Propriedades eletrônicas e estruturais do PbTiO3: teoria do funcional de densidade aplicada a modelos periódicos

Calculations based on density functional theory at the B3LYP hybrid functional level applied to periodic models have been performed to characterize the structural and electronic properties of PbTiO3. Two different slab terminations (PbO and TiO2) have been considered to obtain and discuss the results of band structure, density of states, charge distribution on bulk and surface relaxation. It is observed that the relaxation processes are most prominent for the Ti and Pb surface atoms. The electron density maps confirm the partial covalent character of the Ti-O bonds. The calculated optical band gap and other results are in agreement with experimental data.

On the photoluminescence behavior of samarium-doped strontium titanate nanostructures under UV light. A structural and electronic understanding

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Propriedades eletrônicas e estruturais do PbTiO3: teoria do funcional de densidade aplicada a modelos periódicos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Er3+ as marker for order-disorder determination in the PbTiO3 system

Er3+ ions were added to the PbTiO3 network using the polymeric precursor method to characterize the order-disorder transformation found in this material by means of experimental and theoretical approach. The disordered and ordered material structures were studied by photoluminescence measurements, X-ray diffraction (XRD) and U-V-visible spectroscopy. The Er3+ ions served as a marker to identify the structural short-range order beginning in the PbTiO3 matrix. From photoluminescence results it was concluded that disordered PbTiO3 powders have a certain short range order in the network that are undetected by XRD measurements. The electronic structures were calculated by the ab initio periodic method in DFT level with the non-local B3LYP hybrid approximation for the Ti atom site interpretation using density of states (DOS) results. This analysis enabled understanding that Ti atom sphere coordination can create possible states for radioactive return and trap of electron-holes pair. (c) 2007 Elsevier B.V. All rights reserved.

Correlation among order-disorder, electronic levels, and photoluminescence in amorphous CT : Sm

Ca0.95Sm0.05TiO3 (CT:Sm) powder was prepared by the polymeric precursor method (PPM). Order-disorder at short and long range has been investigated by means of Raman spectroscopy, X-ray diffraction (XRD), and photoluminescence emission (PL) experimental techniques. The broad PL band and the Sm emission spectrum measured at room temperature indicate the increase of structural order with annealing temperature. The measured PL emission reveals that the PL intensity changes with the degree of disorder in the CT: Sm. The electronic structures were performed by the ab initio periodic method in the DFT level with the hybrid nonlocal B3LYP approximation. Theoretical results are analyzed in terms of DOS, charge densities, and Mulliken charges. Localized levels into the band gap of the CT: Sm material favor the creation of the electron-hole pair, supporting the observed room-temperature PL phenomenon.

Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

"Vegeu el resum a l'inici del document del fitxer adjunt."

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.

Preparation of TiO2/SnO2 Thin Films by Sol-Gel Method and Periodic B3LYP Simulations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Some Computational Aspects of the Consistent Mass Finite Element Method for a (semi-)periodic Eigenvalue Problem

We consider a model eigenvalue problem (EVP) in 1D, with periodic or semi–periodic boundary conditions (BCs). The discretization of this type of EVP by consistent mass finite element methods (FEMs) leads to the generalized matrix EVP Kc = λ M c, where K and M are real, symmetric matrices, with a certain (skew–)circulant structure. In this paper we fix our attention to the use of a quadratic FE–mesh. Explicit expressions for the eigenvalues of the resulting algebraic EVP are established. This leads to an explicit form for the approximation error in terms of the mesh parameter, which confirms the theoretical error estimates, obtained in [2].

A new method to calculate the periodic steady state of sequencing batch reactors for biological wastewater treatment : model development and applications

Peer reviewed

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.

UNIQUENESS AND NONUNIQUENESS RESULTS FOR A CERTAIN CLASS OF ALMOST PERIODIC DISTRIBUTIONS

We consider distributions u is an element of S'(R) of the form u(t) = Sigma(n is an element of N) a(n)e(i lambda nt), where (a(n))(n is an element of N) subset of C and Lambda = (lambda n)(n is an element of N) subset of R have the following properties: (a(n))(n is an element of N) is an element of s', that is, there is a q is an element of N such that (n(-q) a(n))(n is an element of N) is an element of l(1); for the real sequence., there are n(0) is an element of N, C > 0, and alpha > 0 such that n >= n(0) double right arrow vertical bar lambda(n)vertical bar >= Cn(alpha). Let I(epsilon) subset of R be an interval of length epsilon. We prove that for given Lambda, (1) if Lambda = O(n(alpha)) with alpha < 1, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (2) if Lambda = O(n) is uniformly discrete, then there exists epsilon > 0 such that u vertical bar I(epsilon) = 0 double right arrow u 0; (3) if alpha > 1 and. is uniformly discrete, then for all epsilon > 0, u vertical bar I(epsilon) = 0 double right arrow u = 0. Since distributions of the above mentioned form are very common in engineering, as in the case of the modeling of ocean waves, signal processing, and vibrations of beams, plates, and shells, those uniqueness and nonuniqueness results have important consequences for identification problems in the applied sciences. We show an identification method and close this article with a simple example to show that the recovery of geometrical imperfections in a cylindrical shell is possible from a measurement of its dynamics.

POSITIVITY PROPERTIES OF THE FOURIER TRANSFORM AND THE STABILITY OF PERIODIC TRAVELLING-WAVE SOLUTIONS

In this paper we establish a method to obtain the stability of periodic travelling-wave solutions for equations of Korteweg-de Vries-type u(t) + u(p)u(x) - Mu(x) = 0, with M being a general pseudodifferential operator and where p >= 1 is an integer. Our approach uses the theory of totally positive operators, the Poisson summation theorem, and the theory of Jacobi elliptic functions. In particular we obtain the stability of a family of periodic travelling waves solutions for the Benjamin Ono equation. The present technique gives a new way to obtain the existence and stability of cnoidal and dnoidal waves solutions associated with the Korteweg-de Vries and modified Korteweg-de Vries equations, respectively. The theory has prospects for the study of periodic travelling-wave solutions of other partial differential equations.