Weber-like interactions and energy conservation

Velocity dependent forces varying as $k(\hat{r}/r)(1 - \mu \dot{r}^2 + \gamma r \ddot{r})$ (such as Weber force), here called Weber-like forces, are examined from the point of view of energy conservation and it is proved that they are conservative if and only if $\gamma=2\mu$. As a consequence, it is shown that gravitational theories employing Weber-like forces cannot be conservative and also yield both the precession of the perihelion of Mercury as well as the gravitational deflection of light.Comment: latex, 11 pages, no figure

The importance of the Ising model

Understanding the relationship which integrable (solvable) models, all of which possess very special symmetry properties, have with the generic non-integrable models that are used to describe real experiments, which do not have the symmetry properties, is one of the most fundamental open questions in both statistical mechanics and quantum field theory. The importance of the two-dimensional Ising model in a magnetic field is that it is the simplest system where this relationship may be concretely studied. We here review the advances made in this study, and concentrate on the magnetic susceptibility which has revealed an unexpected natural boundary phenomenon. When this is combined with the Fermionic representations of conformal characters, it is suggested that the scaling theory, which smoothly connects the lattice with the correlation length scale, may be incomplete for $H \neq 0$.Comment: 33 page

Monthly and Diurnal Variability of Rain Rate and Rain Attenuation during the Monsoon Period in Malaysia

Rain is the major source of attenuation for microwave propagation above 10 GHz. In tropical and equatorial regions where the rain intensity is higher, designing a terrestrial and earth-to-satellite microwave links is very critical and challenging at these frequencies. This paper presents the preliminary results of rain effects in a 23 GHz terrestrial point-to-point communication link 1.3km long. The experimental test bed had been set up at Skudai, Johor Bahru, Malaysia. In this area, a monsoon equatorial climate prevails and the rainfall rate can reach values well above 100mm/h with significant monthly and diurnal variability. Hence, it is necessary to implement a mitigation technique for maintaining an adequate radio link performance for the action of very heavy rain. Since we now know that the ULPC (Up Link Power Control) cannot guarantee the desired performance, a solution based on frequency band diversity is proposed in this paper. Here, a secondary radio link operating in a frequency not affected by rain (C band for instance) is placed parallel with the main link. Under no rain or light rain conditions, the secondary link carries without priority radio signals. When there is an outage of the main link due to rain, the secondary link assumes the priority traffic. The outcome of the research shows a solution for higher operating frequencies during rainy events

Diagonal Ising susceptibility: elliptic integrals, modular forms and Calabi-Yau equations

We give the exact expressions of the partial susceptibilities $\chi^{(3)}_d$ and $\chi^{(4)}_d$ for the diagonal susceptibility of the Ising model in terms of modular forms and Calabi-Yau ODEs, and more specifically, $_3F_2([1/3,2/3,3/2],\, [1,1];\, z)$ and $_4F_3([1/2,1/2,1/2,1/2],\, [1,1,1]; \, z)$ hypergeometric functions. By solving the connection problems we analytically compute the behavior at all finite singular points for $\chi^{(3)}_d$ and $\chi^{(4)}_d$. We also give new results for $\chi^{(5)}_d$. We see in particular, the emergence of a remarkable order-six operator, which is such that its symmetric square has a rational solution. These new exact results indicate that the linear differential operators occurring in the $n$-fold integrals of the Ising model are not only "Derived from Geometry" (globally nilpotent), but actually correspond to "Special Geometry" (homomorphic to their formal adjoint). This raises the question of seeing if these "special geometry" Ising-operators, are "special" ones, reducing, in fact systematically, to (selected, k-balanced, ...) $_{q+1}F_q$ hypergeometric functions, or correspond to the more general solutions of Calabi-Yau equations.Comment: 35 page

The saga of the Ising susceptibility

We review developments made since 1959 in the search for a closed form for the susceptibility of the Ising model. The expressions for the form factors in terms of the nome $q$ and the modulus $k$ are compared and contrasted. The $\lambda$ generalized correlations $C(M,N;\lambda)$ are defined and explicitly computed in terms of theta functions for $M=N=0,1$.Comment: 19 pages, 1 figur

Células de inovação : experiências educacionais em CTS+I

Neste artigo pretende-se mostrar uma investigação que vem sendo feita em escolas de formação profissional brasileiras com o uso de Células de Inovação (CI). As CI's são grupos de estudantes envolvidos com a tarefa de solucionar um problema concreto da de sua escola ou bairro utilizando-se de conhecimentos técnico-científicos. Procurou-se investigar, através de uma metodologia etnográfica, como esses alunos aprendem os conteúdos de ciência ao solucionar seu problema e se a inovação é algo que possa ser aprendido. As situações trabalhados são problematizadas numa perspectiva CTS e, em seguida, são discutidas soluções. A implementação das melhores soluções gera nova discussão CTS sobre seu impacto. O trabalho aqui descrito cobre apenas uma célula. Pretende-se que a partir de 2010 que a investigação estenda-se para várias células trabalhando em rede

Holonomy Transformation in the FRW Metric

In this work we investigate loop variables in Friedman-Robertson-Walker spacetime. We analyze the parallel transport of vectors and spinors in several paths in this spacetime in order to classify its global properties. The band holonomy invariance is analysed in this background.Comment: 8 page

Dynamic range of hypercubic stochastic excitable media

We study the response properties of d-dimensional hypercubic excitable networks to a stochastic stimulus. Each site, modelled either by a three-state stochastic susceptible-infected-recovered-susceptible system or by the probabilistic Greenberg-Hastings cellular automaton, is continuously and independently stimulated by an external Poisson rate h. The response function (mean density of active sites rho versus h) is obtained via simulations (for d=1, 2, 3, 4) and mean field approximations at the single-site and pair levels (for all d). In any dimension, the dynamic range of the response function is maximized precisely at the nonequilibrium phase transition to self-sustained activity, in agreement with a reasoning recently proposed. Moreover, the maximum dynamic range attained at a given dimension d is a decreasing function of d.Comment: 7 pages, 4 figure