A Model for the Voltage Steps in the Breakdown of the Integer Quantum Hall Effect

In samples used to maintain the US resistance standard the breakdown of the dissipationless integer quantum Hall effect occurs as a series of dissipative voltage steps. A mechanism for this type of breakdown is proposed, based on the generation of magneto-excitons when the quantum Hall fluid flows past an ionised impurity above a critical velocity. The calculated generation rate gives a voltage step height in good agreement with measurements on both electron and hole gases. We also compare this model to a hydrodynamic description of breakdown.Comment: 4 pages including 3 figure

Linear Problems and Linear Algorithms

AbstractUsing predicate logic, the concept of a linear problem is formalized. The class of linear problems is huge, diverse, complex, and important. Linear and randomized linear algorithms are formalized. For each linear problem, a linear algorithm is constructed that solves the problem and a randomized linear algorithm is constructed that completely solves it, that is, for any data of the problem, the output set of the randomized linear algorithm is identical to the solution set of the problem. We obtain a single machine, referred to as the Universal (Randomized) Linear Machine, which (completely) solves every instance of every linear problem. Conversely, for each randomized linear algorithm, a linear problem is constructed that the algorithm completely solves. These constructions establish a one-to-one and onto correspondence from equivalence classes of linear problems to equivalence classes of randomized linear algorithms.Our construction of (randomized) linear algorithms to (completely) solve linear problems as well as the algorithms themselves are based on Fourier Elimination and have superexponential complexity. However, there is no evidence that the inefficiency of our methods is unavoidable relative to the difficulty of the problem

Polygonal excitations of spinning and levitating droplets

The shape of a weightless spinning liquid droplet is governed by the balance between the surface tension and centrifugal forces. The axisymmetric shape for slow rotation becomes unstable to a non-axisymmetric distortion above a critical angular velocity, beyond which the droplet progresses through a series of 2-lobed shapes. Theory predicts the existence of a family of 3- and 4-lobed equilibrium shapes at higher angular velocity. We investigate the formation of a triangular-shaped magnetically levitated water droplet, driven to rotate by the Lorentz force on an ionic current within the droplet. We also study equatorial traveling waves which give the droplet 3, 4 and 5-fold symmetry.Comment: Supplementary information at http://www.nottingham.ac.uk/~ppzlev/Drople

Validation of magnetophonon spectroscopy as a tool for analyzing hot-electron effects in devices

It is shown that very high precision hot-electron magnetophonon experiments made on n+n−n+-GaAs sandwich device structures which are customized for magnetoresistance measurements can be very accurately modeled by a new Monte Carlo technique. The latter takes account of the Landau quantization and device architecture as well as material parameters. It is proposed that this combination of experiment and modeling yields a quantitative tool for the direct analysis of spatially localized very nonequilibrium electron distributions in small devices and low dimensional structures

Extended twin study of alcohol use in Virginia and Australia

Drinking alcohol is a normal behavior in many societies, and prior studies have demonstrated it has both genetic and environmental sources of variation. Using two very large samples of twins and their first-degree relatives (Australia ≈ 20,000 individuals from 8,019 families; Virginia ≈ 23,000 from 6,042 families), we examine whether there are differences: (1) in the genetic and environmental factors that influence four interrelated drinking behaviors (quantity, frequency, age of initiation, and number of drinks in the last week), (2) between the twin-only design and the extended twin design, and (3) the Australian and Virginia samples. We find that while drinking behaviors are interrelated, there are substantial differences in the genetic and environmental architectures across phenotypes. Specifically, drinking quantity, frequency, and number of drinks in the past week have large broad genetic variance components, and smaller but significant environmental variance components, while age of onset is driven exclusively by environmental factors. Further, the twin-only design and the extended twin design come to similar conclusions regarding broad-sense heritability and environmental transmission, but the extended twin models provide a more nuanced perspective. Finally, we find a high level of similarity between the Australian and Virginian samples, especially for the genetic factors. The observed differences, when present, tend to be at the environmental level. Implications for the extended twin model and future directions are discussed

Cross-cultural comparison of genetic and cultural transmission of smoking initiation using an extended twin kinship model

Background: Considerable evidence from twin and adoption studies indicates that genetic and shared environmental factors play a role in the initiation of smoking behavior. Although twin and adoption designs are powerful to detect genetic and environmental influences, they do not provide information on the processes of assortative mating and parent–offspring transmission and their contribution to the variability explained by genetic and/or environmental factors. Methods: We examined the role of genetic and environmental factors in individual differences for smoking initiation (SI) using an extended kinship design. This design allows the simultaneous testing of additive and non-additive genetic, shared and individual-specific environmental factors, as well as sex differences in the expression of genes and environment in the presence of assortative mating and combined genetic and cultural transmission, while also estimating the regression of the prevalence of SI on age. A dichotomous lifetime ‘ever’ smoking measure was obtained from twins and relatives in the ‘Virginia 30,000’ sample and the ‘Australian 25,000’. Results: Results demonstrate that both genetic and environmental factors play a significant role in the liability to SI. Major influences on individual differences appeared to be additive genetic and unique environmental effects, with smaller contributions from assortative mating, shared sibling environment, twin environment, cultural transmission, and resulting genotype-environment covariance. Age regression of the prevalence of SI was significant. The finding of negative cultural transmission without dominance led us to investigate more closely two possible mechanisms for the lower parent–offspring correlations compared to the sibling and DZ twin correlations in subsets of the data: (1) age × gene interaction, and (2) social homogamy. Neither of the mechanism provided a significantly better explanation of the data. Conclusions: This study showed significant heritability, partly due to assortment, and significant effects of primarily non-parental shared environment on liability to SI