arXiv subjects
Publications and source records attributed to Mario Garavaglia.
Light tracking systems have been used in recent years to study wandering phenomena in atmospheric optics. We propose to employ this technology in structural deformation sensing.
In this paper we propose an algorithm that correctly discards a set of numbers (from a previously defined sieve) with an interval of integers. Leopoldo's Theorem states that the remaining integer numbers will generate and count the complete list of primes of absolute value greater than 3 in the interval of interest. This algorithm avoids the problem of generating large lists of numbers, and can be used to compute (even in parallel) the prime counting function $π(h)$.
In this paper we review the properties of families of numbers of the form $6n\pm1$, with $n$ integer (in which there are all prime numbers greater than 3 and other compound numbers with particular properties) to later use them in a new sieve that allows the separation of numbers $n$ that generate primes from those that only generate compounds. In principle, this can be used to find the amount of prime numbers up to a given number $h$; this means, $π(h)$.
We will describe an algorithm to arrange all the positive and negative integer numbers. This array of numbers permits grouping them in six different Classes, $α$, $β$, $γ$, $δ$, $ε$, and $ζ$. Particularly, numbers belong to Class $α$ are defined as $α=1+6 n$, and those of Class $β$, as $β=5+6n$, where $n=0,\pm1,\pm2,\pm3,\pm4,...$ These two Classes $α$ and $β$,contain: i) all prime numbers, except + 2, -2 and $\pm$3, which belong to $ε$, $δ$, and $γ$ Classes, respectively, and ii) all the other odd numbers, except those that are multiple of $\pm$3, according to the sequence $\pm$9, $\pm$15, $\pm$21, $\pm$27, ... Besides, products between numbers of the Class $α$, and also those between numbers of the Class $β$, generates numbers belonging to the Class $α$. On the other side, products between numbers of Class $α$ with numbers of Class $β$, result in numbers of Class $β$. Then, both Classes $α$ and $β$ include: i) all the prime numbers except $\pm$2 and $\pm$3, and ii) all the products between $α$ numbers, as $α\cdotα^{\prime}$; all the products between $β$ numbers, as $β\cdotβ^{\prime}$; and also all the products between numbers of Classes $α$ and $β$, as $α\cdotβ$, which necessarily are composite numbers, whose factorization is completely determined.
We analyze, within the wavelet theory framework, the wandering over a screen of the centroid of a laser beam after it has propagated through a time-changing laboratory-generated turbulence. Following a previous work (Fractals 12 (2004) 223) two quantifiers are used, the Hurst parameter, $H$, and the Normalized Total Wavelet Entropy, $\text{NTWS}$. The temporal evolution of both quantifiers, obtained from the laser spot data stream is studied and compared. This allows us to extract information of the stochastic process associated to the turbulence dynamics.
In a recently published paper (J. of Modern Optics 50 (9) (2003) 1477-1486) a qualitative analysis of the moire effect observed by superposing two grids containing Cantor fractal structures was presented. It was shown that the moire effect is sensible to variations in the order of growth, dimension and lacunarity of the Cantor fractal. It was also verified that self-similarity of the original fractal is inherited by the moire pattern. In this work it is shown that these Cantor moire structures are also fractals and the fractal dimension associated with them is theoretically determined and experimentally measured attending the size of rhombuses in the different orders of growth.
We study the functional link between the Hurst parameter and the Normalized Total Wavelet Entropy when analyzing fractional Brownian motion (fBm) time series--these series are synthetically generated. Both quantifiers are mainly used to identify fractional Brownian motion processes (Fractals 12 (2004) 223). The aim of this work is understand the differences in the information obtained from them, if any.
It is discussed the limitations of the widely used markovian approximation applied to model the turbulent refractive index in lightwave propagation. It is well-known the index is a passive scalar field. Thus, the actual knowledge about these quantities is used to propose an alternative stochastic process to the markovian approximation: the fractional Brownian motion. This generalizes the former introducing memory; that is, there is correlation along the propagation path.
The propagation of a laser beam through turbulent media is modeled as a fractional Brownian motion (fBm). Time series corresponding to the center position of the laser spot (coordinates x and y) after traveling across air in turbulent motion, with different strength, are analyzed by the wavelet theory. Two quantifiers are calculated, the Hurst exponent and the mean Normalized Total Wavelet Entropy. It is verified that both quantifiers gives complementary information about the turbulence state.
This paper introduces a general and new formalism to model the turbulent wave-front phase using fractional Brownian motion processes. Moreover, it extends results to non-Kolmogorov turbulence. In particular, generalized expressions for the Strehl ratio and the angle-of-arrival variance are obtained. These are dependent on the dynamic state of the turbulence.