Poisson brackets,Novikov-Leibniz structures and integrable Riemann hydrodynamic systems

A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is closely related to the infinite multi-component Riemann integrable hierarchies. A close relationship to the standard symplectic analysis techniques is also discussed.     

Electromodulation spectroscopy of confined systems

The convolution formalism of Aspnes and Rowe for the dielectric function in the presence of an electric field is applied to electromodulation spectroscopy of confined systems. It is shown that for isolated confined systems where excitonic effects are not important, electromodulation spectroscopy leads to first derivative like optical features of two dimensional critical points. For superlattices in weak fields (neglecting excitonic interactions), the familiar third derivative forms of Aspnes and Rowe are applicable. In contrast, when moderate and high electric fields are applied to superlattices, electromodulation spectroscopy will exhibit optical features characteristic of first derivative line shapes. This phenomenon arises because the electric field causes the envelope functions of the electron and hole states to become spatially localized. The importance of excitons and their inhomogeneous broadening to the experimentally observed line shapes are considered.     

The minimum degree distance of graphs of given order and size

In this note, we study the degree distance of a graph which is a degree analogue of the Wiener index. Given n and e, we determine the minimum degree distance of a connected graph of order n and size e.     

Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

Route to Lambda in conformally coupled phantom cosmology

In this Letter we investigate acceleration in the flat cosmological model with a conformally coupled phantom field and we show that acceleration is its generic feature. We reduce the dynamics of the model to a 3-dimensional dynamical system and analyze it on a invariant 2-dimensional submanifold. Then the concordance FRW model with the cosmological constant Λ   is a global attractor situated on a 2-dimensional invariant space. We also study the behaviour near this attractor, which can be approximated by the dynamics of the linearized part of the system. We demonstrate that trajectories of the conformally coupled phantom scalar field with a simple quadratic potential crosses the cosmological constant barrier infinitely many times in the phase space. The universal behaviour of the scalar field and its potential is also calculated. We conclude that the phantom scalar field conformally coupled to gravity gives a natural dynamical mechanism of concentration of the equation of state coefficient around the magical value weff=−1$w_{\mathrm{eff}}=-1$. We demonstrate route to Lambda through the infinite times crossing the weff=−1$w_{\mathrm{eff}}=-1$ phantom divide.     

Twister quintessence scenario

We study generic solutions in a non-minimally coupled to gravity scalar field cosmology. It is shown that dynamics for both canonical and phantoms scalar fields with the potential can be reduced to the dynamical system from which the exact forms for an equation of the state parameter can be derived. We have found the stationary solutions of the system and discussed their stability. Within the large class of admissible solutions we have found a non-degenerate critical points and we pointed out multiple attractor type of trajectory travelling in neighborhood of three critical points at which we have the radiation dominating universe, the barotropic matter dominating state and finally the de Sitter attractor. We have demonstrated the stability of this trajectory which we call the twister solution. Discovered evolutional path is only realized if there exist the non-minimal coupling constant. We have found simple duality relations between twister solutions in phantom and canonical scalar fields in the radiation domination phase. For the twister trajectory we have found an oscillating regime of approaching the de Sitter attractor.     

Dissipative or conservative cosmology with dark energy?

All evolutional paths for all admissible initial conditions of FRW cosmological models with dissipative dust fluid (described by dark matter, baryonic matter and dark energy) are analyzed using dynamical system approach. With that approach, one is able to see how generic the class of solutions leading to the desired property—acceleration—is. The theory of dynamical systems also offers a possibility of investigating all possible solutions and their stability with tools of Newtonian mechanics of a particle moving in a one-dimensional potential which is parameterized by the cosmological scale factor. We demonstrate that flat cosmology with bulk viscosity can be treated as a conservative system with a potential function of the Chaplygin gas type. We characterize the class of dark energy models that admit late time de Sitter attractor solution in terms of the potential function of corresponding conservative system. We argue that inclusion of dissipation effects makes the model more realistic because of its structural stability. We also confront viscous models with SNIa observations. The best fitted models are obtained by minimizing the χ² function which is illustrated by residuals and χ² levels in the space of model independent parameters. The general conclusion is that SNIa data supports the viscous model without the cosmological constant. The obtained values of χ² statistic are comparable for both the viscous model and ΛCDM model. The Bayesian information criteria are used to compare the models with different power-law parameterization of viscous effects. Our result of this analysis shows that SNIa data supports viscous cosmology more than the ΛCDM model if the coefficient in viscosity parameterization is fixed. The Bayes factor is also used to obtain the posterior probability of the model.     

NIR-FT-SERS of 4″-trimethylsilylethylsulfanyl-4,4′-di(phenyleneethynylene)benzenethiol on Au nanospheres

Oligo(phenyleneethynylene) (OPE) compounds have been identified as promising molecular electronic bridges. Self-assembled monolayers of 4″-trimethylsilylethylsulfanyl-4,4′-phenyleneethynylenebenzene thiol (OPE′) on Au were characterized by surface-enhanced Raman scattering (SERS). The FT-Raman spectrum of OPE′ shows three C–S bands at 834, 1086, and 1131 cm⁻¹. From the FT-Raman to the SERS spectra, the 1086 cm⁻¹ band exhibits a 9 cm⁻¹ red shift. Chemisorption of OPE′ to the gold surface occurs via oxidative cleavage of the disulfide bond and the formation of the Au–S bond. The Au–S vibration is visible in the SERS spectra at 257 cm⁻¹. Peaks due to the S–S and S–H stretch are observed at 544 and 2519 cm⁻¹, respectively, in the FT spectrum, but are unobserved in the surface-enhanced spectra. The C–H stretching region (2700–3350 cm⁻¹) in the spectrum of neat OPE′ shows three distinct bands, whereas the SERS spectra show a single broad band. Assignments of vibrational bands were based on DFT calculations performed at the B3LYP level with good agreement between theoretical and experimental values. An average percent difference of 2.52 was obtained for the non-CH stretching frequencies.     

Rare-earth chloride seeded growth of GaN nano- and micro-crystals

A novel rare-earth chloride seed was employed as a catalyst for growth of GaN nano- and micro-crystals on c-, a- and r-plane sapphire. The ErCl₃ seed on the substrate surface enhanced the growth rate and density of the GaN crystals. Distinctive green photoluminescence was measured, confirming that Er³⁺ ions were active in the GaN matrix. This technique can be adapted to selectively grow GaN crystals with emission tailored to the particular optical transitions of the rare-earth seed.