Note on a paper by Anderson

An error concerning the group of symmetries of a particle moving in a uniform magnetic field is corrected.     

Bivariate probability densities with given margins

We determine the bivariate probability densities with specified margins and show that the Cohen-Zaparovanny class of positive phase-space density functions, with the quantum mechanical marginal distributions of position and momentum, contains all such densities.     

Rejoinder: Comments on a paper by Gruber

An error in Gruber's paper, Quantization in Generalised Coordinates, and the reason for this kind of error are pointed out. A partial answer to the problem posed by the paper is stated.     

Vacuum instability and tachyons: Comments on a paper by Zeldovich

We show that vacuum instabilities possibly arising because of tachyons do not contradict any experimental evidence, and therefore that no objection against tachyon existence can be found even on this ground.     

Comment on a paper by Gonzalez-Gascon

It is shown that the Gonzalez-Gascon effect does not exist and that the involved “distortions” had been measured experimentally.     

Comments on a paper by Collinson

The demonstration of the uniqueness of the Schwarzschild interior metric within conformally flat axisymmetric stationary spacetimes is revised. A complete proof containing the three possible branches of interior fluid solutions is given.     

A note on a paper by Atkin and Bastin

The paper A Homological Foundation for Scale Problems in Physics (Atkin & Bastin, 1970) is criticised on account of several inconsistencies in the argument. Possible applications of the general ideas used are then discussed in the context of a quantum logic type of framework.     

A note on a paper by Massa and Pagani

Massa and Pagani [1] have given a neat refutal to the conjecture [2] that the Riemann tensor is derivable from a tensor potential. Their method consists of assuming such a relationship does exist and examining the resulting integrability conditions; they show that the existence of such a potential will impose nontrivial restrictions on the Riemann tensor and so conclude that, in general, such a potential cannot exist. Although Massa and Pagani posed the problem and interpreted the conclusion in ordinary tensor notation the actual derivation of the crucial constraint equation was carried out in the language of tensor-valued differential forms, and is quite involved. In this note it is shown that the crucial equation can be obtained quite naturally and easily in ordinary tensor notation.     

Probability distributions for the run-and-tumble bacterial dynamics: An analogy to the Lorentz model

In this paper, we exploit an analogy of the run-and-tumble process for bacterial motility with the Lorentz model of electron conduction in order to obtain analytical results for the intermediate scattering function. This allows to obtain an analytical result for the van Hove function in real space for two-dimensional systems. We furthermore consider the 2D circling motion of bacteria close to solid boundaries with tumbling, and show that the analogy to electron conduction in a magnetic field allows to predict the effective diffusion coefficient of the bacteria. The latter is shown to be reduced by the circling motion of the bacteria.     

Most likely ensemble with a given average energy prepared by a single slit

We discuss an ensemble of particle selected by a single slit within the statistical model of quantization reported earlier. We look for the most probable distribution of the position of the particle with a given average energy by applying Jaynes’s maximum entropy principle. We first show that the most likely ensemble with the lowest possible average energy is given by the quantum mechanical ground state of a particle trapped inside the slit. We further show that in general it takes a larger energy to collect the beam of particles into a target position with a higher precision.     

Electronics with and on paper

Today there is a strong interest in the scientific and industrial community concerning the use of biopolymers for electronic applications, driven mainly by low‐cost and disposable applications. Adding to this interest, we must recognise the importance of the dream of wireless auto‐sustained and low‐energy‐consumption electronics. This dream can be fulfilled by cellulose paper, the lightest and the cheapest known substrate material, as well as the Earth's major biopolymer and of tremendous global economic importance. Most of the paper used up to now is optimised in terms of the required mechanical and physical properties to be used as the support of inks of different origins. In the future, specific electronic heterogeneous paper sheets should be fabricated aiming to get paper fibers with required bulk and surface functionalities, proper water/vapour barrier, size and diameter/thickness of the fibrils and full paper thickness. This will be the function of components/devices to be incorporated/integrated such as thin‐film transistors, complementary metal oxide semiconductor devices, passive electronic components (resistances, inductors and capacitors), memory transistors, electrochromics and thin‐film paper batteries. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Note on incoherent photon scattering by a statistical atom

The incoherent X-ray scattering by a statistical atom is studied for the screening function restored by using the experimental energy distribution of atomic electrons.