Compression-induced failure of electro-active polymeric thin films

The insurgence of compression induces wrinkling in actuation devices based on EAPs thin films leading to a sudden decrease of performances up to failure. Based on the classical tension field theory for thin elastic membranes, we provide a general framework for the analysis of the insurgence of in-plane compression in membranes of electroactive polymers (EAPs). Our main result is the deduction of a (voltage-dependent) domain in the stretch space which represents tensile configurations. Under the assumption of Mooney-Rivlin materials, we obtain that for growing values of the applied voltage the domain contracts, vanishing at a critical voltage above which the polymer is wrinkled for any stretch configuration. Our approach can be easily implemented in numerical simulations for more complex material behaviors and provides a tool for the analysis of compression instability as a function of the elastic moduli.Comment: (15 pages, 7 figures

Catastrophic thinning of dielectric elastomers

We provide a clear energetic insight into the catastrophic nature of the so-called creasing and pull-in instabilities in soft electro-active elastomers. These phenomena are ubiquitous for thin electro-elastic plates and are a major obstacle to the development of giant actuators; yet they are not completely understood nor modelled accurately. Here, in complete agreement with experiments, we give a simple formula to predict the voltage thresholds for these instability patterns and model their shape, and show that equilibrium is impossible beyond their onset. Our analysis is fully analytical, does not require finite element simulations, and can be extended to include pre-stretch and to encompass any material behaviour

On the Riemann Hypothesis for the Zeta-Function

The object of this paper is to give a proof of the conjecture made by Riemann in 1859 about the complex zeros of the zeta-functionComment: 22 page

B-Mode Polarization Experiments for the Cosmic Microwave Background: Map-making and Foreground Modeling

The Cosmic Microwave Background (CMB) is a relic radiation generated at the decoupling of matter and radiation as the temperature of the Universe dropped below 3000 K. As a probe of the early phases of the universe, it is made of tiny fluctuations (1 part over 100,000) where the seeds of structure formation are encoded. The study of temperature anisotropies in the CMB carried out by a plethora of satellite and ground-based experiments (COsmic Background Explorer (COBE), Balloon Observations Of Millimetric Extragalactic Radiation ANd Geophysics (BOOMERanG), Millimeter wave Anisotropy eXperiment IMaging Array (MAXIMA), Wilkinson Microwave Anisotropy Probe (WMAP), Planck etc.) has been outstandingly successful measuring average properties of the Universe like geometry, matter-energy content and is one of the cornerstones of what has come to be called the standard cosmological model (known as $\Lambda$ Cold Dark Matter, $\Lambda$CDM). It is worth noticing that the existence of Dark Energy, the latest cosmological component to be discovered, responsible for a late time phase of cosmic acceleration, has been discovered thanks to the CMB anisotropies in combination with high redshift Supernovae data. Linear polarization of CMB anisotropies was expected from theory so that in the last decades efforts for detection intensified and in 2002 the Degree Angular Scale Interferometer (DASI) experiment succeeded for the first time. CMB polarization pattern can be decomposed into two scalar quantities called E- and B-modes. To date, most of the research studies aimed at observing the latter since they are related to the gravitational lensing of large scale structures at the arcminute angular scales, whereas at the degree scales, B-modes are induced by a stochastic background of gravitational waves produced during the inflationary era of the Universe. Unfortunately, the B-modes amplitude is expected to be orders of magnitude smaller, making their detection at large angular scales very challenging. To further worsen the situation and complicate this scenario, it has been found that the polarized emission from the Galaxy emitting at the very same frequencies represents one of the biggest obstacles in observing CMB polarization anisotropies. The list of Galactic foregrounds is long and includes anything between us and the CMB: thermal dust, synchrotron radiation, free-free (or bremsstrahlung) and several molecular line emissions all emanating from our Galaxy. All these emissions are partially polarized: synchrotron and dust are polarized at < 20 % level, molecular lines are expected to be polarized at < 1 %, free-free emission is essentially considered unpolarized. This is the reason of the recent effort to observe the CMB polarization in a very large range of frequencies to accurately know the distribution in the sky and the frequency dependence of each Galactic polarized foreground. Moreover, such an investigation allows us to design data analysis algorithms known as component separation for extracting B-modes out of a multi-frequency experimental setup. On the other hand, in order to constrain the inflation parameters from the faint B-mode signal, the CMB experiments have been constantly increasing the accuracy of the measurements by means of larger and larger samples of number of detectors in the focal plane. Reconstructing CMB maps is computationally expensive since it requires a lot of resources to compress trillions of time samples to pixels in a map: hence, for current and forthcoming CMB experiments, the map-making procedure is required to be computationally efficient and fast. The work presented in this Thesis addresses both the challenges presented above in observing CMB B-modes and it has been further motivated by the needs of a specific CMB experiment, Polarbear, to which we belong. We have participated in the analysis of the first seasons of observations and specifically, we developed and tested a map-making pipeline to process the data of the future seasons of observations. In the context of Galactic foregrounds, we built a model, MCMOLE 3D, aimed at simulating Carbon Monoxide rotational lines emission in molecular clouds taking into account their 3D spatial distribution with different geometrical properties to assess the contamination to B-modes of an undetected molecular cloud which could be eventually observed within a patch of a ground based experiment. Both investigations led to results which have been published and represent major contribution to the data analysis and simulation infrastructure of the experiment. Moreover, they are being further developed and expanded, for application in the ongoing and future Polarbear experiment, and other B-mode observations as well

A conditional result on exponential sums over primes in short intervals

The aim of this work is to illustrate a conditional result involving the exponential sums over primes in short intervals under the assumption that both the Generalized Riemann Hypothesis and the Density Hypothesis for Dirichlet $L$-functions are true.Comment: 15 page