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271.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2008,62(2):179-208
We study a general class of nonlinear mean field
Fokker-Planck equations in relation with an effective generalized
thermodynamical (E.G.T.) formalism. We show that these equations describe
several physical systems such as: chemotaxis of bacterial
populations, Bose-Einstein condensation in the canonical ensemble,
porous media, generalized Cahn-Hilliard equations, Kuramoto model,
BMF model, Burgers equation, Smoluchowski-Poisson system for
self-gravitating Brownian particles, Debye-Hückel theory of
electrolytes, two-dimensional turbulence... In particular, we show
that nonlinear mean field Fokker-Planck equations can provide
generalized Keller-Segel models for the chemotaxis of
biological populations. As an example, we introduce a new model of
chemotaxis incorporating both effects of anomalous diffusion and
exclusion principle (volume filling). Therefore, the notion of
generalized thermodynamics can have applications for concrete
physical systems. We also consider nonlinear mean field
Fokker-Planck equations in phase space and show the passage from
the generalized Kramers equation to the generalized Smoluchowski
equation in a strong friction limit. Our formalism is simple and
illustrated by several explicit examples corresponding to Boltzmann,
Tsallis, Fermi-Dirac and Bose-Einstein entropies among others. 相似文献
272.
Lubricant spreading on solid substrates has drawn considerable attention not only for the microscopic wetting theory but also for the dramatic application in head-disk interface of magnetic storage drive systems. Molecular dynamic simulation based on a coarse-grained bead-spring model has been used to study such a spreading process. The spreading profiles indicate that the hydrogen bonds among lubricant molecules and the hydrogen bonds between lubricant molecules and polar atoms of solid substrates will complicate the spreading process in a tremendous degree. The hydrogen bonds among lubricant molecules will strengthen the lubricant combination intensity, which may hinder most molecules from flowing down to the substrates and diffusing along the substrates. And the hydrogen bonds between lubricant molecules and polar atoms of solid substrates will confine the lubricant molecules around polar atoms, which may hinder the molecules from diffusing along the substrates and cause precursor film to vanish. 相似文献
273.
对约束在曲面上粒子运动的描述可以在内部坐标即曲面局部坐标下进行,也可以在外部坐标即在笛卡尔坐标下进行.在量子力学中,动量和动能算符的表示在这两种描述中各有不同,前者的动量算符仅包含内禀几何量,后者的动量算符包含了曲面的平均曲率.考虑到算符次序问题,动能算符对动量算符的依赖关系也不同,前者的依赖关系仅发现存在一种,后者的依赖关系已经发现有两种. 相似文献
274.
275.
Analogy is used to treat the system of non-interacting integrate-and-fire neurons as an ideal Fermi gas. It allows to obtain the nonlinear gain curve in the form of sigmoid in agreement with biological findings. As the by-product the gain-threshold mechanism in neurons is presented. Surprisingly enough, this is in agreement with new biological findings, too. Besides, the application of this mechanism to the dynamics of neurons leads to the non-monotone transfer function. 相似文献
276.
277.
Ulrich Mohrhoff 《Foundations of Physics》2002,32(2):217-254
Several errors in Stapp's interpretation of quantum mechanics and its application to mental causation (Henry P. Stapp, Quantum theory and the role of mind in nature, Foundations of Physics
31, 1465–1499 (2001)) are pointed out. An interpretation of (standard) quantum mechanics that avoids these errors is presented. 相似文献
278.
Our main aim from this work is to see which theorems in classical probability theory are still valid in fuzzy probability theory. Following Gudder's approach [Demonestratio Mathematica 31(3), 1998, 235–254; Foundations of Physics, 30, 1663–1678] to fuzzy probability theory, the basic concepts of the theory, that is of fuzzy probability measures and fuzzy random variables (observables), are presented. We show that fuzzy random variables extend the usual ones. Moreover, we prove that for any separable metrizable space, the crisp observables coincide with random variables. Then we prove the existence of a joint observable for any collection of observables, and we prove the weak law of large numbers and the central limit theorem in the fuzzy context. We construct a new definition of almost everywhere convergence. After proving that Gudder's definition implies ours and presenting an example that indicates that the converse is not true, we prove the strong law of large numbers according to this definition. 相似文献
279.
The flow between rough surfaces in sliding motion with contacts between these surfaces, is analyzed through the volume averaging method. Assuming a Reynolds (lubrication) approximation at the roughness scale, an average flow model is obtained combining spatial and time average. Time average, which is often omitted in previous works, is specially discussed. It is shown that the effective transport coefficients, traditionally termed flow factors in the lubrication literature, that appear in the average equations can be obtained from the solution to two closure problems. This allows for the numerical determination of flow factors on firmer bases and sheds light on some arguments to the literature. Moreover, fluid flows through fractures form an important subset of problems embodied in the present analysis, for which macroscopisation is given. 相似文献
280.
K. Broderix M. Weigt A. Zippelius 《The European Physical Journal B - Condensed Matter and Complex Systems》2002,29(3):441-455
We consider the gelation of particles which are permanently connected by random crosslinks, drawn from an ensemble of finite-dimensional
continuum percolation. To average over the randomness, we apply the replica trick, and interpret the replicated and crosslink-averaged
model as an effective molecular fluid. A Mayer-cluster expansion for moments of the local static density fluctuations is set
up. The simplest non-trivial contribution to this series leads back to mean-field theory. The central quantity of mean-field
theory is the distribution of localization lengths, which we compute for all connectivities. The highly crosslinked gel is
characterized by a one-to-one correspondence of connectivity and localization length. Taking into account higher contributions
in the Mayer-cluster expansion, systematic corrections to mean-field can be included. The sol-gel transition shifts to a higher
number of crosslinks per particle, as more compact structures are favored. The critical behavior of the model remains unchanged
as long as finite truncations of the cluster expansion are considered. To complete the picture, we also discuss various geometrical
properties of the crosslink network, e.g. connectivity correlations, and relate the studied crosslink ensemble to a wider class of ensembles, including the Deam-Edwards
distribution.
Received on 24 April 2002 Published online 14 October 2002
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ID="b"e-mail: weigt@theorie.physik.uni-goettingen.de 相似文献