Impurity effects in few-electron quantum dots: Incipient Wigner molecule regime

Numerically exact path-integral Monte Carlo data are presented for $N\leq 10$ strongly interacting electrons confined in a 2D parabolic quantum dot, including a defect to break rotational symmetry. Low densities are studied, where an incipient Wigner molecule forms. A single impurity is found to cause drastic effects: (1) The standard shell-filling sequence with magic numbers $N=4,6,9$, corresponding to peaks in the addition energy $\Delta(N)$, is destroyed, with a new peak at N=8, (2) spin gaps decrease, (3) for N=8, sub-Hund's rule spin S=0 is induced, and (4) spatial ordering of the electrons becomes rather sensitive to spin. We also comment on the recently observed bunching phenomenon.Comment: 7 pages, 1 table, 4 figures, accepted for publication in Europhysics Letter

Parameter identification in a semilinear hyperbolic system

We consider the identification of a nonlinear friction law in a one-dimensional damped wave equation from additional boundary measurements. Well-posedness of the governing semilinear hyperbolic system is established via semigroup theory and contraction arguments. We then investigte the inverse problem of recovering the unknown nonlinear damping law from additional boundary measurements of the pressure drop along the pipe. This coefficient inverse problem is shown to be ill-posed and a variational regularization method is considered for its stable solution. We prove existence of minimizers for the Tikhonov functional and discuss the convergence of the regularized solutions under an approximate source condition. The meaning of this condition and some arguments for its validity are discussed in detail and numerical results are presented for illustration of the theoretical findings

Estimating historical changes in physical activity levels.

ObjectiveTo compare activity levels between a simulated “historical” lifestyle and a “modern” lifestyle to try to validate earlier estimates of secular changes in activity.DesignTriaxial accelerometers (TRACMORs) were used to measure activity levels in a “historical” group of seven male actors who were paid to live like early Australian settlers at a theme park north of Sydney (eg, minimising the use of modern technology) for a week. Results were compared with those from a group of seven “modern” sedentary office workers.ResultsActivity levels were up to 2.3 times greater in the historical group than the modern group. Calculations based on body weight and energy expenditure suggest the difference is the equivalent of walking up to 16 km per day more in the past than today.ConclusionsThese findings accord with two previous estimates of changes in daily activity levels over time and suggest that recent public health guidelines for increasing physical activity may be inadequate

A Bayesian dose-response meta-analysis model: simulation study and application

Dose-response models express the effect of different dose or exposure levels on a specific outcome. In meta-analysis, where aggregated-level data is available, dose-response evidence is synthesized using either one-stage or two-stage models in a frequentist setting. We propose a hierarchical dose-response model implemented in a Bayesian framework. We present the model with cubic dose-response shapes for a dichotomous outcome and take into account heterogeneity due to variability in the dose-response shape. We develop our Bayesian model assuming normal or binomial likelihood and accounting for exposures grouped in clusters. We implement these models in R using JAGS and we compare our approach to the one-stage dose-response meta-analysis model in a simulation study. We found that the Bayesian dose-response model with binomial likelihood has slightly lower bias than the Bayesian model with the normal likelihood and the frequentist one-stage model. However, all three models perform very well and give practically identical results. We also re-analyze the data from 60 randomized controlled trials (15,984 participants) examining the efficacy (response) of various doses of antidepressant drugs. All models suggest that the dose-response curve increases between zero dose and 40 mg of fluoxetine-equivalent dose, and thereafter is constant. We draw the same conclusion when we take into account the fact that five different antidepressants have been studied in the included trials. We show that implementation of the hierarchical model in Bayesian framework has similar performance to, but overcomes some of the limitations of the frequentist approaches and offers maximum flexibility to accommodate features of the data

Fluctuation relations and rare realizations of transport observables

Fluctuation relations establish rigorous identities for the nonequilibrium averages of observables. Starting from a general transport master equation with time-dependent rates, we employ the stochastic path integral approach to study statistical fluctuations around such averages. We show how under nonequilibrium conditions, rare realizations of transport observables are crucial and imply massive fluctuations that may completely mask such identities. Quantitative estimates for these fluctuations are provided. We illustrate our results on the paradigmatic example of a mesoscopic RC circuit.Comment: 4 pages, 3 figures; v2: minor changes, published versio

Conductance quantization and snake states in graphene magnetic waveguides

We consider electron waveguides (quantum wires) in graphene created by suitable inhomogeneous magnetic fields. The properties of uni-directional snake states are discussed. For a certain magnetic field profile, two spatially separated counter-propagating snake states are formed, leading to conductance quantization insensitive to backscattering by impurities or irregularities of the magnetic field.Comment: 5 pages, 4 figures, final version accepted as Rapid Comm. in PR

Phonon-phonon interactions and phonon damping in carbon nanotubes

We formulate and study the effective low-energy quantum theory of interacting long-wavelength acoustic phonons in carbon nanotubes within the framework of continuum elasticity theory. A general and analytical derivation of all three- and four-phonon processes is provided, and the relevant coupling constants are determined in terms of few elastic coefficients. Due to the low dimensionality and the parabolic dispersion, the finite-temperature density of noninteracting flexural phonons diverges, and a nonperturbative approach to their interactions is necessary. Within a mean-field description, we find that a dynamical gap opens. In practice, this gap is thermally smeared, but still has important consequences. Using our theory, we compute the decay rates of acoustic phonons due to phonon-phonon and electron-phonon interactions, implying upper bounds for their quality factor.Comment: 15 pages, 2 figures, published versio

Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes

We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J. Phys. Cond. Mat., published versio

Charging effects in quantum wires

We investigate the role of charging effects in a voltage-biased quantum wire. Both the finite range of the Coulomb interaction and the long-ranged nature of the Friedel oscillation imply a finite capacitance, leading to a charging energy. While observable Coulomb blockade effects are absent for a single impurity, they are crucial if islands are present. For a double barrier, we give the resonance condition, fully taking into account the charging of the island.Comment: 6 Pages RevTeX, no figures, Phys. Rev. B (in press

The scaled boundary finite element method for the efficient modeling of linear elastic fracture

In this work, a study of computational and implementational efficiency is presented, on the treatment of Linear Elastic Fracture Mechanics (LEFM) problems. To this end, the Scaled Boundary Finite Element Method (SBFEM), is compared against the popular eXtended Finite Element Method (XFEM) and the standard FEM approach for efficient calculation of Stress Intensity Factors (SIFs). The aim is to examine SBFEM’s potential for inclusion within a multiscale fracture mechanics framework. The above features will be exploited to solve a series of benchmarks in LEFM comparing XFEM, SBFEM and commercial FEM software to analytical solutions. The extent to which the SBFEM lends itself for inclusion within a multiscale framework will further be assessed