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.

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.