A simple topological model with continuous phase transition

In the area of topological and geometric treatment of phase transitions and symmetry breaking in Hamiltonian systems, in a recent paper some general sufficient conditions for these phenomena in $\mathbb{Z}_2$-symmetric systems (i.e. invariant under reflection of coordinates) have been found out. In this paper we present a simple topological model satisfying the above conditions hoping to enlighten the mechanism which causes this phenomenon in more general physical models. The symmetry breaking is testified by a continuous magnetization with a nonanalytic point in correspondence of a critical temperature which divides the broken symmetry phase from the unbroken one. A particularity with respect to the common pictures of a phase transition is that the nonanalyticity of the magnetization is not accompanied by a nonanalytic behavior of the free energy.Comment: 17 pages, 7 figure

Topological conditions for discrete symmetry breaking and phase transitions

In the framework of a recently proposed topological approach to phase transitions, some sufficient conditions ensuring the presence of the spontaneous breaking of a Z_2 symmetry and of a symmetry-breaking phase transition are introduced and discussed. A very simple model, which we refer to as the hypercubic model, is introduced and solved. The main purpose of this model is that of illustrating the content of the sufficient conditions, but it is interesting also in itself due to its simplicity. Then some mean-field models already known in the literature are discussed in the light of the sufficient conditions introduced here

Accurate quadratic-response approximation for the self-consistent pseudopotential of semiconductor nanostructures

Quadratic-response theory is shown to provide a conceptually simple but accurate approximation for the self-consistent one-electron potential of semiconductor nanostructures. Numerical examples are presented for GaAs/AlAs and InGaAs/InP (001) superlattices using the local-density approximation to density-functional theory and norm-conserving pseudopotentials without spin-orbit coupling. When the reference crystal is chosen to be the virtual-crystal average of the two bulk constituents, the absolute error in the quadratic-response potential for Gamma(15) valence electrons is about 2 meV for GaAs/AlAs and 5 meV for InGaAs/InP. Low-order multipole expansions of the electron density and potential response are shown to be accurate throughout a small neighborhood of each reciprocal lattice vector, thus providing a further simplification that is confirmed to be valid for slowly varying envelope functions. Although the linear response is about an order of magnitude larger than the quadratic response, the quadratic terms are important both quantitatively (if an accuracy of better than a few tens of meV is desired) and qualitatively (due to their different symmetry and long-range dipole effects).Comment: 16 pages, 20 figures; v2: new section on limitations of theor

Dynamical-charge neutrality at a crystal surface

For both molecules and periodic solids, the ionic dynamical charge tensors which govern the infrared activity are known to obey a dynamical neutrality condition. This condition enforces their sum to vanish (over the whole finite system, or over the crystal cell, respectively). We extend this sum rule to the non trivial case of the surface of a semiinfinite solid and show that, in the case of a polar surface of an insulator, the surface ions cannot have the same dynamical charges as in the bulk. The sum rule is demonstrated through calculations for the Si-terminated SiC(001) surface.Comment: 4 pages, latex file, 1 postscript figure automatically include

Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion

We describe how to apply the recently developed pole expansion and selected inversion (PEXSI) technique to Kohn-Sham density function theory (DFT) electronic structure calculations that are based on atomic orbital discretization. We give analytic expressions for evaluating the charge density, the total energy, the Helmholtz free energy and the atomic forces (including both the Hellman-Feynman force and the Pulay force) without using the eigenvalues and eigenvectors of the Kohn-Sham Hamiltonian. We also show how to update the chemical potential without using Kohn-Sham eigenvalues. The advantage of using PEXSI is that it has a much lower computational complexity than that associated with the matrix diagonalization procedure. We demonstrate the performance gain by comparing the timing of PEXSI with that of diagonalization on insulating and metallic nanotubes. For these quasi-1D systems, the complexity of PEXSI is linear with respect to the number of atoms. This linear scaling can be observed in our computational experiments when the number of atoms in a nanotube is larger than a few hundreds. Both the wall clock time and the memory requirement of PEXSI is modest. This makes it even possible to perform Kohn-Sham DFT calculations for 10,000-atom nanotubes with a sequential implementation of the selected inversion algorithm. We also perform an accurate geometry optimization calculation on a truncated (8,0) boron-nitride nanotube system containing 1024 atoms. Numerical results indicate that the use of PEXSI does not lead to loss of accuracy required in a practical DFT calculation

Indexação Multidimensional para Problemas da Mochila Multiobjetivo com Paretos de Alta Cardinalidade

"Diversos problemas reais envolvem a otimização simultânea de múltiplos critérios, os quais são, geralmente, conflitantes entre si. Estes problemas são denominados multiobjetivo e não possuem uma única solução, mas um conjunto de soluções de interesse, denominadas soluções eficientes ou não dominadas. Um dos grande desafios a serem enfrentados na resolução deste tipo de problema é o tamanho do conjunto solução, que tende a crescer rapidamente dado o tamanho da instância, degradando a performance dos algoritmos. Dentre os problemas multiobjetivos mais estudados está o problema da mochila multiobjetivo, pelo qual diversos problemas reais podem ser modelados. Este trabalho propõe a aceleração do processo de solução do problema da mochila multiobjetivo, através da utilizando da árvore k-d como estrutura de indexação multidimensional para auxiliar a manipulação das soluções. A performance da abordagem é analisada através de experimentos computacionais, realizados no contexto exato utilizando um algoritmo estado da arte. Testes também são realizados no contexto heurístico, utilizando a adaptação de uma meta-heurística para o problema em questão, sendo esta também uma contribuição do presente trabalho. Segundo os resultados, para o contexto exato a proposta foi eficaz, apresentam speedup de até 2.3 para casos bi-objetivo e 15.5 em casos 3-objetivo, não sendo porém eficaz no contexto heurístico, apresentando pouco impacto no tempo computacional. Em todos os casos, porém, houve considerável redução no número de avaliações de soluções.

Um Estudo da Eficiência da Autocentralidade no Problema de Isomorfismo de Grafos

Este trabalho trata da aplicação da autocentralidade na resolução do Problema de Isomorfismo de Grafos. Esta propriedade, retirada da teoria espectral de grafos, foi utilizada por Philippe Santos em [SANTOS 2010] para a proposta de um algoritmo espectral para resolução deste problema. Uma adaptação do método das potências é proposta para o cálculo das autocentralidades produzindo uma versão competitiva do algoritmo espectral proposto em [SANTOS 2010]. Baseado nesta adaptação, é feito um estudo da eficiência da autocentralidade na resolução do Problema de Isomorfismo. Além disso, é Algoritmo de Rotulação Iterativa Baseado em Medidas de Centralidades, que pode ser aplicado a qualquer tipo de grafo, inclusive grafos regulares. Uma bateria de testes computacionais foi realizada para comparar os dois algoritmos propostos com alguns bemconhecidos na literatura, como o Nauty

Medium polarization isotopic effects on nuclear binding energies

There exist several effective interactions whose parameters are fitted to force mean field predictions to reproduce experimental findings of finite nuclei and calculated properties of infinite nuclear matter. Exploiting this tecnique one can give a good description of nuclear binding energies. We present evidence that further progress can be made by taking into account medium polarization effects associated with surface and pairing vibrations.Comment: 7 pages, 5 figure

Is renalase a novel player in catecholaminergic signaling? The mystery of the catalytic activity of an intriguing new flavoenzyme

Renalase is a flavoprotein recently discovered in humans, preferentially expressed in the proximal tubules of the kidney and secreted in blood and urine. It is highly conserved in vertebrates, with homologs identified in eukaryotic and prokaryotic organisms. Several genetic, epidemiological, clinical and experimental studies show that renalase plays a role in the modulation of the functions of the cardiovascular system, being particularly active in decreasing the catecholaminergic tone, in lowering blood pressure and in exerting a protective action against myocardial ischemic damage. Deficient renalase synthesis might be the cause of the high occurrence of hypertension and adverse cardiac events in kidney disease patients. Very recently, recombinant human renalase has been structurally and functionally characterized in vitro. Results show that it belongs to the p-hydroxybenzoate hydroxylase structural family of flavoenzymes, contains non-covalently bound FAD with redox features suggestive of a dehydrogenase activity, and is not a catecholamine-degrading enzyme, either through oxidase or NAD(P)H-dependent monooxygenase reactions. The biochemical data now available will hopefully provide the basis for a systematic and rational quest toward the identification of the reaction catalyzed by renalase and of the molecular mechanism of its physiological action, which in turn are expected to favor the development of novel therapeutic tools for the treatment of kidney and cardiovascular diseases