An investigation of Lagrangian Riemann methods incorporating material strength

The application of Riemann Methods formulated in the Lagrangian reference frame to the numerical simulation of non-linear events in solid materials is investigated. Here, solids are characterised by their ability to withstand shear distortion since they possess material strength. In particular, numerical techniques are discussed for simulating the transient response of solids subjected to extreme loading. In such circumstances, the response of solids will often be highly non-linear, displaying elastic and plastic behaviour, and even moderate compressions will produce strong shock waves.This work reviews the numerical schemes or 'hydrocodes' which have been adopted in the past in order to simulate such systems, identifying the advantages and limitations of such techniques. One of the most prominent limitations of conventional Lagrangian methods is that the computational mesh or grid has fixed-connectivity i.e. mesh nodes are connected to the same nodes for all time. This has significant disadvantages since the computational mesh can easily become tangled as the simulated material distorts. The majority of conventional hydrocodes are also constructed using outdated artificial viscosity schemes which are known to diffuse shock waves and other steep features which may be present in the solution.In the work presented here, a novel two-dimensional Lagrangian solver has been developed Vucalm-EP which overcomes many of the limitations of conventional techniques. By employing the Free-Lagrange Method, whereby the connectivity of the computational mesh is allowed to evolve as the material distorts, problems of arbitrarily large deformation can be simulated. With the implementation of a spatially second-order accurate, finite-volume, Godunov-type solver, non-linear waves such as shocks are represented with higher resolution than previously possible with contemporary schemes. The Vucalm-EP solver simulates the transient elastic-perfectly plastic response of solids and displays increased accuracy over alternative Lagrangian techniques developed to simulate large material distortion such as Smoothed particle Hydrodynamics (SPH). Via a variety of challenging numerical simulations the Vucalm-EP solver is compared with contemporary Euler, fixed-connectivity Lagrangian, and meshless SPH solvers. These simulations include the solution of one- and two dimensional shock tube problems in aluminium, simulating the collapse of cylindrical shells and modelling high-velocity projectile impacts. Validation against previously published results, solutions obtained using alternative numerical techniques and analytical models illustrates the versatility and accuracy of the technique. Thus, the Vucalm-EP solver provides a numerical scheme for the Lagrangian simulation of extensive material distortion in materials with strength, which has never previously been possible with mesh-based techniques

Rational Curves and (0,2)-Deformations

We compare the count of (0,2)-deformation moduli fields for N=(2,2) conformal field theories on orbifolds and sigma-models on resolutions of the orbifold. The latter involves counting deformations of the tangent sheaf. We see there is generally a discrepancy which is expected to be explained by worldsheet instanton corrections coming from rational curves in the orbifold resolution. We analyze the rational curves on the resolution to determine such corrections and discover that irreducible toric rational curves account for some, but not all, of the discrepancy. In particular, this proves that there must be worldsheet instanton corrections beyond those from smooth isolated rational curves.Comment: 25 pages, PDFLaTe

Mesogranulation and small-scale dynamo action in the quiet Sun

Regions of quiet Sun generally exhibit a complex distribution of small-scale magnetic field structures, which interact with the near-surface turbulent convective motions. Furthermore, it is probable that some of these magnetic fields are generated locally by a convective dynamo mechanism. In addition to the well-known granular and supergranular convective scales, various observations have indicated that there is an intermediate scale of convection, known as mesogranulation, with vertical magnetic flux concentrations accumulating preferentially at mesogranular boundaries. Our aim is to investigate the small-scale dynamo properties of a convective flow that exhibits both granulation and mesogranulation, comparing our findings with solar observations. Adopting an idealised model for a localised region of quiet Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D Cartesian domain, to investigate the parametric dependence of this system (focusing particularly upon the effects of varying the aspect ratio and the Reynolds number). In purely hydrodynamic convection, we find that mesogranulation is a robust feature of this system provided that the domain is wide enough to accommodate these large-scale motions. The mesogranular peak in the kinetic energy spectrum is more pronounced in the higher Reynolds number simulations. We investigate the dynamo properties of this system in both the kinematic and the nonlinear regimes and we find that the dynamo is always more efficient in larger domains, when mesogranulation is present. Furthermore, we use a filtering technique in Fourier space to demonstrate that it is indeed the larger scales of motion that are primarily responsible for driving the dynamo. In the nonlinear regime, the magnetic field distribution compares very favourably to observations, both in terms of the spatial distribution and the measured field strengths.Comment: 12 pages, 11 figures, accepted for publication in Astronomy & Astrophysic

Exact Heavy to Light Meson Form Factors in the Combined Heavy Quark, Large NcN_c and Chiral Limits

We demonstrate that the form factors of local operators between a heavy meson state (like the~$B$) and a light pseudoscalar state (like the pion) are given exactly by a single pole form in the combined heavy quark, large $N_c$ (number of colors) and chiral limits. We discuss the deviations from this exact result from finite heavy quark masses, non-zero light quark masses and finite $N_c$. We comment on some implications of this result.Comment: 12 pages (harvmac), Brown-HET-92

The Microbiota and Health Promoting Characteristics of the Fermented Beverage Kefir

peer-reviewedKefir is a complex fermented dairy product created through the symbiotic fermentation of milk by lactic acid bacteria and yeasts contained within an exopolysaccharide and protein complex called a kefir grain. As with other fermented dairy products, kefir has been associated with a range of health benefits such as cholesterol metabolism and angiotensin-converting enzyme (ACE) inhibition, antimicrobial activity, tumor suppression, increased speed of wound healing, and modulation of the immune system including the alleviation of allergy and asthma. These reports have led to increased interest in kefir as a focus of research and as a potential probiotic-containing product. Here, we review those studies with a particular emphasis on the microbial composition and the health benefits of the product, as well as discussing the further development of kefir as an important probiotic product.The authors are funded through the Teagasc Walsh Fellowship Scheme(2014025)and internal Teagasc funding(RMIS6486). BW is supported by the Canada Research Chairs Program and research in the Cotter laboratory is funded by SFI through the PI award “Obesibiotics”(11/PI/1137)and in the form of a center grant (APC Microbiome Institute Grant Number SFI/12/RC/2273)