Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits

For zero energy, $E=0$, we derive exact, classical solutions for {\em all} power-law potentials, $V(r)=-\gamma/r^\nu$, with $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions lead to the orbits $\r(t)= [\cos \mu (\th(t)-\th_0(t))]^{1/\mu}$, for all $\mu \equiv \nu/2-1 \ne 0$. When $\nu>2$, the orbits are bound and go through the origin. This leads to discrete discontinuities in the functional dependence of $\th(t)$ and $\th_0(t)$, as functions of $t$, as the orbits pass through the origin. We describe a procedure to connect different analytic solutions for successive orbits at the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. Also, we explain why they all must violate the virial theorem. The unbound orbits are also discussed in detail. This includes the unusual orbits which have finite travel times to infinity and also the special $\nu = 2$ case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be generated from Mathematica instructions at end of the fil

Changes over time in socioeconomic inequalities in breast and rectal cancer survival in England and Wales during a 32-year period (1973-2004): the potential role of health care.

BACKGROUND: Socioeconomic inequalities in cancer survival are well documented but they vary for different cancers and over time. Reasons for these differences are poorly understood. PATIENTS AND METHODS: For England and Wales, we examined trends in socioeconomic survival inequalities for breast cancer in women and rectal cancer in men during the 32-year period 1973-2004. We used a theoretical framework based on Victora's 'inverse equity' law, under which survival inequalities could change with the advent of successive new treatments, of varying effectiveness, which are disseminated with different speed among patients of different socioeconomic groups. We estimated 5-year relative survival for patients of different deprivation quintiles and examined trends in survival inequalities in light of major treatment innovations. RESULTS: Inequalities in breast cancer survival (921,611 cases) narrowed steadily during the study (from -10% to -6%). In contrast, inequalities in rectal cancer survival (187,104 cases) widened overall (form -5% to -11%) with fluctuating periods of narrowing inequality. CONCLUSIONS: Trends in socioeconomic differences in tumour or patient factors are unlikely explanations of observed changes over time in survival inequalities. The sequential introduction into clinical practice of new treatments of progressively smaller incremental benefit may partly explain the reduction in inequality in breast cancer survival

Tapasin gene polymorphism in systemic onset juvenile rheumatoid arthritis: a family-based case-control study

Juvenile rheumatoid arthritis (JRA) comprises a group of chronic systemic inflammatory disorders that primarily affect joints and can cause long-term disability. JRA is likely to be a complex genetic trait, or a series of such traits, with both genetic and environmental factors contributing to the risk for developing the disease and to its progression. The HLA region on the short arm of chromosome 6 has been intensively evaluated for genetic contributors to JRA, and multiple associations, and more recently linkage, has been detected. Other genes involved in innate and acquired immunity also map to near the HLA cluster on 6p, and it is possible that variation within these genes also confers risk for developing JRA. We examined the TPSN gene, which encodes tapasin, an endoplasmic reticulum chaperone that is involved in antigen processing, to elucidate its involvement, if any, in JRA. We employed both a case-control approach and the transmission disequilibrium test, and found linkage and association between the TPSN allele (Arg260) and the systemic onset subtype of JRA. Two independent JRA cohorts were used, one recruited from the Rheumatology Clinic at Cincinnati Children's Hospital Medical Center (82 simplex families) and one collected by the British Paediatric Rheumatology Group in London, England (74 simplex families). The transmission disequilibrium test for these cohorts combined was statistically significant (chi(2) = 4.2, one degree of freedom; P = 0.04). Linkage disequilibrium testing between the HLA alleles that are known to be associated with systemic onset JRA did not reveal linkage disequilibrium with the Arg260 allele, either in the Cincinnati systemic onset JRA cohort or in 113 Caucasian healthy individuals. These results suggest that there is a weak association between systemic onset JRA and the TPSN polymorphism, possibly due to linkage disequilibrium with an as yet unknown susceptibility allele in the centromeric part of chromosome 6

A Learning 2.0 Programme: raising library staff awareness of Web 2.0 at Imperial College London

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Distinct human stem cell populations in small and large intestine

The intestine is composed of an epithelial layer containing rapidly proliferating cells that mature into two regions, the small and the large intestine. Although previous studies have identified stem cells as the cell-of-origin for intestinal epithelial cells, no studies have directly compared stem cells derived from these anatomically distinct regions. Here, we examine intrinsic differences between primary epithelial cells isolated from human fetal small and large intestine, after in vitro expansion, using the Wnt agonist R-spondin 2.We utilized flow cytometry, fluorescence-activated cell sorting, gene expression analysis and a three-dimensional in vitro differentiation assay to characterize their stemcell properties. We identified stem cell markers that separate subpopulations of colony-forming cells in the small and large intestine and revealed important differences in differentiation, proliferation and disease pathways using gene expression analysis. Single cells from small and large intestine cultures formed organoids that reflect the distinct cellular hierarchy found in vivo and respond differently to identical exogenous cues. Our characterization identified numerous differences between small and large intestine epithelial stem cells suggesting possible connections to intestinal disease

Physics of Neutron Star Kicks

It is no longer necessary to `sell' the idea of pulsar kicks, the notion that neutron stars receive a large velocity (a few hundred to a thousand km s$^{-1}$) at birth. However, the origin of the kicks remains mysterious. We review the physics of different kick mechanisms, including hydrodynamically driven, neutrino and magnetically driven kicks.Comment: 8 pages including 1 figure. To be published in "Stellar Astrophysics" (Pacific Rim Conference Proceedings), (Kluwer Pub.

Magnetized Domain Walls in the Deconfined Sakai-Sugimoto Model at Finite Baryon Density

The magnetized pure pion gradient ($\mathcal{5}\phi$) phase in the deconfined Sakai-Sugimoto model is explored at zero and finite temperature. We found that the temperature has very small effects on the phase. The thermodynamical properties of the phase shows that the excitations behave like a scalar solitonic free particles. By comparing the free energy of the pion gradient phase to the competing multiquark-pion gradient (MQ-$\mathcal{5}\phi$) phase, it becomes apparent that the pure pion gradient is less thermodynamically preferred than the MQ-$\mathcal{5}\phi$ phase. However, in the parameter space where the baryonic chemical potential is smaller than the onset value of the multiquark, the dominating magnetized nuclear matter is the pion gradient phase.Comment: 20 pages, 9 figure

Nonlinear response of the vacuum Rabi resonance

On the level of single atoms and photons, the coupling between atoms and the electromagnetic field is typically very weak. By employing a cavity to confine the field, the strength of this interaction can be increased many orders of magnitude to a point where it dominates over any dissipative process. This strong-coupling regime of cavity quantum electrodynamics has been reached for real atoms in optical cavities, and for artificial atoms in circuit QED and quantum-dot systems. A signature of strong coupling is the splitting of the cavity transmission peak into a pair of resolvable peaks when a single resonant atom is placed inside the cavity - an effect known as vacuum Rabi splitting. The circuit QED architecture is ideally suited for going beyond this linear response effect. Here, we show that increasing the drive power results in two unique nonlinear features in the transmitted heterodyne signal: the supersplitting of each vacuum Rabi peak into a doublet, and the appearance of additional peaks with the characteristic sqrt(n) spacing of the Jaynes-Cummings ladder. These constitute direct evidence for the coupling between the quantized microwave field and the anharmonic spectrum of a superconducting qubit acting as an artificial atom.Comment: 6 pages, 4 figures. Supplementary Material and Supplementary Movies are available at http://www.eng.yale.edu/rslab/publications.htm