Introduction to Q-tensor theory

This paper aims to provide an introduction to a basic form of the ${\bf Q}$-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the ${\bf Q}$-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated

Factors Driving Sow Breeding Operations to Become Large

This study examines the influences of economic and non-economic variables on the size of U.S. sow breeding operations using a probit model. Data from a national survey of U.S. hog operations identifying two different size categories were used in this study. Findings indicate that factors such as operations located in Delta States, climate controlled facilities, specialized operation, breeding practices, and risk attitudes toward investments influence decisions to establish breeding operations with 500 or more sows. Producers located in Iowa were more likely to choose breeding operations with 499 or less sows.Farm Management,

Genome-wide association study of electrocardiographic and heart rate variability traits: the Framingham Heart Study

BACKGROUND: Heritable electrocardiographic (ECG) and heart rate variability (HRV) measures, reflecting pacemaking, conduction, repolarization and autonomic function in the heart have been associated with risks for cardiac arrhythmias. Whereas several rare monogenic conditions with extreme phenotypes have been noted, few common genetic factors contributing to interindividual variability in ECG and HRV measures have been identified. We report the results of a community-based genomewide association study of six ECG and HRV intermediate traits. METHODS: Genotyping using Affymetrix 100K GeneChip was conducted on 1345 related Framingham Heart Study Original and Offspring cohort participants. We analyzed 1175 Original and Offspring participants with ECG data (mean age 52 years, 52% women) and 548 Offspring participants with HRV data (mean age 48 years, 51% women), in relation to 70,987 SNPs with minor allele frequency ≥ 0.10, call rate ≥ 80%, Hardy-Weinberg p-value ≥ 0.001. We used generalized estimating equations to test association of SNP alleles with multivariable-adjusted residuals for QT, RR, and PR intervals, the ratio of low frequency to high frequency power (LF/HFP), total power (TP) and the standard deviation of normal RR intervals (SDNN). RESULTS: Associations at p < 10-3 were found for 117 (QT), 105 (RR), 111 (PR), 102 (LF/HF), 121 (TP), and 102 (SDNN) SNPs. Several common variants in NOS1AP (4 SNPs with p-values < 10-3; lowest p-value, rs6683968, p = 1 × 10-4) were associated with adjusted QT residuals, consistent with our previously reported finding for NOS1AP in an unrelated sample of FHS Offspring and other cohorts. All results are publicly available at NCBI's dbGaP at. CONCLUSION: In the community-based Framingham Heart Study none of the ECG and HRV results individually attained genomewide significance. However, the presence of bona fide QT-associated SNPs among the top 117 results for QT duration supports the importance of efforts to validate top results from the reported scans. Finding genetic variants associated with ECG and HRV quantitative traits may identify novel genes and pathways implicated in arrhythmogenesis and allow for improved recognition of individuals at high risk for arrhythmias in the general population.National Institutes of Health (K23 N01-HC25195); Doris Duke Charitable Foundation Clinical Scientist Developement Award; Pfizer; National Institutes of Health National Center for Research Resources Shared Instrumentation grant (1S10RR163736-01A1

Number fields with prescribed norms

We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for $100\%$ of $G$-extensions of $k$, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result.Comment: 35 pages, comments welcome

The Hasse norm principle for abelian extensions

We study the distribution of abelian extensions of bounded discriminant of a number field k which fail the Hasse norm principle. For example, we classify those finite abelian groups G for which a positive proportion of G-extensions of k fail the Hasse norm principle. We obtain a similar classification for the failure of weak approximation for the associated norm one tori. These results involve counting abelian extensions of bounded discriminant with infinitely many local conditions imposed, which we achieve using tools from harmonic analysis, building on work of Wright

Number fields with prescribed norms

We study the distribution of extensions of a number field k with fixed abelian Galois group G, from which a given finite set of elements of k are norms. In particular, we show the existence of such extensions. Along the way, we show that the Hasse norm principle holds for 100% of G-extensions of k, when ordered by conductor. The appendix contains an alternative purely geometric proof of our existence result

Magnetic inflation and stellar mass. V. Intensification and saturation of M-dwarf absorption lines with Rossby number

In young Sun-like stars and field M-dwarf stars, chromospheric and coronal magnetic activity indicators such as Hα, X-ray, and radio emission are known to saturate with low Rossby number (Ro lesssim 0.1), defined as the ratio of rotation period to convective turnover time. The mechanism for the saturation is unclear. In this paper, we use photospheric Ti i and Ca i absorption lines in the Y band to investigate magnetic field strength in M dwarfs for Rossby numbers between 0.01 and 1.0. The equivalent widths of the lines are magnetically enhanced by photospheric spots, a global field, or a combination of the two. The equivalent widths behave qualitatively similar to the chromospheric and coronal indicators: we see increasing equivalent widths (increasing absorption) with decreasing Ro and saturation of the equivalent widths for Ro lesssim 0.1. The majority of M dwarfs in this study are fully convective. The results add to mounting evidence that the magnetic saturation mechanism occurs at or beneath the stellar photosphere.Published versio