On the particle paths and the stagnation points in small-amplitude deep-water waves

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the particle motion are provided. All these solutions are not closed curves. Some particle trajectories are peakon-like, others can be expressed with the aid of the Jacobi elliptic functions or with the aid of the hyperelliptic functions. Remarks on the stagnation points of the small-amplitude irrotational deep-water waves are also made.Comment: to appear in J. Math. Fluid Mech. arXiv admin note: text overlap with arXiv:1106.382

Akhet Khufu: Archaeo-astronomical Hints at a Common Project of the Two Main Pyramids of Giza, Egypt

Abstract. The architectural complexes composed by the two main pyramids of Giza together with their temples are investigated from an interdisciplinary point of view, taking into account their astronomical alignments as well as their relationships with the visible landscape. Combining already known facts together with new clues, the work strongly supports the idea that the two complexes were conceived as parts of a common project

Oval Domes: History, Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word Aoval@ comes from the latin Aovum@, egg. Then, an oval dome has an egg-shaped geometry. The first buildings with oval plans were built without a predetermined form, just trying to close an space in the most economical form. Eventually, the geometry was defined by using arcs of circle with common tangents in the points of change of curvature. Later the oval acquired a more regular form with two axis of symmetry. Therefore, an “oval” may be defined as an egg-shaped form, doubly symmetric, constructed with arcs of circle; an oval needs a minimum of four centres, but it is possible also to build polycentric ovals. The above definition corresponds with the origin and the use of oval forms in building and may be applied without problem until, say, the XVIIIth century. Since then, the teaching of conics in the elementary courses of geometry made the cultivated people to define the oval as an approximation to the ellipse, an “imperfect ellipse”: an oval was, then, a curve formed with arcs of circles which tries to approximate to the ellipse of the same axes. As we shall see, the ellipse has very rarely been used in building. Finally, in modern geometrical textbooks an oval is defined as a smooth closed convex curve, a more general definition which embraces the two previous, but which is of no particular use in the study of the employment of oval forms in building. The present paper contains the following parts: 1) an outline the origin and application of the oval in historical architecture; 2) a discussion of the spatial geometry of oval domes, i. e., the different methods employed to trace them; 3) a brief exposition of the mechanics of oval arches and domes; and 4) a final discussion of the role of Geometry in oval arch and dome design

Strong suppression of heat conduction in a laboratory replica of galaxy-cluster turbulent plasmas

In conventional gases and plasmas, it is known that heat fluxes are proportional to temperature gradients, with collisions between particles mediating energy flow from hotter to colder regions and the coefficient of thermal conduction given by Spitzer's theory. However, this theory breaks down in magnetized, turbulent, weakly collisional plasmas, although modifications are difficult to predict from first principles due to the complex, multiscale nature of the problem. Understanding heat transport is important in astrophysical plasmas such as those in galaxy clusters, where observed temperature profiles are explicable only in the presence of a strong suppression of heat conduction compared to Spitzer's theory. To address this problem, we have created a replica of such a system in a laser laboratory experiment. Our data show a reduction of heat transport by two orders of magnitude or more, leading to large temperature variations on small spatial scales (as is seen in cluster plasmas)

Quantitative imaging of concentrated suspensions under flow

We review recent advances in imaging the flow of concentrated suspensions, focussing on the use of confocal microscopy to obtain time-resolved information on the single-particle level in these systems. After motivating the need for quantitative (confocal) imaging in suspension rheology, we briefly describe the particles, sample environments, microscopy tools and analysis algorithms needed to perform this kind of experiments. The second part of the review focusses on microscopic aspects of the flow of concentrated model hard-sphere-like suspensions, and the relation to non-linear rheological phenomena such as yielding, shear localization, wall slip and shear-induced ordering. Both Brownian and non-Brownian systems will be described. We show how quantitative imaging can improve our understanding of the connection between microscopic dynamics and bulk flow.Comment: Review on imaging hard-sphere suspensions, incl summary of methodology. Submitted for special volume 'High Solid Dispersions' ed. M. Cloitre, Vol. xx of 'Advances and Polymer Science' (Springer, Berlin, 2009); 22 pages, 16 fig

Non-local rheology in dense granular flows -- Revisiting the concept of fluidity

Granular materials belong to the class of amorphous athermal systems, like foams, emulsion or suspension they can resist shear like a solid, but flow like a liquid under a sufficiently large applied shear stress. They exhibit a dynamical phase transition between static and flowing states, as for phase transitions of thermodynamic systems, this rigidity transition exhibits a diverging length scales quantifying the degree of cooperatively. Several experiments have shown that the rheology of granular materials and emulsion is non-local, namely that the stress at a given location does not depend only on the shear rate at this location but also on the degree of mobility in the surrounding region. Several constitutive relations have recently been proposed and tested successfully against numerical and experimental results. Here we use discrete elements simulation of 2D shear flows to shed light on the dynamical mechanism underlying non-locality in dense granular flows

Study on a compact and adaptable Thomson Spectrometer for laser-initiated 11B(p,α)8Be reactions and low-medium energy particle detection

Thomson Spectrometers are of primary importance in the discrimination of particles produced by laser-plasma interaction, according to their energy and charge-mass ratio. We describe here a detailed study on a set of Thomson Spectrometers, adaptable to different experimental situations, with the aim of being placed directly within the experimental chamber, rather than in additional extensions, in order to increase the solid angle of observation. These instruments are suitable for detection of low-medium energy particles and can be effectively employed in laser-plasma experiments of 11B(p,α)8Be fusion. They are provided with permanent magnets, have small dimensions and compact design. In these small configurations electric and magnetic fringing fields play a primary role for particle deflection, and their accurate characterization is required. It was accomplished by means of COMSOL electromagnetic solver coupled to an effective analytical model, very suitable for practical use of the spectrometers. Data from experimental measurements of the magnetic fields have been also used. We describe the application of the spectrometers to an experiment of laser-plasma interaction, coupled to Imaging Plate detectors. Data analysis for spectrum and yield of the detected radiation is discussed in detail. © 2016 ENEA

Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility

A series of cryogenic, layered deuterium-tritium (DT) implosions have produced, for the first time, fusion energy output twice the peak kinetic energy of the imploding shell. These experiments at the National Ignition Facility utilized high density carbon ablators with a three-shock laser pulse (1.5 MJ in 7.5 ns) to irradiate low gas-filled (0.3  mg/cc of helium) bare depleted uranium hohlraums, resulting in a peak hohlraum radiative temperature ∼290  eV. The imploding shell, composed of the nonablated high density carbon and the DT cryogenic layer, is, thus, driven to velocity on the order of 380  km/s resulting in a peak kinetic energy of ∼21  kJ, which once stagnated produced a total DT neutron yield of 1.9×10¹⁶ (shot N170827) corresponding to an output fusion energy of 54 kJ. Time dependent low mode asymmetries that limited further progress of implosions have now been controlled, leading to an increased compression of the hot spot. It resulted in hot spot areal density (ρr∼0.3  g/cm²) and stagnation pressure (∼360  Gbar) never before achieved in a laboratory experiment

Guiding of relativistic electron beams in dense matter by laser-driven magnetostatic fields

Intense lasers interacting with dense targets accelerate relativistic electron beams, whichtransport part of the laser energy into the target depth. However, the overall laser-to-targetenergy coupling efficiency is impaired by the large divergence of the electron beam, intrinsicto the laser-plasma interaction. Here we demonstrate that an efficient guiding ofMeV electrons with about 30MA current in solid matter is obtained by imposing a laserdrivenlongitudinal magnetostatic field of 600 T. In the magnetized conditions the transportedenergy density and the peak background electron temperature at the 60-μm-thicktarget's rear surface rise by about a factor of five, as unfolded from benchmarked simulations.Such an improvement of energy-density flux through dense matter paves the ground foradvances in laser-driven intense sources of energetic particles and radiation, driving matter toextreme temperatures, reaching states relevant for planetary or stellar science as yet inaccessibleat the laboratory scale and achieving high-gain laser-driven thermonuclear fusion