Solvable Examples of Drift and Diffusion of Ions in Non-uniform Electric Fields

The drift and diffusion of a cloud of ions in a fluid are distorted by an inhomogeneous electric field. If the electric field carries the center of the distribution in a straight line and the field configuration is suitably symmetric, the distortion can be calculated analytically. We examine the specific examples of fields with cylindrical and spherical symmetry in detail assuming the ion distributions to be of a generally Gaussian form. The effects of differing diffusion coefficients in the transverse and longitudinal directions are included

Pressure dependence of the magnetization in the ferromagnetic superconductor UGe_2

The recent discovery that superconductivity occurs in several clean itinerant ferromagnets close to low temperature magnetic instabilities naturally invites an interpretation based on a proximity to quantum criticality. Here we report measurements of the pressure dependence of the low temperature magnetisation in one of these materials, UGe_2. Our results show that both of the magnetic transitions observed in this material as a function of pressure are first order transitions and do not therefore correspond to quantum critical points. Further we find that the known pressure dependence of the superconducting transition is not reflected in the pressure dependence of the static susceptibility. This demonstrates that the spectrum of excitations giving superconductivity is not that normally associated with a proximity to quantum criticality in weak itinerant ferromagnets. In contrast our data suggest that instead the pairing spectrum might be related to a sharp spike in the electronic density of states that also drives one of the magnetic transitions.Comment: to appear in Phys. Rev. Let

A scanning drift tube apparatus for spatio-temporal mapping of electron swarms

A "scanning" drift tube apparatus, capable of mapping of the spatio-temporal evolution of electron swarms, developing between two plane electrodes under the effect of a homogeneous electric field, is presented. The electron swarms are initiated by photoelectron pulses and the temporal distributions of the electron flux are recorded while the electrode gap length (at a fixed electric field strength) is varied. Operation of the system is tested and verified with argon gas, the measured data are used for the evaluation of the electron bulk drift velocity. The experimental results for the space-time maps of the electron swarms - presented here for the first time - also allow clear observation of deviations from hydrodynamic transport. The swarm maps are also reproduced by particle simulations

Microscopic theories for cubic and tetrahedral superconductors: application to PrOs_4Sb_{12}

We examine weak-coupling theory for unconventional superconducting states of cubic or tetrahedral symmetry for arbitrary order parameters and Fermi surfaces and identify the stable states in zero applied field. We further examine the possibility of having multiple superconducting transitions arising from the weak breaking of a higher symmetry group to cubic or tetrahedral symmetry. Specifically, we consider two higher symmetry groups. The first is a weak crystal field theory in which the spin-singlet Cooper pairs have an approximate spherical symmetry. The second is a weak spin orbit coupling theory for which spin-triplet Cooper pairs have a cubic orbital symmetry and an approximate spherical spin rotational symmetry. In hexagonal UPt_3, these theories easily give rise to multiple transitions. However, we find that for cubic materials, there is only one case in which two superconducting transitions occur within weak coupling theory. This sequence of transitions does not agree with the observed properties of PrOs_4Sb_{12}. Consequently, we find that to explain two transitions in PrOs_4Sb_{12} using approximate higher symmetry groups requires a strong coupling theory. In view of this, we finally consider a weak coupling theory for which two singlet representations have accidentally nearly degenerate transition temperatures (not due to any approximate symmetries). We provide an example of such a theory that agrees with the observed properties of PrOs_4Sb_{12}.Comment: 11 pages,1 figur

Force Dependence of the Michaelis Constant in a Two-State Ratchet Model for Molecular Motors

We present a quantitative analysis of recent data on the kinetics of ATP hydrolysis, which has presented a puzzle regarding the load dependence of the Michaelis constant. Within the framework of coarse grained two-state ratchet models, our analysis not only explains the puzzling data, but provides a modified Michaelis law, which could be useful as a guide for future experiments.Comment: 4 pages, 3 eps figures, accepted for publication on Physical Review Letter

Deviations from the local field approximation in negative streamer heads

Negative streamer ionization fronts in nitrogen under normal conditions are investigated both in a particle model and in a fluid model in local field approximation. The parameter functions for the fluid model are derived from swarm experiments in the particle model. The front structure on the inner scale is investigated in a 1D setting, allowing reasonable run-time and memory consumption and high numerical accuracy without introducing super-particles. If the reduced electric field immediately before the front is >= 50kV/(cm bar), solutions of fluid and particle model agree very well. If the field increases up to 200kV/(cm bar), the solutions of particle and fluid model deviate, in particular, the ionization level behind the front becomes up to 60% higher in the particle model while the velocity is rather insensitive. Particle and fluid model deviate because electrons with high energies do not yet fully run away from the front, but are somewhat ahead. This leads to increasing ionization rates in the particle model at the very tip of the front. The energy overshoot of electrons in the leading edge of the front actually agrees quantitatively with the energy overshoot in the leading edge of an electron swarm or avalanche in the same electric field.Comment: The paper has 17 pages, including 15 figures and 3 table

Analytic solution of the fractional advection diffusion equation for the time-of-flight experiment in a finite geometry

A general analytic solution to the fractional advection diffusion equation is obtained in plane parallel geometry. The result is an infinite series of spatial Fourier modes which decay according to the Mittag-Leffler function, which is cast into a simple closed form expression in Laplace space using the Poisson summation theorem. An analytic expression for the current measured in a time-of-flight experiment is derived, and the sum of the slopes of the two respective time regimes on logarithmic axes is demonstrated to be -2, in agreement with the well known result for a continuous time random walk model. The sensitivity of current and particle number density to variation of experimentally controlled parameters is investigated in general, and the results applied to analyze selected experimental data.Comment: 10 pages, 6 figure

On the error term in Weyl's law for the Heisenberg manifolds (II)

In this paper we study the mean square of the error term in the Weyl's law of an irrational $(2l+1)$-dimensional Heisenberg manifold . An asymptotic formula is established

Coexistence of ferromagnetism and superconductivity

A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the paramagnetic one. The resulting phase diagram is compared with the experimental observations in UGe_2 and ZrZn_2.Comment: 16 pp., REVTeX, 6 eps figs; final version as publishe

Birthweight and risk markers for type 2 diabetes and cardiovascular disease in childhood: the Child Heart and Health Study in England (CHASE).

AIMS/HYPOTHESIS: Lower birthweight (a marker of fetal undernutrition) is associated with higher risks of type 2 diabetes and cardiovascular disease (CVD) and could explain ethnic differences in these diseases. We examined associations between birthweight and risk markers for diabetes and CVD in UK-resident white European, South Asian and black African-Caribbean children. METHODS: In a cross-sectional study of risk markers for diabetes and CVD in 9- to 10-year-old children of different ethnic origins, birthweight was obtained from health records and/or parental recall. Associations between birthweight and risk markers were estimated using multilevel linear regression to account for clustering in children from the same school. RESULTS: Key data were available for 3,744 (66%) singleton study participants. In analyses adjusted for age, sex and ethnicity, birthweight was inversely associated with serum urate and positively associated with systolic BP. After additional height adjustment, lower birthweight (per 100 g) was associated with higher serum urate (0.52%; 95% CI 0.38, 0.66), fasting serum insulin (0.41%; 95% CI 0.08, 0.74), HbA1c (0.04%; 95% CI 0.00, 0.08), plasma glucose (0.06%; 95% CI 0.02, 0.10) and serum triacylglycerol (0.30%; 95% CI 0.09, 0.51) but not with BP or blood cholesterol. Birthweight was lower among children of South Asian (231 g lower; 95% CI 183, 280) and black African-Caribbean origin (81 g lower; 95% CI 30, 132). However, adjustment for birthweight had no effect on ethnic differences in risk markers. CONCLUSIONS/INTERPRETATION: Birthweight was inversely associated with urate and with insulin and glycaemia after adjustment for current height. Lower birthweight does not appear to explain emerging ethnic difference in risk markers for diabetes