相比,优化后的SCS-CN模型效率系数NSE从0.576提升至0.813,决定系数R^(2)为0.858。将模型优化方法验证于气候地形条件相似的凤凰流域,模型NSE值提高117%。通过预测径流深与实测径流深比较,优化模型模拟精度较为理想,对湖南省山区小流域场次降雨产流预报有一定的参考意义。