Stochastic Perturbation of Integrable Systems: A Window to Weakly Chaotic Systems

Integrable non-linear Hamiltonian systems perturbed by additive noise develop a Lyapunov instability, and are hence chaotic, for any amplitude of the perturbation. This phenomenon is related, but distinct, from Taylor’s diffusion in hydrodynamics. We develop expressions for the Lyapunov exponents for the cases of white and colored noise. The situation described here being ‘multi-resonance’—by nature well beyond the Kolmogorov–Arnold–Moser regime, it offers an analytic glimpse on the regime in which many near-integrable systems, such as some planetary systems, find themselves in practice. We show with the aid of a simple example, how one may model in some cases weakly chaotic deterministic systems by a stochastically perturbed one, with good qualitative results.     

Confined-acoustic-phonon-assisted cyclotron resonance via multi-photon absorption process in GaAs quantum well structure

Phonon-assisted cyclotron resonance (PACR) in GaAs quantum well (QW) structure is investigated via multi-photon absorption process when electrons interact with the confined acoustic phonon through deformation potential. The additional peaks in the absorption spectrum due to transitions between Landau levels accompanied with the emission and absorption of phonons are indicated. The dependence of absorption power on the temperature, magnetic field and well width is presented. Using profile method, we obtain PACR-linewidth as profiles of the curves. The temperature, magnetic field and well width dependences of the PACR-linewidth are investigated. The results are compared with those in the case of mono-photon absorption process, as well as in the electron-bulk acoustic phonon interaction. The results show that the multi-photon absorption process is strong enough to be detected in PACR.     

DPPH radical scavenging and xanthine oxidase inhibitory activity of Terminalia macroptera leaves

From a methanol extract of the leaves of the Malian medicinal tree Terminalia macroptera, cis-polyisoprene (1), chebulic acid trimethyl ester (2), methyl gallate (3), shikimic acid (4), corilagin (5), rutin (6), narcissin (7), chebulagic acid (8) and chebulinic acid (9), were isolated. Cispolyisoprene (1) was the major non-polar constituent. The novel compound 2 showed high radical scavenging activity (IC50 4.7 microg/mL), but was inactive as xanthine oxidase inhibitor. The major substituent of the crude extract, substance 5, showed a high radical scavenger effect (IC50 2.7 microg/mL) and weak xanthine oxidase inhibition (IC50 ca 105 microg/mL). The antioxidant and radical scavenging effects of some of the substances identified in this study may to some extent explain the medical use of this tree in West Africa.     

The automorphism group of a certain unbounded non-hyperbolic domain

In this paper we determine the automorphism group of the Fock–Bargmann–Hartogs domain _Dn,m$D_{n,m}$ in Cⁿ×C^m${\mathbb{C}}^n\times {\mathbb{C}}^m$ which is defined by the inequality ‖ζ‖²<e^{−μ‖z‖2}${\Vert \zeta \Vert }^2<e^{-\mu {\Vert z\Vert }^2}$.     

Crystal Structures of Uranyl Ion Complexes of Tetrahydroxy[3.1.3.1]metacyclophane (Homocalix[4]arene)

The first crystal structures of complexes of tetrahydroxy-[3.1.3.1]metacyclophanes, also termed homocalix[4]arenes, are reported. In the two uranyl ion complexes obtained, with different para-substituents, the complex core is analogous to that in tetrahomodioxacalix[4]arene complexes, with the cation in a tetra-phenoxide, distorted square-planar environment. The packing in one of these complexes comprises two different arrangements, one of them being a columnar stacking of complex molecules with sandwiched triethylammonium counter-ions hydrogen bonded to one complex and held by cation–π and CH–π interactions within the cavity of the other neighbouring one.     

Interfacial behavior of OEG-linear dendron monolayers: aggregation, nanostructuring, and electropolymerizability

We report on the interesting interfacial behavior of oligoethylene glycol or OEGylated linear dendron monolayers at the air-water interface as a function of (a) carbazole dendron generation, (b) the length of the OEG units, and (c) the surface pressure applied upon compression. Surface pressure-area isotherms, hysteresis studies, and isobaric creep measurement revealed a structure-property relationship consistent with the hydrophilic-lipophilic balance of a linear dendron with the OEG group serving as the surface anchor to the water subphase. AFM studies revealed that all the OEGylated carbazole dendrons self-assemble into spherical morphology at low surface pressures but form ribbonlike structures as the surface pressure is increased. This nanostructuring is primarily imparted by the increase in van der Waals forces with increasing amount of carbazole units per dendron generation on a hydrophilic mica surface. Further, electrochemical cross-linking of the carbazole molecules by cyclic voltammetery (CV) on doped Si wafer has enabled the formation of an LB film monolayer with a secondary level of organization in the monolayer imparted by the inter- and intramolecular cross-linking among the carbazole units. This study should provide a basis for monolayer film materials based on combining the LB technique and electrochemical cross-linking for nanostructuring superstructures at the air-water interface.     

Comparative investigation of the copper(II) complexes of (R)-, (S)- and (R,S)-1-phenyl-N,N-bis(pyridine-3-ylmethyl)ethanamine along with the related complex of (R,S)-1-cyclohexyl-N,N-bis(pyridine-3-ylmethyl)ethanamine. Synthetic, magnetic, and structural studies

The interaction of the enantiopure (R)- and (S)-1-phenyl-N,N-bis(pyridine-3- ylmethyl)ethanamine ligands, R-L ¹ and S-L ¹ , with copper(II) chloride followed by addition of hexafluorophosphate resulted in the isolation of the corresponding enantiomeric complexes [Cu(R-L ¹ )Cl](PF₆) (1), [Cu(S-L ¹ )Cl](PF₆) (2) and [Cu(S-L ¹ )Cl](PF₆)??0.5Et₂O (3), in which dimerization occurs through two long Cu??????Cl interactions, the ??-chloro bridges being thus strongly asymmetric. The organic ligand is bound to the metal centre via its N₃-donor dipyridylmethylamine fragment in a planar fashion, such that each copper centre is in a square planar environment (or distorted square pyramidal with a long axial bond length if the additional interaction is considered). When R,S-L ¹ was employed in a parallel synthesis, the similar racemic complex [Cu(R,S-L ¹ )Cl](PF₆)??0.5MeOH (4) was obtained, in which the L ¹ ligands in each dimeric unit have opposite hands. In contrast to the complexes of L ¹ , the reaction of Cu(II) chloride with the related ligand, (R)-1-cyclohexyl-N,N-bis(pyridine-3-ylmethyl)ethanamine (R-L ² ), yielded the mononuclear complex [Cu(R,S-L ² )Cl₂] (5), displaying a distorted square pyramidal coordination geometry. The structure of this product along with its corresponding circular dichroism spectrum revealed that racemisation of the starting R-L ² ligand has occurred under the relatively mild (basic) conditions employed for the synthesis. A temperature-dependent magnetic studies of the complexes 1, 2 and 5 indicate that a week ferromagnetic interaction is operative in each dicopper core in 1 and 2 with 2J?=?1.2?cm^?1. On the other hand, a week antiferromagnetic intermolecular interaction is operative for 5.     

The forces on a single interacting Bose–Einstein condensate

Using double parabola approximation for a single Bose–Einstein condensate confined between double slabs we proved that in grand canonical ensemble (GCE) the ground state with Robin boundary condition (BC) is favored, whereas in canonical ensemble (CE) our system undergoes from ground state with Robin BC to the one with Dirichlet BC in small-L region and vice versa for large-L region and phase transition in space of the ground state is the first order. The surface tension force and Casimir force are also considered in both CE and GCE in detail.     

Transformation Kinetics of LiBH4–MgH2 for Hydrogen Storage

The reactive hydride composite (RHC) LiBH₄–MgH₂ is regarded as one of the most promising materials for hydrogen storage. Its extensive application is so far limited by its poor dehydrogenation kinetics, due to the hampered nucleation and growth process of MgB₂. Nevertheless, the poor kinetics can be improved by additives. This work studied the growth process of MgB₂ with varying contents of 3TiCl₃·AlCl₃ as an additive, and combined kinetic measurements, X-ray diffraction (XRD), and advanced transmission electron microscopy (TEM) to develop a structural understanding. It was found that the formation of MgB₂ preferentially occurs on TiB₂ nanoparticles. The major reason for this is that the elastic strain energy density can be reduced to ~4.7 × 10⁷ J/m³ by creating an interface between MgB₂ and TiB₂, as opposed to ~2.9 × 10⁸ J/m³ at the original interface between MgB₂ and Mg. The kinetics of the MgB₂ growth was modeled by the Johnson–Mehl–Avrami–Kolmogorov (JMAK) equation, describing the kinetics better than other kinetic models. It is suggested that the MgB₂ growth rate-controlling step is changed from interface- to diffusion-controlled when the nucleation center changes from Mg to TiB₂. This transition is also reflected in the change of the MgB₂ morphology from bar- to platelet-like. Based on our observations, we suggest that an additive content between 2.5 and 5 mol% 3TiCl₃·AlCl₃ results in the best enhancement of the dehydrogenation kinetics.