The cluster initial mass function of the M82 disk Super Star Clusters

The presence of a population of a large number ($\sim$400) of almost coeval (100--300 Myr) super star clusters (SSCs) in the disk of M82 offers an opportunity to construct the Cluster Initial Mass Function (CIMF) from the observed present-day Cluster Mass Function (CMF). We carry out the dynamical and photometric evolution of the CMF assuming the clusters move in circular orbits under the gravitational potential of the host galaxy using the semi-analytical simulation code EMACSS. We explore power-law and log-normal functions for the CIMFs, and populate the clusters in the disk assuming uniform, power-law, and exponential radial distribution functions. We find that the observed CMF is best produced by a CIMF that is power-law in form with an index of 1.8, for a power-law radial distribution function. More importantly, we establish that the observed turn-over in the present-day CMF is the result of observational incompleteness rather than due to dynamically induced effects, or an intrinsically log-normal CIMF, as was proposed for the fossil starburst region B of this galaxy. Our simulations naturally reproduce the mass-radius relation observed for a sub-sample of M82 SSCs.Comment: 17 pages, 11 figures, accepted to be published on MNRA

Analysis of Dipolar Sources in the Solution of the Electroencephalographic Inverse Problem

In this work, we propose a solution to the problem of identification of sources in the brain from measurements of the electrical potential, recorded on the scalp EEG (electroencephalogram), where boundary problems are used to model the skull, brain region, and scalp, solving the inverse problem from the EEG measurements, the so-called Electroencephalographic Inverse Problem (EIP), which is ill-posed in the Hadamard sense since the problem has numerical instability. We focus on the identification of volumetric dipolar sources of the EEG by constructing and modeling a simplification to reduce the multilayer conductive medium (two layers or regions Ω1 and Ω2) to a problem of a single layer of a homogeneous medium with a null Neumann condition on the boundary. For this simplification purpose, we consider the Cauchy problem to be solved at each time. We compare the results we obtained solving the multiple layers problem with those obtained by our simplification proposal. In both cases, we solve the direct and inverse problems for two different sources, as synthetic results for dipolar sources resembling epileptic foci, and a similar case with an external stimulus (intense light, skin stimuli, sleep problems, etc). For the inverse problem, we use the Tikhonov regularization method to handle its numerical instability. Additionally, we build an algorithm to solve both models (multiple layers problem and our simplification) in time, showing optimization of the problem when considering 128 divisions in the time interval [0,1] s, solving the inverse problem at each time (interval division) and comparing the recovered source with the initial one in the algorithm. We observed a significant decrease in the computation times when simplifying the numerical calculations, resulting in a decrease up to 50% in the execution times, between the EIP multilayer model and our simplification proposal, to a single layer homogeneous problem of a homogeneous medium, which translates into a numerical efficiency in this type of problem

Simulated LCSLM with Inducible Diffractive Theory to Display Super-Gaussian Arrays Applying the Transport-of-Intensity Equation

We simulate a liquid crystal spatial light modulator (LCSLM), previously validated by Fraunhofer diffraction to observe super-Gaussian periodic profiles and analyze the wavefront of optical surfaces applying the transport-of-intensity equation (TIE). The LCSLM represents an alternative to the Ronchi Rulings, allowing to avoid all the related issues regarding diffractive and refractive properties, and noise. To this aim, we developed and numerically simulated a LCSLM resembling a fractal from a generating base. Such a base is constituted by an active square (values equal to one) and surrounded by eight switched-off pixels (zero-valued). We replicate the base in order to form 1 ×N-pixels and the successive rows to build the 1024×1024 LCSLM of active pixels. We visually test the LCSLM with calibration images as a diffractive object that is mathematically inducible, using mathematical induction over the N×N-shape (1×1, 2×2, 3×3, …, n×n pixels for the generalization). Finally, we experimentally generate periodic super-Gaussian profiles to be visualized in the LCSLM (transmission SLM, 1024×768-pixels LC 2012 Translucent SLM), modifying the TIE as an optical test in order to analyze the optical elements by comparing the results with ZYGO/APEX