关于Diophantine方程的解

对于正整数a ,设S(a)是Smarandache函数。证明了 :方程S(1·2 ) +S(2·3) +… +S(x(x +1) ) =S(x(x +1) (x +2 ) /3)仅有正整数解x =1。     

THERIA_G: a software program to numerically model prograde garnet growth

We present the software program THERIA_G, which allows for numerical simulation of garnet growth in a given volume of rock along any pressure–temperature–time (P–T–t) path. THERIA_G assumes thermodynamic equilibrium between the garnet rim and the rock matrix during growth and accounts for component fractionation associated with garnet formation as well as for intracrystalline diffusion within garnet. In addition, THERIA_G keeps track of changes in the equilibrium phase relations, which occur during garnet growth along the specified P–T–t trajectory. This is accomplished by the combination of two major modules: a Gibbs free energy minimization routine is used to calculate equilibrium phase relations including the volume and composition of successive garnet growth increments as P and T and the effective bulk rock composition change. With the second module intragranular multi-component diffusion is modelled for spherical garnet geometry. THERIA_G allows to simulate the formation of an entire garnet population, the nucleation and growth history of which is specified via the garnet crystal size frequency distribution. Garnet growth simulations with THERIA_G produce compositional profiles for the garnet porphyroblasts of each size class of a population and full information on equilibrium phase assemblages for any point along the specified P–T–t trajectory. The results of garnet growth simulation can be used to infer the P–T–t path of metamorphism from the chemical zoning of garnet porphyroblasts. With a hypothetical example of garnet growth in a pelitic rock we demonstrate that it is essential for the interpretation of the chemical zoning of garnet to account for the combined effects of the thermodynamic conditions of garnet growth, the nucleation history and intracrystalline diffusion. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.

Robust adaptive control of underactuated ships on a linear course with comfort

This paper addresses an important problem in ship control application—the robust stabilization of underactuated ships on a linear course with comfort. Specifically, we develop a multivariable controller to stabilize ocean surface ships without a sway actuator on a linear course and to reduce roll and pitch simultaneously. The controller adapts to unknown parameters of the ship and constant environmental disturbances induced by wave, ocean current and wind. It is also robust to time-varying environmental disturbances, time-varying change in ship parameters and other motions of the ship such as surge and heave. The roll and pitch can be made arbitrarily small while the heading angle and sway are kept to be in reasonably small bounds. The controller development is based on Lyapunov’s direct method and backstepping technique. A Lipschitz continuous projection algorithm is used to update the estimate of the unknown parameters to avoid the parameters’ drift due to time-varying environmental disturbances. Simulations on a full-scale catamaran illustrate the effectiveness of our proposed controller.     

Vertical variations of wave-induced radiation stress tensor

INTRODUcrIONThe concept of radiation stress was deve1oPed by tonguet--Higgins and Stewart (1964 ),who intreduced the definition of radiation stress as the excess mornentum due to the presence ofwaves, on the basis of time-averaged laws of Newtonian fluid mechanics and the assmption ofa unifOrm velocity distribution over depth. Subequently, the theory has been applied success-fully in the investigation of phenomena such as wave set-up and set--down (Bowen et al.,l968), longshore currents …     

全球海洋与大气界面的熵通量估算

给出并讨论了海洋系统中由于热量交换、物质交换以及外力做功引起的熵通量的表达式;同时,根据新近调整的全球海 气界面的气候平均资料,估计了全球海洋与大气界面气候年平均的熵通量(熵流),这一熵通量主要取决于海 气界面的热量和物质交换的空间不均匀性。计算结果显示,由热量交换分量引起的熵通量对海洋系统的总熵通量起到主要的贡献作用,其值约为-555.6mW·(m2·K)-1;由海表风应力做功引起的熵通量相对较小,约为-0.09mW·(m2·K)-1;由物质交换引起的熵通量最小,仅为-0.02mW·(m2·K)-1。总的来说,海洋系统从外界获得的总熵通量为-555.7mW·(m2·K)-1,这也就意味着在气候平均定态下,海洋系统内部的熵产生在量值上等于系统的熵交换,即为555.7mW·(m2·K)-1。海洋系统的负熵流与其内部的各种不可逆过程引起的熵产生取得平衡,确保了全球海洋系统处于非平衡热力学定态,并维持着海洋系统中各种尺度的时 空有序现象的消长过程。     

A linear Boltzmann equation to model wave scattering in the marginal ice zone

We present a linear Boltzmann equation to model wave scattering in the Marginal Ice Zone (the region of ocean which consists of broken ice floes). The equation is derived by two methods, the first based on Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991] and second based on Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136]. This linear Boltzmann equation, we believe, is more suitable than the equation presented in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] because of its simpler form, because it is a differential rather than difference equation and because it does not depend on any assumptions about the ice floe geometry. However, the linear Boltzmann equation presented here is equivalent to the equation in Masson and LeBlond [Masson, D., LeBlond, P., 1989. Spectral evolution of wind-generated surface gravity waves in a dispersed ice field. J. Fluid Mech. 202, 111–136] since it is derived from their equation. Furthermore, the linear Boltzmann equation is also derived independently using the argument in Meylan et al. [Meylan, M.H., Squire, V.A., Fox, C., 1997. Towards realism in modeling ocean wave behavior in marginal ice zones. J. Geophys. Res. 102 (C10), 22981–22991]. We also present details of how the scattering kernel in the linear Boltzmann equation is found from the scattering by an individual ice floe and show how the linear Boltzmann equation can be solved straightforwardly in certain cases.     

Calculation of transverse hydrodynamic coefficients using computational fluid dynamic approach

Computational Fluid Dynamic (CFD) based on Reynolds Averaged Navier–Stokes equation is used for determining the transverse hydrodynamic damping force and moment coefficients that are needed in the maneuverability study of marine vehicles. Computations are performed for two geometrical shapes representing typical AUVs presently in use. Results are compared with available data on similar geometries and from some of the available semi-empirical relations. It is found that the CFD predictions compares reasonable well with these results. In particular, the CFD predictions of forces and moments are found to be nonlinear with respect to the transverse velocity, and therefore both linear and nonlinear coefficients can be derived. A discussion on the sources of the component forces reveal that the total force and moment variations should in fact be nonlinear.     

中国对虾配合饲料限制性营养成分分析

以最常用的18种原料为对象,用线性规划的方法对华东沿海中国对虾人工饲料配制过程中的限制营养成分进行了分析。结果表明,粗脂肪、粗灰分、磷、精氨酸、赖氨酸是限制性营养成分,粗纤维和蛋氨酸在以植物性蛋白质为主的配方中是限制性营养成分。因此,在中国对虾人工饵料配方设计中,应注意选用脱脂原料,增加矿物质添加剂中磷的含量以及采用富含精氨酸和赖氨酸的原料。     

多源遥感数据综合解译鄂尔多斯盆地杭锦旗地区地质构造

利用多源遥感数据假彩色合成、融合及纹理分析等增强处理方法提取研究区构造信息,进而对研究区进行综合解译;通过分析水系、色调、纹理、地貌及岩性等特征,判断出杭锦旗地区存在一小一大、内外相套的2个环形构造,发育的北西向、北东向2组共轭断层和一组北北西向断层,与环形构造相互构架,构成研究区特殊的构造体系。经分析预测,这些构造是受周边南北向构造应力共同挤压而形成。     

模拟退火算法在控制网平差中的应用

线性最小二乘估计在对非线性函数进行线性近似的过程中会产生模型误差,而一些非线性参数估计方法可能因为函数复杂而难以求导,法方程系数矩阵秩亏或呈病态矩阵时难以求解,非线性迭代解法有时对初始值的选择存在依赖性,不恰当的初始值会导致迭代无法收敛。针对这些问题,引入了模拟退火算法,介绍了该算法的基本原理、计算步骤和收敛性,并以3个控制网平差应用为例,说明该算法具有无需求导求逆,简洁实用,易于编程等优势,并能实现全局优化,获得高精度的平差结果。