Reactions at surfaces studied by ab initio dynamics calculations

Due to the development of efficient algorithms and the improvement of computer power it is now possible to map out potential energy surfaces (PES) of reactions at surfaces in great detail. This achievement has been accompanied by an increased effort in the dynamical simulation of processes on surfaces. The paradigm for simple reactions at surfaces -- the dissociation of hydrogen on metal surfaces -- can now be treated fully quantum dynamically in the molecular degrees of freedom from first principles, i.e., without invoking any adjustable parameters. This relatively new field of ab initio dynamics simulations of reactions at surfaces will be reviewed. Mainly the dissociation of hydrogen on clean and adsorbate covered metal surfaces and on semiconductor surfaces will be discussed. In addition, the ab initio molecular dynamics treatment of reactions of hydrogen atoms with hydrogen-passivated semiconductor surfaces and recent achievements in the ab initio description of laser-induced desorption and further developments will be addressed.Comment: 33 pages, 19 figures, submitted to Surf. Sci. Rep. Other related publications can be found at http://www.rz-berlin.mpg.de/th/paper.htm

Regularity properties of nonlocal minimal surfaces via limiting arguments

We prove an improvement of flatness result for nonlocal minimal surfaces which is independent of the fractional parameter $s$ when $s\rightarrow 1^-$. As a consequence, we obtain that all the nonlocal minimal cones are flat and that all the nonlocal minimal surfaces are smooth when the dimension of the ambient space is less or equal than 7 and $s$ is close to 1

On rational maps from a general surface in P^3 to surfaces of general type

We study the dominant rational maps from a general surface in P^{3} to surfaces of general type. We prove restrictions on the target surfaces, and special properties of the rational maps. We show that for a small degree the general surface has no such map. Moreover a slight improvement of a result of Catanese, on the number of moduli of a surface of general type, is also obtained.Comment: 19 pages, accepted in Advances in Geometr

Topology of modified helical gears

The topology of several types of modified surfaces of helical gears is proposed. The modified surfaces allow absorption of a linear or almost linear function of transmission errors. These errors are caused by gear misalignment and an improvement of the contact of gear tooth surfaces. Principles and corresponding programs for computer aided simulation of meshing and contact of gears have been developed. The results of this investigation are illustrated with numerical examples

A survey of partial differential equations in geometric design

YesComputer aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling since they offer a number of features from which these areas can benefit. This work summarises the uses given to PDE surfaces as a surface generation technique togethe

The Invariant Measures of some Infinite Interval Exchange Maps

We classify the locally finite ergodic invariant measures of certain infinite interval exchange transformations (IETs). These transformations naturally arise from return maps of the straight-line flow on certain translation surfaces, and the study of the invariant measures for these IETs is equivalent to the study of invariant measures for the straight-line flow in some direction on these translation surfaces. For the surfaces and directions for which our methods apply, we can characterize the locally finite ergodic invariant measures of the straight-line flow in a set of directions of Hausdorff dimension larger than 1/2. We promote this characterization to a classification in some cases. For instance, when the surfaces admit a cocompact action by a nilpotent group, we prove each ergodic invariant measure for the straight-line flow is a Maharam measure, and we describe precisely which Maharam measures arise. When the surfaces under consideration are finite area, the straight-line flows in the directions we understand are uniquely ergodic. Our methods apply to translation surfaces admitting multi-twists in a pair of cylinder decompositions in non-parallel directions.Comment: 107 pages, 11 figures. Minor improvement