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Jablan S.,The Mathematical Institute | Radovic L.,University of Nis | Sazdanovic R.,University of Pennsylvania
Journal of Mathematical Chemistry | Year: 2011

Virtual knot theory offers the possibility to consider knots and links embedded on different surfaces. This paper analyzes nonplanarity of graphs obtained from Gauss codes of virtual knots and links and their potential applications in chemistry. © 2011 Springer Science+Business Media, LLC.

Jablan S.,The Mathematical Institute | Radovic L.,University of Nis | Sazdanovic R.,The Mathematical Institute
Journal of Mathematical Chemistry | Year: 2011

In order to facilitate recognition of polymer graphs and patterns obtained by graphical recombination, we analyze polynomial invariants, graphs and knots associated to polyominoes, polyiamonds, and polyhexes. © 2010 Springer Science+Business Media, LLC.

Jablan S.,The Mathematical Institute | Radovic L.,University of Nis
Kybernetes | Year: 2011

Purpose: The purpose of this paper is to consider the history of certain modular elements: Truchet tiles, Op-tiles, Kufic tiles, and key-patterns, which occur as ornamental archetypes from Paleolithic times until the present. The appearance of the same ornamental archetypes at the same level of the development in different cultures, distant in space and time can be described from the cybernetics point of view as a specific kind of self-referential systems or cellular automata present in the intellectual and cultural development of mankind. The aim of this research is to show a continuity of the development of ornamental structures based on modular elements used as ornamental archetypes. Design/methodology/approach: Research of the material from archaeological findings, history of art, painting, architecture, and applied arts. Findings: Existence of universal geometrical construction principles based on modularity. Practical implications: Creation of new patterns or designs (e.g. TeX-fonts, tiles, etc.) based on modularity. Originality/value: The paper presents a new explanation of constructions of labyrinths and different Islamic patterns. © Emerald Group Publishing Limited.

Singh K.,The Mathematical Institute | Michelin S.,Ecole Polytechnique - Palaiseau | De Langre E.,Ecole Polytechnique - Palaiseau
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2012

The problem of energy harvesting from flutter instabilities in flexible slender structures in axial flows is considered. In a recent study, we used a reduced-order theoretical model of such a system to demonstrate the feasibility for harvesting energy from these structures. Following this preliminary study, we now consider a continuous fluid-structure system. Energy harvesting is modelled as strain-based damping, and the slender structure under investigation lies in a moderate fluid loading range, for which the flexible structure may be destabilized by damping. The key goal of this work is to analyse the effect of damping distribution and intensity on the amount of energy harvested by the system. The numerical results indeed suggest that non-uniform damping distributions may significantly improve the power-harvesting capacity of the system. For low-damping levels, clustered dampers at the position of peak curvature are shown to be optimal. Conversely for higher damping, harvesters distributed over the whole structure are more effective. © 2012 The Royal Society.

Mason L.J.,The Mathematical Institute | Nicolas J.-P.,University of Western Brittany
Journal of Geometry and Physics | Year: 2012

We study the peeling of Dirac and Maxwell fields on a Schwarzschild background following the approach developed by the authors in Mason and Nicolas (2009). [12] for the wave equation. The method combines a conformal compactification with vector field techniques in order to work out the optimal space of initial data for a given transverse regularity of the rescaled field across null infinity. The results show that analogous decay and regularity assumptions in Minkowski and Schwarzschild produce the same regularity across null infinity. The results are valid also for the classes of asymptotically simple spacetimes constructed by Corvino-Schoen/Chruściel-Delay. © 2012 .

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