Poisson Voronoi diagrams are useful for modeling and describing various natural patterns and for generating random lattices. Although this particular space tessellation is intensively studied by mathematicians, in two-and three dimensional spaces there is no exact result known for the size-distribution of Voronoi cells. Motivated by the simple form of the distribution function in the one-dimensional case, a simple and compact analytical formula is proposed for approximating the Voronoi cell's size distribution function in the practically important two-and three dimensional cases as well. Denoting the dimensionality of the space by d (d = 1, 2, 3) the f (y) = Const * y (3d−1)/2 exp(−(3d + 1)y/2) compact form is suggested for the normalized cell-size distribution function. By using large-scale computer simulations the validity of the proposed distribution function is studied and critically discussed.

Patterns generated by a colloidal suspension of nanospheres drying on a frictional substrate are studied by experiments and computer simulations. The obtained two-dimensional self-assembled structures are commonly used for nanosphere lithography. A spring-block stick-slip model is introduced for simulating the phenomenon and the influence of several controllable parameters on the final structure is investigated. The model successfully reproduces the experimentally observed patterns and the dynamics leading to pattern formation is revealed.The so-called bottom-up approach for the fabrication of nanostructures starting from stable building blocks such as molecules or nanoparticles has become an increasingly popular topic in nanoscience and nanotechnology. Thanks to the efforts of nanochemists, during the past decades various nanoparticles of polystyrene, silica, noble-metal and semiconductor, nearly monodisperse in terms of size, shape, internal structure, and surface chemistry, can be produced through a reliable, standard manufacturing process. Using these nanoparticles as building blocks, the synthesis of long-range-ordered monolayers and films of colloidal nanocrystals has been in particular focus. The revolutionary development of photonic crystals triggered efforts to get innovative methods for crystallizing polystyrene colloids and creating new crystal structures [1,2]. The use of two-dimensional (2D) selfassembled array of nanometer-sized polystyrene spheres as deposition mask is known as NanoSphere Lithography (NSL) [3]. The homogeneous arrays of nanoparticles produced using NSL are potentially useful in studies of size-dependent optical, magnetic, catalytic and electrical transport properties of materials [3,4,5,6]. NSL is now recognized as a powerful fabrication technique to inexpensively produce nanoparticle arrays with controlled shape, size and interparticle spacing. A fundamental goal for further progress in NSL is the development of experimental protocols to control the interactions, and thereby the ordering of nanoparticles on solid substrates [7,8]. However, it is more and more clear that due to the rich physics and chemistry underlying the formation of nanoparticle arrays from colloidal suspensions, the likelihood of structures other than close-packed networks forming during solvent evaporation is very high [9, 10]. Therefore a major motivation for theoretical research in this field remains the challenge to understand how ordered or complex structures form spontaneously by selfassembly, and how such processes can be controlled in order to prepare structures with a pre-determined geometry [11]. The present study intends to contribute in this sense by proposing a model that can be easily studied through computer simulations and it is able to qualitatively reproduce the wide variety of observed patterns. We focus on an experimentally simple case, when 2D selfassembled arrays of nanometer-sized polystyrene spheres will form from a colloidal suspension which is drying on a substrate. Some characteristi...

We present a fully differential study of projectile coherence effects in ionization in p + He collisions. The experimental data are qualitatively reproduced by a non-perturbative ab initio time-dependent model, which treats the projectile coherence properties in terms of a wave packet. A comparison between first- and higher-order treatments shows that the observed interference structures are primarily due to a coherent superposition of different impact parameters leading to the same scattering angle. Higher-order contributions have a significant effect on the interference term.

Abstract. Based on the semiclassical, impact parameter method a theoretical model is constructed to calculate fully differential cross sections for single ionization of helium by impact with fast C 6+ ions. Good agreement with the experiment is achieved in the scattering plane, while in the perpendicular plane a similar structure to that observed experimentally is obtained. The contribution of different partial waves to the cross section is also investigated.

Accurate and efficient community detection in networks is a key challenge for complex network theory and its applications. The problem is analogous to cluster analysis in data mining, a field rich in metric space-based methods. Common to these methods is a geometric, distance-based definition of clusters or communities. Here we propose a new geometric approach to graph community detection based on graph Voronoi diagrams. Our method serves as proof of principle that the definition of appropriate distance metrics on graphs can bring a rich set of metric space-based clustering methods to network science. We employ a simple edge metric that reflects the intra-or inter-community character of edges, and a graph density-based rule to identify seed nodes of Voronoi cells. Our algorithm outperforms most network community detection methods applicable to large networks on benchmark as well as real-world networks. In addition to offering a computationally efficient alternative for community detection, our method opens new avenues for adapting a wide range of data mining algorithms to complex networks from the class of centroid-and density-based clustering methods.