PoN-S : a systematic approach for applying the Physics of Notation (PoN)

Visual Modeling Languages (VMLs) are important instruments of communication between modelers and stakeholders. Thus, it is important to provide guidelines for designing VMLs. The most widespread approach for analyzing and designing concrete syntaxes for VMLs is the so-called Physics of Notation (PoN). PoN has been successfully applied in the analysis of several VMLs. However, despite its popularity, the application of PoN principles for designing VMLs has been limited. This paper presents a systematic approach for applying PoN in the design of the concrete syntax of VMLs. We propose here a design process establishing activities to be performed, their connection to PoN principles, as well as criteria for grouping PoN principles that guide this process. Moreover, we present a case study in which a visual notation for representing Ontology Pattern Languages is designed

Icosahedral multi-component model sets

A quasiperiodic packing Q of interpenetrating copies of C, most of them only partially occupied, can be defined in terms of the strip projection method for any icosahedral cluster C. We show that in the case when the coordinates of the vectors of C belong to the quadratic field Q[\sqrt{5}] the dimension of the superspace can be reduced, namely, Q can be re-defined as a multi-component model set by using a 6-dimensional superspace.Comment: 7 pages, LaTeX2e in IOP styl

How model sets can be determined by their two-point and three-point correlations

We show that real model sets with real internal spaces are determined, up to translation and changes of density zero by their two- and three-point correlations. We also show that there exist pairs of real (even one dimensional) aperiodic model sets with internal spaces that are products of real spaces and finite cyclic groups whose two- and three-point correlations are identical but which are not related by either translation or inversion of their windows. All these examples are pure point diffractive. Placed in the context of ergodic uniformly discrete point processes, the result is that real point processes of model sets based on real internal windows are determined by their second and third moments.Comment: 19 page

Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

The rings of n-dimensional polytopes

Points of an orbit of a finite Coxeter group G, generated by n reflections starting from a single seed point, are considered as vertices of a polytope (G-polytope) centered at the origin of a real n-dimensional Euclidean space. A general efficient method is recalled for the geometric description of G- polytopes, their faces of all dimensions and their adjacencies. Products and symmetrized powers of G-polytopes are introduced and their decomposition into the sums of G-polytopes is described. Several invariants of G-polytopes are found, namely the analogs of Dynkin indices of degrees 2 and 4, anomaly numbers and congruence classes of the polytopes. The definitions apply to crystallographic and non-crystallographic Coxeter groups. Examples and applications are shown.Comment: 24 page

Limit-(quasi)periodic point sets as quasicrystals with p-adic internal spaces

Model sets (or cut and project sets) provide a familiar and commonly used method of constructing and studying nonperiodic point sets. Here we extend this method to situations where the internal spaces are no longer Euclidean, but instead spaces with p-adic topologies or even with mixed Euclidean/p-adic topologies. We show that a number of well known tilings precisely fit this form, including the chair tiling and the Robinson square tilings. Thus the scope of the cut and project formalism is considerably larger than is usually supposed. Applying the powerful consequences of model sets we derive the diffractive nature of these tilings.Comment: 11 pages, 2 figures; dedicated to Peter Kramer on the occasion of his 65th birthda

Dark-Matter Decays and Self-Gravitating Halos

We consider models in which a dark-matter particle decays to a slightly less massive daughter particle and a noninteracting massless particle. The decay gives the daughter particle a small velocity kick. Self-gravitating dark-matter halos that have a virial velocity smaller than this velocity kick may be disrupted by these particle decays, while those with larger virial velocities will be heated. We use numerical simulations to follow the detailed evolution of the total mass and density profile of self-gravitating systems composed of particles that undergo such velocity kicks as a function of the kick speed (relative to the virial velocity) and the decay time (relative to the dynamical time). We show how these decays will affect the halo mass-concentration relation and mass function. Using measurements of the halo mass-concentration relation and galaxy-cluster mass function to constrain the lifetime--kick-velocity parameter space for decaying dark matter, we find roughly that the observations rule out the combination of kick velocities greater than 100 km/s and decay times less than a few times the age of the Universe.Comment: 17 pages, 10 figures, replaced with published versio

Possible contractions of quantum orthogonal groups

Possible contractions of quantum orthogonal groups which correspond to different choices of primitive elements of Hopf algebra are considered and all allowed contractions in Cayley--Klein scheme are obtained. Quantum deformations of kinematical groups have been investigated and have shown that quantum analog of (complex) Galilei group G(1,3) do not exist in our scheme.Comment: 10 pages, Latex. Report given at XXIII Int. Colloquium on Group Theoretical Methods in Physics, July 31- August 5, 2000, Dubna (Russia

Reduction of laser intensity scintillations in turbulent atmospheres using time averaging of a partially coherent beam

We demonstrate experimentally and numerically that the application of a partially coherent beam (PCB) in combination with time averaging leads to a significant reduction in the scintillation index. We use a simplified experimental approach in which the atmospheric turbulence is simulated by a phase diffuser. The role of the speckle size, the amplitude of the phase modulation, and the strength of the atmospheric turbulence are examined. We obtain good agreement between our numerical simulations and our experimental results. This study provides a useful foundation for future applications of PCB-based methods of scintillation reduction in physical atmospheres.Comment: 18 pages, 14 figure