Beyond the simple Proximity Force Approximation: geometrical effects on the non-retarded Casimir interaction

We study the geometrical corrections to the simple Proximity Force Approximation for the non-retarded Casimir force. We present analytical results for the force between objects of various shapes and substrates, and between pairs of objects. We compare the results to those from more exact numerical calculations. We treat spheres, spheroids, cylinders, cubes, cones, and wings; the analytical PFA results together with the geometrical correction factors are summarized in a table.Comment: 18 pages, 19 figures, 1 tabl

The non-perturbative corrections to the Bˉ→Xsγ\bar B \to X_s\gamma photon spectrum in a parton-like model

We derive a new parton-like formula, which establishes a simple connection between the electroweak decay rate $\Gamma (\bar B \to X_s\gamma$) and the rate of a free b-quark decay. The main features of our approach are the treatment of the b-quark as an on-mass-shell particle and the inclusion of the effects arising from the b-quark transverse motion in the $\bar B$-meson. Using various b-quark light-front (LF) distribution functions, both phenomenological one and the ones derived from current constituent quark models, and neglecting perturbative corrections we compute the photon energy spectra and the moments of the shape function. It is shown that the parton-like approach is fully consistent with the Heavy Quark Effective Theory (HQET) provided the b-quark constituent mass is redefined in the way similar to that used in HQET to define the pole mass of the b quark. In this way the correction to first order in $1/m_b$ can be eliminated from the total width in agreement with the general statement of HQET. We have also found that the photon energy spectra calculated in the LF approach agree well with the ones obtained in the ACM model, provided the same distribution function is used as input in both cases. In spite of the simplicity of the model our results show a fair good agreement both with the HQET predictions and available experimental data.Comment: 14 pages, LaTeX, 3 ps figure

Associations of gestational glycemia and prepregnancy adiposity with offspring growth and adiposity in an Asian population

Background: maternal obesity and hyperglycemia increase risk of obesity and diabetes in offspring later in life.Objective: we examined the relation between gestational glycemia and prepregnancy body mass index (ppBMI) with offspring growth in an Asian mother-offspring cohort.Design: pregnant mothers undertook a 75-g 2-h oral-glucose-tolerance test at 26–28 wk of gestation. In 937 singleton offspring, ?9 serial measurements of weight and length were obtained from birth until 36 mo of age.Results: gestational fasting plasma glucose (FPG) was positively associated with birth weight (B: 0.17; 95% CI: 0.10, 0.24; P < 0.001) and birth BMI (B: 0.15; 95% CI: 0.06, 0.40; P = 0.001) but not at ?3 mo of age. In contrast, maternal ppBMI was positively associated with birth variables and conditional growth in weight and BMI in the first 36 mo of life. However, gestational FPG and prepregnancy obesity status interacted significantly for the association with offspring growth and overweight status in the first 36 mo of life (P-interaction < 0.01). In nonobese mothers, each unit increase in gestational FPG was associated with increased offspring weight (B: 0.08; 95% CI: 0.008, 0.16; P = 0.03) and BMI (B: 0.08; 95% CI: 0.003, 0.15; P = 0.04) as well as increased risk of overweight in the first 36 mo of life (OR: 1.36; 95% CI: 1.10, 1.68). However, in obese mothers, each unit increase in gestational FPG was associated with decreased offspring weight (B: ?0.01; 95% CI: ?0.02, ?0.003) and BMI (B: ?0.008; 95% CI: ?0.01, ?0.002) velocity (P < 0.01 for both) and decreased risk of overweight (OR: 0.59; 95% CI: 0.41, 0.86) in the first 36 mo of life.Conclusions: prepregnancy adiposity was associated with offspring growth in early childhood. Although pooled analyses showed no demonstrable difference by 3 mo of age, there were contrasting and opposite associations of gestational glycemia with weight and BMI in the first 36 mo of life in offspring of nonobese and obese mothers separately. This study was registered at clinicaltrials.gov as NCT0117487

Detection of NMR signals with a radio-frequency atomic magnetometer

We demonstrate detection of proton NMR signals with a radio frequency atomic magnetometer tuned to the NMR frequency of 62 kHz. High-frequency operation of the atomic magnetometer makes it relatively insensitive to ambient magnetic field noise. We obtain magnetic field sensitivity of 7 fT/Hz$^{1/2}$ using only a thin aluminum shield. We also derive an expression for the fundamental sensitivity limit of a surface inductive pick-up coil as a function of frequency and find that an atomic rf magnetometer is intrinsically more sensitive than a coil of comparable size for frequencies below about 50 MHz.Comment: 7 page

On the One-dimensional Stability of Viscous Strong Detonation Waves

Building on Evans function techniques developed to study the stability of viscous shocks, we examine the stability of viscous strong detonation wave solutions of the reacting Navier-Stokes equations. The primary result, following the work of Alexander, Gardner & Jones and Gardner & Zumbrun, is the calculation of a stability index whose sign determines a necessary condition for spectral stability. We show that for an ideal gas this index can be evaluated in the ZND limit of vanishing dissipative effects. Moreover, when the heat of reaction is sufficiently small, we prove that strong detonations are spectrally stable provided the underlying shock is stable. Finally, for completeness, the stability index calculations for the nonreacting Navier-Stokes equations are includedComment: 66 pages, 7 figure

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map

Thermodynamic and Tunneling Density of States of the Integer Quantum Hall Critical State

We examine the long wave length limit of the self-consistent Hartree-Fock approximation irreducible static density-density response function by evaluating the charge induced by an external charge. Our results are consistent with the compressibility sum rule and inconsistent with earlier work that did not account for consistency between the exchange-local-field and the disorder potential. We conclude that the thermodynamic density of states is finite, in spite of the vanishing tunneling density of states at the critical energy of the integer quantum Hall transition.Comment: 5 pages, 4 figures, minor revisions, published versio

Thermodynamic properties of excess-oxygen-doped La2CuO4.11 near a simultaneous transition to superconductivity and long-range magnetic order

We have measured the specific heat and magnetization {\it versus} temperature in a single crystal sample of superconducting La$_{2}$CuO$_{4.11}$ and in a sample of the same material after removing the excess oxygen, in magnetic fields up to 15 T. Using the deoxygenated sample to subtract the phonon contribution, we find a broad peak in the specific heat, centered at 50 K. This excess specific heat is attributed to fluctuations of the Cu spins possibly enhanced by an interplay with the charge degrees of freedom, and appears to be independent of magnetic field, up to 15 T. Near the superconducting transition $T_{c}$($H$=0)= 43 K, we find a sharp feature that is strongly suppressed when the magnetic field is applied parallel to the crystallographic c-axis. A model for 3D vortex fluctuations is used to scale magnetization measured at several magnetic fields. When the magnetic field is applied perpendicular to the c-axis, the only observed effect is a slight shift in the superconducting transition temperature.Comment: 8 pages, 8 figure

Playing safe: Assessing the risk of sexual abuse to elite child athletes

Young athletes frequently suffer from being seen as athletes first and children second. This has consequences for their legal, civil and human rights as children (Kelly et al., 1995) and for the way in which sport organisations choose to intervene on their behalf to protect them from physical, psychological and sexual abuses (Brackenridge, 1994). Sport careers peak at different ages depending on the sport: in some, children as young as 12 or 13 may reach the highest levels of competitive performance; in others, full maturity as an athlete may come late into adulthood or even middle age. Recognition of this variation has given rise to the concept of ‘sport age’ (Kirby, 1986) referring to sport-specific athlete development. This concept is of significance in helping to identify the developmental process in terms of athletic, rather than chronological, maturity. The risk of sexual abuse in sport, formerly ignored or denied, has now been documented in a number of studies, using both quantitative and qualitative methods (Kirby & Greaves, 1996; Brackenridge, 1997; Volkwein, 1996). Drawing on data from these studies and from the previous work on sport age and athletic maturation, this paper proposes a possible means of identifying and assessing relative risk of sexual abuse to elite young athletes in selected sports. The concept of a ‘stage of imminent achievement’ (SIA) is proposed as the period of peak vulnerability of young athletes to sexual abuse

Hexatic-Herringbone Coupling at the Hexatic Transition in Smectic Liquid Crystals: 4-ϵ\epsilon Renormalization Group Calculations Revisited

Simple symmetry considerations would suggest that the transition from the smectic-A phase to the long-range bond orientationally ordered hexatic smectic-B phase should belong to the XY universality class. However, a number of experimental studies have constantly reported over the past twenty years "novel" critical behavior with non-XY critical exponents for this transition. Bruinsma and Aeppli argued in Physical Review Letters {\bf 48}, 1625 (1982), using a $4-\epsilon$ renormalization-group calculation, that short-range molecular herringbone correlations coupled to the hexatic ordering drive this transition first order via thermal fluctuations, and that the critical behavior observed in real systems is controlled by a `nearby' tricritical point. We have revisited the model of Bruinsma and Aeppli and present here the results of our study. We have found two nontrivial strongly-coupled herringbone-hexatic fixed points apparently missed by those authors. Yet, those two new nontrivial fixed-points are unstable, and we obtain the same final conclusion as the one reached by Bruinsma and Aeppli, namely that of a fluctuation-driven first order transition. We also discuss the effect of local two-fold distortion of the bond order as a possible missing order parameter in the Hamiltonian.Comment: 1 B/W eps figure included. Submitted to Physical Review E. Contact: [email protected]