Classical diamagnetism, magnetic interaction energies, and repulsive forces in magnetized plasmas

The Bohr-van Leeuwen theorem is often summarized as saying that there is no classical magnetic susceptibility, in particular no diamagnetism. This is seriously misleading. The theorem assumes position dependent interactions but this is not required by classical physics. Since the work of Darwin in 1920 it has been known that the magnetism due to classical charged point particles can only be described by allowing velocity dependent interactions in the Lagrangian. Legendre transformation to an approximate Hamiltonian can give an estimate of the Darwin diamagnetism for a system of charged point particles. Comparison with experiment, however, requires knowledge of the number of classically behaving electrons in the sample. A new repulsive effective many-body force, which should be relevant in plasmas, is predicted by the Hamiltonian.Comment: added references, revise

The exact Darwin Lagrangian

Darwin (1920) noted that when radiation can be neglected it should be possible to eliminate the radiation degrees-of-freedom from the action of classical electrodynamics and keep the discrete particle degrees-of-freedom only. Darwin derived his well known Lagrangian by series expansion in $v/c$ keeping terms up to order $(v/c)^2$. Since radiation is due to acceleration the assumption of low speed should not be necessary. A Lagrangian is suggested that neglects radiation without assuming low speed. It cures deficiencies of the Darwin Lagrangian in the ultra-relativistic regime.Comment: 2.5 pages, no figure

The comfortable roller coaster -- on the shape of tracks with constant normal force

A particle that moves along a smooth track in a vertical plane is influenced by two forces: gravity and normal force. The force experienced by roller coaster riders is the normal force, so a natural question to ask is: what shape of the track gives a normal force of constant magnitude? Here we solve this problem. It turns out that the solution is related to the Kepler problem; the trajectories in velocity space are conic sections.Comment: 10 pages, 4 figure

Normal families and fixed points of iterates

Let F be a family of holomorphic functions and let K be a constant less than 4. Suppose that for all f in F the second iterate of f does not have fixed points for which the modulus of the multiplier is greater than K. We show that then F is normal. This is deduced from a result about the multipliers of iterated polynomials.Comment: 5 page

On the regular-geometric-figure solution to the N-body problem

The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of interactions beyond the gravitational ones for some special values of the parameters of the forces. For the harmonic oscillator, in particular, it is shown that the $N$-body problem is reduced to $N$ one-body problems.Comment: To appear in Eur. J. Phys. (5 pages

Static deformation of heavy spring due to gravity and centrifugal force

The static equilibrium deformation of a heavy spring due to its own weight is calculated for two cases. First for a spring hanging in a constant gravitational field, then for a spring which is at rest in a rotating system where it is stretched by the centrifugal force. Two different models are considered. First a discrete model assuming a finite number of point masses connected by springs of negligible weight. Then the continuum limit of this model. In the second case the differential equation for the deformation is obtained by demanding that the potential energy is minimized. In this way a simple application of the variational calculus is obtained.Comment: 11 pages, 2 figure

The non-self-adjointness of the radial momentum operator in n dimensions

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the $n$-dimensional radial momentum operator is not self- adjoint and has no self-adjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on $L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint extensions.Comment: Some text and a reference adde

A forage-only diet alters the metabolic response of horses in training

Most athletic horses are fed a high-starch diet despite the risk of health problems. Replacing starch concentrate with high-energy forage would alleviate these health problems, but could result in a shift in major substrates for muscle energy supply from glucose to short-chain fatty acids (SCFA) due to more hindgut fermentation of fibre. Dietary fat inclusion has previously been shown to promote aerobic energy supply during exercise, but the contribution of SCFA to exercise metabolism has received little attention. This study compared metabolic response with exercise and lactate threshold (VLa4) in horses fed a forage-only diet (F) and a more traditional high-starch, low-energy forage diet (forage–concentrate diet - FC). The hypothesis was that diet F would increase plasma acetate concentration and increase VLa4 compared with diet FC. Six Standardbred geldings in race training were used in a 29-day change-over experiment. Plasma acetate, non-esterified fatty acids (NEFA), lactate, glucose and insulin concentrations and venous pH were measured in samples collected before, during and after a treadmill exercise test (ET, day 25) and muscle glycogen concentrations before and after ET. Plasma acetate concentration was higher before and after exercise in horses on diet F compared with diet FC, and there was a tendency ( P50.09) for increased VLa4 on diet F. Venous pH and plasma glucose concentrations during exercise were higher in horses on diet F than diet FC, as was plasma NEFA on the day after ET. Plasma insulin and muscle glycogen concentrations were lower for diet F, but glycogen utilisation was similar for the two diets. The results show that a high-energy, forage-only diet alters the metabolic response to exercise and, with the exception of lowered glycogen stores, appears to have positive rather than negative effects on performance traits

Mechanics, cosmology and Mach's principle

It is pointed out that recent cosmological findings seem to support the view that the mass/energy distribution of the universe defines the Newtonian inertial frames as originally suggested by Mach. The background concepts of inertial frame, Newton's second law, and fictitious forces are clarified. A precise definition of Mach's principle is suggested. Then an approximation to general relativity discovered by Einstein, Infeld, and Hoffmann is used and it is found that this precise formulation of Mach's principle is realized provided the mass/energy density of the universe has a specific value. This value turns out to be twice the critical density. The implications of this approximate result is put into context.Comment: 9 pages, 34 references, 0 figure

Causes of death among undocumented migrants in Sweden, 1997–2010

Background: Undocumented migrants are one of the most vulnerable groups in Swedish society, where they generally suffer from poor health and limited health care access. Due to their irregular status, such migrants are an under-researched group and are not included in the country's Cause of Death Register (CDR). Objective: To determine the causes of death among undocumented migrants in Sweden and to ascertain whether there are patterns in causes of death that differ between residents and undocumented migrants. Design: This is a cross-sectional study of death certificates issued from 1997 to 2010 but never included in the CDR from which we established our study sample of undocumented migrants. As age adjustments could not be performed due to lack of data, comparisons between residents and undocumented migrants were made at specific age intervals, based on the study sample's mean age at death±a half standard deviation. Results: Out of 7,925 individuals surveyed, 860 were classified as likely to have been undocumented migrants. External causes (49.8%) were the most frequent cause of death, followed by circulatory system diseases, and then neoplasms. Undocumented migrants had a statistically significant increased risk of dying from external causes (odds ratio [OR] 3.57, 95% confidence interval [CI]: 2.83–4.52) and circulatory system diseases (OR 2.20, 95% CI: 1.73–2.82) compared to residents, and a lower risk of dying from neoplasms (OR 0.07, 95% CI: 0.04–0.14). Conclusions: We believe our study is the first to determine national figures on causes of death of undocumented migrants. We found inequity in health as substantial differences in causes of death between undocumented migrants and residents were seen. Legal ambiguities regarding health care provision must be addressed if equity in health is to be achieved in a country otherwise known for its universal health coverage