Evaluation of Navier-Stokes and Euler solutions for leading-edge separation vortices

Extensive study on the numerical simulation of the vortical flow over a double delta wing is carried out using the thin layer Navier-Stokes and Euler equations. Two important flow characteristics, vortex interaction and vortex breakdown, are successfully simulated. Grid resolution is one of the most important factors associated with the vortex problem. Computations were performed on a series of grids with various levels of refinement, coarse, medium, and fine. Computations using either the coarse or medium grids fail to capture the proper physical phenomena. The computed result using a fine grid shows flow unsteadiness once the vortex breakdown takes place. The C sub L - alpha characteristics are well predicted up to the breakdown angle of attack for all the grid distributions. The Euler solutions show fairly good agreement with the experiment on the C sub L - alpha characteristics. However, other aspects of the solution at each angle of attack, such as the locus of the leading edge separation vortex, are not consistent with the experiment. Even for the fine grid Navier-Stokes computations, further grid resolution is required to obtain good quantitative agreement with the experiment

The Liability Threshold Model for Censored Twin Data

Family studies provide an important tool for understanding etiology of diseases, with the key aim of discovering evidence of family aggregation and to determine if such aggregation can be attributed to genetic components. Heritability and concordance estimates are routinely calculated in twin studies of diseases, as a way of quantifying such genetic contribution. The endpoint in these studies are typically defined as occurrence of a disease versus death without the disease. However, a large fraction of the subjects may still be alive at the time of follow-up without having experienced the disease thus still being at risk. Ignoring this right-censoring can lead to severely biased estimates. We propose to extend the classical liability threshold model with inverse probability of censoring weighting of complete observations. This leads to a flexible way of modeling twin concordance and obtaining consistent estimates of heritability. We apply the method in simulations and to data from the population based Danish twin cohort where we describe the dependence in prostate cancer occurrence in twins

Predictions for the First Parker Solar Probe Encounter

We examine Alfv\'en Wave Solar atmosphere Model (AWSoM) predictions of the first Parker Solar Probe (PSP) encounter. We focus on the 12-day closest approach centered on the 1st perihelion. AWSoM (van der Holst et al., 2014) allows us to interpret the PSP data in the context of coronal heating via Alfv\'en wave turbulence. The coronal heating and acceleration is addressed via outward-propagating low-frequency Alfv\'en waves that are partially reflected by Alfv\'en speed gradients. The nonlinear interaction of these counter-propagating waves results in a turbulent energy cascade. To apportion the wave dissipation to the electron and anisotropic proton temperatures, we employ the results of the theories of linear wave damping and nonlinear stochastic heating as described by Chandran et al. (2011). We find that during the first encounter, PSP was in close proximity to the heliospheric current sheet (HCS) and in the slow wind. PSP crossed the HCS two times, namely at 2018/11/03 UT 01:02 and 2018/11/08 UT 19:09 with perihelion occuring on the south of side of the HCS. We predict the plasma state along the PSP trajectory, which shows a dominant proton parallel temperature causing the plasma to be firehose unstable.Comment: 16 pages, 5 figures; accepted for publication in the Astrophysical Journal Letter

TAIR: A transonic airfoil analysis computer code

The operation of the TAIR (Transonic AIRfoil) computer code, which uses a fast, fully implicit algorithm to solve the conservative full-potential equation for transonic flow fields about arbitrary airfoils, is described on two levels of sophistication: simplified operation and detailed operation. The program organization and theory are elaborated to simplify modification of TAIR for new applications. Examples with input and output are given for a wide range of cases, including incompressible, subcritical compressible, and transonic calculations

Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Computer model for simulating the long-term dynamics of annual weeds under different cultivation practices

A model is being developed which describes the population dynamics of annual weeds and how it is affected by crop rotation, cultivation practices and weed control. The model aims to predict the development of a certain weed species in order to plan crop rotation and cultivation practices to minimize the risk of proliferation. The model does not predict the exact number of weeds expected to be found in a certain year or crop, but rather the general development over a number of years. The model includes documented knowledge, as well as informal expert knowledge, on seed survival in the soil, seed placement in soil after tillage, seed germination with respect to placement in soil, time of year and tillage, weed development in response to crop competitiveness and seed production of the weeds. The model is at present only accounting for the development of one weed species at a time, and only a few weed species are parameterised. However, the model can easily be extended with more weed species, crops and cultivation practices. Model predictions should match what knowledgeable weed scientists already know, perhaps with a little new insight

Topological states of multiband superconductors with interband pairing

We study the effects of interband pairing in two-band s-wave and d-wave superconductors with D4h symmetry in both time-reversal invariant as well as time-reversal symmetry breaking states. The presence of interband pairing qualitatively changes the nodal structure of the superconductor: nodes can (dis)appear, merge, and leave high-symmetry locations when interband pairing is tuned. Furthermore, in the d-wave case, we find that also the boundary modes change qualitatively when interband pairing increases: flat zero-energy Andreev bound states gap out and transition to helical edge states.Comment: 19 pages, 11 figure

Linguistic models and short story analysis: approaches to literature in teaching English as a second language

This thesis sets out to apply procedures and concepts derived from\ud contemporary linguistics in the analysis of short stories. The goal is\ud to arrive at an approach to the teaching of literature within the context\ud of English language teaching. Theory is drawn from the French structuralists\ud and Russian formalists, and from contemporary stylistics.\ud The opening section is concerned with various theoretical approaches to\ud literary study as they relate to three levels of analysis. The focus,\ud initially, is on the underlying structures of narrative and the attempts\ud of structuralists to isolate these and relate them to patterns and\ud conventions discernible in literature as a whole. The advantages and\ud limitations in such an approach ore discussed. chapter 2 deals with\ud discourse structure in the light of Genette's categories of time, mode\ud and voice, and Uspensky's planes of perspective. The formalists' views\ud on the devices of composition and the estranging function of literature\ud are considered in this context. The third approach surveyed focusses on\ud the language of narrative texts, and some contemporary stylistic studies\ud of prose are discussed.\ud The middle section is practical, and demonstrates an eclectic methodology,\ud derived from those reviewed, in extensive analysis of nine stories in the\ud Penguin collections. Several different starting points for analysis ore\ud tested. First, an approach to story is demonstrated, using propositional\ud analysis along the lines suggested by Todorov, and, subsequently, structuration\ud of action sequences as described by Barthes. Chapter 5 focusses on\ud discourse structure, and examines time relations and other dominant\ud structural elements in stories. The last chapter in this section explores\ud linguistic features foregrounded in the text, and shows how analysis can\ud progress from this point to more abstract levels of organization in the\ud works exomined.\ud The final section of the thesis argues for the place of literature as on\ud integral part of the language teaching programme, offers practical\ud suggestions about how the approach demonstrated here might be implemented\ud in the classroom, and concludes with a tentative,graded teaching sequence\ud which, it is suggested, could form the basis of a literature programe