MASS DISTRIBUTION IN HICKSON COMPACT GROUPS OF GALAXIES

This study presents the mass distribution for a sample of 18 late-type galaxies in nine Hickson compact groups. We used Ha rotation curves (RCs) from high-resolution two-dimensional velocity fields of Fabry-Perot observations and the J-band photometry from the Two Micron All Sky Survey, in order to determine the dark halo and the visible matter distributions. The study compares two halo density profiles, an isothermal core-like distribution, and a cuspy one. We also compare their visible and dark matter distributions with those of galaxies belonging to cluster and field galaxies coming from two samples: 40 cluster galaxies of Barnes et al. and 35 field galaxies of Spano et al. The central halo surface density is found to be constant with respect to the total absolute magnitude similar to what is found for the isolated galaxies. This suggests that the halo density is independent of galaxy type and environment. We have found that core-like density profiles better fit the RCs than cuspy-like ones. No major differences have been found between field, cluster, and compact group galaxies with respect to their dark halo density profiles.

Star formation in the intragroup medium and other diagnostics of the evolutionary stages of compact groups of galaxies

Context. Compact groups of galaxies are entities that have high densities of galaxies and serve as laboratories to study galaxy interactions, intergalactic star formation and galaxy evolution. Aims. The main goal of this study is to search for young objects in the intragroup medium of seven compact groups of galaxies: HCG 2, 7, 22, 23, 92, 100 and NGC 92 as well as to evaluate the stage of interaction of each group. Methods. We used Fabry-Perot velocity fields and rotation curves together with GALEX NUV and FUV images and optical R-band and HI maps. Results. (i) HCG 7 and HCG 23 are in early stages of interaction; (ii) HCG 2 and HCG 22 are mildly interacting; and (iii) HCG 92, HCG 100 and NGC 92 are in late stages of evolution. We find that all three evolved groups contain populations of young blue objects in the intragroup medium, consistent with ages < 100 Myr, of which several are younger than < 10 Myr. We also report the discovery of a tidal dwarf galaxy candidate in the tail of NGC 92. These three groups, besides containing galaxies that have peculiar velocity fields, also show extended HI tails. Conclusions. Our results indicate that the advanced stage of evolution of a group, together with the presence of intragroup HI clouds, may lead to star formation in the intragroup medium. A table containing all intergalactic HII regions and tidal dwarf galaxies confirmed to date is appended.

FLOWS WITHOUT WANDERING POINTS ON COMPACT CONNECTED SURFACES

Given a compact 2 dimensional manifold M we classify all continuous flows phi without wandering points on M. This classification is performed by finding finitely many pairwise disjoint open phi-invariant subsets {U(1), U(2), ..., U(n)} of M such that U(i=1)(n) (U(i)) over bar = M and each U(i) is either a suspension of an interval exchange transformation, or a maximal open cylinder made up of closed trajectories of phi.

Hyperpolarizabilities of the methanol molecule: A CCSD calculation including vibrational corrections

In this work we present the results for hyperpolarizabilities of the methanol molecule including vibrational corrections and electron correlation effects at the CCSD level. Comparisons to random phase approximation results previously reported show that the electron correlation is in general important for both electronic contribution and vibrational corrections. The role played by the anharmonicities on the calculations of the vibrational corrections has also been analyzed and the obtained results indicate that the anharmonic terms are important for the dc-Pockels and dc-Kerr effects. For the other nonlinear optical properties studied the double-harmonic approximation is found to be suitable. Comparison to available experimental result in gas phase for the dc-second harmonic generation second hyperpolarizability shows a very good agreement with the electronic contribution calculated here while our total value is 14% larger than the experimental value.

Approximation to density functional theory for the calculation of band gaps of semiconductors

The local-density approximation (LDA) together with the half occupation (transitionstate) is notoriously successful in the calculation of atomic ionization potentials. When it comes to extended systems, such as a semiconductor infinite system, it has been very difficult to find a way to half ionize because the hole tends to be infinitely extended (a Bloch wave). The answer to this problem lies in the LDA formalism itself. One proves that the half occupation is equivalent to introducing the hole self-energy (electrostatic and exchange correlation) into the Schrodinger equation. The argument then becomes simple: The eigenvalue minus the self-energy has to be minimized because the atom has a minimal energy. Then one simply proves that the hole is localized, not infinitely extended, because it must have maximal self-energy. Then one also arrives at an equation similar to the self- interaction correction equation, but corrected for the removal of just 1/2 electron. Applied to the calculation of band gaps and effective masses, we use the self- energy calculated in atoms and attain a precision similar to that of GW, but with the great advantage that it requires no more computational effort than standard LDA.

Nonuniversal behavior for aperiodic interactions within a mean-field approximation

We study the spin-1/2 Ising model on a Bethe lattice in the mean-field limit, with the interaction constants following one of two deterministic aperiodic sequences, the Fibonacci or period-doubling one. New algorithms of sequence generation were implemented, which were fundamental in obtaining long sequences and, therefore, precise results. We calculate the exact critical temperature for both sequences, as well as the critical exponents beta, gamma, and delta. For the Fibonacci sequence, the exponents are classical, while for the period-doubling one they depend on the ratio between the two exchange constants. The usual relations between critical exponents are satisfied, within error bars, for the period-doubling sequence. Therefore, we show that mean-field-like procedures may lead to nonclassical critical exponents.

Spin gaps and spin-flip energies in density-functional theory

Energy gaps are crucial aspects of the electronic structure of finite and extended systems. Whereas much is known about how to define and calculate charge gaps in density-functional theory (DFT), and about the relation between these gaps and derivative discontinuities of the exchange-correlation functional, much less is known about spin gaps. In this paper we give density-functional definitions of spin-conserving gaps, spin-flip gaps and the spin stiffness in terms of many-body energies and in terms of single-particle (Kohn-Sham) energies. Our definitions are as analogous as possible to those commonly made in the charge case, but important differences between spin and charge gaps emerge already on the single-particle level because unlike the fundamental charge gap spin gaps involve excited-state energies. Kohn-Sham and many-body spin gaps are predicted to differ, and the difference is related to derivative discontinuities that are similar to, but distinct from, those usually considered in the case of charge gaps. Both ensemble DFT and time-dependent DFT (TDDFT) can be used to calculate these spin discontinuities from a suitable functional. We illustrate our findings by evaluating our definitions for the Lithium atom, for which we calculate spin gaps and spin discontinuities by making use of near-exact Kohn-Sham eigenvalues and, independently, from the single-pole approximation to TDDFT. The many-body corrections to the Kohn-Sham spin gaps are found to be negative, i.e., single-particle calculations tend to overestimate spin gaps while they underestimate charge gaps.

Density functional theory investigation of 3d, 4d, and 5d 13-atom metal clusters

The knowledge of the atomic structure of clusters composed by few atoms is a basic prerequisite to obtain insights into the mechanisms that determine their chemical and physical properties as a function of diameter, shape, surface termination, as well as to understand the mechanism of bulk formation. Due to the wide use of metal systems in our modern life, the accurate determination of the properties of 3d, 4d, and 5d metal clusters poses a huge problem for nanoscience. In this work, we report a density functional theory study of the atomic structure, binding energies, effective coordination numbers, average bond lengths, and magnetic properties of the 3d, 4d, and 5d metal (30 elements) clusters containing 13 atoms, M(13). First, a set of lowest-energy local minimum structures (as supported by vibrational analysis) were obtained by combining high-temperature first- principles molecular-dynamics simulation, structure crossover, and the selection of five well-known M(13) structures. Several new lower energy configurations were identified, e. g., Pd(13), W(13), Pt(13), etc., and previous known structures were confirmed by our calculations. Furthermore, the following trends were identified: (i) compact icosahedral-like forms at the beginning of each metal series, more opened structures such as hexagonal bilayerlike and double simple-cubic layers at the middle of each metal series, and structures with an increasing effective coordination number occur for large d states occupation. (ii) For Au(13), we found that spin-orbit coupling favors the three-dimensional (3D) structures, i.e., a 3D structure is about 0.10 eV lower in energy than the lowest energy known two-dimensional configuration. (iii) The magnetic exchange interactions play an important role for particular systems such as Fe, Cr, and Mn. (iv) The analysis of the binding energy and average bond lengths show a paraboliclike shape as a function of the occupation of the d states and hence, most of the properties can be explained by the chemistry picture of occupation of the bonding and antibonding states.

Transition-metal 13-atom clusters assessed with solid and surface-biased functionals

First-principles density-functional theory studies have reported open structures based on the formation of double simple-cubic (DSC) arrangements for Ru(13), Rh(13), Os(13), and Ir(13), which can be considered an unexpected result as those elements crystallize in compact bulk structures such as the face-centered cubic and hexagonal close-packed lattices. In this work, we investigated with the projected augmented wave method the dependence of the lowest-energy structure on the local and semilocal exchange-correlation (xc) energy functionals employed in density-functional theory. We found that the local-density approximation (LDA) and generalized-gradient formulations with different treatment of the electronic inhomogeneities (PBE, PBEsol, and AM05) confirm the DSC configuration as the lowest-energy structure for the studied TM(13) clusters. A good agreement in the relative total energies are obtained even for structures with small energy differences, e. g., 0.10 eV. The employed xc functionals yield the same total magnetic moment for a given structure, i.e., the differences in the bond lengths do not affect the moments, which can be attributed to the atomic character of those clusters. Thus, at least for those systems, the differences among the LDA, PBE, PBEsol, and AM05 functionals are not large enough to yield qualitatively different results. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3577999]

The role of electron localization in the atomic structure of transition-metal 13-atom clusters: the example of Co(13), Rh(13), and Hf(13)

The crystalline structure of transition-metals (TM) has been widely known for several decades, however, our knowledge on the atomic structure of TM clusters is still far from satisfactory, which compromises an atomistic understanding of the reactivity of TM clusters. For example, almost all density functional theory (DFT) calculations for TM clusters have been based on local (local density approximation-LDA) and semilocal (generalized gradient approximation-GGA) exchange-correlation functionals, however, it is well known that plain DFT fails to correct the self-interaction error, which affects the properties of several systems. To improve our basic understanding of the atomic and electronic properties of TM clusters, we report a DFT study within two nonlocal functionals, namely, the hybrid HSE (Heyd, Scuseria, and Ernzerhof) and GGA + U functionals, of the structural and electronic properties of the Co(13), Rh(13), and Hf(13) clusters. For Co(13) and Rh(13), we found that improved exchange-correlation functionals decrease the stability of open structures such as the hexagonal bilayer (HBL) and double simple-cubic (DSC) compared with the compact icosahedron (ICO) structure, however, DFT-GGA, DFT-GGA + U, and DFT-HSE yield very similar results for Hf(13). Thus, our results suggest that the DSC structure obtained by several plain DFT calculations for Rh(13) can be improved by the use of improved functionals. Using the sd hybridization analysis, we found that a strong hybridization favors compact structures, and hence, a correct description of the sd hybridization is crucial for the relative energy stability. For example, the sd hybridization decreases for HBL and DSC and increases for ICO in the case of Co(13) and Rh(13), while for Hf(13), the sd hybridization decreases for all configurations, and hence, it does not affect the relative stability among open and compact configurations.

COMPLETE ISOMORPHIC CLASSIFICATIONS OF SOME SPACES OF COMPACT OPERATORS

This paper is a continuation and a complement of our previous work on isomorphic classification of some spaces of compact operators. We improve the main result concerning extensions of the classical isomorphic classification of the Banach spaces of continuous functions on ordinals. As an application, fixing an ordinal a and denoting by X(xi), omega(alpha) <= xi < omega(alpha+1), the Banach space of all X-valued continuous functions defined in the interval of ordinals [0,xi] and equipped with the supremum, we provide complete isomorphic classifications of some Banach spaces K(X(xi),Y(eta)) of compact operators from X(xi) to Y(eta), eta >= omega. It is relatively consistent with ZFC (Zermelo-Fraenkel set theory with the axiom of choice) that these results include the following cases: 1.X* contains no copy of c(0) and has the Mazur property, and Y = c(0)(J) for every set J. 2. X = c(0)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < infinity. 3. X = l(p)(I) and Y = l(q)(J) for any infinite sets I and J and 1 <= q < p < infinity.

ON ISOMORPHIC CLASSIFICATIONS OF SPACES OF COMPACT OPERATORS

We prove an extension of the classical isomorphic classification of Banach spaces of continuous functions on ordinals. As a consequence, we give complete isomorphic classifications of some Banach spaces K(X,Y(n)), eta >= omega, of compact operators from X to Y(eta), the space of all continuous Y-valued functions defined in the interval of ordinals [1, eta] and equipped with the supremum norm. In particular, under the Continuum Hypothesis, we extend a recent result of C. Samuel by classifying, up to isomorphism, the spaces K(X(xi), c(0)(Gamma)(eta)), where omega <= xi < omega(1,) eta >= omega, Gamma is a countable set, X contains no complemented copy of l(1), X* has the Mazur property and the density character of X** is less than or equal to N(1).

ON SPACES OF COMPACT OPERATORS ON C(K, X) SPACES

This paper concerns the spaces of compact operators kappa(E,F), where E and F are Banach spaces C([1, xi], X) of all continuous X-valued functions defined on the interval of ordinals [1, xi] and equipped with the supremun norm. We provide sufficient conditions on X, Y, alpha, beta, xi and eta, with omega <= alpha <= beta < omega 1 for the following equivalence: (a) kappa(C([1, xi], X), C([1, alpha], Y)) is isomorphic to kappa(C([1,eta], X), C([1, beta], Y)), (b) beta < alpha(omega). In this way, we unify and extend results due to Bessaga and Pelczynski (1960) and C. Samuel (2009). Our result covers the case of the classical spaces X = l(p) and Y = l(q) with 1 < p, q < infinity.

POLAR ACTIONS ON CERTAIN PRINCIPAL BUNDLES OVER SYMMETRIC SPACES OF COMPACT TYPE

We study polar actions with horizontal sections on the total space of certain principal bundles G/K -> G/H with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locally irreducible homogeneous spaces with nonnegative curvature which are not homeomorphic to symmetric spaces.

Age-related difference on weight transfer during unconstrained standing

The ability to transfer weight from one lower limb to the other is essential for the execution of daily life activities and little is known about how weight transfer during unconstrained natural standing is affected by age. This study examined the weight transfer ability of elderly individuals during unconstrained standing (for 30 mill) in comparison to young adults. The subjects (19 healthy elderly adults, range 65-80 years, and 19 healthy young adults, range 18-30 years) stood with each foot on a separate force plate and were allowed to change their posture freely at any time. The limits of stability and base of support width during standing, measures of mobility (using the timed up and go and the preferred walking speed tests), and fear of falling were also measured. In comparison to the young adults, during unconstrained standing the elderly adults produced four times fewer weight transfers of large amplitude (greater than,half of their body weight). The limits of stability and base of support width were significantly smaller for the elderly adults but there were no significant differences in the measures of mobility and in the fear of falling score compared to young adults. The observed significant age-related decrease in the use of weight transfer during unconstrained standing, despite any difference in the measured mobility of the subjects, suggests that this task reveals unnoticed and subtle differences in postural control, which may help to better understand age related impairments in balance that the elderly population experiences. (C) 2010 Elsevier B.V. All rights reserved.