On Polynomial Relations in the Heisenberg Algebra

Polynomial relations between the generators of the classical and quantum Heisenberg algebras are presented. Some of those relations can have a meaning of the formulas of the normal ordering for the creation/annihilation operators occurred in the method of the second quantization.Comment: 10 pages, Preprint CRN 94/08 and IFUNAM FT 94-41 (corrected), LaTeX The title is changed, the paper is expanded, extra references are added, typos are correcte

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200

Dynamics of vascular branching morphogenesis: the effect of blood and tissue flow

Vascularization of embryonic organs or tumors starts from a primitive lattice of capillaries. Upon perfusion, this lattice is remodeled into branched arteries and veins. Adaptation to mechanical forces is implied to play a major role in arterial patterning. However, numerical simulations of vessel adaptation to haemodynamics has so far failed to predict any realistic vascular pattern. We present in this article a theoretical modeling of vascular development in the yolk sac based on three features of vascular morphogenesis: the disconnection of side branches from main branches, the reconnection of dangling sprouts ('dead ends'), and the plastic extension of interstitial tissue, which we have observed in vascular morphogenesis. We show that the effect of Poiseuille flow in the vessels can be modeled by aggregation of random walkers. Solid tissue expansion can be modeled by a Poiseuille (parabolic) deformation, hence by deformation under hits of random walkers. Incorporation of these features, which are of a mechanical nature, leads to realistic modeling of vessels, with important biological consequences. The model also predicts the outcome of simple mechanical actions, such as clamping of vessels or deformation of tissue by the presence of obstacles. This study offers an explanation for flow-driven control of vascular branching morphogenesis

Physical Acoustics

Contains reports on two research projects.U. S. Navy (Office of Naval Research) under Contract Nonr-1841(42)National Aeronautics and Space Administratio

Goldstone-Mode Phonon Dynamics in the Pyrochlore Cd2Re2O7

We have measured the polarized Raman scattering spectra of Cd2Re2O7, the first superconducting pyrochlore, as a function of temperature. For temperatures below the cubic-to-tetragonal structural phase transition (SPT) at 200K, a peak with B1 symmetry develops at zero frequency with divergent intensity. We identify this peak as the first observation of the Goldstone phonon in a crystalline solid. The Goldstone phonon is a collective excitation that exists due to the breaking of the continuous symmetry with the SPT. Its emergence coincides with that of a Raman-active soft mode. The order parameter for both features derives from an unstable doubly-degenerate vibration (with Eu symmetry) of the O1 atoms which drives the SPT.Comment: 4+ pages, 4 figures. Updated figures and text. Accepted to PR

Biharmonic pattern selection

A new model to describe fractal growth is discussed which includes effects due to long-range coupling between displacements $u$. The model is based on the biharmonic equation $\nabla^{4}u =0$ in two-dimensional isotropic defect-free media as follows from the Kuramoto-Sivashinsky equation for pattern formation -or, alternatively, from the theory of elasticity. As a difference with Laplacian and Poisson growth models, in the new model the Laplacian of $u$ is neither zero nor proportional to $u$. Its discretization allows to reproduce a transition from dense to multibranched growth at a point in which the growth velocity exhibits a minimum similarly to what occurs within Poisson growth in planar geometry. Furthermore, in circular geometry the transition point is estimated for the simplest case from the relation $r_{\ell}\approx L/e^{1/2}$ such that the trajectories become stable at the growing surfaces in a continuous limit. Hence, within the biharmonic growth model, this transition depends only on the system size $L$ and occurs approximately at a distance $60 \%$ far from a central seed particle. The influence of biharmonic patterns on the growth probability for each lattice site is also analysed.Comment: To appear in Phys. Rev. E. Copies upon request to [email protected]

Facebook, a nova arquibancada para o marketing de relacionamento

This paper aims to relate the marketing strategies adopted by football teams in social media networks with an increasing number of users and their interactions on the fanpage of each football club. Information was gathered from the top Brazilian football teams in the first and second divisions in 2013 on Facebook. The findings show that Authenticity, Disclosure and Information Dissemination are positively related to increasing the number of users. Authenticity impacts directly in the number of interactions, reinforcing the need for an active management of the fanpages. The findings show that the professional management of a Facebook page contributes positively to the increase in the number of fans on its pages. This allows clubs to model new relationship strategies with their fans and sponsors.Keywords: social media, social network sites, relationship marketing, marketing strategy, Facebook, sports management.Este artigo tem como objetivo relacionar as estratégias de marketing adotadas por equipes de futebol em redes sociais com o aumento no número de usuários e de suas interações na fanpage de cada clube. Para atingir esse objetivo, coletaram-se informações das principais equipes da primeira e segunda divisão de futebol brasileiro em 2013 no Facebook. As descobertas mostram que a Autenticidade, a Divulgação e a Informação são positivamente relacionadas com o aumento de usuários. A Autenticidade impacta diretamente no número de interações, reforçando a necessidade de uma gestão ativa das páginas. As descobertas mostram que o gerenciamento profissional de páginas do Facebook contribui positivamente para o aumento do número de fãs em suas páginas. Isso permite aos clubes modelar novas estratégias de relacionamento com seus fãs e patrocinadores.Palavras-chave: mídia social, sites de redes sociais, marketing de relacionamento, estratégia de marketing, Facebook, marketing esportivo

Strategy for Enhancing Ultrahigh-Molecular-Weight Block Copolymer Chain Mobility to Access Large Period Sizes (>100 nm)

Assembling ultrahigh-molecular-weight (UHMW) block copolymers (BCPs) in rapid time scales is perceived as a grand challenge in polymer science due to slow kinetics. Through surface engineering and identifying a nonvolatile solvent (propylene glycol methyl ether acetate, PGMEA), we showcase the impressive ability of a series of lamellar poly(styrene)-block-poly(2-vinylpyridine) (PS-b-P2VP) BCPs to self-assemble directly after spin-coating. In particular, we show the formation of large-period (≈111 nm) lamellar structures from a neat UHMW PS-b-P2VP BCP. The significant influence of solvent–polymer solubility parameters are explored to enhance the polymer chain mobility. After optimization using solvent vapor annealing, increased feature order of ultralarge-period PS-b-P2VP BCP patterns in 1 h is achieved. Isolated metallic and dielectric features are also demonstrated to exemplify the promise that large BCP periods offer for functional applications. The methods described in this article center on industry-compatible patterning schemes, solvents, and deposition techniques. Thus, our straightforward UHMW BCP strategy potentially paves a viable and practical path forward for large-scale integration in various sectors, e.g., photonic band gaps, polarizers, and membranes that demand ultralarge period sizes

Theory of Non-Reciprocal Optical Effects in Antiferromagnets: The Case Cr_2O_3

A microscopic model of non-reciprocal optical effects in antiferromagnets is developed by considering the case of Cr_2O_3 where such effects have been observed. These effects are due to a direct coupling between light and the antiferromagnetic order parameter. This coupling is mediated by the spin-orbit interaction and involves an interplay between the breaking of inversion symmetry due to the antiferromagnetic order parameter and the trigonal field contribution to the ligand field at the magnetic ion. We evaluate the matrix elements relevant for the non-reciprocal second harmonic generation and gyrotropic birefringence.Comment: accepted for publication in Phys. Rev.