Optimal Explicit Strong Stability Preserving Runge--Kutta Methods with High Linear Order and optimal Nonlinear Order

High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The search for high order strong stability time-stepping methods with large allowable strong stability coefficient has been an active area of research over the last two decades. This research has shown that explicit SSP Runge--Kutta methods exist only up to fourth order. However, if we restrict ourselves to solving only linear autonomous problems, the order conditions simplify and this order barrier is lifted: explicit SSP Runge--Kutta methods of any linear order exist. These methods reduce to second order when applied to nonlinear problems. In the current work we aim to find explicit SSP Runge--Kutta methods with large allowable time-step, that feature high linear order and simultaneously have the optimal fourth order nonlinear order. These methods have strong stability coefficients that approach those of the linear methods as the number of stages and the linear order is increased. This work shows that when a high linear order method is desired, it may be still be worthwhile to use methods with higher nonlinear order

The Higgs System in and Beyond the Standard Model

After the discovery of the Higgs boson particle on the 4th of July of 2012 at the Large Hadron Collider, sited at the european CERN laboratory, we are entering in a fascinating period for Particle Physics where both theorists and experimentalists are devoted to fully understand the features of this new particle and the possible consequences for High Energy Physics of the Higgs system both within and beyond the Standard Model of fundamental particle interactions. This paper is a summary of the lectures given at the third IDPASC school (Santiago de Compostela, Feb. 2013, Spain) addressed to PhD students, and contains a short introduction to the main basic aspects of the Higgs boson particle in and beyond the Standard Model.Comment: 62 pages, 31 figures, Lectures of the IDPASC School at Santiago de Compostela, Spain, February 201

Modelling coevolution in multispecies communities

We introduce the Webworld model, which links together the ecological modelling of food web structure with the evolutionary modelling of speciation and extinction events. The model describes dynamics of ecological communities on an evolutionary timescale. Species are defined as sets of characteristic features, and these features are used to determine interaction scores between species. A simple rule is used to transfer resources from the external environment through the food web to each of the species, and to determine mean population sizes. A time step in the model represents a speciation event. A new species is added with features similar to those of one of the existing species and a new food web structure is then calculated. The new species may (i) add stably to the web, (ii) become extinct immediately because it is poorly adapted, or (iii) cause one or more other species to become extinct due to competition for resources. We measure various properties of the model webs and compare these with data on real food webs. These properties include the proportions of basal, intermediate and top species, the number of links per species and the number of trophic levels. We also study the evolutionary dynamics of the model ecosystem by following the fluctuations in the total number of species in the web. Extinction avalanches occur when novel organisms arise which are significantly better adapted than existing ones. We discuss these results in relation to the observed extinction events in the fossil record, and to the theory of self-organized criticality.Comment: 21 pages, 3 Postscript figures, uses psfig.sty Affiliations correcte

The Influence of Predator-Prey Population Dynamics on the Long-term Evolution of Food Web Structure

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are non-linear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary timescale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organised criticality.Comment: 40 pages, preprint forma

Laurel and Thorn: The Athlete in American Literature

To examine the social and cultural significance of the athlete hero in American literature, Robert J. Higgs turns to the works of Ring Lardner, Ernest Hemingway, F. Scott Fitzgerald, Thomas Wolfe, William Faulkner, Robert Penn Warren, Arthur Miller, and Tennessee Williams. Higgs views the athlete in literature not as an artistic creation but as one who reflects the tastes, attainments, beliefs, and ideals of his society. The athletes he describes as Apollonian are the know-it-alls, of whom Lardner’s Busher Keefe is an example; the Dyonisian, as exemplified by Irwin Shaw’s Christian Darling, worships his body as an end in itself. The Adonic seeks knowledge for the sake of self-realization and lives in a world of tension, pain, struggle, and hope. Such a figure is Wolfe’s Nebraska Crane. Higgs finds in contemporary American literature a clear rejection of the Apollonian and Dyonisian models and an acceptance of the Adonic. Robert J. Higgs is professor of English at East Tennessee State University.https://uknowledge.uky.edu/upk_english_language_and_literature_north_america/1024/thumbnail.jp

Next-to-leading Corrections to the Higgs Boson Transverse Momentum Spectrum in Gluon Fusion

We present a fully analytic calculation of the Higgs boson transverse momentum and rapidity distributions, for nonzero Higgs $p_\perp$, at next-to-leading order in the infinite-top-mass approximation. We separate the cross section into a part that contains the dominant soft, virtual, collinear, and small-$p_\perp$-enhanced contributions, and the remainder, which is organized by the contributions due to different parton helicities. We use this cross section to investigate analytically the small-$p_\perp$ limit and compare with the expectation from the resummation of large logarithms of the type $\ln{m_H/p_\perp}$. We also compute numerically the cross section at moderate $p_\perp$ where a fixed-order calculation is reliable. We find a $K$-factor that varies from $\approx1.6-1.8$, and a reduction in the scale dependence, as compared to leading order. Our analysis suggests that the contribution of current parton distributions to the total uncertainty on this cross section at the LHC is probably less than that due to uncalculated higher orders.Comment: 40 pages, 10 figures, JHEP style (minor changes, added reference

Modeling, Stability, and Control of a Rotatable Tail on a Micro Air Vehicle

This research uses existing experimental wind tunnel data to develop a non-linear model that is used to characterize the stability of a flexible wing Micro Air Vehicle (MAV) with a rotatable tail. The experimental data are curve fit based on either angle of attack or angle of sideslip, and the coupled effect of tail rotation and tail deflection on the force and moment coefficients. Static optimization trims the input and state variables for Steady Level Unaccelerated Flight (SLUF). The resulting initial conditions are fed to an open loop non-linear Simulink/Matlab simulation. The study found that the bare MAV design is unstable, but parametric studies identified practical modifications that could be made to the MAV to improve its open loop stability characteristics. The study found that the coupling effect due to the dihedreal derivative played a large role in destabilizing the lateral-directional dynamics and a feedback Stability Augmentation System is required for flight

New Mechanism of Flavor Symmetry Breaking from Supersymmetric Strong Dynamics

We present a class of supersymmetric models in which flavor symmetries are broken dynamically, by a set of composite flavon fields. The strong dynamics that is responsible for confinement in the flavor sector also drives flavor symmetry breaking vacuum expectation values, as a consequence of a quantum-deformed moduli space. Yukawa couplings result as a power series in the ratio of the confinement to Planck scale, and the fermion mass hierarchy depends on the differing number of preons in different flavor symmetry-breaking operators. We present viable non-Abelian and Abelian flavor models that incorporate this mechanism.Comment: 24 pp. LaTe

The role of irrational beliefs in the relationship between attention deficit hyperactivity disorder (ADHD) symptoms and disordered eating in two general student samples

Attention deficit hyperactivity disorder (ADHD) symptoms are associated with disordered eating and negative mood. The purpose of this study was to examine whether irrational beliefs mediate this relationship along with previously reported mediators such as depression and impulsivity. Irrational beliefs trigger negative automatic thoughts which are believed, in cognitive behavior therapies, to be a source of psychopathology. Challenges brought about by symptoms of ADHD may lead to habitual emotion-eliciting thought patterns which, in turn, could lead to negative mood and disordered eating. Undergraduate students (N = 127) completed online questionnaires assessing ADHD symptoms and disordered eating and several potential mediators including irrational beliefs, depression, impulsivity, interoceptive accuracy, and reward responsiveness. The results, which were replicated in a second study (N = 254), indicated that irrational beliefs and depression mediated the relationship between ADHD symptoms and disordered eating. In the second study, impulsivity due to negative urgency was also a mediator. These findings support the theory that the symptoms of ADHD lead to enhancement of irrational beliefs, depression, and negative urgency which are linked to disordered eating.</p