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1.
A numerical scheme is developed in order to simulate fluid flow in three dimensional (3‐D) microstructures. The governing equations for steady incompressible flow are solved using the semi‐implicit method for pressure‐linked equations (SIMPLE) finite difference scheme within a non‐staggered grid system that represents the 3‐D microstructure. This system allows solving the governing equations using only one computational cell. The numerical scheme is verified through simulating fluid flow in idealized 3‐D microstructures with known closed form solutions for permeability. The numerical factors affecting the solution in terms of convergence and accuracy are also discussed. These factors include the resolution of the analysed microstructure and the truncation criterion. Fluid flow in 2‐D X‐ray computed tomography (CT) images of real porous media microstructure is also simulated using this numerical model. These real microstructures include field cores of asphalt mixes, laboratory linear kneading compactor (LKC) specimens, and laboratory Superpave gyratory compactor (SGC) specimens. The numerical results for the permeability of the real microstructures are compared with the results from closed form solutions. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
2.
A coupled continuum‐discrete hydromechanical model was employed to analyse the liquefaction of a saturated loose deposit of cohesionless particles when subjected to a dynamic base excitation. The pore fluid flow was idealized using averaged Navier–Stokes equations and the discrete element method was employed to model the solid phase particles. A well established semi‐empirical relationship was utilized to quantify the fluid–particle interactions. The conducted simulations revealed a number of salient micro‐mechanical mechanisms and response patterns associated with the deposit liquefaction. Space and time variation of porosity was a major factor which affected the coupled response of the solid and fluid phases. Pore fluid flow was within Darcy's regime. The predicted response exhibited macroscopic patterns consistent with experimental results and case histories of the liquefaction of granular soil deposits. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
3.
Jean-Francois Guéguen Pho Hoang-Trong Hilaire Legros 《Geophysical Journal International》1987,89(3):839-855
Summary. A first-order form of the Euler's equations for rays in an ellipsoidal model of the Earth is obtained. The conditions affecting the velocity law for a monotonic increase, with respect to the arc length, in the angular distance to the epicentre, and in the angle of incidence, are the same in the ellipsoidal and spherical models. It is therefore possible to trace rays and to compute travel times directly in an ellipsoidal earth as in the spherical model. Thus comparison with the rays of the same coordinates in a spherical earth provides an estimate of the various deviations of these rays due to the Earth's flattening, and the corresponding travel-time differences, for mantle P -waves and for shallow earthquakes. All these deviations are functions both of the latitude and of the epicentral distance. The difference in the distance to the Earth's centre at points with the same geocentric latitude on rays in the ellipsoidal and in the spherical model may reach several kilometres. Directly related to the deformation of the isovelocity surfaces, this difference is the only cause of significant perturbation in travel times. Other differences, such as that corresponding to the ray torsion, are of the first order in ellipticity, and may exceed 1 km. They induce only small differences in travel time, less than 0.01s. Thus, we show that the ellipticity correction obtained by Jeffreys (1935) and Bullen (1937) by a perturbational method can be recovered by a direct evaluation of the travel times in an ellipsoidal model of the Earth. Moreover, as stated by Dziewonski & Gilbert (1976), we verify the non-dependence of this correction on the choice of the velocity law. 相似文献
4.
This study explores garnet coronas around hedenbergite, which were formed by the reaction plagioclase + hedenbergite→garnet + quartz, to derive information about diffusion paths that allowed for material redistribution during reaction progress. Whereas quartz forms disconnected single grains along the garnet/hedenbergite boundaries, garnet forms ~20‐μm‐wide continuous polycrystalline rims along former plagioclase/hedenbergite phase boundaries. Individual garnet crystals are separated by low‐angle grain boundaries, which commonly form a direct link between the reaction interfaces of the plagioclase|garnet|hedenbergite succession. Compositional variations in garnet involve: (i) an overall asymmetric compositional zoning in Ca, Fe2+, Fe3+ and Al across the garnet layer; and (ii) micron‐scale compositional variations in the near‐grain boundary regions and along plagioclase/garnet phase boundaries. These compositional variations formed during garnet rim growth. Thereby, transfer of the chemical components occurred by a combination of fast‐path diffusion along grain boundaries within the garnet rim, slow diffusion through the interior of the garnet grains, and by fast diffusion along the garnet/plagioclase and the garnet/hedenbergite phase boundaries. Numerical simulation indicates that diffusion of Ca, Al and Fe2+ occurred about three to four, four and six to seven orders of magnitude faster along the grain boundaries than through the interior of the garnet grains. Fast‐path diffusion along grain boundaries contributed substantially to the bulk material transfer across the growing garnet rim. Despite the contribution of fast‐path diffusion, bulk diffusion through the garnet rim was too slow to allow for chemical equilibration of the phases involved in garnet rim formation even on a micrometre scale. Based on published garnet volume diffusion data the growth interval of a 20‐μm‐wide garnet rim is estimated at ~103–104 years at the inferred reaction conditions of 760 ± 50 °C at 7.6 kbar. Using the same parameterization of the growth law, 100‐μm‐ and 1‐mm‐thick garnet rims would grow within 105–106 and 106–107 years respectively. 相似文献
5.
Mauro Lo Cascio Yan Liang Nobumichi Shimizu Paul C. Hess 《Contributions to Mineralogy and Petrology》2008,156(1):87-102
The grain-scale processes of peridotite melting were examined at 1,340°C and 1.5 GPa using reaction couples formed by juxtaposing
pre-synthesized clinopyroxenite against pre-synthesized orthopyroxenite or harzburgite in graphite and platinum-lined molybdenum
capsules. Reaction between the clinopyroxene and orthopyroxene-rich aggregates produces a melt-enriched, orthopyroxene-free,
olivine + clinopyroxene reactive boundary layer. Major and trace element abundance in clinopyroxene vary systematically across
the reactive boundary layer with compositional trends similar to the published clinopyroxene core-to-rim compositional variations
in the bulk lherzolite partial melting studies conducted at similar P–T conditions. The growth of the reactive boundary layer takes place at the expense of the orthopyroxenite or harzburgite and
is consistent with grain-scale processes that involve dissolution, precipitation, reprecipitation, and diffusive exchange
between the interstitial melt and surrounding crystals. An important consequence of dissolution–reprecipitation during crystal-melt
interaction is the dramatic decrease in diffusive reequilibration time between coexisting minerals and melt. This effect is
especially important for high charged, slow diffusing cations during peridotite melting and melt-rock reaction. Apparent clinopyroxene-melt
partition coefficients for REE, Sr, Y, Ti, and Zr, measured from reprecipitated clinopyroxene and coexisting melt in the reactive
boundary layer, approach their equilibrium values reported in the literature. Disequilibrium melting models based on volume
diffusion in solid limited mechanism are likely to significantly underestimate the rates at which major and trace elements
in residual minerals reequilibrate with their surrounding melt.
Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users. 相似文献
6.
D. J. Cherniak 《Physics and Chemistry of Minerals》2008,35(4):179-187
Self-diffusion of Si under anhydrous conditions at 1 atm has been measured in natural zircon. The source of diffusant for
experiments was a mixture of ZrO2 and 30Si-enriched SiO2 in 1:1 molar proportions; experiments were run in crimped Pt capsules in 1-atm furnaces. 30Si profiles were measured with both Rutherford backscattering spectrometry (RBS) and nuclear reaction analysis with the resonant
nuclear reaction 30Si(p,γ)31P. For Si diffusion normal to c over the temperature range 1,350–1,550°C, we obtain an Arrhenius relation D = 5.8 exp(−702 ± 54 kJ mol−1/RT) m2 s−1 for the NRA measurements, which agrees within uncertainty with an Arrhenius relation determined from the RBS measurements
[62 exp(−738 ± 61 kJ mol−1/RT) m2 s−1]. Diffusion of Si parallel to c appears slightly faster, but agrees within experimental uncertainty at most temperatures
with diffusivities for Si normal to c. Diffusion of Si in zircon is similar to that of Ti, but about an order of magnitude faster than diffusion of Hf and two
orders of magnitude faster than diffusion of U and Th. Si diffusion is, however, many orders of magnitude slower than oxygen
diffusion under both dry and hydrothermal conditions, with the difference increasing with decreasing temperature because of
the larger activation energy for Si diffusion. If we consider Hf as a proxy for Zr, given its similar charge and size, we
can rank the diffusivities of the major constituents in zircon as follows: D
Zr < D
Si << D
O, dry < D
O, ‘wet’. 相似文献
7.
8.
In this study, we investigate two internal wave generation methods in numerical modeling of time-dependent equations for water wave propagation, i.e., delta source function method and source term addition method, the latter of which has been called the line source method in literatures. We derive delta source functions for the Boussinesq-type equations and extended mild-slope equations. By applying the fractional step splitting method, we show that the delta source function method is equivalent to the source term addition method employing the energy velocity. This suggests that the energy velocity should be used rather than the phase velocity for the transport of incident wave energy in the source term addition method. Finally, the performance of the delta source function method is verified by accurately generating nonlinear cnoidal waves as well as linear waves for horizontally one-dimensional cases. 相似文献
9.
A new set of equations of motion for wave propagation in water with varying depth is derived in this study. The equations expressed by the velocity potentials and the wave surface elevations include first-order non-linearity of waves and have the same dispersion characteristic to the extended Boussinesq equations. Compared to the extended Boussinesq equations, the equations have only two unknown scalars and do not contain spatial derivatives with an order higher than 2. The wave equations are solved by a finite element method. Fourth-order predictor–corrector method is applied in the time integration and a damping layer is applied at the open boundary for absorbing the outgoing waves. The model is applied to several examples of wave propagation in variable water depth. The computational results are compared with experimental data and other numerical results available in literature. The comparison demonstrates that the new form of the equations is capable of calculating wave transformation from relative deep water to shallow water. 相似文献
10.
In this paper, we analyse the ability of the nonlinear shallow-water (NSW) equations to predict wave distortion and energy dissipation of periodic broken waves in the inner surf zone. This analysis is based on the weak-solution theory for conservative equations. We derive a new one-way model, which applies to the transformation of non-reflective periodic broken waves on gently sloping beaches. This model can be useful to develop breaking-wave parameterizations (in particular broken-wave celerity expression) in both time-averaged wave models and time-dependent Boussinesq-type models. We also derive a new wave set-up equation which provides a simple and explicit relation between wave set-up and energy dissipation. Finally, we compare numerical simulations of both, the NSW model and the simplified one-way model, with spilling wave breaking experiments and we find a good agreement. 相似文献