Monochromatic Clique Decompositions of Graphs

Let $G$ be a graph whose edges are coloured with $k$ colours, and $\mathcal H=(H_1,\dots , H_k)$ be a $k$-tuple of graphs. A monochromatic $\mathcal H$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms a monochromatic copy of $H_i$ in colour $i$, for some $1\le i\le k$. Let $\phi_{k}(n,\mathcal H)$ be the smallest number $\phi$, such that, for every order-$n$ graph and every $k$-edge-colouring, there is a monochromatic $\mathcal H$-decomposition with at most $\phi$ elements. Extending the previous results of Liu and Sousa ["Monochromatic $K_r$-decompositions of graphs", Journal of Graph Theory}, 76:89--100, 2014], we solve this problem when each graph in $\mathcal H$ is a clique and $n\ge n_0(\mathcal H)$ is sufficiently large.Comment: 14 pages; to appear in J Graph Theor

Exponential Distributions in a Mechanical Model for Earthquakes

We study statistical distributions in a mechanical model for an earthquake fault introduced by Burridge and Knopoff [R. Burridge and L. Knopoff, {\sl Bull. Seismol. Soc. Am.} {\bf 57}, 341 (1967)]. Our investigations on the size (moment), time duration and number of blocks involved in an event show that exponential distributions are found in a given range of the paramenter space. This occurs when the two kinds of springs present in the model have the same, or approximately the same, value for the elastic constants. Exponential distributions have also been seen recently in an experimental system to model earthquake-like dynamics [M. A. Rubio and J. Galeano, {\sl Phys. Rev. E} {\bf 50}, 1000 (1994)].Comment: 11 pages, uuencoded (submitted to Phys. Rev. E

A simple deterministic self-organized critical system

We introduce a new continuous cellular automaton that presents self-organized criticality. It is one-dimensional, totally deterministic, without any kind of embedded randomness, not even in the initial conditions. This system is in the same universality class as the Oslo rice pile system, boundary driven interface depinning and the train model for earthquakes. Although the system is chaotic, in the thermodynamic limit chaos occurs only in a microscopic level.Comment: System slightly modified. New results on Liapunov exponents. Submitted for publication (8 pages

Site-dependent hydrogenation on graphdiyne

Graphene is one of the most important materials in science today due to its unique and remarkable electronic, thermal and mechanical properties. However in its pristine state, graphene is a gapless semiconductor, what limits its use in transistor electronics. In part due to the revolution created by graphene in materials science, there is a renewed interest in other possible graphene-like two-dimensional structures. Examples of these structures are graphynes and graphdiynes, which are two-dimensional structures, composed of carbon atoms in sp2 and sp-hybridized states. Graphdiynes (benzenoid rings connecting two acetylenic groups) were recently synthesized and some of them are intrinsically nonzero gap systems. These systems can be easily hydrogenated and the relative level of hydrogenation can be used to tune the band gap values. We have investigated, using fully reactive molecular dynamics (ReaxFF), the structural and dynamics aspects of the hydrogenation mechanisms of graphdiyne membranes. Our results showed that the hydrogen bindings have different atom incorporation rates and that the hydrogenation patterns change in time in a very complex way. The formation of correlated domains reported to hydrogenated graphene is no longer observed in graphdiyne cases.Comment: Submitted to Carbo

Photochemical studies of cis-[Ru(bpy)2(4-bzpy)(CO)](PF6)2 and cis-[Ru(bpy)2(4-bzpy)(Cl)](PF6): Blue light-induced nucleobase binding.

The ruthenium(II) compounds cis-[Ru(bpy)2(4-bzpy)(CO)](PF6)2 (I) and cis-[Ru(bpy)2(4-bzpy)(Cl)](PF6) (II) (4-bzpy=4-benzoylpyridine, bpy=2,2'-bipyridine) were synthesized and characterized by spectroscopic and electrochemical techniques. The crystal structure of II was determined by X-ray diffraction. The photochemical behavior of I in aqueous solution shows that irradiation with ultraviolet light (365nm) releases both CO and 4-bzpy leading to the formation of the cis-[Ru(bpy)2(H2O)2]2+ ion as identified by NMR and electronic spectroscopy. Carbon monoxide release was confirmed with the myoglobin method and by gas chromatographic analysis of the headspace. CO release was not observed when aqueous I was irradiated with blue light (453nm). Changes in the electronic and 1H NMR spectra indicate that I undergoes photoaquation of 4-bzpy to form cis-[Ru(bpy)2(CO)(H2O)]2+. Blue light irradiation of aqueous II released the coordinated 4-bzpy to give the cis-[Ru(bpy)2(H2O)(Cl)]2+ ion. When the latter reaction was carried out in the presence of the nucleobase guanine, Ru-guanine adducts were formed, indicating that the metal containing photoproduct may also participate in biologically relevant reactions. The photochemical behavior of I indicates that it can release either CO or 4-bzpy depending on the wavelength chosen, a feature that may have therapeutic application