Fundamental solutions of homogeneous elliptic differential operators

We compute fundamental solutions of homogeneous elliptic differential operators, with constant coefficients, on $\mathbb{R}^n$ by mean of analytic continuation of distributions. The result obtained is valid in any dimension, for any degree and can be extended to pseudodifferential operators of the same type.Comment: 5 pages, perhaps to be revise

Fields and rings with few types

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It is shown here that a field extension of finite degree of a weakly small field either is a finite field or has no Artin-Schreier extension. A weakly small field of characteristic 2 is finite or algebraically closed. Every weakly small division ring of positive characteristic is locally finite dimensional over its centre. The Jacobson radical of a weakly small ring is locally nilpotent. Every weakly small division ring is locally, modulo its Jacobson radical, isomorphic to a product of finitely many matrix rings over division rings

A modification of the convective constraint release mechanism in the molecular stress function model giving enhanced vortex growth

The molecular stress function model with convective constraint release (MSF with CCR) constitutive model [J. Rheol. 45 (2001), 1387] is capable of fitting all viscometric data for IUPAC LDPE, with only two adjustable parameters (with difference found only on reported ¿steady-state¿ elongational viscosities). The full MSF with CCR model is implemented in a backwards particle-tracking implementation, using an adaptive method for the computation of relative stretch that reduces simulation time many-fold, with insignificant loss of accuracy. The model is shown to give improved results over earlier versions of the MSF (without CCR) when compared to well-known experimental data from White and Kondo [J. non-Newt. Fluid Mech., 3 (1977), 41]; but still to under-predict contraction flow opening angles. The discrepancy is traced to the interaction between the rotational dissipative function and the large stretch levels caused by the contraction flow. A modified combination of dissipative functions in the constraint release mechanism is proposed, which aims to reduce this interaction to allow greater strain hardening in a mixed flow. The modified constraint release mechanism is shown to fit viscometric rheological data equally well, but to give opening angles in the complex contraction flow that are much closer to the experimental data from White and Kondo. It is shown (we believe for the first time) that a constitutive model demonstrates an accurate fit to all planar elongational, uniaxial elongational and shear viscometric data, with a simultaneous agreement with this well-known experimental opening angle data. The sensitivity of results to inaccuracies caused by representing the components of the deformation gradient tensor to finite precision is examined; results are found to be insensitive to even large reductions in the precision used for the representation of components. It is shown that two models that give identical response in elongational flow, and a very similar fit to available shear data, give significantly different results in flows containing a mix of deformation modes. The implication for constitutive models is that evaluation against mixed deformation mode flow data is desirable in addition to evaluation against viscometric measurements

A First Synoptic Blazar Study Comprising Thirteen Blazars Visible in E>100 GeV Gamma-Rays

Since 2002, the number of detected blazars at E_\gamma > 100 GeV has more than doubled. I study all currently known BL Lac-type objects with published energy spectra. Their intrinsic energy spectra are reconstructed by removing extragalactic background light attenuation effects. The emission properties are then compared and correlated among each other, with X-ray data, and with the individual black hole masses. In addition, I consider temporal properties of the very high energy gamma-ray flux. Key findings concern the flux--black hole mass and variability scale--black hole mass connections and the correlation of the spectral slope and the luminosity. As a specific application, the study allows to constrain the still undetermined redshift of the blazar PG 1553+113.Comment: 4 pages, 4 figures, to appear in the proceedings of the 30th International Cosmic Ray Conference, Merida, July 200

Forecasting and Intercepting the 28 May 2013 Bennington, KS Tornadic Supercell: A Student Perspective

This project examines the 28 May 2013 mesoscale case over north-central Kansas and focuses on the step-by-step process from a student perspective. The project describes the tools, models, parameters, and observations used to determine the focus for the day, including a classic loaded-gun sounding measured and observed by the field team. The decisions made by the team on this day placed them in position to observe an EF-3 tornado near Bennington, Kansas. The main goal of the project is to educate students about how to forecast and safely observe severe weather events through a how-to-guide compiled from experiences in the Valparaiso University Meteorology Department program, Severe Convective Storms Field Study. The project will demonstrate how to apply the knowledge from the course to a real-time, in the field, forecast. Although forecasting is not an exact science just yet, the guide will help educate future students and others on how to utilize various tools and techniques in order to accurately forecast for convective weather

Fermionic fields in the pseudoparticle approach

The pseudoparticle approach is a numericalmethod to compute path integrals without discretizing spacetime. The basic idea is to consider only those field configurations, which can be represented as a linear superposition of a small number of localized building blocks (pseudoparticles), and to replace the functional integration by an integration over the pseudoparticle degrees of freedom. In previous papers we have successfully applied the pseudoparticle approach to SU(2) Yang-Mills theory. In this work we discuss the inclusion of fermionic fields in the pseudoparticle approach. To test our method, we compute the phase diagram of the 1+1-dimensional Gross-Neveu model in the large-N limit as well as the chiral condensate in the crystal phase

Generalised model-independent characterisation of strong gravitational lenses IV: formalism-intrinsic degeneracies

Based on the standard gravitational lensing formalism with its effective, projected lensing potential in a given background cosmology, we investigate under which transformations of the source position and of the deflection angle the observable properties of the multiple images, i.e. the time delay differences, the relative image positions, relative shapes, and magnification ratios, remain invariant. As these observables only constrain local lens properties, we derive general, local invariance transformations in the areas covered by the multiple images. We show that the known global invariance transformations, e.g. the mass sheet transformation or the source position transformation, are contained in our invariance transformations, when they are restricted to the areas covered by the multiple images and when lens-model-based degeneracies are ignored, like the freedom to add or subtract masses in unconstrained regions without multiple images. Hence, we have identified the general class of invariance transformations that can occur, in particular in our model-independent local characterisation of strong gravitational lenses.Comment: 10 pages, 4 figures, in press in A&A, comments very welcome (update to accepted and improved version

Generalised model-independent characterisation of strong gravitational lenses III: perturbed axisymmetric lenses

In galaxy-galaxy strong gravitational lensing, Einstein rings are generated when the lensing galaxy has an axisymmetric lensing potential and the source galaxy is aligned with its symmetry centre along the line of sight. Using a Taylor expansion around the Einstein radius and eliminating the unknown source, I derive a set of analytic equations that determine differences of the deflection angle of the perturber weighted by the convergence of the axisymmetric lens and ratios of the convergences at the positions of the arcs from the measurable thickness of the arcs. In the same manner, asymmetries in the brightness distributions along an arc determine differences in the deflection angle of the perturber if the source has a symmetric brightness profile and is oriented parallel to or orthogonal to the caustic. These equations are the only model-independent information retrievable from observations to leading order in the Taylor expansion. General constraints on the derivatives of the perturbing lens are derived such that the perturbation does not change the number of critical curves. To infer physical properties such as the mass of the perturber or its position, models need to be inserted. The same conclusions about the scale of detectable masses and model-dependent degeneracies as in other approaches are then found and supported by analysing B1938 as an example. Yet, the model-independent equations show that there is a fundamental degeneracy between the main lens and the perturber that can only be broken if their relative position is known. This explains the degeneracies between lens models already found in simulations from a more general viewpoint. Depending on the properties of the pertuber, this degeneracy can be broken by characterising the surrounding of the lens or by measuring the time delay between quasar images embedded in the perturbed Einstein ring of the host galaxy.Comment: 10 pages, 3 figures, 1 table, accepted for publication in Astronomy & Astrophysics, comments welcom