To the University of London Graduates' Committee.

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Slack Dynamics on an Unfurling String

An arch will grow on a rapidly deployed thin string in contact with a rigid plane. We present a qualitative model for the growing structure involving the amplification, rectification, and advection of slack in the presence of a steady stress field, validate our assumptions with numerical experiments, and pose new questions about the spatially developing motions of thin objects.Comment: significant changes. removed one figur

The Rare Decay D^0 -> gamma gamma

We present a calculation of the rare decay mode D^0 -> gamma gamma, in which the long distance contributions are expected to be dominant. Using the Heavy Quark Chiral Perturbation Theory Lagrangian with a strong g coupling as recently determined by CLEO from the D^* -> D pi width, we consider both the anomaly contribution which relates to the annihilation part of the weak Lagrangian and the one-loop pi, K diagrams. The loop contributions which are proportional to g and contain the a_1 Wilson coefficient are found to dominate the decay amplitude, which turns out to be mainly parity violating. The branching ratio is then calculated to be (1.0+-0.5)x10^(-8). Observation of an order of magnitude larger branching ratio could be indicative of new physics.Comment: 16 pages, 5 figures, additional reference and several remarks added, results unchange

The falling chain of Hopkins, Tait, Steele and Cayley

A uniform, flexible and frictionless chain falling link by link from a heap by the edge of a table falls with an acceleration $g/3$ if the motion is nonconservative, but $g/2$ if the motion is conservative, $g$ being the acceleration due to gravity. Unable to construct such a falling chain, we use instead higher-dimensional versions of it. A home camcorder is used to measure the fall of a three-dimensional version called an $xyz$-slider. After frictional effects are corrected for, its vertical falling acceleration is found to be $a_x/g = 0.328 \pm 0.004$. This result agrees with the theoretical value of $a_x/g = 1/3$ for an ideal energy-conserving $xyz$-slider.Comment: 17 pages, 5 figure

Progress in Classical and Quantum Variational Principles

We review the development and practical uses of a generalized Maupertuis least action principle in classical mechanics, in which the action is varied under the constraint of fixed mean energy for the trial trajectory. The original Maupertuis (Euler-Lagrange) principle constrains the energy at every point along the trajectory. The generalized Maupertuis principle is equivalent to Hamilton's principle. Reciprocal principles are also derived for both the generalized Maupertuis and the Hamilton principles. The Reciprocal Maupertuis Principle is the classical limit of Schr\"{o}dinger's variational principle of wave mechanics, and is also very useful to solve practical problems in both classical and semiclassical mechanics, in complete analogy with the quantum Rayleigh-Ritz method. Classical, semiclassical and quantum variational calculations are carried out for a number of systems, and the results are compared. Pedagogical as well as research problems are used as examples, which include nonconservative as well as relativistic systems

Transient peak-strain matching partially recovers the age-impaired mechanoadaptive cortical bone response

Mechanoadaptation maintains bone mass and architecture; its failure underlies age-related decline in bone strength. It is unclear whether this is due to failure of osteocytes to sense strain, osteoblasts to form bone or insufficient mechanical stimulus. Mechanoadaptation can be restored to aged bone by surgical neurectomy, suggesting that changes in loading history can rescue mechanoadaptation. We use non-biased, whole-bone tibial analyses, along with characterisation of surface strains and ensuing mechanoadaptive responses in mice at a range of ages, to explore whether sufficient load magnitude can activate mechanoadaptation in aged bone. We find that younger mice adapt when imposed strains are lower than in mature and aged bone. Intriguingly, imposition of short-term, high magnitude loading effectively primes cortical but not trabecular bone of aged mice to respond. This response was regionally-matched to highest strains measured by digital image correlation and to osteocytic mechanoactivation. These data indicate that aged bone’s loading response can be partially recovered, non-invasively by transient, focal high strain regions. Our results indicate that old murine bone does respond to load when the loading is of sufficient magnitude, and bones’ age-related adaptation failure may be due to insufficient mechanical stimulus to trigger mechanoadaptation

KRAS/BRAF mutation status and ERK1/2 activation as biomarkers for MEK1/2 inhibitor therapy in colorectal cancer

Phase II clinical trials of MEK inhibitors are ongoing and ERK1/2 activation is frequently used as a biomarker. In light of the mutational activation of BRAF and KRAS in colorectal cancer (CRC), inhibitors of the Raf-MEK-ERK mitogen-activated protein kinase are anticipated to be promising. Previous studies in pancreatic cancer have found little correlation between BRAF/KRAS mutation status and ERK1/2 activation, suggesting that identifying biomarkers of MEK inhibitor response may be more challenging than previously thought. The purpose of this study was to evaluate the effectiveness of MEK inhibitor therapy for CRC and BRAF/KRAS mutation status and ERK1/2 activation as biomarkers for MEK inhibitor therapy. First, we found that MEK inhibitor treatment impaired the anchorage-independent growth of nearly all KRAS/BRAF mutant, but not wild-type, CRC cells. There was a correlation between BRAF, but not KRAS, mutation status and ERK1/2 activation. Second, neither elevated ERK1/2 activation nor reduction of ERK1/2 activity correlated with MEK inhibition of anchorage-independent growth. Finally, we validated our cell line observations and found that ERK1/2 activation correlated with BRAF, but not KRAS, mutation status in 190 patient CRC tissues. Surprisingly, we also found that ERK activation was elevated in normal colonic epithelium, suggesting that normal cell toxicity may be a complication for CRC treatment. Our results suggest that although MEK inhibitors show promise in CRC, KRAS/BRAF mutation status, but not ERK activation as previously thought, may be useful biomarkers for MEK inhibitor sensitivity