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1.
The system containing six benzylideneanilines (BA) has been studied: Group 1:
The crystal structures of Group 1 are isostructural. They crystallize in a monoclinic cell, space groupP21. They are rare examples of planar benzylideneanilines in a nondisordered crystal structure. The crystal structures exhibit an intermolecular ring containing five atoms and hal- - - hal. C-H- - - hal interactions, which may contribute to the planarity of the molecule. The structures in Group 2 crystallize in a monoclinic cell, space groupP21/c. The conformation is nonplanar and there are no intermolecular halogen- - -halogen interactions. The abovementioned five atom pattern ring does not occur in these structures. These two groups of structures show that the type and mode of molecular substitution can lead to specific intermolecular interactions which in turn stabilize an otherwise unfavorable molecular conformation. 相似文献
I: | N-(p-Chlorobenzylideneaniline)m-chloroaniline (BA, X=4-Cl, Y=3-Cl) |
II: | N-(p-Bromobenzylideneaniline)m-bromoaniline (BA, X=4-Br, Y=3-Br) |
III: | N-(p-Bromobenzylideneaniline)m-chloroaniline (BA, X=4-Br, Y=3-Cl) |
IV: | N-(p-Chlorobenzylideneaniline)m-bromoaniline (BA, X=4-Cl, Y=3-Br) Group 2: |
V: | N-(m-Chlorobenzylideneaniline)p-bromoaniline (BA, X=3-Cl, Y=4-Br) |
VI: | N-(m-Bromobenzylidencaniline)p-chloroaniline (BA, X=3-Br, Y=4-Br) |
2.
Model order reduction of the two‐dimensional Burgers equation is investigated. The mathematical formulation of POD/discrete empirical interpolation method (DEIM)‐reduced order model (ROM) is derived based on the Galerkin projection and DEIM from the existing high fidelity‐implicit finite‐difference full model. For validation, we numerically compared the POD ROM, POD/DEIM, and the full model in two cases of Re = 100 and Re = 1000, respectively. We found that the POD/DEIM ROM leads to a speed‐up of CPU time by a factor of O(10). The computational stability of POD/DEIM ROM is maintained by means of a careful selection of POD modes and the DEIM interpolation points. The solution of POD/DEIM in the case of Re = 1000 has an accuracy with error O(10?3) versus O(10?4) in the case of Re = 100 when compared with the high fidelity model. For this turbulent flow, a closure model consisting of a Tikhonov regularization is carried out in order to recover the missing information and is developed to account for the small‐scale dissipation effect of the truncated POD modes. It is shown that the computational results of this calibrated ROM exhibit considerable agreement with the high fidelity model, which implies the efficiency of the closure model used. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
3.
Aleksey K. Alekseev I. Michael Navon 《International Journal of Computational Fluid Dynamics》2013,27(2):113-117
The uncertainty of temperature prediction from the heat flux error is estimated using first and second order adjoint equations. The adjoint codes developed for the inverse heat transfer problems provide the uncertainty estimation for the corresponding forward problems. Numerical tests corroborate the feasibility of fast uncertainty estimation using Hessian maximum eigenvalue obtained via second order adjoint equations. 相似文献
4.
An improved algorithm for the shallow water equations model reduction: Dynamic Mode Decomposition vs POD
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We propose an improved framework for dynamic mode decomposition (DMD) of 2‐D flows for problems originating from meteorology when a large time step acts like a filter in obtaining the significant Koopman modes, therefore, the classic DMD method is not effective. This study is motivated by the need to further clarify the connection between Koopman modes and proper orthogonal decomposition (POD) dynamic modes. We apply DMD and POD to derive reduced order models (ROM) of the shallow water equations. Key innovations for the DMD‐based ROM introduced in this paper are the use of the Moore–Penrose pseudoinverse in the DMD computation that produced an accurate result and a novel selection method for the DMD modes and associated amplitudes and Ritz values. A quantitative comparison of the spatial modes computed from the two decompositions is performed, and a rigorous error analysis for the ROM models obtained is presented. Copyright © 2015 John Wiley & Sons, Ltd. 相似文献
5.
Non‐intrusive reduced‐order modeling for multiphase porous media flows using Smolyak sparse grids
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Dunhui Xiao Zhi Lin Fangxin Fang Christopher C. Pain Ionel M. Navon Pablo Salinas Ann Muggeridge 《国际流体数值方法杂志》2017,83(2):205-219
In this article, we describe a non‐intrusive reduction method for porous media multiphase flows using Smolyak sparse grids. This is the first attempt at applying such an non‐intrusive reduced‐order modelling (NIROM) based on Smolyak sparse grids to porous media multiphase flows. The advantage of this NIROM for porous media multiphase flows resides in that its non‐intrusiveness, which means it does not require modifications to the source code of full model. Another novelty is that it uses Smolyak sparse grids to construct a set of hypersurfaces representing the reduced‐porous media multiphase problem. This NIROM is implemented under the framework of an unstructured mesh control volume finite element multiphase model. Numerical examples show that the NIROM accuracy relative to the high‐fidelity model is maintained, whilst the computational cost is reduced by several orders of magnitude. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
6.
The effect of proton exchange on the measurement of 1H-1H, 1H-2H, and 2H-2H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the 1H-1H and 1H-2H residual dipolar interactions and the proton exchange rate at a temperature of 24 degrees C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24 degrees C were 300 and 50 Hz and 3000 s-1, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5 degrees C, where the spectra of the H2O molecules were well resolved, so that the 1H-1H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5 degrees C, where the proton exchange was in the intermediate regime for the 1H-2H dipolar interaction, confirmed the result obtained at 24 degrees C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T2) depend on the orientation as the square of the second-rank Legendre polynomial. 相似文献
7.
Taler G Eliav U Navon G 《Journal of magnetic resonance (San Diego, Calif. : 1997)》1999,141(2):228-238
The application of multiple quantum filtered (MQF) NMR to the identification and characterization of the binding of ligands containing quadrupolar nuclei to proteins is demonstrated. Using relaxation times measured by MQF NMR multiple binding of boric acid and borate ion to ferri and ferrocytochrome c was detected. Borate ion was found to have two different binding sites. One of them was in slow exchange, k(diss) = 20 +/- 3 s(-1) at 5 degrees C and D(2)O solution, in agreement with previous findings by (1)H NMR (G. Taler et al., 1998, Inorg. Chim. Acta 273, 388-392). The triple quantum relaxation of the borate in this site was found to be governed by dipolar interaction corresponding to an average B-H distance of 2.06 +/- 0.07 A. Other, fast exchanging sites for borate and boric acid could be detected only by MQF NMR. The binding equilibrium constants at these sites at pH 9.7 were found to be 1800 +/- 200 M(-1) and 2.6 +/- 1.5 M(-1) for the borate ion and boric acid, respectively. Thus, detection of binding by MQF NMR proved to be sensitive to fast exchanging ligands as well as to very weak binding that could not be detected using conventional methods. 相似文献
8.
The extinction of a single species due to demographic stochasticity is analyzed. The discrete nature of the individual agents
and the Poissonian noise related to the birth-death processes result in local extinction of a metastable population, as the
system hits the absorbing state. The Fokker-Planck formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the absorbing state become, in general, invalid as the
population becomes large. To connect these two regimes, a real space WKB method based on the master equation is presented,
and is shown to yield an excellent approximation for the decay rate and the extreme events statistics all the way down to
the absorbing state. The details of the underlying microscopic process, smeared out in a mean field treatment, are shown to
be crucial for an exact determination of the extinction exponent. This general scheme is shown to reproduce the known results
in the field, to yield new corollaries and to fit quite precisely the numerical solutions. Moreover it allows for systematic
improvement via a series expansion where the small parameter is the inverse of the number of individuals in the metastable
state. 相似文献
9.
Yosef E. Maruvka Nadav M. Shnerb Sorin Solomon Gur Yaari David A. Kessler 《Journal of statistical physics》2011,142(6):1302-1316
The inference of past demographic parameters from current genetic polymorphism is a fundamental problem in population genetics.
The standard techniques utilize a reconstruction of the gene-genealogy, a cumbersome process that may be applied only to small
numbers of sequences. We present a method that compares the total number of haplotypes (distinct sequences) with the model
prediction. By chopping the DNA sequence into pieces we condense the immense information hidden in sequence space into a function
for the number of haplotypes versus subsequence size. The details of this curve are robust to statistical fluctuations and
are seen to reflect the process parameters. This procedure allows for a clear visualization of the quality of the fit and,
crucially, the numerical complexity grows only linearly with the number of sequences. Our procedure is tested against both
simulated data as well as empirical mtDNA data from China and provides excellent fits in both cases. 相似文献
10.
Degenerate band edges (DBEs) of a photonic bandgap have the form (ω-ω(D)) ∝k(2m) for integers m>1, with ω(D) the frequency at the band edge. We show theoretically that DBEs lead to efficient coupling into slow-light modes without a transition region, and that the field strength in the slow mode can far exceed that in the incoming medium. A method is proposed to create a DBE of arbitrary order m by coupling m optical modes with multiple superimposed gratings. The enhanced coupling near a DBE occurs because of the presence of one or more evanescent modes, which are absent at conventional quadratic band edges. We furthermore show that the coupling can be increased or suppressed by varying the number of excited evanescent waves. 相似文献