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101.
Philipp Bader Arieh Iserles Karolina Kropielnicka Pranav Singh 《Foundations of Computational Mathematics》2014,14(4):689-720
The computation of the semiclassical Schrödinger equation presents major challenges because of the presence of a small parameter. Assuming periodic boundary conditions, the standard approach consists of semi-discretisation with a spectral method, followed by an exponential splitting. In this paper we sketch an alternative strategy. Our analysis commences with the investigation of the free Lie algebra generated by differentiation and by multiplication with the interaction potential: it turns out that this algebra possesses a structure which renders it amenable to a very effective form of asymptotic splitting: exponential splitting where consecutive terms are scaled by increasing powers of the small parameter. This leads to methods which attain high spatial and temporal accuracy and whose cost scales as \({\mathcal {O}}\!\left( M\log M\right) \) , where \(M\) is the number of degrees of freedom in the discretisation. 相似文献
102.
Taking into account softening effects in connection with conventional inelastic material models can cause ill-posed boundary value problems. These problems can be established by obtaining no unique solution for the resulting algebraic system or by having a strong mesh dependence of the numerical results. This is the consequence of losing ellipticity of the governing field equations. A possible approach to solve these problems is to introduce a non-local field function in the model which includes an internal material length scale. For this purpose a gradient-enhanced free energy function is used for the current continuum damage model from which two variational equations are resulting. Calculations with less effort can be achieved due to the enhancement of the free energy function in comparison to other approaches. The mentioned model is applied to a material with locally varying damage properties (yield limits). Furthermore, the model is able to describe crack propagation in cases of completely damaged material. Therewith, a matrix material including precipitates, such as carbides, is modeled. This allows to investigate ship screws, which usually exhibit the mentioned composition, with regard to the influence of cavitation. Cavitation describes the implosion of risen vapor bubbles, whereby the impact on screws causes heavy damages which can lead to a complete destruction. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
103.
Ferdinand H. Lutter Lucie Grokenberger Philipp Spieß Jeffrey M. Hammann Konstantin Karaghiosoff Paul Knochel 《Angewandte Chemie (International ed. in English)》2020,59(14):5546-5550
A combination of 10 % CoCl2 and 20 % 2,2′‐bipyridine ligands enables cross‐coupling of functionalized primary and secondary alkylzinc reagents with various (hetero)aryl halides. Couplings with 1,3‐ and 1,4‐substituted cycloalkylzinc reagents proceeded diastereoselectively leading to functionalized heterocycles with high diastereoselectivities of up to 98:2. Furthermore, alkynyl bromides react with primary and secondary alkylzinc reagents providing the alkylated alkynes. 相似文献
104.
105.
Kowalewski J Effemey M Jokisaari J 《Journal of magnetic resonance (San Diego, Calif. : 1997)》2002,157(2):171-177
Multiple-field (4.7, 9.4, 14.1 T) carbon-13 relaxation data are reported for hexamethylenetetramine (HMTA) in the cryosolvent D(2)O/DMSO at 243 K. Under these conditions, the reorientational motion of HMTA is outside of the extreme narrowing range and the relaxation data can be subjected to a quantitative interpretation. Because of the high symmetry of the HMTA molecule, the reorientation must be isotropic. Treating the reorientation as a small-step rotational diffusion of a rigid body, we obtain a rotational correlation time of 1.0 ns and a carbon-proton dipole-dipole coupling constant corresponding to an effective internuclear distance of 114. 2 pm. The harmonic vibrational correction to the dipole-dipole coupling constant, based on a known force field, yields an NMR estimate of the r(alpha) distance of 110.8 +/- 0.3 pm. 相似文献
106.
In this article we study the regularity of stationary points of the knot energies E (α) introduced by O’Hara (Topology 30(2):241–247, 1991; Topol Appl 48(2):147–161, 1992; Topol Appl 56(1):45–61, 1994) in the range ${\alpha\in(2,3)}$ . In a first step we prove that E (α) is C 1 on the set of all regular embedded curves belonging to ${{H^{(\alpha+1)/2,2}(\mathbb {R}{/}\mathbb {Z}, \mathbb {R}^n)}}$ and calculate its derivative. After that we use the structure of the Euler-Lagrange equation to study the regularity of stationary points of E (α) plus a positive multiple of the length. We show that stationary points of finite energy are of class C ∞—so especially all local minimizers of E (α) among curves with fixed length are smooth. 相似文献
107.
We report on a 3.3 μm laser/optical parametric oscillator system with 4.7 mJ pulse energy for laser ultrasound measurements of carbon-fiber-reinforced materials. The OPO was pumped by a compact diode-pumped Nd:YAG master-oscillator power-amplifier system with two amplifier stages. First results of laser ultrasound measurements are presented. 相似文献
108.
Friedrich Philipp 《PAMM》2014,14(1):833-834
We prove by means of elementary methods that phase retrieval of complex polynomials p of degree less than N is possible with 4N − 4 phaseless Fourier measurements of p and p′. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
109.
110.
Ivanovskaya VV Zobelli A Wagner P Heggie MI Briddon PR Rayson MJ Ewels CP 《Physical review letters》2011,107(6):065502
We demonstrate that free graphene sheet edges can curl back on themselves, reconstructing as nanotubes. This results in lower formation energies than any other nonfunctionalized edge structure reported to date in the literature. We determine the critical tube size and formation barrier and compare with density functional simulations of other edge terminations including a new reconstructed Klein edge. Simulated high resolution electron microscopy images show why such rolled edges may be difficult to detect. Rolled zigzag edges serve as metallic conduction channels, separated from the neighboring bulk graphene by a chain of insulating sp(3)-carbon atoms, and introduce van Hove singularities into the graphene density of states. 相似文献