The Study of the Heisenberg-Euler Lagrangian and Some of its Applications

The Heisenberg-Euler Lagrangian is not only a topic of fundamental interest, but also has a rich variety of diverse applications in astrophysics, nonlinear optics and elementary particle physics etc. We discuss the series representation of this Lagrangian and a few of its applications in this study. [In an appendix, we discuss issues related to the renormalization - and the renormalization-group invariance - of the Heisenberg-Euler Lagrangian and its two-loop generalization.]Comment: 12 pages, LaTeX; Proceedings of the MRST-2003 conference; talk given by S. R. Vallur

Model-Independent Bounds on R(J/ψ)R(J/\psi)

We present a model-independent bound on $R(J/\psi) \! \equiv \! \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \tau^+\nu_\tau)/ \mathcal{BR} (B_c^+ \rightarrow J/\psi \, \mu^+\nu_\mu)$. This bound is constructed by constraining the form factors through a combination of dispersive relations, heavy-quark relations at zero-recoil, and the limited existing determinations from lattice QCD. The resulting 95\% confidence-level bound, $0.20\leq R(J/\psi)\leq0.39$, agrees with the recent LHCb result at $1.3 \, \sigma$, and rules out some previously suggested model form factors.Comment: 19 pages, 4 figures, JHEP format, revised to match published versio

Age spreads in star forming regions?

Rotation periods and projected equatorial velocities of pre-main-sequence (PMS) stars in star forming regions can be combined to give projected stellar radii. Assuming random axial orientation, a Monte-Carlo model is used to illustrate that distributions of projected stellar radii are very sensitive to ages and age dispersions between 1 and 10 Myr which, unlike age estimates from conventional Hertzsprung-Russell diagrams, are relatively immune to uncertainties due to extinction, variability, distance etc. Application of the technique to the Orion Nebula cluster reveals radius spreads of a factor of 2--3 (FWHM) at a given effective temperature. Modelling this dispersion as an age spread suggests that PMS stars in the ONC have an age range larger than the mean cluster age, that could be reasonably described by the age distribution deduced from the Hertzsprung-Russell diagram. These radius/age spreads are certainly large enough to invalidate the assumption of coevality when considering the evolution of PMS properties (rotation, disks etc.) from one young cluster to another.Comment: To appear in "The Ages of Stars", E.E. Mamajek, D.R. Soderblom, R.F.G. Wyse (eds.), IAU Symposium 258, CU

Derivatives of Knots and Second-order Signatures

We define a set of "second-order" L^(2)-signature invariants for any algebraically slice knot. These obstruct a knot's being a slice knot and generalize Casson-Gordon invariants, which we consider to be "first-order signatures". As one application we prove: If K is a genus one slice knot then, on any genus one Seifert surface, there exists a homologically essential simple closed curve of self-linking zero, which has vanishing zero-th order signature and a vanishing first-order signature. This extends theorems of Cooper and Gilmer. We introduce a geometric notion, that of a derivative of a knot with respect to a metabolizer. We also introduce a new equivalence relation, generalizing homology cobordism, called null-bordism.Comment: 40 pages, 22 figures, typographical corrections, to appear in Alg. Geom. Topolog

Existence of immersed spheres minimizing curvature functionals in compact 3-manifolds

We study curvature functionals for immersed 2-spheres in a compact, three-dimensional Riemannian manifold M. Under the assumption that the sectional curvature of M is strictly positive, we prove the existence of a smoothly immersed sphere minimizing the L^{2} integral of the second fundamental form. Assuming instead that the sectional curvature is less than or equal to 2, and that there exists a point in M with scalar curvature bigger than 6, we obtain a smooth 2-sphere minimizing the integral of 1/4|H|^{2} +1, where H is the mean curvature vector

Targeting determinants of dosage compensation in Drosophila

The dosage compensation complex (DCC) in Drosophila melanogaster is responsible for up-regulating transcription from the single male X chromosome to equal the transcription from the two X chromosomes in females. Visualization of the DCC, a large ribonucleoprotein complex, on male larval polytene chromosomes reveals that the complex binds selectively to many interbands on the X chromosome. The targeting of the DCC is thought to be in part determined by DNA sequences that are enriched on the X. So far, lack of knowledge about DCC binding sites has prevented the identification of sequence determinants. Only three binding sites have been identified to date, but analysis of their DNA sequence did not allow the prediction of further binding sites. We have used chromatin immunoprecipitation to identify a number of new DCC binding fragments and characterized them in vivo by visualizing DCC binding to autosomal insertions of these fragments, and we have demonstrated that they possess a wide range of potential to recruit the DCC. By varying the in vivo concentration of the DCC, we provide evidence that this range of recruitment potential is due to differences in affinity of the complex to these sites. We were also able to establish that DCC binding to ectopic high-affinity sites can allow nearby low-affinity sites to recruit the complex. Using the sequences of the newly identified and previously characterized binding fragments, we have uncovered a number of short sequence motifs, which in combination may contribute to DCC recruitment. Our findings suggest that the DCC is recruited to the X via a number of binding sites of decreasing affinities, and that the presence of high-and moderate-affinity sites on the X may ensure that lower-affinity sites are occupied in a context-dependent manner. Our bioinformatics analysis suggests that DCC binding sites may be composed of variable combinations of degenerate motifs

Lamm, Valluri, Jentschura and Weniger comment on "A Convergent Series for the QED Effective Action" by Cho and Pak [Phys. Rev. Lett. vol. 86, pp. 1947-1950 (2001)]

Complete results were obtained by us in [Can. J. Phys. 71, 389 (1993)] for convergent series representations of both the real and the imaginary part of the QED effective action; these derivations were based on correct intermediate steps. In this comment, we argue that the physical significance of the "logarithmic correction term" found by Cho and Pak in [Phys. Rev. Lett. 86, 1947 (2001)] in comparison to the usual expression for the QED effective action remains to be demonstrated. Further information on related subjects can be found in Appendix A of hep-ph/0308223 and in hep-th/0210240.Comment: 1 page, RevTeX; only "meta-data" update

Identifying Advantages and Disadvantages of Variable Rate Irrigation – An Updated Review

Variable rate irrigation (VRI) sprinklers on mechanical move irrigation systems (center pivot or lateral move) have been commercially available since 2004. Although the number of VRI, zone or individual sprinkler, systems adopted to date is lower than expected there is a continued interest to harness this technology, especially when climate variability, regulatory nutrient management, water conservation policies, and declining water for agriculture compound the challenges involved for irrigated crop production. This article reviews the potential advantages and potential disadvantages of VRI technology for moving sprinklers, provides updated examples on such aspects, suggests a protocol for designing and implementing VRI technology and reports on the recent advancements. The advantages of VRI technology are demonstrated in the areas of agronomic improvement, greater economic returns, environmental protection and risk management, while the main drawbacks to VRI technology include the complexity to successfully implement the technology and the lack of evidence that it assures better performance in net profit or water savings. Although advances have been made in VRI technologies, its penetration into the market will continue to depend on tangible and perceived benefits by producers

Knot Concordance and Higher-Order Blanchfield Duality

In 1997, T. Cochran, K. Orr, and P. Teichner defined a filtration {F_n} of the classical knot concordance group C. The filtration is important because of its strong connection to the classification of topological 4-manifolds. Here we introduce new techniques for studying C and use them to prove that, for each natural number n, the abelian group F_n/F_{n.5} has infinite rank. We establish the same result for the corresponding filtration of the smooth concordance group. We also resolve a long-standing question as to whether certain natural families of knots, first considered by Casson-Gordon and Gilmer, contain slice knots.Comment: Corrected Figure in Example 8.4, Added Remark 5.11 pointing out an important strengthening of Theorem 5.9 that is needed in a subsequent pape