van der Waals corrections to density functional theory calculations: Methane,ethane, ethylene,benzene, formaldehyde,ammonia, water,PBE, and CPMD

Parameters are developed for a practical application of the empirical van der Waals (vdW) correction infrastructure available in the CPMD density functional theory (DFT) code. The binding energy, geometry, and potential energy surface (PES) are examined for methane, ethane, ethylene, formaldehyde, ammonia, three benzene dimer geometries, and three benzene–water geometries. The vdW corrected results compare favorably with MP2 and CCSD(T) calculations near the complete basis set limits, and with experimental results where they are available.     

An asymptotic definition of K-groups of automorphisms and a non-Bernoullian counter-example

Summary Let GZⁿ be a group of measure preserving transformations of a Lebesgue space. J. P. Conze [1] has developed an entropy theory for such groups and described a class of groups obeying a form of the Kolmogorov zero-one law called K-groups. A Bernoulli group is a group isomorphic to the group of translates (shifts) of elements of the space with product measure where X _g =X is a probability space. Bernoulli groups are also K-groups. Katznelson and Weiss [3] have shown entropy is a complete invariant for isomorphism classes of Bernoulli groups. We give an asymptotic definition of K-groups in terms of finite -algebras and justify this definition in terms of entropy and Conze's formulation. This definition s used to help us construct a K-group GZ ⁿ that is completely non-Bernoulli, that is one that contains no Bernoulli subgroup.     

Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion

Summary Conventional numerical methods, when applied to the ordinary differential equations of motion of classical mechanics, conserve the total energy and angular momentum only to the order of the truncation error. Since these constants of the motion play a central role in mechanics, it is a great advantage to be able to conserve them exactly. A new numerical method is developed, which is a generalization to arbitrary order of the discrete mechanics described in earlier work, and which conserves the energy and angular momentum to all orders. This new method can be applied much like a corrector as a modification to conventional numerical approximations, such as those obtained via Taylor series, Runge-Kutta, or predictor-corrector formulae. The theory is extended to a system of particles in Part II of this work.     

Zur Minimalität trigonometrischer Polynomoperatoren

Cheney and others [2] have shown that, with respect to the norm of uniform convergence, the Fourier operator F_n:C₂p_n is the only minimal projection. For a more detailed study of operators A:C₂P_n we investigate the evaluation functionals respectively the mean of their norms . We give a complete characterization of polynomial operators which minimize this quantity. As an application we can simplify the proof in [2]. Moreover, we show that the trigonometric interpolation operators, having the above minimal-property,are exactly those with equidistant nodes.

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Diese Arbeit enthält die wesentlichen Resultate einer Diplomarbeit, die der Verfasser an der Eberhard-Karls-Universität Tübingen unter der Anleitung von A.Schönhage angefertigt hat.     

über die Striktionslinien von einparametrigen Scharen linearer Räume

A generalisation of a ruled surface in n-dimensional euclidean space may be generated by euclidean motion of a s-plane A_s. For this one-parametric family {A_s} the curve of striction is defined and the following theorems are proved:

1. The generators A_s are parallel along the curve of striction, i.e. the multivectors representing A_s form a parallel vector field along the curve of striction.
2. If the curve of striction is geodesic on {A_s}, it is also an isogonal trajectory of the family of generators {A_s}.

     

Meromorphic Traveling Wave Solutions of the Complex Cubic-Quintic Ginzburg-Landau Equation

We look for singlevalued solutions of the squared modulus M of the traveling wave reduction of the complex cubic-quintic Ginzburg-Landau equation. Using Clunie??s lemma, we first prove that any meromorphic solution M is necessarily elliptic or degenerate elliptic. We then give the two canonical decompositions of the new elliptic solution recently obtained by the subequation method.     

Separable geodesic action slicing in stationary spacetimes

A simple observation about the action for geodesics in a stationary spacetime with separable geodesic equations leads to a natural class of slicings of that spacetime whose orthogonal geodesic trajectories represent the world lines of freely falling fiducial observers. The time coordinate function can then be taken to be the observer proper time, leading to a unit lapse function, although the time coordinate lines still follow Killing trajectories to retain the explicitly stationary nature of the coordinate grid. This explains some of the properties of the original Painlevé-Gullstrand coordinates on the Schwarzschild spacetime and their generalization to the Kerr-Newman family of spacetimes, reproducible also locally for the Gödel spacetime. For the static spherically symmetric case the slicing can be chosen to be intrinsically flat with spherically symmetric geodesic observers, leaving all the gravitational field information in the shift vector field.     

Effect of flame-sprayed Al–12Si coatings on the failure behaviour of pressurized fibre-reinforced composite tubes

Internal pressurization testing at room temperature was performed to evaluate the effect of flame-spraying aluminum-12silicon on the leakage behavior of fibre-reinforced composite tubes fabricated by filament winding, and covered with garnet sand. A group of specimens were completely coated with flame-sprayed metal particles and another set remained uncoated. t-tests were conducted at a significance level of α = 0.05 to analyze the effect of the coating on the leakage behavior of the specimens. Ultraviolet imaging was used to illustrate a characteristic leakage pattern of the composite tubes. Coated specimens exhibited slightly higher mean leakage and burst pressures than the uncoated specimens. The t-test results provided strong statistical evidence that the flame spraying process employed did not damage the filament wound tubes covered with garnet sand.