椭球谐和球谐系数之间一个简单的转换关系

本文推导的椭球谐系数和球谐系数相互之间转换关系的核心思想是在ε~2量级下利用Legendre函数的正交性,从球谐系数求解的积分表示出发,将积分中的椭球坐标变量与球坐标变量相互转换,从而得出椭球谐系数与球谐系数之间的转换关系。本文导出的转换关系有以下优点:①对于第二类Legendre函数的计算采用Laurent级数表示,使计算第二类Legendre函数更为简单;②保留了ε~2量级下,导出的转换关系相比文献[2]的形式更简单,满足物理大地测量边值问题线性化的要求;③顾及了余纬和归化余纬的区别。     

利用气象要素计算五道梁地区土壤热流量的试验

根据五道梁地区1994—1997年的热流板测量土壤热流值,初步分析了该地区土壤热流随时间的变化特征。利用1994—1996年的月平均资料分别分析了总辐射、地表温度、地表温度和80 cm深度温度差和2 cm、10 cm深度的土壤热流的相关性,并建立了相应的回归方程;利用得到的回归方程对1997年的土壤热流作计算检验,就月平均资料来说,用总辐射和地温差来计算浅层土壤热流结果是比较可靠的。     

斜坡平台波浪破碎数值模拟

波浪在斜坡地形上破碎,破波后稳定波高多采用物理模型试验方法进行研究,利用近岸波浪传播变形的抛物型缓坡方程和波能流平衡方程,导出了适用于斜坡上波浪破碎的数值模拟方法。首先根据波能流平衡方程和缓坡方程基本型式分析波浪在破波带内的波能变化和衰减率,推导了波浪传播模型中波能衰减因子和破波能量流衰减因子之间的关系;其次,利用陡坡地形上的高阶抛物型缓坡方程建立了波浪传播和波浪破碎数学模型;最后,根据物理模型试验实测数据对数值模拟的效果进行验证。数值计算与试验资料比较表明,该模型可以较好地模拟斜坡地形的波浪传播波高变化。     

A Modified Form of Mild-Slope Equation with Weakly Nonlinear Effect

Nonlinear effect is of importance to waves propagating from deep water to shallow water.Thenon-linearity of waves is widely discussed due to its high precision in application.But there are still someproblems in dealing with the nonlinear waves in practice.In this paper,a modified form of mild-slope equa-tion with weakly nonlinear effect is derived by use of the nonlinear dispersion relation and the steady mild-slope equation containing energy dissipation.The modified form of mild-slope equation is convenient to solvenonlinear effect of waves.The model is tested against the laboratory measurement for the case of a submergedelliptical shoal on a slope beach given by Berkhoff et al,The present numerical results are also comparedwith those obtained through linear wave theory.Better agreement is obtained as the modified mild-slope e-quation is employed.And the modified mild-slope equation can reasonably simulate the weakly nonlinear ef-fect of wave propagation from deep water to coast.     

微扰Kepler系统轨道微分方程的近似Lie对称性与近似不变量

把极角θ视为独立变量,得到Kepler系统的轨道微分方程. 首先讨论Kepler系统轨道微分方程的Lie对称性和不变量,微扰Kepler系统轨道微分方程的精确Lie对称性和精确不变量,其次讨论微扰Kepler系统轨道微分方程的近似Lie对称性和近似不变量,并得到了微扰Kepler系统的9个一阶近似Lie对称性和6个一阶近似不变量,其中1个实为精确不变量,而其余5个分别等于微扰系数ε乘以Kepler系统相应的5个不变量.     

mKdV-sine-Gordon方程丰富的相互作用解

基于mKdV-sine-Gordon方程的Wronsk解的形式和结构,提出了Wronsk形式展开法,通过这一方法求得了该方程的丰富的相互作用解,该方法的主要特征是不要求Wronsk行列式元素满足线性偏微分方程组。     

Interaction of water waves with vertical cylinders using null-field integral equations

The scattering of water waves by bottom-mounted vertical circular cylinders is solved by using the null-field integral equations in conjunction with degenerate kernels and Fourier series to avoid calculating the Cauchy and Hadamard principal values. In the implementation, the null-field point can be exactly located on the real boundary owing to the introduction of degenerate kernels for fundamental solutions. An adaptive observer system of polar coordinates is considered to fully employ the properties of degenerate kernels. For the hypersingular equation, vector decomposition for the radial and tangential gradients is carefully considered. This method can be seen as a semi-analytical approach since errors attribute from the truncation of Fourier series. Neither hypersingularity in the Burton and Miller approach nor the CHIEF concept was required to deal with the problem of irregular frequencies. Five advantages of free of calculating principal value, well-posed algebraic system, convergence rate of exponential order, meshfree and elimination of boundary-layer effect, are achieved by using the present approach. Numerical results are given for the forces and free-surface elevation around the circular boundaries. Also, the near-trapped behavior arisen from the physical resonance is detected. A general-purpose program for water wave impinging several circular cylinders with arbitrary number, radii, and positions was developed. Several examples of water wave structure interaction by vertical circular cylinders were demonstrated to see the validity of the present formulation.     

四川盆地东部再生稻高温伏旱区腋芽萌发期气象适宜度

以四川盆地东部再生稻高温伏旱区为研究区,基于气象条件对腋芽萌发期再生稻生长发育的影响机理,采用结构方程模型探明了腋芽萌发的影响因素、影响路径及影响强度。进一步结合隶属函数和层次分析法,构建了再生稻腋芽萌发气象适宜度模型,并分析了1981—2021年研究区腋芽萌发期气象影响因素及气象适宜度的变化特征。结果表明：气温、空气湿度、降水是四川盆地东部再生稻高温伏旱区腋芽萌发的关键影响因素,基于以上因素的气象适宜度模型能较好地评价再生稻腋芽萌发期的气象影响。1981—2021年研究区气温适宜度、空气湿度适宜度及综合气象适宜度均呈下降趋势,降水适宜度没有表现出明显的变化趋势。气温适宜度、空气湿度适宜度及综合气象适宜度总体呈“西高东低”的空间分布特征,降水适宜度则表现为“东西高、中部低”。1981—2021年研究区气温上升趋势与空气湿度下降趋势显著,导致致害高温（日平均气温≥32℃）积温和致害低湿（日平均相对湿度≤65％）日数明显增加,这是再生稻腋芽萌发期气象适宜度总体呈下降趋势的诱因。     

Applications of Lodrigues Matrix in 3D Coordinate Transformation

Three transformation models (Bursa-Wolf, Molodensky, and WTUSM) are generally used between two data systems transformation. The linear models are used when the rotation angles are small; however, when the rotation angles get bigger, model errors will be produced. In this paper, we present a method with three main terms: ① the traditional rotation angles θ , φ ,ψ are substituted with a , b, c which are three re-spective values in the anti-symmetrical or Lodrigues matrix; ② directly and accurately calculating the formula of seven parameters in any value of rotation angles; and ③ a corresponding adjustment model is established. This method does not use the triangle function. Instead it uses addition, subtraction, multiplication and division, and the complexity of the equation is reduced, making the calculation easy and quick.