Extrema statistics in the dynamics of a non-Gaussian random field

When the equations that govern the dynamics of a random field are nonlinear, the field can develop with time non-Gaussian statistics even if its initial condition is Gaussian. Here, we provide a general framework for calculating the effect of the underlying nonlinear dynamics on the relative densities of maxima and minima of the field. Using this simple geometrical probe, we can identify the size of the non-Gaussian contributions in the random field, or alternatively the magnitude of the nonlinear terms in the underlying equations of motion. We demonstrate our approach by applying it to an initially Gaussian field that evolves according to the deterministic KPZ equation, which models surface growth and shock dynamics.Comment: 9 pages, 3 figure

Topological mechanics of gyroscopic metamaterials

Topological mechanical metamaterials are artificial structures whose unusual properties are protected very much like their electronic and optical counterparts. Here, we present an experimental and theoretical study of an active metamaterial -- comprised of coupled gyroscopes on a lattice -- that breaks time-reversal symmetry. The vibrational spectrum of these novel structures displays a sonic gap populated by topologically protected edge modes which propagate in only one direction and are unaffected by disorder. We present a mathematical model that explains how the edge mode chirality can be switched via controlled distortions of the underlying lattice. This effect allows the direction of the edge current to be determined on demand. We envision applications of these edges modes to the design of loss-free, one-way, acoustic waveguides and demonstrate this functionality in experiment

Analysis for Liquefaction: Empirical Approach

An improved analytical method to calculate the likelihood of soil liquefaction is described. The method is based on an expanded list of case histories of liquefaction and no-liquefaction and employs earthquake magnitude and hypocentral distance to describe the intensity of shaking at a site. The new list of case histories is compiled from a complete re-evaluation of previously published case histories and field data observed in more recent earthquakes. Specific applications of the proposed procedure are described and an example analysis is presented

THE COMPLEX POINT CLOUD FOR THE KNOWLEDGE OF THE ARCHITECTURAL HERITAGE. SOME EXPERIENCES

The present paper aims to present a series of experiences and experimentations that a group of PhD from the University of Naples Federico II conducted over the past decade. This work has concerned the survey and the graphic restitution of monuments and works of art, finalized to their conservation. The targeted query of complex point cloud acquired by 3D scanners, integrated with photo sensors and thermal imaging, has allowed to explore new possibilities of investigation. In particular, we will present the scientific results of the experiments carried out on some important historical artifacts with distinct morphological and typological characteristics. According to aims and needs that emerged during the connotative process, with the support of archival and iconographic historical research, the laser scanner technology has been used in many different ways. New forms of representation, obtained directly from the point cloud, have been tested for the elaboration of thematic studies for documenting the pathologies and the decay of materials, for correlating visible aspects with invisible aspects of the artifact

Stochastic geometry and topology of non-Gaussian fields

Gaussian random fields pervade all areas of science. However, it is often the departures from Gaussianity that carry the crucial signature of the nonlinear mechanisms at the heart of diverse phenomena, ranging from structure formation in condensed matter and cosmology to biomedical imaging. The standard test of non-Gaussianity is to measure higher order correlation functions. In the present work, we take a different route. We show how geometric and topological properties of Gaussian fields, such as the statistics of extrema, are modified by the presence of a non-Gaussian perturbation. The resulting discrepancies give an independent way to detect and quantify non-Gaussianities. In our treatment, we consider both local and nonlocal mechanisms that generate non-Gaussian fields, both statically and dynamically through nonlinear diffusion.Comment: 8 pages, 4 figure

Shocks near Jamming

Non-linear sound is an extreme phenomenon typically observed in solids after violent explosions. But granular media are different. Right when they jam, these fragile and disordered solids exhibit a vanishing rigidity and sound speed, so that even tiny mechanical perturbations form supersonic shocks. Here, we perform simulations in which two-dimensional jammed granular packings are dynamically compressed, and demonstrate that the elementary excitations are strongly non-linear shocks, rather than ordinary phonons. We capture the full dependence of the shock speed on pressure and impact intensity by a surprisingly simple analytical model.Comment: Revised version. Accepted for publication in Phys. Rev. Let