Collective phase-like mode and the role of lattice distortions at TN ~TC in RMn2O5 (R= Pr, Sm, Gd, Tb, Bi)

We report on electronic collective excitations in RMn(2)O(5) (R =Pr, Sm, Gd, Tb) showing condensation starting at and below ~T(N) ~T(C)~ 40-50 K. Their origin is understood as partial delocalized e(g) electron orbitals in the Jahn-Teller distortion of the pyramid dimer with strong hybridized Mn(3+)-O bonds. Our local probes, Raman, infrared, and x-ray absorption, back the conclusion that there is no structural phase transition at T(N)~T(C). Ferroelectricity is magnetically assisted by electron localization triggering lattice polarizability by unscreening. We have also found phonon hardening as the rare earth is sequentially replaced. This is understood as a consequence of lanthanide contraction. It is suggested that partially f-electron screened rare earth nuclei might be introducing a perturbation to e(g) electrons prone to delocalize as the superexchange interaction takes place.     

Reversible electron-induced cis-trans isomerization mediated by intermolecular interactions

Reversible isomerization processes are rarely found when organic molecular switches are adsorbed on metal surfaces. One obstacle is the large energy difference of the isomeric forms, since usually the most planar conformer has the largest adsorption energy. In the example of an imine derivative, we show a strategy for also stabilizing the non-planar isomer by intermolecular bonding to its neighbors. Tunneling electrons from the tip of a scanning tunneling microscope can then be used to induce reversible switching between the trans?and cis-like state. Supported by model force-field calculations, we illustrate that the most probable cause of the enhanced stability of the three-dimensional cis?state at specific adsorption sites is the electrostatic interaction with N sites of the neighboring molecule.     

Wood typification by Venturi easy ambient sonic spray ionization mass spectrometry: the case of the endangered Mahogany tree

Venturi easy ambient sonic spray ionization mass spectrometry in both its liquid (V(L) -EASI-MS) and solid sample modes (V(S) -EASI-MS) is shown to provide nearly immediate and secure typification of woods, as demonstrated for Mahogany, an endangered and most valuable type of tropical wood. This reddish wood displays unique phytochemical markers (phragmalin-type limonoids) which are rapidly detected from the wood surface by V(S) -EASI-MS or from a simple methanol extract of a tiny wood chip by V(L) -EASI-MS. Unique profiles were obtained for Mahogany (Swietenia macrophylla) whereas genuine samples of six other similar types of woods, which are commonly falsified by artificial coloring and commercialized as Mahogany, display also typical but dissimilar pythochemical profiles as compared to that of the authentic wood. Variable and atypical chemical profiles were observed for artificially colored woods. Secure chemical characterization via V(S) -EASI-MS or V(s) -EASI-MS fingerprints of Mahogany and other types of woods with similar appearance should help to control the illegal logging and trade of this and other endangered woods and their falsification, and to create certified standards.     

Statistical characterization of an ensemble of functional neural networks

The Ginzburg-Landau free energy functional with two order parameters has been widely used to describe surfactant adsorption phenomena at the interface between two immiscible fluids such as oil and water. To model surfactant adsorption, additional surfactant related terms are added to the original free energy functional which models an immiscible binary mixture. In this paper, we present a detailed comparison of phase-field models for an immiscible binary mixture with surfactant. In particular, we investigate the effects of mathematical model parameters on equilibrium surfactant profile across the interface between the immiscible binary mixture. Most previous models have severe time-step constraints due to the nonlinear coupling of order parameters. To solve these stability problems, we propose a special case of these models which allows the use of a much larger time-step size. We also apply a type of unconditionally gradient stable scheme and a fast multigrid method to solve the proposed model efficiently and accurately.     

Analysis of eigenmodes in a relativistic gas

The eigenmodes of a relativistic gas within a five-, thirteen- and fourteen-field theories are analyzed in the ultra-relativistic, relativistic and non-relativistic regimes. The five-field theory furnishes one non-propagating and two propagating hydrodynamic modes and there appear sound propagation gaps caused by a coupling of thermal and pressure fluctuations at large wavenumbers. Apart from the three hydrodynamic modes of the five-field theory in the fourteen-field theory emerge more three kinetic sound modes, which at small wavenumbers are purely non-propagating diffusive modes. In the thirteen-field theory, there appear the three hydrodynamic of the five-field theory and two kinetic sound modes, which do not propagate for small values of the wavenumber. It is shown that the fourteen- and the thirteen-field theories exhibit no sound propagation gaps, so that these gaps are shortcomings that arise from the five-field theory.     

The eigenvalue problem for solitary waves of a boussinesq equation,via a generalization of the rouché theorem

We consider the study of an eigenvalue problem obtained by linearizing about solitary wave solutions of a Boussinesq equation. Instead of using the technique of Evans functions as done by Pego and Weinstein in [R. Pego and M. Weinstein, Convective Linear Stability of Solitary Waves for Boussinesq equation. AMS, 99, 311–375] for this particular problem, we perform Fourier analysis to characterize solutions of the eigenvalue problem in terms of a multiplier operator and use the strong relationship between the eigenvalue problem for the linearized Boussinesq equation and the eigenvalue problem associated with the linearization about solitary wave solutions of a special form of the KdV equation. By using a generalization of the Rouché Theorem and the asymptotic behavior of the Fourier symbol corresponding to the eigenvalues problem for the Boussinesq equation and the Fourier symbol corresponding to the eigenvalues problem for the KdV equation, we show nonexistence of eigenvalues with respect to weighted space in a planar region containing the right-half plane.     

A novel approach to obtain analytical-numerical solutions of nonlinear Lorenz system

In this research we apply an analytic approach to solve the well-known Lorenz system in the non-chaotic regime. The proposed approach is based on modal expansion by infinite series. The analytical-numerical results show that for real initial conditions and under the non-convective regime the modal expansion series reproduce correctly the dynamical behavior of the solution of the Lorenz system. The validity and reliability of the proposed analytical approach with few terms is tested by its application to the convective and non-convective regime with various parameter values. The main advantage is that the obtained solution is global and is presented in analytical form.     

On a singular minimizing problem

We investigate the non-homogeneous modular Dirichlet problem Δ _p (·)u(x) = f (x) (where Δ _p (·)u(x) = div(|?u|^p(x-2)?u(x)) from the functional analytic point of view and we prove the stability of the solutions \({\left( {{u_{{p_i}}}} \right)_i}\) of the equation \({\Delta _{{p_i}\left( \cdot \right)}}{u_{{p_i}\left( \cdot \right)}} = f\) as p _i (·) → q(·) via Gamma-convergence of sequence of appropriate functionals.     

Proper holomorphic mappings between generalized pseudoellipsoids

Summary We characterize the existence of proper holomorphic mappings between pseudoellipsoids of the form . If f:()() is any such mapping, the existence of a subgroup of Aut (()) such that is shown equivalent to a condition on the branch locus of f.     

Structure and dynamics of the missing-row reconstruction on O/Cu(0 0 1) and O/Ag(0 0 1)

The geometry and the vibrational properties of missing row reconstructed O/Cu(0 0 1) and O/Ag(0 0 1) surfaces are investigated by means of density functional theory and density functional perturbation theory, using the local density and the generalized-gradient approximations. Our results predict very similar structural and vibrational properties for the two reconstructed surfaces. In the case of copper our calculations reproduce quite accurately the experimental results, while for the missing row reconstructed O/Ag(0 0 1) surface the agreement between theory and experiment is less satisfactory.