The hyperbolic meteor orbits among the 4,581 photographic and 62,906 radar meteors of the IAU MDC have been analysed using
statistical methods. It was shown that the vast majority of hyperbolic orbits has been caused by the dispersion of determined
velocities. The large proportion of hyperbolic orbits among the known meteor showers strongly suggests the hyperbolicity of
the meteors is not real. The number of apparent hyperbolic orbits increases inversely proportional to the difference between
the mean heliocentric velocity of meteor shower and the parabolic velocity limit. The number of hyperbolic meteors in the
investigated catalogues does not, in any case, represent the number of interstellar meteors in observational data. The apparent
hyperbolicity of these orbits is caused by a high spread in velocity determination, shifting a part of the data through the
parabolic limit. 相似文献
This study presents results of field tests conducted on anchors used to support wire mesh and cable net rockfall protection systems. The load transfer and failure characteristics of these anchors are different from those used in most civil applications in that loads are often applied transversely to the top of tendon rather than axially. The study included vertical as well as horizontal series of tests conducted on some anchors widely used in wire mesh and cable net rockfall protect systems. It was found that the deformation characteristics of these anchors under vertical loading are nonlinear. They are approximated by a hyperbolic formulation and used to calculate the ultimate capacity. Top-downward progressive cracking of the grout was observed during loading and influences the deformation characteristics of these anchors under horizontal loading. The anchors deflected excessively before they could attain their ultimate capacity in the horizontal direction. Based on the field tests, it appears that the deformation under horizontal loading in the systems can be limited by using an enlarged grout zone at the top. 相似文献
A dolerite sill cutting slightly older basalt in west-central Sweden shows a strong chemical variation (54% < SiO2 < 73%) within a restricted area (< 100 × 100 m2). The linear correlation among almost all elements is extremely high; in addition, NdT is strongly correlated with the SiO2 content. Least-square hyperbolic-ratio and three-element ratio modelling (common denominator) suggests that most of the chemical variation is explained by mixing and/or micro-mingling. In all, we test 407 hyperbolas, of which 402 are fitted. The five ratio pairs, which could not be fitted to a hyperbola using a least-square fitting procedure, have the ratio Th / Eu in common. Testing the goodness of fit is problematic for hyperbolic distributions; for comparing purposes we sum the distances to chords approximating the hyperbola. Mobile and immobile elements behave similarly, suggesting that no elements are lost or added from outside the system. The data suggests that already the most mafic of the analysed rocks is a mixture of the ‘normal’ dolerite and a siliceous crustal rock. A mafic magma intruded into the base of the crust, where it fractionated resulting in a decreased Mg number. The magma was then contaminated with country rocks in an intermediate magma chamber due to country rock melting; during mixing/mingling almost no fractionation took place. The contaminated rock suggests the presence of a fluid phase. This was probably a prerequisite for country-rock melting. Enrichment in some incompatible elements suggests that besides major mixing/mingling a thermochemical separation process has affected the most felsic rock enriching it in light rare earths and Zr. 相似文献
The present paper focuses on the governing equations for the sensitivity of the variables to the parameters in flow models that can be described by one-dimensional scalar, hyperbolic conservation laws. The sensitivity is shown to obey a hyperbolic, scalar conservation law. The sensitivity is a conserved scalar except in the case of discontinuous flow solutions, where an extra, point source term must be added to the equations in order to enforce conservation. The propagation speed of the sensitivity waves being identical to that of the conserved variable in the original conservation law, the system of conservation laws formed by the original hyperbolic equation and the equation satisfied by the sensitivity is linearly degenerate. A consequence on the solution of the Riemann problem is that rarefaction waves for the variable of the original equation result in vacuum regions for the sensitivity. The numerical solution of the hyperbolic conservation law for the sensitivity by finite volume methods requires the implementation of a specific shock detection procedure. A set of necessary conditions is defined for the discretisation of the source term in the sensitivity equation. An application to the one-dimensional kinematic wave equation shows that the proposed numerical technique allows analytical solutions to be reproduced correctly. The computational examples show that first-order numerical schemes do not yield satisfactory numerical solutions in the neighbourhood of moving shocks and that higher-order schemes, such as the MUSCL scheme, should be used for sharp transients. 相似文献
The growth of magnetic field is considered in the stretch–fold–shear map in the limit of weak diffusion. Numerical results are given for insulating, perfectly conducting and periodic boundary conditions. The resulting eigenvalue branches and magnetic fields are related to eigenvalue branches for perfect dynamo action, obtained for zero diffusion using a complex variable formulation.
The effect of diffusion on these perfect dynamo modes depends on their structure, growth rate and the diffusive boundary conditions employed. In some cases, the effect of diffusion is a small perturbation, giving a correction going to zero in the limit of weak diffusion, with a scaling exponent given analytically. In other cases weak diffusion can entirely destroy a perfect dynamo branch. Diffusive boundary layers can also generate entirely new branches.
These different cases are elucidated, and within the framework of the asymptotic approximations used (which do not constitute a rigorous proof), it is seen that for all three boundary conditions employed, the stretch–fold–shear map is a fast dynamo. 相似文献
The sensitivity of a model output (called a variable) to a parameter can be defined as the partial derivative of the variable with respect to the parameter. When the governing equations are not differentiable with respect to this parameter, problems arise in the numerical solution of the sensitivity equations, such as locally infinite values or instability. An approximate Riemann solver is thus proposed for direct sensitivity calculation for hyperbolic systems of conservation laws in the presence of discontinuous solutions. The proposed approach uses an extra source term in the form of a Dirac function to restore sensitivity balance across the shocks. It is valid for systems such as the Euler equations for gas dynamics or the shallow water equations for free surface flow. The method is first detailed and its application to the shallow water equations is proposed, with some test cases such as dike- or dam-break problems with or without source terms. An application to a two-dimensional flow problem illustrates the superiority of direct sensitivity calculation over the classical empirical approach. 相似文献
This paper presents a closed-form relationship between small and finite strain cavity expansion solutions. Its derivation is based on the non-linearly elastic–perfectly plastic cylindrical (or spherical) problem considering a general Mohr’s criterion and constant plastic dilatancy. It is shown, however, that it is sufficiently accurate for general expansion problems not obeying plane-strain rotationally (or spherically) symmetric conditions and involving strain-hardening/softening constitutive behaviour. Therefore, this relationship quantifies the error stemming from the computational assumption of small deformations and provides a simple and efficient way of accounting for geometric non-linearity based entirely on conventional computational methods: ‘self-correction’ of small strain analyses results. 相似文献