Deconstructing Non-Abelian Gauge Theories at One Loop

Deconstruction of 5D Yang-Mills gauge theories is studied in next-to-leading order accuracy. We calculate one-loop corrections to the mass spectrum of the non-linear gauged sigma-model, which is the low energy effective theory of the deconstructed theory. Renormalization is carried out following the standard procedure of effective field theories. The relation between the radius of the compactified fifth dimension and the symmetry breaking scale of the non-linear sigma-model is modified by radiative corrections. We demonstrate that one can match the low lying spectrum of the gauge boson masses of the effective 4D gauged non-linear sigma-model to the Kaluza-Klein modes of the 5D theory at one-loop accuracy

Non-linear analysis of two-layer timber beams considering interlayer slip and uplift

A new mathematical model and its finite element formulation for the non-linear analysis of mechanical behaviour of a two-layer timber planar beam is presented. A modified principle of virtual work is employed in formulating the finite element method. The basic unknowns are strains. The following assumptions are adopted in the mathematical model: materials are taken to be non-linear and can differ from layer to layer; interacting shear and normal contact tractions between layers are derived from the non-linear shear contact traction-slip and the non-linear normal contact traction-uplift characteristics of the connectors; the geometrically linear and materially non-linear Bernoulli's beam theory is assumed for each layer. The formulation is found to be accurate, reliable and computationally effective. The suitability of the theory is validated by the comparison of the numerical solution and the experimental results of full-scale laboratory tests on a simply supported beam. An excellent agreement between measured and calculated results is observed for all load levels. The further objective of the paper is the analysis of the effect of different normal contact traction-uplift constitutive relationships on the kinematic and static quantities in a statically determined and undetermined structure. While the shear contact traction-slip constitutive relationship dictates the deformability of the composite beam and has a substantial influence on most of the static and kinematic quantities of the composite beam, a variable normal contact traction-uplift constitutive relationship is in most cases negligible

Dynamics of granular avalanches caused by local perturbations

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. Following previous studies, we use mass and momentum conservation to derive St-Venant like equations for the evolution of the thickness R of the mobile layer and the profile Z of the static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.Comment: 25 pages, 12 figure

On the role of specific drug binding in modelling arterial eluting stents

In this paper we consider drug binding in the arterial wall following delivery by a drug-eluting stent. Whilst it is now generally accepted that a non-linear saturable reversible binding model is required to properly describe the binding process, the precise form of the binding model varies between authors. Our particular interest in this manuscript is in assessing to what extent modelling specific and non-specific binding in the arterial wall as separate phases is important. We study this issue by extending a recently developed coupled model of drug release and arterial tissue distribution, and comparing simulated profiles of drug concentration and drug mass in each phase within the arterial tissue

Using Random Forests to Describe Equity in Higher Education: A Critical Quantitative Analysis of Utah’s Postsecondary Pipelines

The following work examines the Random Forest (RF) algorithm as a tool for predicting student outcomes and interrogating the equity of postsecondary education pipelines. The RF model, created using longitudinal data of 41,303 students from Utah\u27s 2008 high school graduation cohort, is compared to logistic and linear models, which are commonly used to predict college access and success. Substantially, this work finds High School GPA to be the best predictor of postsecondary GPA, whereas commonly used ACT and AP test scores are not nearly as important. Each model identified several demographic disparities in higher education access, most significantly the effects of individual-level economic disadvantage. District- and school-level factors such as the proportion of Low Income students and the proportion of Underrepresented Racial Minority (URM) students were important and negatively associated with postsecondary success. Methodologically, the RF model was able to capture non-linearity in the predictive power of school- and district-level variables, a key finding which was undetectable using linear models. The RF algorithm outperforms logistic models in prediction of student enrollment, performs similarly to linear models in prediction of postsecondary GPA, and excels both models in its descriptions of non-linear variable relationships. RF provides novel interpretations of data, challenges conclusions from linear models, and has enormous potential to further the literature around equity in postsecondary pipelines