Dynamics of Coupled Maps with a Conservation Law

A particularly simple model belonging to a wide class of coupled maps which obey a local conservation law is studied. The phase structure of the system and the types of the phase transitions are determined. It is argued that the structure of the phase diagram is robust with respect to mild violations of the conservation law. Critical exponents possibly determining a new universality class are calculated for a set of independent order parameters. Numerical evidence is produced suggesting that the singularity in the density of Lyapunov exponents at $\lambda=0$ is a reflection of the singularity in the density of Fourier modes (a ``Van Hove'' singularity) and disappears if the conservation law is broken. Applicability of the Lyapunov dimension to the description of spatiotemporal chaos in a system with a conservation law is discussed.Comment: To be published in CHAOS #7 (31 page, 16 figures

Internal conversion coefficients for superheavy elements

The internal conversion coefficients (ICC) were calculated for all atomic subshells of the elements with 104<=Z<=126, the E1...E4, M1...M4 multipolarities and the transition energies between 10 and 1000 keV. The atomic screening was treated in the relativistic Hartree-Fock-Slater model. The Tables comprising almost 90000 subshell and total ICC were recently deposited at LANL preprint server.Comment: 6 pages including 3 figures, needs files myown.sty and epsfig.sty (both included

Functoriality and duality in Morse-Conley-Floer homology

In~\cite{rotvandervorst} a homology theory --Morse-Conley-Floer homology-- for isolated invariant sets of arbitrary flows on finite dimensional manifolds is developed. In this paper we investigate functoriality and duality of this homology theory. As a preliminary we investigate functoriality in Morse homology. Functoriality for Morse homology of closed manifolds is known~\cite{abbondandoloschwarz, aizenbudzapolski,audindamian, kronheimermrowka, schwarz}, but the proofs use isomorphisms to other homology theories. We give direct proofs by analyzing appropriate moduli spaces. The notions of isolating map and flow map allows the results to generalize to local Morse homology and Morse-Conley-Floer homology. We prove Poincar\'e type duality statements for local Morse homology and Morse-Conley-Floer homology.Comment: To appear in the Journal of Fixed Point theory and its Application