Hausdorff Dimension of Non-Hyperbolic Repellers. I: Maps with Holes

This is the first paper in a two-part series devoted to studying the Hausdorff dimension of invariant sets of non-uniformly hyperbolic, non-conformal maps. Here we consider a general abstract model, that we call piecewise smooth maps with holes. We show that the Hausdorff dimension of the repeller is strictly less than the dimension of the ambient manifold. Our approach also provides information on escape rates and dynamical dimension of the repeller.     

Periodicity detection on the parameter-space of a forced Chua’s circuit

We report a Periodicity-Detection algorithm, implemented in a LabVIEW routine for real-time data analysis on experimental chaos, to evaluate the periodicity P of experimental time series. The Periodicity-Detector (PD) algorithm was applied to the forced Chua’s circuit with the aim to build the Periodicity-parameter-space (P-parameter-space). As results of the P-parameter-space, we could observe very complex dynamical behaviors, as regions of periodic structures, a new sequence of accumulation boundary, and the periodic structures organizing themselves in a period-adding bifurcation cascade. Those results agree with the maximal Lyapunov exponent and the bifurcation diagram analysis, presented in a previous work.     

SRB measures for partially hyperbolic systems whose central direction is mostly contracting

We consider partially hyperbolic diffeomorphisms preserving a splitting of the tangent bundle into a strong-unstable subbundleE ^uu (uniformly expanding) and a subbundleE ^c, dominated byE ^uu. We prove that if the central directionE ^c is mostly contracting for the diffeomorphism (negative Lyapunov exponents), then the ergodic Gibbsu-states are the Sinai-Ruelle-Bowen measures, there are finitely many of them, and their basins cover a full measure subset. If the strong-unstable leaves are dense, there is a unique Sinai-Ruelle-Bowen measure. We describe some applications of these results, and we also introduce a construction of robustly transitive diffeomorphisms in dimension larger than three, having no uniformly hyperbolic (neither contracting nor expanding) invariant subbundles. Work partially supported by CNRS and CNPq/PRONEX-Dynamical Systems, and carried out at Laboratoire de Topologie, Dijon, and IMPA, Rio de Janeiro.     

Exploring the reaction channels between arsine and the hydroxyl radical

The aim of this study was to present the reaction mechanism channels between arsine (AsH₃) and hydroxyl (OH) which was evaluated at CCSD(T)/CBS//CCSD/cc-pVTZ level. One potential channel is the hydrogen abstraction pathway (R1), leading to AsH₂ and H₂O products, which occurs due to the formation of an entrance complex (AsH₃OH) followed by a 1,2-hydrogen shift pathway (involving the proton transfer from the arsine group to hydroxyls, with one leading to the products). Additional channels are accessed via H-elimination pathways of the entrance complexes, forming arsinous acid (AsH₂OH; R2) and arsine oxide (AsH₃O; R3). In this respect, R2 is the only exoergic route of the three exit channels, representing the major branching ratio at 200–1000 K and, after 2000 K, R1 increases gradually becoming the major route of this reaction. In contrast, even at 4000 K, R3 is a highly unfeasible pathway. Therefore, the information predicted here provides new insights into the neutral–neutral chemical reaction dynamics regarding the Group V hydrides. On the other side, the R2 pathway may have some potential to solve the arsine oxidation puzzle as a possible primary pathway to the arsenic-oxygen species formation.     

Magnetohydrostatic Equilibrium with External Gravitational Fields in Symmetric Systems

We present a general formulation for magnetohydrostatic equilibria with external gravitational fields in symmetric systems with one ignorable coordinate, using non-orthogonal coordinate systems. We consider the cases of isothermal as well as adiabatic processes. Analytical exact solutions for the ideal magnetohydrodynamical equilibrium equation are presented for rectangular, cylindrical, and spherical coordinates.     

Synaptic Plasticity and Spike Synchronisation in Neuronal Networks

Brain plasticity, also known as neuroplasticity, is a fundamental mechanism of neuronal adaptation in response to changes in the environment or due to brain injury. In this review, we show our results about the effects of synaptic plasticity on neuronal networks composed by Hodgkin-Huxley neurons. We show that the final topology of the evolved network depends crucially on the ratio between the strengths of the inhibitory and excitatory synapses. Excitation of the same order of inhibition revels an evolved network that presents the rich-club phenomenon, well known to exist in the brain. For initial networks with considerably larger inhibitory strengths, we observe the emergence of a complex evolved topology, where neurons sparsely connected to other neurons, also a typical topology of the brain. The presence of noise enhances the strength of both types of synapses, but if the initial network has synapses of both natures with similar strengths. Finally, we show how the synchronous behaviour of the evolved network will reflect its evolved topology.     

STM investigations of Au(1 1 1) electrodes coated with vitamin B12 derivatives

Vitamin B₁₂ derivatives immobilized at flame-annealed Au(1 1 1) electrode surfaces have been investigated in close correlation with their structural properties and spatial arrangement at the electrode substrate by scanning tunneling microscopy (STM) in air and in aqueous 0.1 M NaClO₄ solution. The investigated compounds were symmetrical (B₁₂C₁₀S-SC₁₀B₁₂) and nonsymmetrical (B₁₂C₁₀S-SC₁₀) dialkyl disulfide derivatives of vitamin B₁₂, attached to the electrode surfaces by the S-Au bond. The ex situ and in situ STM experiments show the formation of a surface layer, whose packing density and structure is presumably controlled by the spatial arrangement of the large cobyrinate head groups. In presence of the symmetrical B₁₂ compound, a disordered surface layer is observed. Voltammetric investigations show that, in 0.1 M NaClO₄, this layer becomes unstable at potentials approximately ? −1000 mV vs. MSE and is almost completely removed at more negative potentials. The STM imaging properties of the nonsymmetrical B₁₂ surface layer show a significant dependence on the tunneling distance. In particular, at small tunneling distances, a highly regular hexagonal surface pattern is observed that suggests strongly the presence of an ordered surface assembly. Modeling of the B₁₂ head group has been performed to provide information for a structure-related interpretation of the high-resolution STM images. The investigations are first STM results obtained at such B₁₂ modified electrodes.     

New insights in the formation of thioxophosphine: a quantum chemical study

The investigation of the thioxophosphine (PS) formation from different reaction paths is successfully performed and presented in this paper. The PH(3)+SH(1) reaction is likely to yield the intermediates PH(2) (2)+H(2)S through an energy barrier of 2.8 kcal mol(-1). However, the next step is the H(2)PS(2) formation, which has a too high energy barrier, 52.6 kcal mol(-1). The PH(3)+S(1) reaction path is the likely source of the HPS(1) molecule. The other possibilities are the PH(1)+H(2)S, PH(2) (2)+SH(1), and PH(3)+H(2)S reactions, but they are spin forbidden and energetically unfavorable for the HPS(1) and PSH(1) formations. On the other hand, the PS(2) formation is more likely to happen by the PH(1)+SH(1) reaction. The PH(2) (2)+S(1), PH(3)+SH(1), P(2)+H(2)S, and P(4)+H(2)S reactions are also favorable in terms of energetics; however, these reactions are spin forbidden. The chemical mechanism for the PS(2) formation is now presented in more details, which is of great importance in the atmosphere of Jupiter and Saturn, and in interstellar medium.