Large Scale Features of Rotating Forced Turbulence

Large scale features of a randomly isotropically forced incompressible and unbounded rotating fluid are examined in perturbation theory. At first order in both the random force amplitude and the angular velocity we find two types of modifications to the fluid equation of motion. The first correction transforms the molecular shear viscosity into a (rotation independent) effective viscosity. The second perturbative correction leads to a new large scale non-dissipative force proportional to the fluid angular velocity in the slow rotation regime. This effective force does no net work and alters the dispersion relation of inertial waves propagating in the fluid. Both dynamically generated corrections can be identified with certain components of the most general axisymmetric ``viscosity tensor'' for a Newtonian fluid.Comment: 12 pages, 2 figures, RevTeX, and accepted for publication in Phys. Rev.

Relation between obesity and the oestrogen receptor status of breast cancer

Introduction: Obesity is a growing problem in the Western world. Correlations have been found between increasing body mass index (BMI) and breast cancer. The objectives were to establish whether a relationship exists between BMI and breast cancer and to investigate any association between BMI and tumour oestrogen receptor expression. Method: Clinical and socio-demographic details (age, menopausal status, height and weight) of a sample of women with breast cancer operated in 2010 were collected, dividing the group into oestrogen receptor positive (ER+) and negative (ER–) subgroups. The average BMI of each subgroup was compared to the mean BMI of a sample of the general Maltese female population obtained from the European Health Examination Survey 2010 Report (Pilot Study) by virtue of an ANOVA test. Subsequently, the relations between oestrogen receptor expression and each of menopausal status, age and BMI were statistically analysed using chi-squared analysis and two-sample t-tests. Results: A total of 103 patients were studied. 72 patients (age range: 40 – 90 years) had ER+ malignancy and 31 patients (29 – 81 years) had ER- malignancy. The mean BMI’s of the ER+ and ER- subgroups were 30.1 and 27.1 respectively, while that of the female general population (29 – 90 years) was 28.4. Analysis revealed a significant difference between the BMI’s of the ER+ and ER- subgroups (p<0.05) but no difference between each receptor subgroup and the general population. Neither menopausal status nor age was found to correlate with positive oestrogen receptor expression. Conclusions: Women with ER+ malignancy tended to be significantly more obese than those with ER- breast cancer. However, neither subgroup had a mean BMI significantly different from that of the general population.peer-reviewe

Every countable model of set theory embeds into its own constructible universe

The main theorem of this article is that every countable model of set theory M, including every well-founded model, is isomorphic to a submodel of its own constructible universe. In other words, there is an embedding $j:M\to L^M$ that is elementary for quantifier-free assertions. The proof uses universal digraph combinatorics, including an acyclic version of the countable random digraph, which I call the countable random Q-graded digraph, and higher analogues arising as uncountable Fraisse limits, leading to the hypnagogic digraph, a set-homogeneous, class-universal, surreal-numbers-graded acyclic class digraph, closely connected with the surreal numbers. The proof shows that $L^M$ contains a submodel that is a universal acyclic digraph of rank $Ord^M$. The method of proof also establishes that the countable models of set theory are linearly pre-ordered by embeddability: for any two countable models of set theory, one of them is isomorphic to a submodel of the other. Indeed, they are pre-well-ordered by embedability in order-type exactly $\omega_1+1$. Specifically, the countable well-founded models are ordered by embeddability in accordance with the heights of their ordinals; every shorter model embeds into every taller model; every model of set theory $M$ is universal for all countable well-founded binary relations of rank at most $Ord^M$; and every ill-founded model of set theory is universal for all countable acyclic binary relations. Finally, strengthening a classical theorem of Ressayre, the same proof method shows that if $M$ is any nonstandard model of PA, then every countable model of set theory---in particular, every model of ZFC---is isomorphic to a submodel of the hereditarily finite sets $HF^M$ of $M$. Indeed, $HF^M$ is universal for all countable acyclic binary relations.Comment: 25 pages, 2 figures. Questions and commentary can be made at http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe. (v2 adds a reference and makes minor corrections) (v3 includes further changes, and removes the previous theorem 15, which was incorrect.

Effective action for stochastic partial differential equations

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. In this paper we set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these non-quantum field theories are fully interacting. Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues, and furthermore offers marked technical advantages: We can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the BRST formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this ``direct approach'' is the SPDE analog of canonical quantization using physical fields.) We show how to define the effective action to all loops, and then focus on the one-loop effective action, and its specialization to constant fields: the effective potential. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant hbar in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT.Comment: 24 pages, latex 209, ReV_TeX 3.2; Cosmetic revisions to improve the handling of the Faddeev-Popov ghost determinant; References updated; Accepted for publication in Physical Review E; This version essentially identical to the published versio

Centennial- to millennial-scale hard rock erosion rates deduced from luminescence-depth profiles

The measurement of erosion and weathering rates in different geomorphic settings and over diverse temporal and spatial scales is fundamental to the quantification of rates and patterns of earth surface processes. A knowledge of the rates of these surface processes helps one to decipher their relative contribution to landscape evolution – information that is crucial to understanding the interaction between climate, tectonics and landscape. Consequently, a wide range of techniques has been developed to determine short- (&lt;102 a) and long-term (&gt;104 a) erosion rates. However, no method is available to quantify hard rock erosion rates at centennial to millennial timescales. Here we propose a novel technique, based on the solar bleaching of luminescence signals with depth into rock surfaces, to bridge this analytical gap. We apply our technique to glacial and landslide boulders in the Eastern Pamirs, China. The calculated erosion rates from the smooth varnished surfaces of 7 out of the 8 boulders sampled in this study vary between &lt;0.038±0.002 and 1.72±0.04 mmka-1 (the eighth boulder gave an anomalously high erosion rate, possibly due to a recent chipping/cracking loss of surface). Given this preferential sampling of smooth surfaces, assumed to arise from grain-by-grain surface loss, we consider these rates as minimum estimates of rock surface denudation rates in the Eastern Pamirs, China

Renormalization Group Improving the Effective Action

The existence of fluctuations together with interactions leads to scale-dependence in the couplings of quantum field theories for the case of quantum fluctuations, and in the couplings of stochastic systems when the fluctuations are of thermal or statistical nature. In both cases the effects of these fluctuations can be accounted for by solutions of the corresponding renormalization group equations. We show how the renormalization group equations are intimately connected with the effective action: given the effective action we can extract the renormalization group equations; given the renormalization group equations the effects of these fluctuations can be included in the classical action by using what is known as improved perturbation theory (wherein the bare parameters appearing in tree-level expressions are replaced by their scale-dependent running forms). The improved action can then be used to reconstruct the effective action, up to finite renormalizations, and gradient terms.Comment: 25 pages, ReV-TeX 3.