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81.
This paper develops a novel return mapping algorithm for the numerical integration of general isotropic finite strain elastoplastic constitutive models for geomaterials. The constitutive formulation is founded on multiplicative decomposition of the deformation gradient. The logarithmic strain measure as well as the exponential approximation of the plastic flow rule is utilized to restore the standard infinitesimal format return mapping algorithm. Central to the algorithm is the exploitation of a set of three mutually orthogonal unit base tensors for the representation of constitutive relations and the corresponding integration of the rate form of the constitutive equations. The base tensors constitute a local cylindrical coordinate system in the principal space, which allows to formulate the return mapping algorithm in the three‐dimensional space and reduce the dimension of the problem to be analyzed from six down to three. With the proposed approach, direct determination of the principal axes and the transformation procedure between the general space and the principal space, as required in traditional spectral decomposition, are avoided. Furthermore, the matrices that are involved in the inversion evaluation take simple forms, leading to extremely easy inverse computation. As a result, the consistent tangent operator can be streamlined into a form simpler and more compact than those by conventional integration methods. Following the formulation of the integration procedure, a numerical experiment is performed to assess the accuracy and efficiency of the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
82.
PETREL,a winged hybrid-driven underwater glider is a novel and practical marine survey platform which combines the features of legacy underwater glider and conventional AUV (autonomous underwater vehicle).It can be treated as a multi-rigid-body system with a floating base and a particular hydrodynamic profile.In this paper,theorems on linear and angular momentum are used to establish the dynamic equations of motion of each rigid body and the effect of translational and rotational motion of internal masses on the attitude control are taken into consideration.In addition,due to the unique external shape with fixed wings and deflectable rudders and the dual-drive operation in thrust and glide modes,the approaches of building dynamic model of conventional AUV and hydrodynamic model of submarine are introduced,and the tailored dynamic equations of the hybrid glider are formulated.Moreover,the behaviors of motion in glide and thrust operation are analyzed based on the simulation and the feasibility of the dynamic model is validated by data from lake field trials. 相似文献
83.
Navin Chandra 《Planetary and Space Science》2004,52(8):747-760
The non-linear stability of the triangular libration point L4 of the restricted three-body problem is studied under the presence of third- and fourth-order resonances, when the more massive primary is a triaxial rigid body and source of radiation. In this study, Markeev's theorems are applied with the help of Moser's theorem. It is found that the stability of the triangular libration point is unstable in the third-order resonance case and in the fourth-order resonance case, this is stable or unstable depending on A1 and A2, and a source of radiation parameter α, where A1, A2 depend upon the lengths of the semi-axes of the triaxial rigid body. 相似文献
84.
A new approach is demonstrated that permits a reliable estimate of specific yield using published values of the van Genuchten water retention parameters and effective grain sizes and the measured effective grain sizes of soil samples. The specific yield distribution of the soil texture was computed using the published values of the van Genuchten parameters. The specific yield values and the published values of effective grain sizes were then used to construct a specific yield–effective grain size curve, which estimates the ‘point’ specific yield of the soil samples. Applying the central limit theorem, the point specific yields could be transformed into an ‘areal’ specific yield for a study area. Compared with other commonly used approaches, the present procedure requires relatively low computational efforts and readily obtainable data. It is cost effective and does not depend on soil texture classification. More importantly, it incorporates the depth to water table and the variations in grain sizes inherent in natural soil conditions in the estimation. The approach developed was applied for estimating the specific yield of an unconfined sandy aquifer created by land reclamation in the equatorial region. The values obtained were compared with field measurements and the typical ranges of specific yield from the literature. Instead of a single estimate of the specific yield, the method yields a confidence interval with a high confidence level of 95% and with a narrower range than the typical ranges from the literature. In addition, the estimated values are close to the field measurements; hence, the procedure provides a cost‐effective alternative to field measurement. The applicability of the present approach could be extended to sites with heterogeneity in the horizontal direction. Nevertheless, the applicability of the present approach for layered soil profiles requires further evaluations. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
85.
《New Astronomy》2022
In this paper, we study the weak deflection angle in the spacetime of improved Schwarzschild black hole using the method derived by Gibbons and Werner. To do so, we derive the optical curvature from the optical metric and calculate deflection angle in weak field limits by using the Gauss–Bonnet theorem. Moreover, we study the effect of the plasma medium on the weak gravitational lensing using the Gauss–Bonnet theorem. Furthermore, we also study the graphical analysis of the deflection angle in both the plasma and non-plasma mediums. Moreover, we obtain the bound on greybody for improved Schwarzschild black hole. 相似文献
86.
M. M. Vishik 《地球物理与天体物理流体动力学》2013,107(1-3):151-167
Abstract Using an asymptotic expansion of Green's function for the problem of magnetic field generation by 3D steady flow of highly conducting fluid a general antidynamo theorem is proved in the case of no exponential stretching of liquid particles. Explicit formulae connecting the spectrum of the magnetic modes with the geometry of the Lagrangian trajectories are obtained. The existence of the fast dynamo action for special flows with exponential stretching is proved under the condition of smoothness of the fields of stretching and non-stretching directions. 相似文献
87.
基于岩土塑性极限分析上限理论的基本原理,考虑预应力锚索的加固效应,分析了单预应力锚索加固措施条件下边坡的稳定性特性,并由此探讨了多预应力锚索共同加固边坡的稳定性能量分析方法。结合强度折减技术,采用内点迭代方法和序列二次规划优化迭代法对锚固边坡安全系数目标函数进行了能量耗散最小化意义上的优化计算。典型算例的分析计算表明:锚索加固效应可以有效地提高边坡的稳定性,预应力锚索设置位置对边坡安全系数、临界滑裂面位置和锚索长度有显著影响。综合考虑锚索设置位置对边坡安全系数和锚索长度的影响,单锚索的最优设置位置应位于边坡中下部区域。采用多排锚索加固既可以保证边坡的安全储备,也可有效避免局部稳定性问题。 相似文献
88.
对目前已有的4种中国剩余定理的求解方法,即传统中国剩余定理算法、闭式解的中国剩余定理算法、高效中国剩余定理算法以及多频中国剩余定理算法,进行了较详细的理论分析与性能比较。将上述算法应用于无线传感与激励网络中对未知节点进行测距,设计了相应的测距算法,分析了各算法的性能特点,并通过仿真实验分析比较了各自在估计精度、计算复杂度以及鲁棒性等方面的差异,并讨论了各算法的适用场景。 相似文献
89.
Nonlinear dynamical analysis and the control problem for a displaced orbit above a planet are discussed. It is indicated that
there are two equilibria for the system, one hyperbolic (saddle) and one elliptic (center), except for the degenerate h
z
max, a saddle-node bifurcation point. Motions near the equilibria for the nonresonance case are investigated by means of the
Birkhoff normal form and dynamical system techniques. The Kolmogorov–Arnold–Moser (KAM) torus filled with quasiperiodic trajectories
is measured in the τ 1 and τ 2 directions, and a rough algorithm for calculating τ 1 and τ 2 is proposed. A general iterative algorithm to generate periodic Lyapunov orbits is also presented. Transitions in the neck
region are demonstrated, respectively, in the nonresonance, resonance, and degradation cases. One of the important contributions
of the paper is to derive necessary and sufficiency conditions for stability of the motion near the equilibria. Another contribution
is to demonstrate numerically that the critical KAM torus of nontransition is filled with the (1,1)-homoclinic orbits of the
Lyapunov orbit. 相似文献
90.
Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well. 相似文献