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241.
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We consider the classical coupled, combined‐field integral equation formulations for time‐harmonic acoustic scattering by a sound soft bounded obstacle. In recent work, we have proved lower and upper bounds on the L2 condition numbers for these formulations and also on the norms of the classical acoustic single‐ and double‐layer potential operators. These bounds to some extent make explicit the dependence of condition numbers on the wave number k, the geometry of the scatterer, and the coupling parameter. For example, with the usual choice of coupling parameter they show that, while the condition number grows like k1/3 as k, when the scatterer is a circle or sphere, it can grow as fast as k7/5 for a class of “trapping” obstacles. In this article, we prove further bounds, sharpening and extending our previous results. In particular, we show that there exist trapping obstacles for which the condition numbers grow as fast as exp(γk), for some γ > 0, as k through some sequence. This result depends on exponential localization bounds on Laplace eigenfunctions in an ellipse that we prove in the appendix. We also clarify the correct choice of coupling parameter in 2D for low k. In the second part of the article, we focus on the boundary element discretisation of these operators. We discuss the extent to which the bounds on the continuous operators are also satisfied by their discrete counterparts and, via numerical experiments, we provide supporting evidence for some of the theoretical results, both quantitative and asymptotic, indicating further which of the upper and lower bounds may be sharper. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010  相似文献   
243.
Solvation of small and large clusters are studied by simulation, considering a range of solvent-solute attractive energy strengths. Over a wide range of conditions, both for solvation in the Lennard-Jones liquid and in the SPC model of water, it is shown that the mean solvent density varies linearly with changes in solvent-solute adhesion or attractive energy strength. This behavior is understood from the perspective of Weeks' theory of solvation (Annu. Rev. Phys. Chem. 2002, 53, 533) and supports theories based upon that perspective.  相似文献   
244.
Herein we report the synthesis of a fluorescent organic salt through anion exchange and the subsequent fabrication of 1D-nanostructures via a facile templating method.  相似文献   
245.
We prepare metastable glassy states in a model glass former made of Lennard-Jones particles by sampling biased ensembles of trajectories with low dynamical activity. These trajectories form an inactive dynamical phase whose "fast" vibrational degrees of freedom are maintained at thermal equilibrium by contact with a heat bath, while the "slow" structural degrees of freedom are located in deep valleys of the energy landscape. We examine the relaxation to equilibrium and the vibrational properties of these metastable states. The glassy states we prepare by our trajectory sampling method are very stable to thermal fluctuations and also more mechanically rigid than low-temperature equilibrated configurations.  相似文献   
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In recent papers, we have argued that kinetically constrained coarse-grained models can be applied to understand dynamic properties of glass-forming materials, and we have used this approach in various applications that appear to validate this view. In one such paper [J. P. Garrahan and D. Chandler, Proc. Natl. Acad. Sci. U.S.A. 100, 9710 (2003)], among other things we argued that this approach also explains why the heat-capacity discontinuity at the glass transition is generally larger for fragile materials than for strong materials. In the preceding article, Biroli, Bouchaud, and Tarjus have objected to our explanation on this point, arguing that the class of models we apply is inconsistent with both the absolute size and the temperature dependence of the experimental specific heat. Their argument, however, neglects parameters associated with the coarse graining. Accounting for these parameters, we show here that our treatment of dynamics is not inconsistent with heat-capacity discontinuities.  相似文献   
248.
We present a coarse-grained lattice model of solvation thermodynamics and the hydrophobic effect that implements the ideas of Lum-Chandler-Weeks theory [J. Phys. Chem. B 134, 4570 (1999)] and improves upon previous lattice models based on it. Through comparison with molecular simulation, we show that our model captures the length-scale and curvature dependence of solvation free energies with near-quantitative accuracy and 2-3 orders of magnitude less computational effort, and further, correctly describes the large but rare solvent fluctuations that are involved in dewetting, vapor tube formation, and hydrophobic assembly. Our model is intermediate in detail and complexity between implicit-solvent models and explicit-water simulations.  相似文献   
249.
    
Current experimental vitreous substitutes only replace the physical functions of the natural vitreous humor. Removal of the native vitreous disrupts oxygen homeostasis in the eye, causing oxidative damage to the lens that likely results in cataract formation. Neither current clinical treatments nor other experimental vitreous substitutes consider the problem of oxidative stress after vitrectomy. To address this problem, biomimetic hydrogels are prepared by free radical polymerization of poly(ethylene glycol) methacrylate and poly(ethylene glycol) diacrylate. These hydrogels have similar mechanical and optical properties to the vitreous. The hydrogels are injectable through small‐gauge needles and demonstrate in vitro biocompatibility with human retinal and lens epithelial cells. The hydrogels and added vitamin C, an antioxidant, show a synergistic effect in protecting ocular cells against reactive oxygen species, which fulfills a chemical function of the natural vitreous. These hydrogels have the potential to prevent post‐vitrectomy cataract formation and reduce the cost of additional surgeries.  相似文献   
250.
This paper presents a novel, yet thermodynamically consistent, model of the isothermal compaction of loose granular material based on the principle of maximum dissipation rate. The method is first tested out on a simple version of the Bingham model and a hard particle model of rate-independent granular flow where it is seen that only the dissipation function and dilatancy rule are required in either case and the procedures are identical. This hard particle model is subsequently modified by the introduction of damage. Yield surface and flow rules are produced that are broadly in accordance with experimental findings. The key to the above modification is the concept of a dilatancy rule with two contributions. (1) A shear induced negative dilatancy, where any shear deformation has a tendency to produce densification. (2) Under many circumstances, this is countered by positive dilatancy such as at the critical state where the two mechanisms balance. This modification uses the idea that the first contribution is encouraged by microscopic damage local to the particle contacts that might permit compaction to occur under hydrostatic pressure alone. A mechanism is postulated whereby shear stresses operating at the microscopic level, while cancelling out at the macroscopic level, might occur with low levels of damage but produce no overall shear strains.  相似文献   
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