Shrimp-shape domains in a dissipative kicked rotator

Some dynamical properties for a dissipative kicked rotator are studied. Our results show that when dissipation is taken into account a drastic change happens in the structure of the phase space in the sense that the mixed structure is modified and attracting fixed points and chaotic attractors are observed. A detailed numerical investigation in a two-dimensional parameter space based on the behavior of the Lyapunov exponent is considered. Our results show the existence of infinite self-similar shrimp-shaped structures corresponding to periodic attractors, embedded in a large region corresponding to the chaotic regime.     

High‐energy‐resolution diced spherical quartz analyzers for resonant inelastic X‐ray scattering

A novel diced spherical quartz analyzer for use in resonant inelastic X‐ray scattering (RIXS) is introduced, achieving an unprecedented energy resolution of 10.53 meV at the Ir L₃ absorption edge (11.215 keV). In this work the fabrication process and the characterization of the analyzer are presented, and an example of a RIXS spectrum of magnetic excitations in a Sr₃Ir₂O₇ sample is shown.     

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards.     

Scalar Quantum Electrodynamics on the lattice as classical statistical mechanics

Wilson's lattice approximation allows us to apply classical statistical mechanics ideas to the study of Scalar Quantum Electrodynamics. Our main tools are Griffiths-Kelly-Sherman inequalities, the transfer matrix formalism and exponential bounds. Our main result is the existence of the infinite volume limit for every value of the coupling parameters.     

Nonreductive Enantioselective Ring Opening of N-(Methylsulfonyl)dicarboximides with Diisopropoxytitanium α,α,α′,α′-Tetraaryl-1,3-dioxolane-4,5-dimethanolate

The bicyclic and tricyclic meso-N-(methylsulfonyl)dicarboximides 1a–f are converted enantioselectively to isopropyl [(sulfonamido)carbonyl]-carboxylates 2a–f by diisopropoxytitanium TADDOLate (75–92% yield; see Scheme 3). The enantiomer ratios of the products are between 86:14 and 97:3, and recrystallization from CH₂Cl₂/hexane leads to enantiomerically pure sulfonamido esters 2 (Scheme 3). The enantioselectivity shows a linear relationship with the enantiomer excess of the TADDOL employed (Fig.3). Reduction of the ester and carboxamide groups (LiAlH₄) and additional reductive cleavage of the sulfonamido group (Red-Al) in the products 2 of imide-ring opening gives hydroxy-sulfonamides 3 and amino alcohols 4 , respectively (Scheme 4). The absolute configuration of the sulfonamido esters 2 is determined by chemical correlation (with 2a,b ; Scheme 6), by the X-ray analysis of the camphanate of 3e (Fig. 1), and by comparative ¹⁹F-NMR analysis of the Mosher esters of the hydroxy-sulfonamides 3 (Table 1). A general proposal for the assignment of the absolute configuration of primary alcohols and amines of Formula HXCH₂CHR¹R², X = O, NH, is suggested (see 11 in Table 1). It follows from the assignment of configuration of 2 that the Re carbonyl group of the original imide 1 is converted to an isopropyl ester group. This result is compatible with a rule previously put forward for the stereochemical course of reactions involving titanium TADDOLate activated chelating electrophiles ( 12 in Scheme 7). A tentative mechanistic model is proposed ( 13 and 14 in Scheme 7).