New representations of pi and Dirac delta using the nonextensive-statistical-mechanics q-exponential function

We present a generalization of the representation in plane waves of Dirac delta, $\delta(x)=(1/2\pi)\int_{-\infty}^\infty e^{-ikx}\,dk$, namely $\delta(x)=(2-q)/(2\pi)\int_{-\infty}^\infty e_q^{-ikx}\,dk$, using the nonextensive-statistical-mechanics $q$-exponential function, $e_q^{ix}\equiv[1+(1-q)ix]^{1/(1-q)}$ with $e_1^{ix}\equiv e^{ix}$, being $x$ any real number, for real values of $q$ within the interval $[1,2[$. Concomitantly with the development of these new representations of Dirac delta, we also present two new families of representations of the transcendental number $\pi$. Incidentally, we remark that the $q$-plane wave form which emerges, namely $e_q^{ikx}$, is normalizable for $1<q<3$, in contrast with the standard one, $e^{ikx}$, which is not.Comment: 13 pages, 6 figures. Accepted for publication in the Journal of Mathematical Physics. Some misprints have been eliminate

q-Moments remove the degeneracy associated with the inversion of the q-Fourier transform

It was recently proven [Hilhorst, JSTAT, P10023 (2010)] that the q-generalization of the Fourier transform is not invertible in the full space of probability density functions for q > 1. It has also been recently shown that this complication disappears if we dispose of the q-Fourier transform not only of the function itself, but also of all of its shifts [Jauregui and Tsallis, Phys. Lett. A 375, 2085 (2011)]. Here we show that another road exists for completely removing the degeneracy associated with the inversion of the q-Fourier transform of a given probability density function. Indeed, it is possible to determine this density if we dispose of some extra information related to its q-moments.Comment: 11 pages, 12 figure

Particle creation by moving spherical shell in the dynamical Casimir effect

The creation of massless scalar particles from the quantum vacuum by spherical shell with time varying radius is studied. In the general case of motion the equations are derived for the instantaneous basis expansion coefficients. The examples are considered when the mean number of particles can be explicitly evaluated in the adiabatic approximation.Comment: 9 pages, LaTeX, no figures, typos corrected, discussion added. Journal-ref adde

Fermion Particle Production in Dynamical Casimir Effect in a Three Dimensional Box

In this paper we investigate the problem of fermion creation inside a three dimensional box. We present an appropriate wave function which satisfies the Dirac equation in this geometry with MIT bag model boundary condition. We consider walls of the box to have dynamic and introduce the time evolution of the quantized field by expanding it over the 'instantaneous basis'. We explain how we can obtain the average number of particles created. In this regard we find the Bogliubove coefficients. We consider an oscillation and determine the coupling conditions between different modes that can be satisfied depending on the cavity's spectrum. Assuming the parametric resonance case we obtain an expression for the mean number of created fermions in each mode of an oscillation and their dynamical Casimir energy.Comment: 5 pages, no figur

q-Generalization of the inverse Fourier transform

A wide class of physical distributions appears to follow the q-Gaussian form, which plays the role of attractor according to a Central Limit Theorem generalized in the presence of specific correlations between the relevant random variables. In the realm of this theorem, a q-generalized Fourier transform plays an important role. We introduce here a method which univocally determines a distribution from the knowledge of its q-Fourier transform and some supplementary information. This procedure involves a recently q-generalized Dirac delta and the class of functions on which it acts. The present method conveniently extends the inverse of the standard Fourier transform, and is therefore expected to be very useful in the study of many complex systems.Comment: 6 pages, 3 figures. To appear in Physics Letters

In Vivo Tissue-Specific Chromatin Profiling in Drosophila Melanogaster Using GFP-Tagged Nuclei

The chromatin landscape defines cellular identity in multicellular organisms with unique patterns of DNA accessibility and histone marks decorating the genome of each cell type. Thus, profiling the chromatin state of different cell types in an intact organism under disease or physiological conditions can provide insight into how chromatin regulates cell homeostasis in vivo. To overcome the many challenges associated with characterizing chromatin state in specific cell types, we developed an improved approach to isolate Drosophila melanogaster nuclei tagged with a GFPKASH protein. The perinuclear space-localized KASH domain anchors GFP to the outer nuclear membrane, and expression of UAS-GFPKASH can be controlled by tissue-specific Gal4 drivers. Using this protocol, we profiled chromatin accessibility using an improved version of Assay for Transposable Accessible Chromatin followed by sequencing (ATAC-seq), called Omni-ATAC. In addition, we examined the distribution of histone marks using Chromatin immunoprecipitation followed by sequencing (ChIP-seq) and Cleavage Under Targets and Tagmentation (CUT&Tag) in adult photoreceptor neurons. We show that the chromatin landscape of photoreceptors reflects the transcriptional state of these cells, demonstrating the quality and reproducibility of our approach for profiling the transcriptome and epigenome of specific cell types in Drosophila

Paper and toner three-dimensional fluidic devices: Programming fluid flow to improve point-of-care diagnostics

We present a new method for fabricating three-dimensional paper-based fluidic devices that uses toner as a thermal adhesive to bond multiple layers of patterned paper together. The fabrication process is rapid, involves minimal equipment (a laser printer and a laminator) and produces complex channel networks with dimensions down to 1 mm. The devices can run multiple diagnostic assays on one or more samples simultaneously, can incorporate positive and negative controls and can be programmed to display the results of the assays in a variety of patterns. The patterns of the results can encode information, which could be used to identify counterfeit devices, identify samples, encrypt the results for patient privacy or monitor patient compliance

Effect of oxygen plasma etching on graphene studied with Raman spectroscopy and electronic transport

We report a study of graphene and graphene field effect devices after exposure to a series of short pulses of oxygen plasma. We present data from Raman spectroscopy, back-gated field-effect and magneto-transport measurements. The intensity ratio between Raman "D" and "G" peaks, I(D)/I(G) (commonly used to characterize disorder in graphene) is observed to increase approximately linearly with the number (N(e)) of plasma etching pulses initially, but then decreases at higher Ne. We also discuss implications of our data for extracting graphene crystalline domain sizes from I(D)/I(G). At the highest Ne measured, the "2D" peak is found to be nearly suppressed while the "D" peak is still prominent. Electronic transport measurements in plasma-etched graphene show an up-shifting of the Dirac point, indicating hole doping. We also characterize mobility, quantum Hall states, weak localization and various scattering lengths in a moderately etched sample. Our findings are valuable for understanding the effects of plasma etching on graphene and the physics of disordered graphene through artificially generated defects.Comment: 10 pages, 5 figure