Plane curve diagrams and geometrical applications

We look at plane curve diagrams (f,alpha), which are given by a plane curve multigerm alpha : (R, S) -> R(2) and a function on it f : (R, S) -> R. We obtain a classification of all such diagrams, where alpha has e-codimension <= 2 and f has finite order. Then we define an equivalence between plane curves which we call Ah(alpha)-equivalence and which is determined by the class of the diagram (h(alpha), alpha). Here, h alpha denotes the height function of alpha with respect to its normal vector. This is an equivalence which not only takes into account the topology of the singularity of alpha, but also its flat geometry. Finally, we apply our results in order to obtain a classification of all the plane projections of a generic space curve gamma embedded in R(3).

Rotation effect on geodesic and zonal flow modes in tokamak plasmas with isothermal magnetic surfaces

The electrostatic geodesic mode oscillations are investigated in rotating large aspect ratio tokamak plasmas with circular isothermal magnetic surfaces. The analysis is carried out within the magnetohydrodynamic model including heat flux to compensate for the non-adiabatic pressure distribution along the magnetic surfaces in plasmas with poloidal rotation. Instead of two standard geodesic modes, three geodesic continua are found. The two higher branches of the geodesic modes have a small frequency up-shift from ordinary geodesic acoustic and sonic modes due to rotation. The lower geodesic continuum is a newzonal flowmode (geodesic Doppler mode) in plasmas with mainly poloidal rotation. Limits to standard geodesic modes are found. Bifurcation of Alfven continuum by geodesic modes at the rational surfaces is also discussed. Due to that, the frequency of combined geodesic continuum extends from the poloidal rotation frequency to the ion-sound band that can have an important role in suppressing plasma turbulence.

A simplified description of the evolution of organic aerosol composition in the atmosphere

Organic aerosol (OA) in the atmosphere consists of a multitude of organic species which are either directly emitted or the products of a variety of chemical reactions. This complexity challenges our ability to explicitly characterize the chemical composition of these particles. We find that the bulk composition of OA from a variety of environments (laboratory and field) occupies a narrow range in the space of a Van Krevelen diagram (H: C versus O:C), characterized by a slope of similar to-1. The data show that atmospheric aging, involving processes such as volatilization, oxidation, mixing of air masses or condensation of further products, is consistent with movement along this line, producing a more oxidized aerosol. This finding has implications for our understanding of the evolution of atmospheric OA and representation of these processes in models. Citation: Heald, C. L., J. H. Kroll, J. L. Jimenez, K. S. Docherty, P. F. DeCarlo, A. C. Aiken, Q. Chen, S. T. Martin, D. K. Farmer, and P. Artaxo (2010), A simplified description of the evolution of organic aerosol composition in the atmosphere, Geophys. Res. Lett., 37, L08803, doi: 10.1029/2010GL042737.

Micelles forming biaxial lyotropic nematic phases

The paper by Yu and Saupe on the first biaxial nematic phase created excitement for a number of reasons. Some theories of biaxial phases already existed, but experimental observation was still lacking. The phase was discovered in a lyotropic system with three components, which in theory is difficult. Lyotropic liquid crystals are composed of supramolecular assemblies of amphiphilic molecules, which may change shape and size as a function of concentration and temperature. The experimental phase diagram of the lyotropic biaxial phase was rather complex, with the biaxial region inserted between nematic cylindrical and nematic discotic phases via second-order transitions. In addition, re-entrant behaviour was evident. Saupe investigated further systems experimentally, observing that the biaxial phase might be absent in cases where a direct transition between the cylindrical and discotic phases occurred. He provided a range of theoretical and experimental contributions on the properties of these lyotropics, but was very cautious regarding the detailed amphiphilic assemblies involved. The present paper reviews this area, focusing on proposals for the structure of the micellar assemblies. Emphasis is placed on recent papers which indicate a transformation of the two uniaxial shapes, in mixing conditions, both from the theoretical and the experimental point of view, and to questions still requiring further study.

Phase behavior of the orange essential oil/sodium bis(2-ethylhexyl)sulfosuccinate/water system

The ternary phase diagram for the orange essential oil (OEO)/sodium bis(2-ethylhexyl)sulfosuccinate (AOT)/water system was constructed at 25 degrees C. It indicates a large single phase region, comprising an isotropic water-in-oil (W/O) microemulsion (ME) phase (L(2)), a liquid crystal (LC) (lamellar or hexagonal) and a large unstable emulsion phase that separates in two phases of normal and reverse micelles (L(1) and L(2)). In this communication the properties of the ME are investigated by viscosity, electric conductivity and small angle X-ray scattering (SAXS) indicating that the isotropic ME phase exhibits different behaviors depending on composition. At low water content low viscous ""dry"" surfactant structures are formed, whereas at higher water content higher viscous water droplets are formed. The experimental data allow the determination of the transition from ""dry"" to the water droplet structures within the L(2) phase. SAXS analyses have also been performed for selected LC samples. (C) 2009 Elsevier B.V. All rights reserved.

Bubbling transition to spatial mode excitation in an extended dynamical system

We investigated the transition to spatio-temporal chaos in spatially extended nonlinear dynamical systems possessing an invariant subspace with a low-dimensional attractor. When the latter is chaotic and the subspace is transversely stable we have a spatially homogeneous state only. The onset of spatio-temporal chaos, i.e. the excitation of spatially inhomogeneous modes, occur through the loss of transversal stability of some unstable periodic orbit embedded in the chaotic attractor lying in the invariant subspace. This is a bubbling transition, since there is a switching between spatially homogeneous and nonhomogeneous states with statistical properties of on-off intermittency. Hence the onset of spatio-temporal chaos depends critically both on the existence of a chaotic attractor in the invariant subspace and its being transversely stable or unstable. (C) 2008 Elsevier B.V. All rights reserved.

Hybrid reflections in InGaP/GaAs(001) by synchrotron radiation multiple diffraction

Hybrid reflections (HRs) involving substrate and layer planes (SL type) [Morelhao et al., Appl. Phys. Len. 73 (15), 2194 (1998)] observed in Chemical Beam Epitaxy (CBE) grown InGaP/GaAs(001) structures were used as a three-dimensional probe to analyze structural properties of epitaxial layers. A set of (002) rocking curves (omega-scan) measured for each 15 degrees in the azimuthal plane was arranged in a pole diagram in phi for two samples with different layer thicknesses (#A -58 nm and #B - 370 nm) and this allowed us to infer the azimuthal epilayer homogeneity in both samples. Also, it was shown the occurrence of (1 (1) over bar3) HR detected even in the thinner layer sample. Mappings of the HR diffraction condition (omega:phi) allowed to observe the crystal truncation rod through the elongation of HR shape along the substrate secondary reflection streak which can indicate in-plane match of layer/substrate lattice parameters. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Mixture of changing uniaxial micellar forms in lyotropic biaxial nematics

Lyotropic nematics consisting of surfactant-cosurfactant water solutions may present a biaxial phase or direct U(+) <-> U(-) transitions, in different regions of the temperature-relative concentration phase diagram, for different systems and compositions. We propose that these may be related to changes of uniaxial micellar form, which may occur either smoothly or abruptly. Smooth change of cylinder-like into disc-like shapes requires a distribution of Maier-Saupe interaction constants and we consider two limiting cases for the distribution of forms: a single Gaussian and a double Gaussian. Alternatively, an abrupt change of form is described by a discontinuous distribution of interaction constants. Our results show that the dispersive distributions yield a biaxial phase, while an abrupt change of shape leads to coexistence of uniaxial phases. Fitting the theory to the experiment for the ternary system KL/decanol/D2O leads to transition lines in very good agreement with experimental results. In order to rationalise the results of the comparison, we analyse temperature and concentration form dependence, which connects micellar and experimental macroscopic parameters. Physically consistent variations of micellar asymmetry, amphiphile partitioning and volume are obtained. To the best of the authors` knowledge, this is the first truly statistical microscopic approach that is able to model experimentally observed lyotropic biaxial nematic phases.

Aging and stationary properties of non-equilibrium symmetrical three-state models

We consider a non-equilibrium three-state model whose dynamics is Markovian and displays the same symmetry as the three-state Potts model, i.e. the transition rates are invariant under the cyclic permutation of the states. Unlike the Potts model, detailed balance is, in general, not satisfied. The aging and the stationary properties of the model defined on a square lattice are obtained by means of large-scale Monte Carlo simulations. We show that the phase diagram presents a critical line, belonging to the three-state Potts universality class, that ends at a point whose universality class is that of the Voter model. Aging is considered on the critical line, at the Voter point and in the ferromagnetic phase.

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.

Emergence and loss of assortative mating in sympatric speciation

We have studied an agent model which presents the emergence of sexual barriers through the onset of assortative mating, a condition that might lead to sympatric speciation. In the model, individuals are characterized by two traits, each determined by a single locus A or B. Heterozygotes on A are penalized by introducing an adaptive difference from homozygotes. Two niches are available. Each A homozygote is adapted to one of the niches. The second trait, called the marker trait has no bearing on the fitness. The model includes mating preferences, which are inherited from the mother and subject to random variations. A parameter controlling recombination probabilities of the two loci is also introduced. We study the phase diagram by means of simulations, in the space of parameters (adaptive difference, carrying capacity, recombination probability). Three phases are found, characterized by (i) assortative mating, (ii) extinction of one of the A alleles and (iii) Hardy-Weinberg like equilibrium. We also make perturbations of these phases to see how robust they are. Assortative mating can be gained or lost with changes that present hysteresis loops, showing the resulting equilibrium to have partial memory of the initial state and that the process of going from a polymorphic panmictic phase to a phase where assortative mating acts as sexual barrier can be described as a first-order transition. (C) 2009 Published by Elsevier Ltd.

Compressible Sherrington-Kirkpatrick spin-glass model

We introduce a Sherrington-Kirkpatrick spin-glass model with the addition of elastic degrees of freedom. The problem is formulated in terms of an effective four-spin Hamiltonian in the pressure ensemble, which can be treated by the replica method. In the replica-symmetric approximation, we analyze the pressure-temperature phase diagram, and obtain expressions for the critical boundaries between the disordered and the ordered (spin-glass and ferromagnetic) phases. The second-order para-ferromagnetic border ends at a tricritical point, beyond which the transition becomes discontinuous. We use these results to make contact with the temperature-concentration phase diagrams of mixtures of hydrogen-bonded crystals.

Fractional quantum Hall effect in second subband of a 2DES

In the present paper we report on the experimental electron sheet density vs. magnetic field diagram for the magnetoresistance R(xx) of a two-dimensional electron system (2DES) with two occupied subbands. For magnetic fields above 9T, we found fractional quantum Hall levels centered around the filing factor v = 3/2 in both the two occupied electric subbands. We focused specially on the fractional levels of the second subband, whose experimental values of the magnetic field B of their minima do not obey a periodicity law in 1/|B-B(c)|, where B(c) is the critical field at the filling factor v = 3/2, and we explain this fact entirely in the framework of the composite fermions theory. We use a simple theoretical model to give a possible explanation for the fact. Copyright (c) EPLA, 2011

2-(4,5,6,7-tetrafluorobenzimidazol-2-yl)-4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazole-3-oxide-1-oxyl, a hydrogen-bonded organic quasi-1D ferromagnet

The title radical (F4BlmNN) is a stable nitronylnitroxide that forms hydrogen-bonded NH center dot center dot center dot ON chains in the solid state. The chains assemble the F4BlmNN molecules to form stacked contacts between the radical groups, in a geometry that is expected to exhibit ferromagnetic (FM) exchange based on spin polarization (SP) models. The experimental magnetic susceptibility of F4BlmNN confirms the expectation, showing 1-D Heisenberg chain FM exchange behavior over 1.8-300 K with an intrachain exchange constant Of J(chain)/k = +22 K. At lower temperatures, ac magnetic susceptibility and variable field heat capacity measurements show that F4BlmNN acts as a quasi-1-D ferromagnet. The dominant ferromagnetic exchange interaction is attributable to overlap between spin orbitals of molecules within the hydrogen-bonded chains, consistent with the SP model expectations. The chains appear to be antiferromagnetically exchange coupled, giving cusps in the ac susceptibility and zero field heat capacity at lower temperatures. The results indicate that the sample orders magnetically at about 0.7 K. The magnetic heat capacity ordering cusp shifts to lower temperatures as external magnetic field increases, consistent with forming a bulk antiferromagnetic phase below a Neel temperature of T-N(0) = 0.72 K, with a critical field of H-c approximate to 1800 Oe. The interchain exchange is estimated to be zJ/k congruent to (-)0.1 K.