Analytical Results for the Statistical Distribution Related to Memoryless Deterministic Tourist Walk: Dimensionality Effect and Mean Field Models

Consider a medium characterized by N points whose coordinates are randomly generated by a uniform distribution along the edges of a unitary d-dimensional hypercube. A walker leaves from each point of this disordered medium and moves according to the deterministic rule to go to the nearest point which has not been visited in the preceding \mu steps (deterministic tourist walk). Each trajectory generated by this dynamics has an initial non-periodic part of t steps (transient) and a final periodic part of p steps (attractor). The neighborhood rank probabilities are parameterized by the normalized incomplete beta function I_d = I_{1/4}[1/2,(d+1)/2]. The joint distribution S_{\mu,d}^{(N)}(t,p) is relevant, and the marginal distributions previously studied are particular cases. We show that, for the memory-less deterministic tourist walk in the euclidean space, this distribution is: S_{1,d}^{(\infty)}(t,p) = [\Gamma(1+I_d^{-1}) (t+I_d^{-1})/\Gamma(t+p+I_d^{-1})] \delta_{p,2}, where t=0,1,2,...,\infty, \Gamma(z) is the gamma function and \delta_{i,j} is the Kronecker's delta. The mean field models are random link model, which corresponds to d \to \infty, and random map model which, even for \mu = 0, presents non-trivial cycle distribution [S_{0,rm}^{(N)}(p) \propto p^{-1}]: S_{0,rm}^{(N)}(t,p) = \Gamma(N)/\{\Gamma[N+1-(t+p)]N^{t+p}\}. The fundamental quantities are the number of explored points n_e=t+p and I_d. Although the obtained distributions are simple, they do not follow straightforwardly and they have been validated by numerical experiments.Comment: 9 pages and 4 figure

Derivative expansion of the electromagnetic Casimir energy for two thin mirrors

We extend our previous work on a derivative expansion for the Casimir energy, to the case of the electromagnetic field coupled to two thin, imperfect mirrors. The latter are described by means of vacuum polarization tensors localized on the mirrors. We apply the results so obtained to compute the first correction to the proximity force approximation to the static Casimir effect.Comment: Version to appear in Phys. Rev.

Astrophysics from data analysis of spherical gravitational wave detectors

The direct detection of gravitational waves will provide valuable astrophysical information about many celestial objects. Also, it will be an important test to general relativity and other theories of gravitation. The gravitational wave detector SCHENBERG has recently undergone its first test run. It is expected to have its first scientific run soon. In this work the data analysis system of this spherical, resonant mass detector is tested through the simulation of the detection of gravitational waves generated during the inspiralling phase of a binary system. It is shown from the simulated data that it is not necessary to have all six transducers operational in order to determine the source's direction and the wave's amplitudes.Comment: 8 pages and 3 figure

The proximity force approximation for the Casimir energy as a derivative expansion

The proximity force approximation (PFA) has been widely used as a tool to evaluate the Casimir force between smooth objects at small distances. In spite of being intuitively easy to grasp, it is generally believed to be an uncontrolled approximation. Indeed, its validity has only been tested in particular examples, by confronting its predictions with the next to leading order (NTLO) correction extracted from numerical or analytical solutions obtained without using the PFA. In this article we show that the PFA and its NTLO correction may be derived within a single framework, as the first two terms in a derivative expansion. To that effect, we consider the Casimir energy for a vacuum scalar field with Dirichlet conditions on a smooth curved surface described by a function $\psi$ in front of a plane. By regarding the Casimir energy as a functional of $\psi$, we show that the PFA is the leading term in a derivative expansion of this functional. We also obtain the general form of corresponding NTLO correction, which involves two derivatives of $\psi$. We show, by evaluating this correction term for particular geometries, that it properly reproduces the known corrections to PFA obtained from exact evaluations of the energy.Comment: Minor changes. Version to appear in Phys. Rev.

An explicit Schr\"odinger picture for Aharonov's Modular Variable concept

We propose to address in a natural manner, the modular variable concept explicitly in a Schr\"odinger picture. The idea of Modular Variables was introduced in 1969 by Aharonov, Pendleton and Petersen to explain certain non-local properties of quantum mechanics. Our approach to this subject is based on Schwinger's finite quantum kinematics and it's continuous limit.Comment: 16 pages, 9 figure

Hybrid Systems Based on Talc and Chitosan for Controlled Drug Release

Inorganic matrices and biopolymers have been widely used in pharmaceutical fields. They show properties such as biocompatibility, incorporation capacity, and controlled drug release, which can become more attractive if they are combined to form hybrid materials. This work proposes the synthesis of new drug delivery systems (DDS) based on magnesium phyllosilicate (Talc) obtained by the sol–gel route method, the biopolymer chitosan (Ch), and the inorganic-organic hybrid formed between this matrix (Talc + Ch), obtained using glutaraldehyde as a crosslink agent, and to study their incorporation/release capacity of amiloride as a model drug. The systems were characterized by X-ray diffraction (XRD), Therma analysis TG/DTG, and Fourier-transform infrared spectroscopy (FTIR) that supported the DDS’s formation. The hybrid showed a better drug incorporation capacity compared to the precursors, with a loading of 55.74, 49.53, and 4.71 mg g-1 for Talc + Ch, Talc, and Ch, respectively. The release assays were performed on a Hanson Research SR-8 Plus dissolver using apparatus I (basket), set to guarantee the sink conditions. The in vitro release tests showed a prolongation of the release rates of this drug for at least 4 h. This result proposes that the systems implies the slow and gradual release of the active substance, favoring the maintenance of the plasma concentration within a therapeutic window.This research was funded by FAPEPI to Caio C. Coelho for Scientific Initiation scholarshi

Insetos bentônicos do Rio El Tala (Catamarca, Argentina): Variação longitudinal de sua estrutura e seu uso para avaliar a qualidade da água

The aim of this work was to determine the structure of the benthic entomofauna and its variation along the El Tala River (Catamarca, Argentina). Five sampling stations were established, considering the location of nearby housing with respect to the watercourse. The following variables were determined in situ: altitude, latitude and longitude, bedstream width, river depth, river-current speed, water and air temperatures. Benthic insects were collected with a square parcel sampler of 0.09-m2 area and 300-μm net opening and identified to the family level. Faunal density, richness, and diversity exhibited a longitudinal variation. From sampling Stations 1 (reference site) to 3, the number of orders and families decreased, whereas in sampling Station 4 those values increased and continued to do so through to Station 5 (downstream station). Station 5 showed the highest family richness (17) and the highest value for the Shannon-Wiener index (2.74) and the lowest value in Simpson's Dominance index (D = 0.22). These values could be explained because of the self-cleansing capabilities of the river downstream. The water quality of El Tala River is Class I (very clean and non-impacted), according to the results obtained from the application of the biotic Biological-Monitoring-Working-Party and Average-Store-per-Taxon indices.O objetivo deste trabalho foi determinar a estrutura da entomofauna bentônica do Rio El Tala (Catamarca, Argentina) e sua variação longitudinal. Cinco estações de amostragem foram estabelecidas considerando-se a localização da habitação em relação ao curso de água. As seguintes variáveis foram determinadas in situ: altitude, latitude e longitude; largura do leito; profundidade do rio; velocidade da correnteza, e temperatura da água e do ar. Insetos bentônicos foram coletados em cinco estações de amostragem, utilizando-se um coletor tipo Surber de 0,09 m2 , com rede de malha 300 μm, tendo sido identificados em laboratório até o nível de Família. Densidade, riqueza e diversidade da fauna exibiram variação longitudinal. Da estação de amostragem 1 (site de referência) à 3, uma tendência decrescente no número de ordens e famílias foi observada, enquanto que as estações de amostragem 4 e 5 apresentaram uma tendência crescente. As amostras da estação 5 (estação rio abaixo) apresentaram a maior riqueza de famílias (17), o valor mais elevado do Índice de Shannon (2,74) e o menor valor de Dominância de Simpson (D = 0,22). Estes valores podem ser explicados pela capacidade de autopurificação de rio a jusante. A qualidade da água do Rio El Tala é Classe I (muito limpo e água sem impacto), de acordo com os resultados obtidos pela aplicação de índices bióticos BMWP’ e ASPT’.Facultad de Ciencias Naturales y Muse