Numerical Diagonalisation Study of the Trimer Deposition-Evaporation Model in One Dimension

We study the model of deposition-evaporation of trimers on a line recently introduced by Barma, Grynberg and Stinchcombe. The stochastic matrix of the model can be written in the form of the Hamiltonian of a quantum spin-1/2 chain with three-spin couplings given by H= \sum\displaylimits_i [(1 - \sigma_i^-\sigma_{i+1}^-\sigma_{i+2}^-) \sigma_i^+\sigma_{i+1}^+\sigma_{i+2}^+ + h.c]. We study by exact numerical diagonalization of $H$ the variation of the gap in the eigenvalue spectrum with the system size for rings of size up to 30. For the sector corresponding to the initial condition in which all sites are empty, we find that the gap vanishes as $L^{-z}$ where the gap exponent $z$ is approximately $2.55\pm 0.15$. This model is equivalent to an interfacial roughening model where the dynamical variables at each site are matrices. From our estimate for the gap exponent we conclude that the model belongs to a new universality class, distinct from that studied by Kardar, Parisi and Zhang.Comment: 11 pages, 2 figures (included

Analytic Solutions to the Constraint Equation for a Force-Free Magnetosphere around a Kerr Black Hole

The Blandford-Znajek constraint equation for a stationary, axisymmetric black-hole force-free magnetosphere is cast in a 3+1 absolute space and time formulation, following Komissarov (2004). We derive an analytic solution for fields and currents to the constraint equation in the far-field limit that satisfies the Znajek condition at the event horizon. This solution generalizes the Blandford-Znajek monopole solution for a slowly rotating black hole to black holes with arbitrary angular momentum. Energy and angular momentum extraction through this solution occurs mostly along the equatorial plane. We also present a nonphysical, reverse jet-like solution.Comment: 6 pages, accepted for publication in Ap

Outcomes and complications of fibular head resection

The fibular head is often used as donor graft material for reconstruction of defects of the distal radius. However little is known on the safety of such a procedure. This report describes the long-term donor-site morbidity following the procedure. Fourteen patients who underwent simple or marginal resections of the proximal fibula between 1990 and 2007 were reviewed. Subjective donor-site morbidity, knee and ankle range of motion and instability, presence of sensory or motor function loss, gait and fibular regeneration were assessed. The mean age at surgery was 25 years; six were male, eight were female and the mean follow-up was 11 years. Abnormal clinical findings were present in 10 patients (71.4 %): nine patients (64.3 %) had Grade 2 varus laxity at the knee confirmed by stress radiographs; one had sensory loss in the distribution of the superficial peroneal nerve. Patients with varus laxity had significantly higher mean age at surgery than those without varus laxity (p = 0.001). None had deformity at the knee or ankle. The range of joint movements was normal. All had a normal tibiotalar angle and none had proximal migration of the fibula. One patient demonstrated near-complete regeneration of the fibula. Donor-site morbidity following simple and marginal resection of the proximal fibula is acceptable. Older patients had a higher risk of demonstrable varus laxity at the knee but proximal fibula resection in children appears to be safe

The Irreducible String and an Infinity of Additional Constants of Motion in a Deposition-Evaporation Model on a Line

We study a model of stochastic deposition-evaporation with recombination, of three species of dimers on a line. This model is a generalization of the model recently introduced by Barma {\it et. al.} (1993 {\it Phys. Rev. Lett.} {\bf 70} 1033) to $q\ge 3$ states per site. It has an infinite number of constants of motion, in addition to the infinity of conservation laws of the original model which are encoded as the conservation of the irreducible string. We determine the number of dynamically disconnected sectors and their sizes in this model exactly. Using the additional symmetry we construct a class of exact eigenvectors of the stochastic matrix. The autocorrelation function decays with different powers of $t$ in different sectors. We find that the spatial correlation function has an algebraic decay with exponent 3/2, in the sector corresponding to the initial state in which all sites are in the same state. The dynamical exponent is nontrivial in this sector, and we estimate it numerically by exact diagonalization of the stochastic matrix for small sizes. We find that in this case $z=2.39\pm0.05$.Comment: Some minor errors in the first version has been correcte

Optimal symmetric flight studies

Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory

Capillary deformations of bendable films

We address the partial wetting of liquid drops on ultrathin solid sheets resting on a deformable foundation. Considering the membrane limit of sheets that can relax compression through wrinkling at negligible energetic cost, we revisit the classical theory for the contact of liquid drops on solids. Our calculations and experiments show that the liquid-solid-vapor contact angle is modified from the Young angle, even though the elastic bulk modulus (E) of the sheet is so large that the ratio between the surface tension γ and E is of molecular size. This finding establishes a new type of “soft capillarity” that stems from the bendability of thin elastic bodies rather than from material softness. We also show that the size of the wrinkle pattern that emerges in the sheet is fully predictable, thus resolving a puzzle noticed in several previous attempts to model “drop-on-a-floating-sheet” experiments, and enabling a reliable usage of this setup for the metrology of ultrathin films

Cerebral oxygen vasoreactivity and cerebral tissue oxygen reactivity†

There has long been an appreciation that cerebral blood flow is modulated to ensure adequate cerebral oxygen delivery in the face of systemic hypoxaemia. There is increasing appreciation of the modulatory role of hyperoxia in the cerebral circulation and a consideration of the effects of such modulation on the maintenance of cerebral tissue oxygen concentration. These newer findings are particularly important in view of the fact that cerebrovascular and tissue oxygen responses to hyperoxia may change in disease. Such alterations provide important insights into pathophysiological mechanisms and may provide novel targets for therapy. However, before the modulatory effects of hyperoxia can be used for diagnosis, to predict prognosis or to direct therapy, a more detailed analysis and understanding of the physiological concepts behind this modulation are required, as are the limitations of the measurement tools used to define the modulation. This overview summarizes the available information in this area and suggests some avenues for further research. Br J Anaesth 2003; 90: 774-8

Clinical and economic consequences of hospital-acquired resistant and multidrug-resistant Pseudomonas aeruginosa infections: a systematic review and meta-analysis

Background Increasing rates of resistant and multidrug-resistant (MDR) P. aeruginosa in hospitalized patients constitute a major public health threat. We present a systematic review of the clinical and economic impact of this resistant pathogen. Methods Studies indexed in MEDLINE and Cochrane databases between January 2000-February 2013, and reported all-cause mortality, length of stay, hospital costs, readmission, or recurrence in at least 20 hospitalized patients with laboratory confirmed resistant P. aeruginosa infection were included. We accepted individual study definitions of MDR, and assessed study methodological quality. Results The most common definition of MDR was resistance to more than one agent in three or more categories of antibiotics. Twenty-three studies (7,881 patients with susceptible P. aeruginosa, 1,653 with resistant P. aeruginosa, 559 with MDR P. aeruginosa, 387 non-infected patients without P. aeruginosa) were analyzed. A random effects model meta-analysis was feasible for the endpoint of all-cause in-hospital mortality. All-cause mortality was 34% (95% confidence interval (CI) 27% – 41%) in patients with any resistant P. aeruginosa compared to 22% (95% CI 14% – 29%) with susceptible P. aeruginosa. The meta-analysis demonstrated a > 2-fold increased risk of mortality with MDR P. aeruginosa (relative risk (RR) 2.34, 95% CI 1.53 – 3.57) and a 24% increased risk with resistant P. aeruginosa (RR 1.24, 95% CI 1.11 – 1.38), compared to susceptible P. aeruginosa. An adjusted meta-analysis of data from seven studies demonstrated a statistically non-significant increased risk of mortality in patients with any resistant P. aeruginosa (adjusted RR 1.24, 95% CI 0.98 – 1.57). All three studies that reported infection-related mortality found a statistically significantly increased risk in patients with MDR P. aeruginosa compared to those with susceptible P. aeruginosa. Across studies, hospital length of stay (LOS) was higher in patients with resistant and MDR P. aeruginosa infections, compared to susceptible P. aeruginosa and control patients. Limitations included heterogeneity in MDR definition, restriction to nosocomial infections, and potential confounding in analyses. Conclusions Hospitalized patients with resistant and MDR P. aeruginosa infections appear to have increased all-cause mortality and LOS. The negative clinical and economic impact of these pathogens warrants in-depth evaluation of optimal infection prevention and stewardship strategies