Statistical thermodynamics of lattice models in zeolites: Implications of local versus global mean field interactions

The statistical thermodynamics of adsorption in caged zeolites is developed by treating the zeolite as an ensemble of M identical cages or subsystems. Within each cage adsorption is assumed to occur onto a lattice of n identical sites. Expressions for the average occupancy per cage are obtained by minimizing the Helmholtz free energy in the canonical ensemble subject to the constraints of constant M and constant number of adsorbates N. Adsorbate-adsorbate interactions in the Brag-Williams or mean field approximation are treated in two ways. The local mean field approximation (LMFA) is based on the local cage occupancy and the global mean field approximation (GMFA) is based on the average coverage of the ensemble. The GMFA is shown to be equivalent in formulation to treating the zeolite as a collection of interacting single site subsystems. In contrast, the treatment in the LMFA retains the description of the zeolite as an ensemble of identical cages, whose thermodynamic properties are conveniently derived in the grand canonical ensemble. For a z coordinated lattice within the zeolite cage, with epsilon(aa) as the adsorbate-adsorbate interaction parameter, the comparisons for different values of epsilon(aa)(*)=epsilon(aa)z/2kT, and number of sites per cage, n, illustrate that for -1 0. We compare the isotherms predicted with the LMFA with previous GMFA predictions [K. G. Ayappa, C. R. Kamala, and T. A. Abinandanan, J. Chem. Phys. 110, 8714 (1999)] (which incorporates both the site volume reduction and a coverage-dependent epsilon(aa)) for xenon and methane in zeolite NaA. In all cases the predicted isotherms are very similar, with the exception of a small steplike feature present in the LMFA for xenon at higher coverages. (C) 1999 American Institute of Physics. [S0021-9606(99)70333-8].

Electronic structure of Mn-doped ZnO quantum wires: A mean-field theory study

Based on the effective-mass model and the mean-field approximation, we investigate the energy levels of the electron and hole states of the Mn-doped ZnO quantum wires (x=0.0018) in the presence of the external magnetic field. It is found that either twofold degenerated electron or fourfold degenerated hole states split in the field. The splitting energy is about 100 times larger than those of undoped cases. There is a dark exciton effect when the radius R is smaller than 16.6 nm, and it is independent of the effective doped Mn concentration. The lowest state transitions split into six Zeeman components in the magnetic field, four sigma(+/-) and two pi polarized Zeeman components, their splittings depend on the Mn-doped concentration, and the order of pi and sigma(+/-) polarized Zeeman components is reversed for thin quantum wires (R < 2.3 nm) due to the quantum confinement effect.

Synthesis, crystal structure and magnetic properties of a chain coordination polymer {[Cu4L2(H2O)] center dot H2O}(n)

A chain coordination polymer with the chemical formula {[Cu4L2(H2O)] (.) H2O)(n), has been synthesized by the assembly reaction of K(2)CuL(.)1.5H(2)O and Cu(OAC)(2)(H2O)-H-. with a 1:1 mole ratio in methanol., where H4L=2-hydroxy-3-[(E)-({2-[(2-hydroxybenzoyl)imino]ethyl I imino)methyl] benzoic acid, OAC(-) = CH3COO-. The crystal structure was determined by single-crystal X-ray diffraction analysis, the compound has chain molecular structure formed by dissymmetrical tetranuclear units. The magnetic measurements showed that Cu-Cu of the complex exhibit antiferromagnetic interactions, and satisfactory fittings to the observed magnetic susceptibility data were obtained by assuming a binuclear system, and further using molecular field approximation to deal with magnetic exchange interactions between binuclear systems.

A combined DFT and SCRF study of solvent effects on 4-methyl-3-penten-2-one

The IR spectrum of 4-methyl-3-penten-2-one is interpreted with the aid of normal coordinate calculations within the Onsager self-consistent reaction field (SCRF) model, using a density functional theory (DFT) method at the Becke3LYP/6-31G* level. The solvent effects on the geometry, energy, dipole moment, and vibrational frequencies of 4-methyl-3-penten-2-one in the solution and in the liquid phase are calculated using the Onsager SCRF model. The calculated vibrational frequencies in the liquid-phase are in good agreement with the experimental values. The solvent reaction field has generally weak influence. For the two main bands of C=C and C=O mixed vibrational modes, small frequency shifts (5-6 cm(-1)), but relatively large changes in IR intensities (up to 101 km mol(-1) in the liquid phase) are found. (C) 1999 Elsevier Science BV. All rights reserved.

Testing numerical implementations of strong-field electrodynamics

We test current numerical implementations of laser-matter interactions by comparison with exact analytical results. Focusing on photon emission processes, it is found that the numerics accurately reproduce analytical emission spectra in all considered regimes, except for the harmonic structures often singled out as the most significant high-intensity (multiphoton) effects. We find that this discrepancy originates in the use of the locally constant field approximation.

Electric field alignment in thin films of cylinder-forming diblock copolymer

We investigate thin films of cylinder-forming diblock copolymer confined between electrically charged parallel plates, using self-consistent-field theory ( SCFT) combined with an exact treatment for linear dielectric materials. Our study focuses on the competition between the surface interactions, which tend to orient cylinder domains parallel to the plates, and the electric field, which favors a perpendicular orientation. The effect of the electric field on the relative stability of the competing morphologies is demonstrated with equilibrium phase diagrams, calculated with the aid of a weak-field approximation. As hoped, modest electric fields are shown to have a significant stabilizing effect on perpendicular cylinders, particularly for thicker films. Our improved SCFT-based treatment removes most of the approximations implemented by previous approaches, thereby managing to resolve outstanding qualitative inconsistencies among different approximation schemes.

pK determination. A mean field, Poisson-Boltzmann approach

A model describing dissociation of monoprotonic acid and a method for the determination of its pK value are presented. The model is based on a mean field approximation. The Poisson-Boltzmann equation, adopting spherical symmetry, is numerically solved, and the solution of its linearized form is written. By use of the pH values of a dilution experiment of galacturonic acid as the entry data, the proposed method allowed estimation of the value of pK = 3.25 at a temperature of 25 degrees C. Values for the complex dimensions and dissociation degree are calculated using experimental pH values for solution concentration values ranging from 0.1 to 60 mM. The present analysis leads to the conclusion that the Poisson-Boltzmann equation or its linear form is equally suited for the description of such systems.

Dynamical mean-field study of strongly interacting Bose-Einstein condensate

The experimental results of Rb-85 Bose-Einstein condensates are analyzed within the mean-field approximation with time-dependent two-body interaction and dissipation due to three-body recombination. We found that the magnitude of the dissipation is consistent with the three-body theory for longer rise times. However, for shorter rise times, it occurs an enhancement of this parameter, consistent with a coherent dimer formation. (C) 2004 Elsevier B.V. All rights reserved.

ON THE INDEPENDENT-PARTICLE APPROXIMATION OF GAUGE-THEORIES - A SIMPLE EXAMPLE

In this work the independent particle model formulation is studied as a mean-field approximation of gauge theories using the path integral approach in the framework of quantum electrodynamics in 1 + 1 dimensions. It is shown how a mean-field approximation scheme can be applied to fit an effective potential to an independent particle model, building a straightforward relation between the model and the associated gauge field theory. An example is made considering the problem of massive Dirac fermions on a line, the so called massive Schwinger model. An interesting result is found, indicating a behaviour of screening of the charges in the relativistic limit of strong coupling. A forthcoming application of the method developed to confining potentials in independent quark models for QCD is in view and is briefly discussed.

Dinâmica das transições quiral e de desconfinamento da cromodinâmica quântica com o modelo Polyakov-Nambu-Jona-Lasinio

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the motion of particles in covariant Horava-Lifshitz gravity and the meaning of the A-field

We studied the low energy motion of particles in the general covariant. version of Horava-Lifshitz gravity proposed by Horava and Melby-Thompson. Using a scalar field coupled to gravity according to the minimal substitution recipe proposed by da Silva and taking the geometrical optics limit, we could write an effective relativistic metric for a general solution. As a result, we discovered that the equivalence principle is not in general recovered at low energies, unless the spatial Laplacian of A vanishes. Finally, we analyzed the motion on the spherical symmetric solution proposed by Horava and Melby-Thompson, where we could find its effective line element and compute spin-0 geodesics. Using standard methods we have shown that such an effective metric cannot reproduce Newton's gravity law even in the weak gravitational field approximation. (C) 2011 Elsevier B.V All rights reserved.

Pair approximation for a model of vertical and horizontal transmission of parasites.

We apply Stochastic Dynamics method for a differential equations model, proposed by Marc Lipsitch and collaborators (Proc. R. Soc. Lond. B 260, 321, 1995), for which the transmission dynamics of parasites occurs from a parent to its offspring (vertical transmission), and by contact with infected host (horizontal transmission). Herpes, Hepatitis and AIDS are examples of diseases for which both horizontal and vertical transmission occur simultaneously during the virus spreading. Understanding the role of each type of transmission in the infection prevalence on a susceptible host population may provide some information about the factors that contribute for the eradication and/or control of those diseases. We present a pair mean-field approximation obtained from the master equation of the model. The pair approximation is formed by the differential equations of the susceptible and infected population densities and the differential equations of pairs that contribute to the former ones. In terms of the model parameters, we obtain the conditions that lead to the disease eradication, and set up the phase diagram based on the local stability analysis of fixed points. We also perform Monte Carlo simulations of the model on complete graphs and Erdös-Rényi graphs in order to investigate the influence of population size and neighborhood on the previous mean-field results; by this way, we also expect to evaluate the contribution of vertical and horizontal transmission on the elimination of parasite. Pair Approximation for a Model of Vertical and Horizontal Transmission of Parasites.

3-D wind field simulation over complex terrain

[EN]A new methodology for wind field simulation or forecasting over complex terrain is introduced. The idea is to use wind measurements or predictions of the HARMONIE mesoscale model as the input data for an adaptive finite element mass consistent wind model. The method has been recently implemented in the freely-available Wind3D code. A description of the HARMONIE Non-Hydrostatic Dynamics can be found in. HARMONIE provides wind prediction with a maximum resolution about 1 Km that is refined by the finite element model in a local scale (about a few meters). An interface between both models is implemented such that the initial wind field approximation is obtained by a suitable interpolation of the HARMONIE results…

Solvent induced NMR chemical shifts that arise from molecular encounters

Recently Homer and Percival have postulated that intermolecular van der Waals dispersion forces can be characterized by three mechanisms. The first arises via the mean square reaction field < R1; 2> due to the transient dipole of a particular solute molecule that is considered situated in a cavity surrounded by solvent molecules; this was characterized by an extended Onsager approach. The second stems from the extra cavity mean square reaction field < R2; 2> of the near neighbour solvent molecules. The third originates from square field electric fields E2BI due to a newly characterized effect in which solute atoms are `buffeted' by the peripheral atoms of adjacent solvent molecules. The present work concerns more detailed studies of the buffeting screening, which is governed by sterically controlled parameter (2T - T)2, where and are geometric structural parameters. The original approach is used to characterise the buffeting shifts induced by large solvent molecules and the approach is found to be inadequate. Consequently, improved methods of calculating and are reported. Using the improved approach it is shown that buffeting is dependent on the nature of the solvent as well as the nature of the solute molecule. Detailed investigation of the buffeting component of the van der Waals chemical shifts of selected solutes in a range of solvents containing either H or Cl as peripheral atoms have enabled the determination of a theoretical acceptable value for the classical screening coefficient B for protons. 1H and 13C resonance studies of tetraethylmethane and 1H, 13C and 29Si resonance studies of TMS have been used to support the original contention that three (< R1; 2> , < R2; 2> and E2BI) components of intermolecular van der Waals dispersion fields are required to characterise vdW chemical shifts.

Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.