Descripción: The linear response within the elimination of the small component formalism is aimed at obtaining the leading order relativistic corrections to magnetic molecular properties in the context of the elimination of the small component approximation. In the present work we extend the method in order to include two-body effects in the form of a mean field one-body operator. To this end we consider the four-component Dirac-Hartree-Fock operator as the starting point in the evaluation of the second order relativistic expression of magnetic properties. The approach thus obtained is the fully consistent leading order approximation of the random phase approximation four-component formalism. The mean field effect on the relativistic corrections to both the diamagnetic and paramagnetic terms of magnetic properties taking into account both the Coulomb and Breit two-body interactions is considered. © 2006 American Institute of Physics.

Descripción: The notion of p-compact sets arises naturally from Grothendieck's characterization of compact sets as those contained in the convex hull of a norm null sequence. The definition, due to Sinha and Karn (2002), leads to the concepts of p-approximation property and p-compact operators (which form an ideal with its ideal norm κ p). This paper examines the interaction between the p-approximation property and certain space of holomorphic functions, the p-compact analytic functions. In order to understand these functions we define a p-compact radius of convergence which allows us to give a characterization of the functions in the class. We show that p-compact holomorphic functions behave more like nuclear than compact maps. We use the ε-product of Schwartz, to characterize the p-approximation property of a Banach space in terms of p-compact homogeneous polynomials and in terms of p-compact holomorphic functions with range on the space. Finally, we show that p-compact holomorphic functions fit into the framework of holomorphy types which allows us to inspect the κ p-approximation property. Our approach also allows us to solve several questions posed by Aron, Maestre and Rueda (2010). © 2012 Elsevier Inc.

Descripción: We give a new proof of the NP-hardness of deciding the existence of real roots of an integer univariate polynomial encoded by a straight line program based on certain properties of the Tchebychev polynomials. These techniques allow us to prove some new NP-hardness results related to real root approximation for polynomials given by straight line programs. © 2006 Elsevier B.V. All rights reserved.

Descripción: General constraints for invariance of magnetic properties in a gauge transformation are analyzed. Sum rules relative to the transformation from Coulomb to Landau gauges are examined in particular. Numerical tests for hydrogen fluoride, water, ammonia, and methane molecule have been carried out in large basis set calculations, using random-phase approximation. The conditions for invariance are severe conditions for accuracy of variational molecular wave functions. © 1995 American Institute of Physics.

Descripción: In the present work a set of formal relations connecting different approaches to calculate relativistic effects on magnetic molecular properties are proven. The linear response (LR) within the elimination of the small component (ESC), Breit Pauli, and minimal-coupling approaches are compared. To this end, the leading order ESC reduction of operators within the minimal-coupling four-component approach is carried out. The equivalence of all three approaches within the ESC approximation is proven. It is numerically verified for the NMR nuclear-magnetic shielding tensor taking HX and C H3 X (X=Br,I) as model compounds. Formal relations proving the gauge origin invariance of the full relativistic effect on the NMR nuclear-magnetic shielding tensor within the LR-ESC approach are presented. © 2006 American Institute of Physics.

Descripción: We have calculated the electrical conductivity in the current-in-plane geometry of multilayered granular alloys composed of Co clusters embedded in Ag alternating with pure Ag layers. In particular, we have paid attention to the conductivity behavior as a function of Ag layer thickness, Co clusters' size, and degree of percolation. The electronic structure is self-consistently calculated within the unrestricted Hartree-Fock approximation using a parametrized tight binding Hamiltonian which includes a Hubbard-like term. The conductivity tensor is obtained by using the semiclassical Boltzmann equation in the anisotropic relaxation time approximation. We have used a s-d Mott-like scattering model for the electronic mean free path taking into account the Sondheimer's picture for electronic transport in thin films. We find that the experimental conductivity behavior at coalescence can be explained through the electronic band contribution. The conductivity behavior of continuous multilayers is already attained in the very early stage of percolation, as in the experiments. © 2007 American Institute of Physics.

Descripción: We determine how the differences in the treatment of the subfilter-scale physics affect the properties of the flow for three closely related regularizations of Navier-Stokes. The consequences on the applicability of the regularizations as subgrid-scale (SGS) models are also shown by examining their effects on superfilter-scale properties. Numerical solutions of the Clark-α model are compared to two previously employed regularizations, the Lagrangian-averaged Navier-Stokes α-model (LANS-α) and Leray-α, albeit at significantly higher Reynolds number than previous studies, namely, Re≈3300, Taylor Reynolds number of Re≈790, and to a direct numerical simulation (DNS) of the Navier-Stokes equations. We derive the de Kármán-Howarth equation for both the Clark-α and Leray-α models. We confirm one of two possible scalings resulting from this equation for Clark-α as well as its associated k-1 energy spectrum. At subfilter scales, Clark-α possesses similar total dissipation and characteristic time to reach a statistical turbulent steady state as Navier-Stokes, but exhibits greater intermittency. As a SGS model, Clark-α reproduces the large-scale energy spectrum and intermittency properties of the DNS. For the Leray-α model, increasing the filter width α decreases the nonlinearity and, hence, the effective Reynolds number is substantially decreased. Therefore, even for the smallest value of α studied Leray-α was inadequate as a SGS model. The LANS-α energy spectrum ∼k1, consistent with its so-called "rigid bodies," precludes a reproduction of the large-scale energy spectrum of the DNS at high Re while achieving a large reduction in numerical resolution. We find, however, that this same feature reduces its intermittency compared to Clark-α (which shares a similar de Kármán-Howarth equation). Clark-α is found to be the best approximation for reproducing the total dissipation rate and the energy spectrum at scales larger than α, whereas high-order intermittency properties for larger values of α are best reproduced by LANS-α. © 2008 American Institute of Physics.

Descripción: Relativistic effects on nuclear magnetic shielding constants in HX and CH 3X, where X is either Br or I, were investigated using elimination of small component (ESC) approach. The values of σ(X) were found to affected by relativistic corrections. Large negative contributions correcting the dimagnetic terms were observed that when the effect of electron-positron rotations was included within RC-ESC approach. The results show that some overall shifts from HX to CH 3X is dominated by nonrelativistic effects.

Descripción: A two-component theory for shielding calculations starting from a four-component Rayleigh-Schrodinger perturbation theory (RSPT) formalism is presented. Thus, a set of operators entering the RSPT expressions in terms of the Schrodinger molecular spectrum are derived by expanding such four-component expression as a power series in c-1. All formal expressions are retained, without neglecting any terms in the intermediate steps of the derivation.

Descripción: A simple model based on an approximation of the dropletlike model is formulated for studying adsorption of fluids into cylindrical pores. This model yields a nearly universal description of capillary condensation transitions for noble gases confined by alkali metals. The system’s thermodynamical behavior is predicted from the values of two dimensionless parameters: [formula presented] (the reduced asymptotic strength of the fluid-adsorber interaction, a function of temperature) and [formula presented] (the reduced radius of the pore). The phenomenon of hysteresis inherently related to capillary condensation is discussed. The connection to a previously proposed universality for cylindrical pores is also established. © 2002 The American Physical Society.

Descripción: Fil:Mocskos, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.

Descripción: The conventional random phase approximation (RPA) of the polarization propagator theory and a computational method based on continuous transformation of origin for the current density (CTOCD) induced within the electron cloud by an external homogeneous, static magnetic field has been employed to calculate atomic contributions to magnetic susceptibilities. The diamagnetic part of the magnetic susceptibility is written in terms of the polarization propagator. Since the paramagnetic term may also be obtained from the propagator it is thus possible to compute both contributions at the same level of approximation. The evaluated average susceptibility is independent of the origin of the vector potential, but depends on the origin of the reference frame. The atomic contributions to the diamagnetic and paramagnetic parts of the magnetic susceptibility are derived by applying off-diagonal hypervirial relations which are exactly fulfilled if the state functions are exact eigenfunctions of a model Hamiltonian. The rationalization of the magnetic susceptibilities into atomic contributions is applied to some small molecules: HF, H2O, NH3 and CH4, and the sum of these contributions is compared to the corresponding calculated total values and the experimental data for the molecular magnetic susceptibility for the same compounds. Computations are performed using basis sets of increasing quality. A series of sum rules for gauge independence of the computed results and charge-current conservation have been tested to document the accuracy of the calculation of magnetic properties. © 1999 American Institute of Physics.

Descripción: A biclique is a maximal induced complete bipartite subgraph of a graph. We investigate the intersection structure of edge-sets of bicliques in a graph. Specifically, we study the associated edge-biclique hypergraph whose hyperedges are precisely the edge-sets of all bicliques. We characterize graphs whose edge-biclique hypergraph is conformal (i.e., it is the clique hypergraph of its 2-section) by means of a single forbidden induced obstruction, the triangular prism. Using this result, we characterize graphs whose edge-biclique hypergraph is Helly and provide a polynomial time recognition algorithm. We further study a hereditary version of this property and show that it also admits polynomial time recognition, and, in fact, is characterized by a finite set of forbidden induced subgraphs. We conclude by describing some interesting properties of the 2-section graph of the edge-biclique hypergraph. © 2011 Elsevier B.V. All rights reserved.

Descripción: An alternative approach for the calculation of the electron-positron (e-p) contribution to magnetic properties based on two-component Breit-Pauli spinors is presented. In it, the elimination of the small component scheme is applied to the inverse propagator matrix of e-p pairs. The effect of the positronic manifold is expressed as an operator acting on Breit-Pauli spinors. The operator form thus obtained sums up the relativistic correction as a geometric series and as a result a totally different behavior in the vicinity of a nucleus is obtained as compared to the one of the linear response approximation. This feature has deep influence in numerical values of the e-p contribution to the nuclear magnetic shielding of heavy atoms. Numerical calculations carried out for Kr, Xe, and I show that with this approach, the e-p contributions to this property are in good agreement with those of four-component methods. © 2009 American Institute of Physics.

Descripción: In order to describe the development of plateaus such as the Tibet and the Altiplano we extend the two-layer model used in a previous paper [C. A. Perazzo and J. Gratton, Phys. Fluids22, 056603 (2010)] to reproduce the evolution of mountain ranges. As before, we consider the convergent motion of a system of two liquid layers to simulate the crust and the upper mantle that form a lithospheric plate, but now we assume that the viscosity of the crust falls off abruptly at a specified depth. We derive a nonlinear differential equation for the evolution of the thickness of the crust. The solution of this equation shows that the process consists of a first stage in which a peaked range is formed and grows until its root reaches the depth where its viscosity drops. After that the range ceases to grow in height and a flat plateau appears at its top. In this second stage the plateau width increases linearly with time as its sides move outward as traveling waves. We derive simple approximate formulas for various properties of the plateau and its evolution. © 2011 American Institute of Physics.

Descripción: A novel method for simulating the statistical mechanics of molecular systems in which both nuclear and electronic degrees of freedom are treated quantum mechanically is presented. The scheme combines a path integral description of the nuclear variables with a first-principles adiabatic description of the electronic structure. The electronic problem is solved for the ground state within a density functional approach, with the electronic orbitals expanded in a localized (Gaussian) basis set. The discretized path integral is computed by a METROPOLIS Monte Carlo sampling technique on the normal modes of the isomorphic ring polymer. An effective short-time action correct to order τ4 is used. The validity and performance of the method are tested by studying two small lithium clusters, namely Li4 and Li5+. Structural and electronic properties computed within this fully quantum-mechanical scheme are presented and compared to those obtained within the classical nuclei approximation. Quantum delocalization effects turn out to be significant as shown by the fact that quantum simulation results at 50 K approximately correspond to those of classical simulations carried out at 150 K. The scaling factor depends, however, on the specific physical property, thus evidencing the different character of quantum and thermal correlations. Tunneling turns out to be irrelevant in the temperature range investigated (50-200 K). © 1998 American Institute of Physics.

Descripción: We investigate an unsteady plane viscous gravity current of silicone oil on a horizontal glass substrate. Within the lubrication approximation with gravity as the dominant force, this current is described by the nonlinear diffusion equation [Formula Presented]=([Formula Presented][Formula Presented][Formula Presented] (φ is proportional to the liquid thickness h and m=3>0), which is of interest in many other physical processes. The solutions of this equation display a fine example of the competition between diffusive smoothening and nonlinear steepening. This work concerns the so-called waiting-time solutions, whose distinctive character is the presence of an interface or front, separating regions with h≠/0 and h=0, that remains motionless for a finite time interval [Formula Presented] meanwhile a redistribution of h takes place behind the interface. We start the experiments from an initial wedge-shape configuration [h(x)≊[Formula Presented]([Formula Presented]-x)] with a small angle ([Formula Presented]⩽0.12 rad). In this situation, the tip of the wedge, situated at [Formula Presented] from the rear wall (15 cm⩽[Formula Presented]⩽75 cm), waits at least several seconds before moving. During this waiting stage, a region characterized by a strong variation of the free surface slope (corner layer) develops and propagates toward the front while it gradually narrows and [Formula Presented]h/∂[Formula Presented] peaks. The stage ends when the corner layer overtakes the front. At this point, the liquid begins to spread over the uncovered substrate. We measure the slope of the free surface in a range ≊10 cm around [Formula Presented], and, by integration, we determine the fluid thickness h(x) there. We find that the flow tends to a self-similar behavior when the corner layer position tends to [Formula Presented]; however, near the end of the waiting stage, it is perturbed by capillarity. Even if some significant effects are not included in the above equation, the main properties of its solutions are well displayed in the experiments © 1996 The American Physical Society.