9,158 research outputs found
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
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
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
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
The importance of the classical channel in the impurity transport of optimized stellarators
In toroidal magnetic confinement devices, such as tokamaks and stellarators,
neoclassical transport is usually an order of magnitude larger than its
classical counterpart. However, when a high-collisionality species is present
in a stellarator optimized for low Pfirsch-Schl\"uter current, its classical
transport can be comparable to the neoclassical transport. In this letter, we
compare neoclassical and classical fluxes and transport coefficients calculated
for Wendelstein 7-X (W7-X) and Large Helical Device (LHD) cases. In W7-X, we
find that the classical transport of a collisional impurity is comparable to
the neoclassical transport for all radii, while it is negligible in the LHD
cases, except in the vicinity of radii where the neoclassical transport changes
sign. In the LHD case, electrostatic potential variations on the flux-surface
significantly enhance the neoclassical impurity transport, while the classical
transport is largely insensitive to this effect in the cases studied.Comment: 10 pages, 2 figure
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
An improved sum-product estimate for general finite fields
This paper improves on a sum-product estimate obtained by Katz and Shen for
subsets of a finite field whose order is not prime
Influence of branch points in the complex plane on the transmission through double quantum dots
We consider single-channel transmission through a double quantum dot system
consisting of two single dots that are connected by a wire and coupled each to
one lead. The system is described in the framework of the S-matrix theory by
using the effective Hamiltonian of the open quantum system. It consists of the
Hamiltonian of the closed system (without attached leads) and a term that
accounts for the coupling of the states via the continuum of propagating modes
in the leads. This model allows to study the physical meaning of branch points
in the complex plane. They are points of coalesced eigenvalues and separate the
two scenarios with avoided level crossings and without any crossings in the
complex plane. They influence strongly the features of transmission through
double quantum dots.Comment: 30 pages, 14 figure
Surface roughness and interfacial slip boundary condition for quartz crystal microbalances
The response of a quartz crystal microbalance (QCM) is considered using a wave equation for the substrate and the Navier-Stokes equations for a finite liquid layer under a slip boundary condition. It is shown that when the slip length to shear wave penetration depth is small, the first order effect of slip is only present in the frequency response. Importantly, in this approximation the frequency response satisfies an additivity relation with a net response equal to a Kanazawa liquid term plus an additional Sauerbrey "rigid" liquid mass. For the slip length to result in an enhanced frequency decrease compared to a no-slip boundary condition, it is shown that the slip length must be negative so that the slip plane is located on the liquid side of the interface. It is argued that the physical application of such a negative slip length could be to the liquid phase response of a QCM with a completely wetted rough surface. Effectively, the model recovers the starting assumption of additivity used in the trapped mass model for the liquid phase response of a QCM having a rough surface. When applying the slip boundary condition to the rough surface problem, slip is not at a molecular level, but is a formal hydrodynamic boundary condition which relates the response of the QCM to that expected from a QCM with a smooth surface. Finally, possible interpretations of the results in terms of acoustic reflectivity are developed and the potential limitations of the additivity result should vapour trapping occur are discussed
Theoretical mass sensitivity of Love wave and layer guided acoustic plate mode sensors
A model for the mass sensitivity of Love wave and layer guided shear horizontal acoustic plate mode (SH–APM) sensors is developed by considering the propagation of shear horizontally polarized acoustic waves in a three layer system. A dispersion equation is derived for this three layer system and this is shown to contain the dispersion equation for the two layer system of the substrate and the guiding layer plus a term involving the third layer, which is regarded as a perturbing mass layer. This equation is valid for an arbitrary thickness perturbing mass layer. The perturbation, Δν, of the wave speed for the two-layer system by a thin third layer of density, ρp and thickness Δh is shown to be equal to the mass per unit area multiplied by a function dependent only on the properties of the substrate and the guiding layer, and the operating frequency of the sensor. The independence of the function from the properties of the third layer means that the mass sensitivity of the bare, two-layer, sensor operated about any thickness of the guiding layer can be deduced from the slope of the numerically or experimentally determined dispersion curve. Formulas are also derived for a Love wave on an infinite thickness substrate describing the change in mass sensitivity due to a change in frequency. The consequences of the various formulas for mass sensing applications are illustrated using numerical calculations with parameters describing a (rigid) poly(methylmethacrylate) wave-guiding layer on a finite thickness quartz substrate. These calculations demonstrate that a layer-guided SH–APM can have a mass sensitivity comparable to, or higher, than that of Love waves propagating on the same substrate. The increase in mass sensitivity of the layer guided SH–APMs over previously studied SH–APM sensors is of significance, particularly for liquid sensing applications. The relevance of the dispersion curve to experiments using higher frequencies or frequency hopping and to experiments using thick guiding layers is discussed
- …