Symbolic analysis of reduced forms of the Navier-Stokes equations

AbstractA unified development of symbolic analysis is presented. Symbolic analysis is used to identify reduced forms of the linearized steady Navier-Stokes equations which permit computational solutions to be obtained in a single spatial march in the dominant flow direction. In particular it is demonstrated that the “parabolized” form of the Navier-Stokes equations, although not parabolic, is well-posed as an initial-value problem in space, provided the solution is restricted to functions with compact support. The effectiveness of symbolic analysis for determining the well-posedness of complex systems of equations, such as the Navier-Stokes equations, is clearly demonstrated

Recent Advances in Understanding Particle Acceleration Processes in Solar Flares

We review basic theoretical concepts in particle acceleration, with particular emphasis on processes likely to occur in regions of magnetic reconnection. Several new developments are discussed, including detailed studies of reconnection in three-dimensional magnetic field configurations (e.g., current sheets, collapsing traps, separatrix regions) and stochastic acceleration in a turbulent environment. Fluid, test-particle, and particle-in-cell approaches are used and results compared. While these studies show considerable promise in accounting for the various observational manifestations of solar flares, they are limited by a number of factors, mostly relating to available computational power. Not the least of these issues is the need to explicitly incorporate the electrodynamic feedback of the accelerated particles themselves on the environment in which they are accelerated. A brief prognosis for future advancement is offered.Comment: This is a chapter in a monograph on the physics of solar flares, inspired by RHESSI observations. The individual articles are to appear in Space Science Reviews (2011

Quantum Vacuum Experiments Using High Intensity Lasers

The quantum vacuum constitutes a fascinating medium of study, in particular since near-future laser facilities will be able to probe the nonlinear nature of this vacuum. There has been a large number of proposed tests of the low-energy, high intensity regime of quantum electrodynamics (QED) where the nonlinear aspects of the electromagnetic vacuum comes into play, and we will here give a short description of some of these. Such studies can shed light, not only on the validity of QED, but also on certain aspects of nonperturbative effects, and thus also give insights for quantum field theories in general.Comment: 9 pages, 8 figur

Identification and targeted management of a neurodegenerative disorder caused by biallelic mutations in SLC5A6

We describe a sibling pair displaying an early infantile-onset, progressive neurodegenerative phenotype, with symptoms of developmental delay and epileptic encephalopathy developing from, to, months of age. Using whole exome sequencing, compound heterozygous variants were identified in SLC, A, which encodes the sodium-dependent multivitamin transporter, SMVT, protein. SMVT is an important transporter of the B-group vitamins biotin, pantothenate, and lipoate. The protein is ubiquitously expressed and has major roles in vitamin uptake in the digestive system, as well as transport of these vitamins across the blood, brain barrier. Pathogenicity of the identified variants was demonstrated by impaired biotin uptake of mutant SMVT. Identification of this vitamin transporter as the genetic basis of this disorder guided targeted therapeutic intervention, resulting clinically in improvement of the patient, s neurocognitive and neuromotor function. This is the second report of biallelic mutations in SLC, A, leading to a neurodegenerative disorder due to impaired biotin, pantothenate and lipoate uptake. The genetic and phenotypic overlap of these cases confirms mutations in SLC, A, as the genetic cause of this disease phenotype. Recognition of the genetic disorder caused by SLC, A, mutations is essential for early diagnosis and to facilitate timely intervention by triple vitamin, biotin, pantothenate, and lipoate, replacement therapy.Steven W. Polyak ... Andreas W. Schreiber ... Christopher N. Hahn ... Dylan A. Mordaunt ... Drago Bratkovic, Grant W. Booker, Nicholas J. Smith, Hamish S. Scot

All-particle cosmic ray energy spectrum measured with 26 IceTop stations

We report on a measurement of the cosmic ray energy spectrum with the IceTop air shower array, the surface component of the IceCube Neutrino Observatory at the South Pole. The data used in this analysis were taken between June and October, 2007, with 26 surface stations operational at that time, corresponding to about one third of the final array. The fiducial area used in this analysis was 0.122 km^2. The analysis investigated the energy spectrum from 1 to 100 PeV measured for three different zenith angle ranges between 0{\deg} and 46{\deg}. Because of the isotropy of cosmic rays in this energy range the spectra from all zenith angle intervals have to agree. The cosmic-ray energy spectrum was determined under different assumptions on the primary mass composition. Good agreement of spectra in the three zenith angle ranges was found for the assumption of pure proton and a simple two-component model. For zenith angles {\theta} < 30{\deg}, where the mass dependence is smallest, the knee in the cosmic ray energy spectrum was observed between 3.5 and 4.32 PeV, depending on composition assumption. Spectral indices above the knee range from -3.08 to -3.11 depending on primary mass composition assumption. Moreover, an indication of a flattening of the spectrum above 22 PeV were observed.Comment: 38 pages, 17 figure

Flux-rope twist in eruptive flares and CMEs : due to zipper and main-phase reconnection

Funding: UK Science and Technology Facilities CouncilThe nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.PostprintPublisher PDFPeer reviewe