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We give the widest geometrical generalization of the notion of connection in fiber spaces that allows one to adequately construct
the geometry of ordinary differential systems of any order. In this area, there is a theory of nonlinear stable connections
developed by the first author. Here we apply it to fourth-order systems. 相似文献
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A solution to the BBGKY hierarchy for nonequilibrium distribution functions is obtained within modified boundary conditions. The boundary conditions take into account explicitly both the nonequilibrium one-particle distribution function as well as local conservation laws. As a result, modified group expansions are proposed. On the basis of these expansions, a generalized kinetic equation for hard spheres and a generalized Bogolubov–Lenard–Balescu kinetic equation for a dense electron gas are derived within the polarization approximation. 相似文献
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Recent research has shown that a phase transformation of diamond to a different form of carbon is involved when diamonds are polished in the traditional fashion. The question as to how this phase transformation is activated and maintained to produce high wear rates is of great technological interest since it may radically change the way we view the processing of diamond. This paper describes the use of Raman spectroscopy to examine debris produced on the diamond polishing wheel, both during its preparation and during polishing. In addition, polished diamond surfaces were examined for the possible existence of non-diamond surface layers in an attempt to identify material removal mechanisms. Raman spectroscopy proves ideal for these analyses because its relatively high spatial resolution is well suited to the analysis of small wear features and debris particles, and because of the wealth of information it reveals about chemical structure. This level of structural information has been lacking in previous analyses of diamond polishing debris. In addition to the non-diamond carbon found in the wear debris, significant quantities of two iron oxides, magnetite (Fe3O4) and haematite (α-Fe2O3), were also found. An interesting observation was that a transformation from magnetite to haematite could be induced either by using high power laser excitation or by frictional heating during polishing. It is suggested that some of the Raman peaks previously attributed to lonsdaleite might better be explained by the presence of these oxides. 相似文献
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Omelyan IP 《The Journal of chemical physics》2007,127(4):044102
A novel approach is developed to integrate the equations of motion in many-body systems of interacting rigid polyatomic molecules. It is based on an advanced gradient-like decomposition technique in the presence of translational and orientational degrees of freedom. As a result, a new class of reversible phase-space volume preserving fourth-order algorithms for rotational motion is introduced. Contrary to standard nongradient decomposition integrators, the algorithms derived take into account additional analytically integrable terms in the exponential propagators, while the arising gradients are expressed in terms of forces and torques. This allows one to increase significantly the precision of the integration and, at the same time, reduce the increased computational costs. The optimized second-order integrator is also presented. The gradient-like and optimized algorithms are tested in molecular dynamics simulations of water versus well-established integrators known previously. It is shown that the new algorithms lead to the best efficiency in the rigid-body integration. 相似文献
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We have developed several multiple time stepping techniques to overcome the limitations on efficiency of molecular dynamics simulations of complex fluids. They include the modified canonical and isokinetic schemes, as well as the extended isokinetic Nosé-Hoover chain approach. The latter generalizes the method of Minary, Tuckerman, and Martyna for translational motion [Phys. Rev. Lett. 93, 150201 (2004)] to systems with both translational and orientational degrees of freedom. Although the microcanonical integrators are restricted to relatively small outer time steps of order of 16 fs, we show on the basis of molecular dynamics simulations of ambient water that in the canonical and isokinetic thermostats the size of these steps can be increased to 50 and 75 fs, respectively (at the same inner time step of 4 fs). Within the generalized isokinetic Nosé-Hoover chain algorithm we have derived, huge outer time steps of order of 500 fs can be used without losing numerical stability and affecting equilibrium properties. 相似文献
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I. P. Omelyan W. Fenz R. Folk I. M. Mryglod 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,51(1):101-110
An integral equation approach is developed to investigate phase
coexistence properties of Ising spin fluids with Yukawa ferromagnetic
and Lennard-Jones nonmagnetic interactions in the presence of an
external field. The calculations are carried out on the basis of
the Duh and Henderson closure with a specific Duh-like partitioning
of the total potential. The coupled set of the Ornstein-Zernike
equation, the closure relation and the external field constraint
are solved using an efficient numerical algorithm. The phase
diagrams are evaluated in a wide range of varying the external
field and the ratio of strengths of Yukawa to Lennard-Jones
interactions. Different types of the phase diagram topology
as well as various external field dependencies of critical
temperatures and densities are identified. The complexity with
respect to simple Lennard-Jones fluids is explained by coupling
between spatial and spin degrees of freedom in the system. A
comparison of the obtained theoretical results with simulation
data is made and a good agreement is observed. 相似文献
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IP Waicheung 《中国科学A辑(英文版)》2006,49(9):1211-1222
In the nonparametric regression models, a homoscedastic structure is usually assumed. However, the homoscedasticity cannot be guaranteed a priori. Hence, testing the heteroscedasticity is needed. In this paper we propose a consistent nonparametric test for heteroscedasticity, based on wavelets. The empirical wavelet coefficients of the conditional variance in a regression model are defined first. Then they are shown to be asymptotically normal, based on which a test statistic for the heteroscedasticity is constructed by using Fan's wavelet thresholding idea. Simulations show that our test is superior to the traditional nonparametric test. 相似文献
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