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51.
The nonlinear free vibration of double-walled carbon nanotubes based on the nonlocal elasticity theory is studied in this paper. The nonlinear equations of motion of the double-walled carbon nanotubes are derived by using Euler beam theory and Hamilton principle, with considering the von Kármán type geometric nonlinearity and the nonlinear van der Waals forces. The surrounding elastic medium is formulated as the Winkler model. The harmonic balance method and Davidon–Fletcher–Powell method are utilized for the analysis and simulation of the nonlinear vibration. The simulation results show that the nonlocal parameter, aspect ratio and surrounding elastic medium play more important roles in the nonlinear noncoaxial vibration than those in the coaxial vibration of the double-walled carbon nanotubes. The noncoaxial vibration amplitudes of only considering nonlinear van der Waals forces are larger than those of considering both geometric nonlinearity and nonlinear van der Waals forces. 相似文献
52.
General local convergence theorems with order of convergence r≥1 are provided for iterative processes of the type xn+1=Txn, where T:D⊂X→X is an iteration function in a metric space X. The new local convergence theory is applied to Newton iteration for simple zeros of nonlinear operators in Banach spaces as well as to Schröder iteration for multiple zeros of polynomials and analytic functions. The theory is also applied to establish a general theorem for the uniqueness ball of nonlinear equations in Banach spaces. The new results extend and improve some results of [K. Do?ev, Über Newtonsche Iterationen, C. R. Acad. Bulg. Sci. 36 (1962) 695–701; J.F. Traub, H. Wo?niakowski, Convergence and complexity of Newton iteration for operator equations, J. Assoc. Comput. Mach. 26 (1979) 250–258; S. Smale, Newton’s method estimates from data at one point, in: R.E. Ewing, K.E. Gross, C.F. Martin (Eds.), The Merging of Disciplines: New Direction in Pure, Applied, and Computational Mathematics, Springer, New York, 1986, pp. 185–196; P. Tilli, Convergence conditions of some methods for the simultaneous computation of polynomial zeros, Calcolo 35 (1998) 3–15; X.H. Wang, Convergence of Newton’s method and uniqueness of the solution of equations in Banach space, IMA J. Numer. Anal. 20 (2000) 123–134; I.K. Argyros, J.M. Gutiérrez, A unified approach for enlarging the radius of convergence for Newton’s method and applications, Nonlinear Funct. Anal. Appl. 10 (2005) 555–563; M. Giusti, G. Lecerf, B. Salvy, J.-C. Yakoubsohn, Location and approximation of clusters of zeros of analytic functions, Found. Comput. Math. 5 (3) (2005) 257–311], and others. 相似文献
53.
The ground state of the van der Waals-type lanthanide dimer Yb2 has been studied by means of relativistic energy-consistent ab initio pseudopotentials using three different core definitions.
Electron correlation was treated by coupled-cluster theory, whereby core-valence correlation effects have been accounted for
either explicitly by correlating the energetically highest coreorbitals or implicitly by means of an effective core-polarization
potential. Results for the first and second atomic ionization potentials, the atomic dipole polarizability, and the spectroscopic
constants of the molecular ground state are reported. Low-lying excited states have been investigated with spin-orbit configuration
interaction calculations. It is also demonstrated for the whole lanthanide series that correlation effects due to the atomic-like,
possibly open 4f-shell in lanthanides can be modeled effectively by adding a core-polarization potential to pseudopotentials attributing the
4f-shell to the core.
Received: 3 April 1998 / Accepted: 27 July 1998 / Published online: 9 October 1998 相似文献
54.
The deformation, drainage, and rupture of an axisymmetrical film between colliding drops in the presence of insoluble surfactants under the influence of van der Waals forces is studied numerically at small capillary and Reynolds numbers and small surfactant concentrations. Constant-force collisions of Newtonian drops in another Newtonian fluid are considered. The mathematical model is based on the lubrication equations in the gap between drops and the creeping flow approximation of Navier–Stokes equations in the drops, coupled with velocity and stress boundary conditions at the interfaces. A nonuniform surfactant concentration on the interfaces, governed by a convection–diffusion equation, leads to a gradient of the interfacial tension which in turn leads to additional tangential stress on the interfaces (Marangoni effects). The mathematical problem is solved by a finite-difference method on a nonuniform mesh at the interfaces and a boundary-integral method in the drops. The whole range of the dispersed to continuous-phase viscosity ratios is investigated for a range of values of the dimensionless surfactant concentration, Peclét number, and dimensionless Hamaker constant (covering both “nose” and “rim” rupture). In the limit of the large Peclét number and the small dimensionless Hamaker constant (characteristic of drops in the millimeter size range) a fair approximation to the results is provided by a simple expression for the critical surfactant concentration, drainage being virtually uninfluenced by the surfactant for concentrations below the critical surfactant concentration and corresponding to that for immobile interfaces for concentrations above it. 相似文献
55.
The ground state ab initio CCSD(T) potential curves using various basis sets (aug-cc-pVXZ-PP (X = D, T, Q, 5)) is obtained for the dimers of helium with IIb group metals. The effect of the position of the (mid) bond-functions on the interaction energy is discussed. A Symmetry Adapted Perturbation Theory decomposition of the interaction energy is provided and the trends in the dimer stabilizing and destabilizing contributions are depicted. The spline fitted potential curves are applied together with rigorous statistical formulae in order to obtain the transport coefficients (viscosity coefficients, diffusion coefficients) and the second virial coefficient both for pure constituents and mixtures. The obtained theoretical results are compared with available experimental data. Molecular dynamics is used to obtain reliable values of the diffusion coefficients for all the systems under study. 相似文献
56.
Dieter Hauchecorne Dr. Roman Szostak Dr. Wouter A. Herrebout Prof. Benjamin J. van der Veken Prof. 《Chemphyschem》2009,10(12):2105-2115
The formation of weakly bound molecular complexes between dimethyl ether (DME) and the trifluoromethyl halides CF3Cl, CF3Br and CF3I dissolved in liquid argon and in liquid krypton is investigated, using Raman and FTIR spectroscopy. For all halides evidence is found for the formation of C? X???O halogen‐bonded 1:1 complexes. At higher concentrations of CF3Br, a weak absorption due to a 1:2 complex is also observed. Using spectra recorded at temperatures between 87 and 125 K, the complexation enthalpies for the complexes are determined to be ?6.8(3) kJ mol?1 (DME?CF3Cl), ?10.2(1) kJ mol?1 (DME?CF3Br), ?15.5(1) kJ mol?1 (DME?CF3I), and ?17.8(5) kJ mol?1 [DME(?CF3Br)2]. Structural and spectral information on the complexes is obtained from ab initio calculations at the MP2/ 6‐311++G(d,p) and MP2/6‐311++G(d,p)+LanL2DZ* levels. By applying Monte Carlo free energy perturbation calculations to account for the solvent influences, and statistical thermodynamics to estimate the zero‐point vibrational and thermal influences, the ab initio complexation energies are converted into complexation enthalpies for the solutions in liquid argon. The resulting values are compared with the experimental data deduced from the cryosolutions. 相似文献
57.
Peter Möller 《Fresenius' Journal of Analytical Chemistry》1974,268(1):28-30
Zusammenfassung Über den Ca2+-Mg2+-Ionenaustausch wurde der Mg2+-Ionengehalt in Calcitoberflächen in Abhängigkeit von der Mg2+-Konzentration in Ca-45-markierten Lösungen bestimmt. Es wurde gefunden, daß der Anstieg des Molverhältnisses Mg/Ca in der Calcit-Oberfläche bei steigendem Mg2+-Gehalt in der Lösung jeweils bei Erreichen von Mg/Ca 1 und 3 deutlich verringert wird. Die ermittelte Austauschisotherme kann benutzt werden, um über eine Bestimmung des Mg/Ca-Verhältnisses in der Lösung auf dasjenige in der Oberfläche zu schließen.Vortrag anläßlich der Tagung Spurenanalyse, 2. bis 5. April 1973 in Erlangen. 相似文献
58.
A mass conservative well‐balanced reconstruction at wet/dry interfaces for the Godunov‐type shallow water model 下载免费PDF全文
This paper presents a novel mass conservative, positivity preserving wetting and drying treatment for Godunov‐type shallow water models with second‐order bed elevation discretization. The novel method allows to compute water depths equal to machine accuracy without any restrictions on the time step or any threshold that defines whether the finite volume cell is considered to be wet or dry. The resulting scheme is second‐order accurate in space and keeps the C‐property condition at fully flooded area and also at the wet/dry interface. For the time integration, a second‐order accurate Runge–Kutta method is used. The method is tested in two well‐known computational benchmarks for which an analytical solution can be derived, a C‐property benchmark and in an additional example where the experimental results are reproduced. Overall, the presented scheme shows very good agreement with the reference solutions. The method can also be used in the discontinuous Galerkin method. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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