In search of the ideal periosteal flap for bone non-union: the chimeric fibula-periosteal flap

Vascularized periosteal flaps may increase union rates in recalcitrant long bone non-union. The fibula-periosteal chimeric flap utilizes periosteum raised on an independent periosteal vessel. This allows the periosteum to be inset freely around the osteotomy site, thereby facilitating bone consolidation. Patients and Methods: 10 patients underwent fibula-periosteal chimeric flaps (2016 – 2022) at Canniesburn Plastic Surgery Unit, UK. Preceding non-union 18.6 months, with bone gap 7.5 cm. Patients underwent pre-operative CT angiography to identify periosteal branches. A case-control approach was used. Patients acted as their own controls with one osteotomy covered by the chimeric periosteal flap and one without, although in two patients both osteotomies were covered by a long periosteal flap. Results: A chimeric periosteal flap was used in 12 of 20 osteotomy sites. Periosteal flap osteotomies had a primary union rate of 100% (11/11) versus those without 28.6% (2/7) (p=0.0025). Union occurred in the chimeric periosteal flaps at 8.5 months versus 16.75 in the control group (p=0.023). 1 case excluded from primary analysis due to recurrent mycetoma. Number needed to treat = 2, indicating that 2 patients would require a chimeric periosteal flap to avoid one non-union. Survival curves with hazards ratio 4.1, equating to 4 times higher chance of union with periosteal flaps (log rank p=0.0016). Conclusions: The chimeric fibula-periosteal flap may increase consolidation rates in difficult cases of recalcitrant non-union. This elegant modification of the fibula flap uses periosteum that is normally discarded, and adds to accumulating data supporting the use of vascularised periosteal flaps in non-union

Radio relics in cosmological simulations

Radio relics have been discovered in many galaxy clusters. They are believed to trace shock fronts induced by cluster mergers. Cosmological simulations allow us to study merger shocks in detail since the intra-cluster medium is heated by shock dissipation. Using high resolution cosmological simulations, identifying shock fronts and applying a parametric model for the radio emission allows us to simulate the formation of radio relics. We analyze a simulated shock front in detail. We find a rather broad Mach number distribution. The Mach number affects strongly the number density of relativistic electrons in the downstream area, hence, the radio luminosity varies significantly across the shock surface. The abundance of radio relics can be modeled with the help of the radio power probability distribution which aims at predicting radio relic number counts. Since the actual electron acceleration efficiency is not known, predictions for the number counts need to be normalized by the observed number of radio relics. For the characteristics of upcoming low frequency surveys we find that about thousand relics are awaiting discovery.Comment: 10 pages, 4 figures, Invited talk at the conference "Diffuse Relativistic Plasmas", Bangalore, 1-4 March 2011; in press in special issue of Journal of Astrophysics and Astronom

High Energy Cosmic Rays From Supernovae

Cosmic rays are charged relativistic particles that reach the Earth with extremely high energies, providing striking evidence of the existence of effective accelerators in the Universe. Below an energy around $\sim 10^{17}$ eV cosmic rays are believed to be produced in the Milky Way while above that energy their origin is probably extragalactic. In the early '30s supernovae were already identified as possible sources for the Galactic component of cosmic rays. After the '70s this idea has gained more and more credibility thanks to the the development of the diffusive shock acceleration theory, which provides a robust theoretical framework for particle energization in astrophysical environments. Afterwards, mostly in recent years, much observational evidence has been gathered in support of this framework, converting a speculative idea in a real paradigm. In this Chapter the basic pillars of this paradigm will be illustrated. This includes the acceleration mechanism, the non linear effects produced by accelerated particles onto the shock dynamics needed to reach the highest energies, the escape process from the sources and the transportation of cosmic rays through the Galaxy. The theoretical picture will be corroborated by discussing several observations which support the idea that supernova remnants are effective cosmic ray factories.Comment: Final draft of a chapter in "Handbook of Supernovae" edited by Athem W. Alsabti and Paul Murdi

Rayleigh-Taylor Instabilities in Type Ia Supernova Remnants undergoing Cosmic-Ray Particle Acceleration - Low Adiabatic Index Solutions

This study investigates the evolution of Rayleigh-Taylor (R-T) instabilities in Type Ia supernova remnants that are associated with a low adiabatic index gamma, where gamma < 5/3, which reflects the expected change in the supernova shock structure as a result of cosmic-ray particle acceleration. Extreme cases, such as the case with the maximum compression ratio that corresponds to gamma=1.1, are examined. As gamma decreases, the shock compression ratio rises, and an increasingly narrow inter shock region with a more pronounced initial mixture of R-T unstable gas is produced. Consequently, the remnant outline may be perturbed by small-amplitude, small-wavelength bumps. However, as the instability decays over time, the extent of convective mixing in terms of the ratio of the radius of the R-T fingers to the blast wave does not strongly depend on the value of gamma for gamma >= 1.2. As a result of the age of the remnant, the unstable gas cannot extend sufficiently far to form metal-enriched filaments of ejecta material close to the periphery of Tycho's supernova remnant. The consistency of the dynamic properties of Tycho's remnant with the adiabatic model gamma=5/3 reveals that the injection of cosmic rays is too weak to alter the shock structure. Even with very efficient acceleration of cosmic rays at the shock, significantly enhanced mixing is not expected in Type Ia supernova remnants.Comment: 11 pages, 10 figures, MNRAS, accepte

Restrictions and extensions of semibounded operators

We study restriction and extension theory for semibounded Hermitian operators in the Hardy space of analytic functions on the disk D. Starting with the operator zd/dz, we show that, for every choice of a closed subset F in T=bd(D) of measure zero, there is a densely defined Hermitian restriction of zd/dz corresponding to boundary functions vanishing on F. For every such restriction operator, we classify all its selfadjoint extension, and for each we present a complete spectral picture. We prove that different sets F with the same cardinality can lead to quite different boundary-value problems, inequivalent selfadjoint extension operators, and quite different spectral configurations. As a tool in our analysis, we prove that the von Neumann deficiency spaces, for a fixed set F, have a natural presentation as reproducing kernel Hilbert spaces, with a Hurwitz zeta-function, restricted to FxF, as reproducing kernel.Comment: 63 pages, 11 figure

Fast responsive and morphologically robust thermo-responsive hydrogel nanofibres from poly(N-isopropylacrylamide) and POSS crosslinker

Stable thermo-responsive hydrogel nanofibres have been prepared by electrospinning of commercial poly(N-isopropylacrylamide) (PNIPAM) in the presence of a polyhedral oligomeric silsesquioxane (POSS) possessing eight epoxide groups and of an organic-base catalyst, followed by a heat curing treatment. The nanofibres showed excellent hydrogel characteristics with fast swelling and de-swelling responses triggered by temperature changes. They were also morphologically robust as their physical integrity was preserved upon repeated hydration/dehydration cycles and exposure to solvents.<br /

Relics as probes of galaxy cluster mergers

Galaxy clusters grow by mergers with other clusters and galaxy groups. These mergers create shocks within the intracluster medium (ICM). It is proposed that within the shocks particles can be accelerated to extreme energies. In the presence of a magnetic field these particles should then form large regions emitting synchrotron radiation, creating so-called radio relics. An example of a cluster with relics is CIZA J2242.8+5301. Here we present hydrodynamical simulations of idealized binary cluster collisions with the aim of constraining the merger scenario for this cluster. We conclude that by using the location, size and width of double radio relics we can set constraints on the mass ratios, impact parameters, timescales, and viewing geometries of binary cluster merger events.Comment: Accepted for publication in special issue of Journal of Astrophysics and Astronomy: conference proceedings of "Diffuse Relativistic Plasmas" conference, Bangalore, 1-4 March 2011, 4 pages, 2 figure

Using performance-based regulation to reduce childhood obesity

BackgroundWorldwide, the public health community has recognized the growing problem of childhood obesity. But, unlike tobacco control policy, there is little evidence about what public policies would work to substantially reduce childhood obesity. Public health leaders currently tend to support traditional "command and control" schemes that order private enterprises and governments to stop or start doing specific things that, is it hoped, will yield lower childhood obesity rates. These include measures such as 1) taking sweetened beverages out of schools, 2) posting calorie counts on fast-food menu boards, 3) labeling foods with a "red light" if they contain high levels of fat or sugar, 4) limiting the density of fast food restaurants in any neighborhood, 5) requiring chain restaurants to offer "healthy" alternatives, and 6) eliminating junk food ads on television shows aimed at children. Some advocates propose other regulatory interventions such as 1) influencing the relative prices of healthy and unhealthy foods through taxes and/or subsidies and 2) suing private industry for money damages as a way of blaming childhood obesity on certain practices of the food industry (such as its marketing, product composition, or portion size decisions). The food industry generally seeks to deflect blame for childhood obesity onto others, such as parents and schools

Radio emission from Supernova Remnants

The explosion of a supernova releases almost instantaneously about 10^51 ergs of mechanic energy, changing irreversibly the physical and chemical properties of large regions in the galaxies. The stellar ejecta, the nebula resulting from the powerful shock waves, and sometimes a compact stellar remnant, constitute a supernova remnant (SNR). They can radiate their energy across the whole electromagnetic spectrum, but the great majority are radio sources. Almost 70 years after the first detection of radio emission coming from a SNR, great progress has been achieved in the comprehension of their physical characteristics and evolution. We review the present knowledge of different aspects of radio remnants, focusing on sources of the Milky Way and the Magellanic Clouds, where the SNRs can be spatially resolved. We present a brief overview of theoretical background, analyze morphology and polarization properties, and review and critical discuss different methods applied to determine the radio spectrum and distances. The consequences of the interaction between the SNR shocks and the surrounding medium are examined, including the question of whether SNRs can trigger the formation of new stars. Cases of multispectral comparison are presented. A section is devoted to reviewing recent results of radio SNRs in the Magellanic Clouds, with particular emphasis on the radio properties of SN 1987A, an ideal laboratory to investigate dynamical evolution of an SNR in near real time. The review concludes with a summary of issues on radio SNRs that deserve further study, and analyzing the prospects for future research with the latest generation radio telescopes.Comment: Revised version. 48 pages, 15 figure

A Jet-ADAF model for Sgr A*

The recent {\em Chandra} observation of the radio source at the center of our Galaxy, Sgr A$^*$, puts new constraints on its theoretical models. The spectrum is very soft, and the source is rapidly variable. We consider different models to explain the observations. We find that the features of the x-ray spectrum can be marginally explained with an advection-dominated accretion flow (ADAF) model while it does not well fit the radio spectrum. An ADAF with strong winds (ADIOS) model is not favored if we assume that the wind does not radiate. Alternatively, we propose a coupled jet plus accretion disk model to explain the observations for Sgr A$^*$. The accretion flow is described as an ADAF fed by Bondi-Hoyle accretion of hot plasma in the Galactic Center region. A small fraction of the accretion flow is ejected near the black hole, forming a jet after passing through a shock. As a result, the electron temperature increases to $\sim 2 \times 10^{11}{\rm K}$, which is about 10 times higher than the highest temperature attained in the ADAF. The model is self-consistent since the main jet parameters are determined by the underlying accretion disk at the inner edge. The emergent spectrum of Sgr A$^*$ is the sum of the emission from jet and underlying ADAF. The very strong Comptonization of synchrotron emission from the jet dominates the bremsstrahlung from the ADAF, therefore, a very short variability timescale is expected and the predicted X-ray slope and the radio spectrum is in very good agreement with the observations.Comment: 10 pages, 3 figures, accepted by Astronomy & Astrophysic