A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Scattering of charge carriers by point defects in bilayer graphene

Theory of scattering of massive chiral fermions in bilayer graphene by radial symmetric potential is developed. It is shown that in the case when the electron wavelength is much larger than the radius of the potential the scattering cross-section is proportional to the electron wavelength. This leads to the mobility independent on the electron concentration. In contrast with the case of single-layer, neutral and charged defects are, in general, equally relevant for the resistivity of the bilayer graphene.Comment: final versio

Edge momentum transport by neutrals: an interpretive numerical framework

Due to their high cross-field mobility, neutrals can contribute to momentum transport even at the low relative densities found inside the separatrix and they can generate intrinsic rotation. We use a charge-exchange dominated solution to the neutral kinetic equation, coupled to neoclassical ions, to evaluate the momentum transport due to neutrals. Numerical solutions to the drift-kinetic equation allow us to cover the full range of collisionality, including the intermediate levels typical of the tokamak edge. In the edge there are several processes likely to contribute to momentum transport in addition to neutrals. Therefore, we present here an interpretive framework that can evaluate the momentum transport through neutrals based on radial plasma profiles. We demonstrate its application by analysing the neutral angular momentum flux for an L-mode discharge in the ASDEX Upgrade tokamak. The magnitudes of the angular momentum fluxes we find here due to neutrals of 0.6 – 2 Nm are comparable to the net torque on the plasma from neutral beam injection, indicating the importance of neutrals for rotation in the edge.Vetenskapsrådet and Marie Sklodowska Curie Actions, Cofund, Project INCA 60039

Spectrum of an open disordered quasi-two-dimensional electron system: strong orbital effect of the weak in-plane magnetic field

The effect of an in-plane magnetic field upon open quasi-two-dimensional electron and hole systems is investigated in terms of the carrier ground-state spectrum. The magnetic field, classified as weak from the viewpoint of correlation between size parameters of classical electron motion and the gate potential spatial profile is shown to efficiently cut off extended modes from the spectrum and to change singularly the mode density of states (MDOS). The reduction in the number of current-carrying modes, right up to zero in magnetic fields of moderate strength, can be viewed as the cause of magnetic-field-driven metal-to-insulator transition widely observed in two-dimensional systems. Both the mode number reduction and the MDOS singularity appear to be most pronounced in the mode states dephasing associated with their scattering by quenched-disorder potential. This sort of dephasing is proven to dominate the dephasing which involves solely the magnetic field whatever level of the disorder.Comment: RevTeX-4 class, 12 pages, 5 eps figure

ST Quartz Acoustic Wave Sensors with Sectional Guiding Layers

We report the effect of removing a section of guiding layer from the propagation paths of ST-quartz Love wave sensors; this offers the ease of fabrication of a polymer guiding layer whilst retaining the native surface of the quartz which may then be used for the attachment of a sensitizing layer. Data is presented for rigid and viscous loading, which indicates a small reduction in mass sensitivity compared to a Love wave device. Biosensing capabilities of these discontinuous ‘sectional’ guiding layer devices are demonstrated using protein adsorption from solution

Surveying the solar system by measuring angles and times: from the solar density to the gravitational constant

A surprisingly large amount of information on our solar system can be gained from simple measurements of the apparent angular diameters of the sun and the moon. This information includes the average density of the sun, the distance between earth and moon, the radius of the moon, and the gravitational constant. In this note it is described how these and other quantities can be obtained by simple earthbound measurements of angles and times only, without using any explicit information on distances between celestial bodies. The pedagogical and historical aspects of these results are also discussed briefly.Comment: 12 pges, one figur

Duality Between Spatial and Angular Shift in Optical Reflection

We report a unified representation of the spatial and angular Goos-Hanchen and Imbert-Fedorov shifts that occur when a light beam reflects from a plane interface. We thus reveal the dual nature of spatial and angular shifts in optical beam reflection. In the Goos-Hanchen case we show theoretically and experimentally that this unification naturally arises in the context of reflection from a lossy surface (e.g., a metal).Comment: 4 pages, 3 figure

Self-organization of hydrophobic soil and granular surfaces

Soil can become extremely water repellent following forest fires or oil spillages, thus preventing penetration of water and increasing runoff and soil erosion. Here the authors show that evaporation of a droplet from the surface of a hydrophobic granular material can be an active process, lifting, self-coating, and selectively concentrating small solid grains. Droplet evaporation leads to the formation of temporary liquid marbles and, as droplet volume reduces, particles of different wettabilities compete for water-air interfacial surface area. This can result in a sorting effect with self-organization of a mixed hydrophobic-hydrophilic aggregate into a hydrophobic shell surrounding a hydrophilic core

High frequency limit of the Transport Cross Section and boundedness of the Total Cross Section in scattering by an obstacle with impedance boundary conditions

The scalar scattering of the plane wave by a strictly convex obstacle with impedance boundary conditions is considered. The uniform boundedness of the Total Cross Section for all values of frequencies is proved. The high frequency limit of the Transport Cross Section is founded and presented as a classical functional of the variational theory