State/event based versus purely Action or State based Logics

Although less studied than purely action or state based logics, state/event based logics are becoming increasingly important. Some systems are best studied using structures with information on both states and transitions, and it is these structures over which state/event based logics are defined. The logic UCTL and its variants are perhaps the most widely studied and implemented of these logics to date. As yet, however, no-one seems to have defined UCTL*, a trivial step but a worthwhile one. Here we do just that, but prove in the cases of both UCTL and UCTL* that these logics are no more expressive than their more commonplace fragments. Also, acknowledging the importance of modal transition systems, we define a state/event based logic over a modified modal transition system as a precursor to further work.Comment: 9 pages, 6 figure

Chaotic Dynamics in Multidimensional Transition States

The crossing of a transition state in a multidimensional reactive system is mediated by invariant geometric objects in phase space: An invariant hyper-sphere that represents the transition state itself and invariant hyper-cylinders that channel the system towards and away from the transition state. The existence of these structures can only be guaranteed if the invariant hyper-sphere is normally hyperbolic, i.e., the dynamics within the transition state is not too strongly chaotic. We study the dynamics within the transition state for the hydrogen exchange reaction in three degrees of freedom. As the energy increases, the dynamics within the transition state becomes increasingly chaotic. We find that the transition state first looses and then, surprisingly, regains its normal hyperbolicity. The important phase space structures of transition state theory will therefore exist at most energies above the threshold

Solid-liquid phase coexistence and structural transitions in palladium clusters

We use molecular dynamics with an embedded atom potential to study the behavior of palladium nanoclusters near the melting point in the microcanonical ensemble. We see transitions from both fcc and decahedral ground state structures to icosahedral structures prior to melting over a range of cluster sizes. In all cases this transition occurs during solid-liquid phase coexistence and the mechanism for the transition appears to be fluctuations in the molten fraction of the cluster and subsequent recrystallization into the icosahedral structure.Comment: 8 pages, 6 figure

Two-Stage Melting in Systems of Strongly Interacting Rydberg Atoms

We analyze the ground state properties of a one-dimensional cold atomic system in a lattice, where Rydberg excitations are created by an external laser drive. In the classical limit, the ground state is characterized by a complete devil's staircase for the commensurate solid structures of Rydberg excitations. Using perturbation theory and a mapping onto an effective low energy Hamiltonian, we find a transition of these commensurate solids into a floating solid with algebraic correlations. For stronger quantum fluctuations the floating solid eventually melts within a second quantum phase transition and the ground state becomes paramagnetic.Comment: 4 pages, 3 figure

Quasimolecular states in the 12C-12C system

Quasimolecular resonance structures in the 12C-12C system are studied in the framework of the coupled channel formalism in the energy range Ec.m.=5-14 MeV. The influence of the coupling of the first excited 2+ state in 12C on the resonance structures is investigated by choosing various types of coupling potentials. The intermediate structures in the reflection and transition coefficients and cross sections can be interpreted with the double resonance mechanism. NUCLEAR REACTIONS 12C(12C, 12C), quasimolecular states, coupling potentials, coupled channel calculations for σ(θ)

Nucleation of Spatio-Temporal Structures From Defect Turbulence in the Two-dimensional Complex Ginzburg-Landau Equation

We numerically investigate nucleation processes in the transient dynamics of the two-dimensional complex Ginzburg-Landau equation towards its "frozen" state with quasi-stationary spiral structures. We study the transition kinetics from either the defect turbulence regime or random initial configurations to the frozen state with a well-defined low density of quasi-stationary topological defects. Nucleation events of spiral structures are monitored using the characteristic length between the emerging shock fronts. We study two distinct situations, namely either when the system is quenched far away from the transition limit or near it. In the former deeply quenched case, the average nucleation time for different system sizes is measured over many independent realizations. We employ an extrapolation method as well as a phenomenological formula to account for and eliminate finite-size effects. The non-zero (dimensionless) barrier for the nucleation of single spiral droplets in the extrapolated infinite system size limit suggests that the transition to the frozen state is discontinuous. We also investigate the nucleation of spirals for systems that are quenched close to but beyond the crossover limit, and of target waves which emerge if a specific spatial inhomogeneity is introduced. In either of these cases, we observe long, "fat" tails in the distribution of nucleation times, which also supports a discontinuous transition scenario.Comment: 16 pages, 9 figure

Collective effects in cellular structure formation mediated by compliant environments: a Monte Carlo study

Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial structure formation for cell communities on soft elastic substrates as a function of elastic moduli, cell density, noise and cell position geometry. In general, we find a disordered structure as well as ordered string-like and ring-like structures. The transition between ordered and disordered structures is controlled both by cell density and noise level, while the transition between string- and ring-like ordered structures is controlled by the Poisson ratio. Similar effects are observed in three dimensions. Our results suggest that in regard to elastic effects, healthy connective tissue usually is in a macroscopically disordered state, but can be switched to a macroscopically ordered state by appropriate parameter variations, in a way that is reminiscent of wound contraction or diseased states like contracture.Comment: 45 pages, 7 postscript figures included, revised version accepted for publication in Acta Biomateriali

Experimental Determination of Electron Transition Probabilities in Elementary Electron-Phonon Scattering Processes Using Electron-Energy-Loss Spectroscopy: The Example of Graphite

We have investigated coupling constants in elementary electron-phonon scattering processes on a graphite surface by the combined use of high-resolution electron-energy-loss spectroscopy (HREELS) and very low-energy electron diffraction (VLEED). HREELS is used to measure the modulations of electron transition probabilities from incoming electrons in vacuum to outgoing electrons in vacuum where the transition includes one-phonon scattering processes inside a solid. Determining the electronic band structures of graphite with VLEED, we defined electronic states of the solid surface that electrons entered before and after scattering off phonons. Thus, we observed that the measured electron transition probabilities significantly depended on whether the electrons were in a bulk Bloch state or an evanescent state before scattering off the phonons. This result clearly indicates that the measured electron transition probabilities reflect the strength of the coupling constants in the solid.Comment: 4 pages, 4 figure

Biconical structures in two-dimensional anisotropic Heisenberg antiferromagnets

Square lattice Heisenberg and XY antiferromagnets with uniaxial anisotropy in a field along the easy axis are studied. Based on ground state considerations and Monte Carlo simulations, the role of biconical structures in the transition region between the antiferromagnetic and spin--flop phases is analyzed. In particular, adding a single--ion anisotropy to the XXZ antiferromagnet, one observes, depending on the sign of that anisotropy, either an intervening biconical phase or a direct transition of first order separating the two phases. In case of the anisotropic XY model, the degeneracy of the ground state, at a critical field, in antiferromagnetic, spin--flop, and bidirectional structures seems to result, as in the case of the XXZ model, in a narrow disordered phase between the antiferromagnetic and spin--flop phases, dominated by bidirectional fluctuations.Comment: 4 pages, 5 figures, accepted by Phys. Rev.