Granular Rayleigh-Taylor Instability: Experiments and Simulations

A granular instability driven by gravity is studied experimentally and numerically. The instability arises as grains fall in a closed Hele-Shaw cell where a layer of dense granular material is positioned above a layer of air. The initially flat front defined by the grains subsequently develops into a pattern of falling granular fingers separated by rising bubbles of air. A transient coarsening of the front is observed right from the start by a finger merging process. The coarsening is later stabilized by new fingers growing from the center of the rising bubbles. The structures are quantified by means of Fourier analysis and quantitative agreement between experiment and computation is shown. This analysis also reveals scale invariance of the flow structures under overall change of spatial scale.Comment: 4 pages, 11 figure

Nonextensive statistics in viscous fingering

Measurements in turbulent flows have revealed that the velocity field in nonequilibrium systems exhibits $q$-exponential or power law distributions in agreement with theoretical arguments based on nonextensive statistical mechanics. Here we consider Hele-Shaw flow as simulated by the Lattice Boltzmann method and find similar behavior from the analysis of velocity field measurements. For the transverse velocity, we obtain a spatial $q$-Gaussian profile and a power law velocity distribution over all measured decades. To explain these results, we suggest theoretical arguments based on Darcy's law combined with the non-linear advection-diffusion equation for the concentration field. Power law and $q$-exponential distributions are the signature of nonequilibrium systems with long-range interactions and/or long-time correlations, and therefore provide insight to the mechanism of the onset of fingering processes.Comment: 8 pages including 3 figures; to appear in PHYSICA

Self-Adjointness of the Dirac Hamiltonian and Fermion Number Fractionization in the Background of a Singular Magnetic Vortex

The method of self-adjoint extensions is employed to determine the vacuum quantum numbers induced by a singular static magnetic vortex in $2+1$-dimensional spinor electrodynamics. The results obtained are gauge-invariant and, for certain values of the extension parameter, both periodic in the value of the vortex flux and possessing definite parity with respect to the charge conjugation.Comment: LaTe

Continuum-particle hybrid coupling for mass, momentum and energy transfers in unsteady fluid flow

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C->P and P->C) which conveys mass, momentum and energy fluxes. The contribution of the hybrid scheme hereby presented is two-fold: first it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.Comment: LaTex, 12 pages, 9 figure

Vacuum polarization for neutral particles in 2+1 dimensions

In 2+1 dimensions there exists a duality between a charged Dirac particle coupled minimally to a background vector potential and a neutral one coupled nonminimally to a background electromagnetic field strength. A constant uniform background electric current induces in the vacuum of the neutral particle a fermion current which is proportional to the background one. A background electromagnetic plane wave induces no current in the vacuum. For constant but nonuniform background electric charge, known results for charged particles can be translated to give the induced fermion number. Some new examples with infinite background electric charge are presented. The induced spin and total angular momentum are also discussed.Comment: REVTeX, 7 pages, no figur

Urban–rural differences in pediatric traumatic head injuries: A prospective nationwide study

Jonas G Halldorsson1, Kjell M Flekkoy2, Kristinn R Gudmundsson3, Gudmundur B Arnkelsson4, Eirikur Orn Arnarson1,51Psychological Health Services, Landspitali University Hospital, Reykjavik, Iceland; 2Department of Psychology, University of Oslo, Oslo, Norway; 3Department of Neurosurgery, Landspitali University Hospital, Reykjavik, Iceland; 4Faculty of Social Science, University of Iceland, Reykjavik, Iceland; 5Faculty of Medicine, University of Iceland, Reykjavik, IcelandAims: To estimate differences in the incidence of recorded traumatic head injuries by gender, age, severity, and geographical area.Methods: The study was prospective and nationwide. Data were collected from all hospitals, emergency units and healthcare centers in Iceland regarding all Icelandic children and adolescents 0–19 years old consecutively diagnosed with traumatic head injuries (N = 550) during a one-year period.Results: Annual incidence of minimal, mild, moderate/severe, and fatal head injuries (ICD-9 850–854) was 6.41 per 1000, with 95% confi dence interval (CI) 5.9, 7.0. Annual incidence of minimal head injuries (ICD-9 850) treated at emergency units was 4.65 (CI 4.2, 5.1) per 1000, mild head injuries admitted to hospital (ICD-9 850) was 1.50 (CI 1.3, 1.8) per 1000, and moderate/severe nonfatal injuries (ICD-9 851–854) was 0.21 (CI 0.1, 0.3) per 1000. Death rate was 0.05 (CI 0.0, 0.1) per 1000. Young children were at greater risk of sustaining minimal head injuries than older ones. Boys were at greater risk than girls were. In rural areas, incidence of recorded minimal head injuries was low.Conclusions: Use of nationwide estimate of the incidence of pediatric head injury shows important differences between urban and rural areas as well as between different age groups.Keywords: incidence, nationwide, pediatric, prospective, traumatic head injuries, urban-rural difference

The prognostic value of injury severity, location of event, and age at injury in pediatric traumatic head injuries

Jonas G Halldorsson1, Kjell M Flekkoy2, Gudmundur B Arnkelsson3, Kristinn Tomasson4, Kristinn R Gudmundsson5, Eirikur Orn Arnarson1,61Psychological Health Services, Landspitali University Hospital, Reykjavik, Iceland; 2Department of Psychology, University of Oslo, and Department of Geriatric Medicine, Ulleval University Hospital, Oslo, Norway; 3Department of Psychology, University of Iceland, Reykjavik, Iceland; 4Administration of Occupational Safety and Health, Reykjavik, Iceland; 5Department of Neurosurgery, Landspitali University Hospital, Reykjavik, Iceland; 6Faculty of Medicine, University of Iceland, Reykjavik, IcelandAims: To estimate the prognostic value of injury severity, location of event, and demographic parameters, for symptoms of pediatric traumatic head injury (THI) 4 years later.Methods: Data were collected prospectively from Reykjavik City Hospital on all patients age 0–19 years, diagnosed with THI (n = 408) during one year. Information was collected on patient demographics, location of traumatic event, cause of injury, injury severity, and ICD-9 diagnosis. Injury severity was estimated according to the Head Injury Severity Scale (HISS). Four years post-injury, a questionnaire on late symptoms attributed to the THI was sent.Results: Symptoms reported were more common among patients with moderate/severe THI than among others (p < 0.001). The event location had prognostic value (p < 0.05). Overall, 72% of patients with moderate/severe motor vehicle-related THI reported symptoms. There was a curvilinear age effect (p < 0.05). Symptoms were least frequent in the youngest age group, 0–4 years, and most frequent in the age group 5–14 years. Gender and urban/rural residence were not significantly related to symptoms.Conclusions: Motor vehicle related moderate/severe THI resulted in a high rate of late symptoms. Location had a prognostic value. Patients with motor vehicle-related THI need special consideration regardless of injury severity.Keywords: follow-up, pediatric, symptoms, traumatic head injur

Fractionalization of angular momentum at finite temperature around a magnetic vortex

Ambiguities in the definition of angular momentum of a quantum-mechanical particle in the presence of a magnetic vortex are reviewed. We show that the long-standing problem of the adequate definition is resolved in the framework of the second-quantized theory at nonzero temperature. Planar relativistic Fermi gas in the background of a point-like magnetic vortex with arbitrary flux is considered, and we find thermal averages, quadratic fluctuations, and correlations of all observables, including angular momentum, in this system. The kinetic definition of angular momentum is picked out unambiguously by the requirement of plausible behaviour for the angular momentum fluctuation and its correlation with fermion number.Comment: 32 pages, submitted to Annals of Physic