General Polytropic Magnetofluid under Self-Gravity: Voids and Shocks

We study the self-similar magnetohydrodynamics (MHD) of a quasi-spherical expanding void (viz. cavity or bubble) in the centre of a self-gravitating gas sphere with a general polytropic equation of state. We show various analytic asymptotic solutions near the void boundary in different parameter regimes and obtain the corresponding void solutions by extensive numerical explorations. We find novel void solutions of zero density on the void boundary. These new void solutions exist only in a general polytropic gas and feature shell-type density profiles. These void solutions, if not encountering the magnetosonic critical curve (MCC), generally approach the asymptotic expansion solution far from the central void with a velocity proportional to radial distance. We identify and examine free-expansion solutions, Einstein-de Sitter expansion solutions, and thermal-expansion solutions in three different parameter regimes. Under certain conditions, void solutions may cross the MCC either smoothly or by MHD shocks, and then merge into asymptotic solutions with finite velocity and density far from the centre. Our general polytropic MHD void solutions provide physical insight for void evolution, and may have astrophysical applications such as massive star collapses and explosions, shell-type supernova remnants and hot bubbles in the interstellar and intergalactic media, and planetary nebulae.Comment: 21 pages, 15 figures, accepted for publication on New Astronom

Perturbation Analysis of a General Polytropic Homologously Collapsing Stellar Core

For dynamic background models of Goldreich & Weber and Lou & Cao, we examine 3-dimensional perturbation properties of oscillations and instabilities in a general polytropic homologously collapsing stellar core of a relativistic hot medium with a polytropic index of 4/3. We identify acoustic p-modes and surface f-modes as well as internal gravity g$^{+}-$ and g$^{-}-$modes. We demonstrate that the global energy criterion of Chandrasehkar is insufficient to warrant the stability of general polytropic equilibria. We confirm the acoustic p-mode stability of Goldreich & Weber, even though their p-mode eigenvalues appear in systematic errors. Unstable modes include g$^{-}-$modes and high-order g$^{+}-$modes. Such instabilities occur before the stellar core bounce, in contrast to instabilities in other models of supernova explosions. The breakdown of spherical symmetry happens earlier than expected in numerical simulations so far. The formation and motion of the central compact object are speculated to be much affected by such g-mode instabilities. By estimates of typical parameters, unstable low-order l=1 g-modes may produce initial kicks of the central compact object

Observational study of the association of first insulin type in uncontrolled type 2 diabetes with macrovascular and microvascular disease

<p>Aims: To compare the risk of vascular disease, HbA1c and weight change, between first prescribed insulins in people with type 2 diabetes.</p> <p>Methods: People included in THIN United Kingdom primary care record database who began insulin (2000–2007) after poor control on oral glucose-lowering agents (OGLD) were grouped by the number of OGLDs in their treatment regimen immediately before starting insulin (n = 3,485). Within OGLD group, Cox regression compared macrovascular (all-cause mortality, myocardial infarction, acute coronary syndrome and stroke) and microvascular disease (peripheral neuropathy, nephropathy, and retinopathy) between insulin type (basal, pre-mix or Neutral Protamine Hagedorn, NPH) while ANCOVAs compared haemoglobin A1c (HbA1c) and weight change.</p> <p>Results: Mean follow-up was 3.6 years. Rates of incident macrovascular events were similar when basal insulin was compared to pre-mix or NPH, adjusted hazard ratio versus basal: pre-mix 1.08 (95% CI 0.73, 1.59); NPH 1.00 (0.63, 1.58) after two OGLDs, and pre-mix 0.97 (0.46, 2.02); NPH 0.77 (0.32, 1.86) after three OGLDs. An increased risk of microvascular disease in NPH versus basal after 3 OGLDs, adjusted hazard ratio1.87 (1.04, 3.36), was not seen after two agents or in comparisons of basal and pre-mix. At one year, after two OGLDs, weight increase was less with basal compared with pre-mix. After three OGLDs, mean HbA1c had reduced less in basal versus pre-mix or NPH at 6–8 and at 9–11 months, and versus pre-mix at 12–14 months.</p> <p>Conclusion: We found no difference in the risk of macrovascular events between first insulins in the medium term when started during poor glycaemia control. The increased risk of microvascular events with NPH warrants further study. In certain groups, first use of basal insulin was associated with less gain in weight and decrease in HbA1c compared to other insulins.</p&gt

Dynamic Evolution of a Quasi-Spherical General Polytropic Magnetofluid with Self-Gravity

In various astrophysical contexts, we analyze self-similar behaviours of magnetohydrodynamic (MHD) evolution of a quasi-spherical polytropic magnetized gas under self-gravity with the specific entropy conserved along streamlines. In particular, this MHD model analysis frees the scaling parameter $n$ in the conventional polytropic self-similar transformation from the constraint of $n+\gamma=2$ with $\gamma$ being the polytropic index and therefore substantially generalizes earlier analysis results on polytropic gas dynamics that has a constant specific entropy everywhere in space at all time. On the basis of the self-similar nonlinear MHD ordinary differential equations, we examine behaviours of the magnetosonic critical curves, the MHD shock conditions, and various asymptotic solutions. We then construct global semi-complete self-similar MHD solutions using a combination of analytical and numerical means and indicate plausible astrophysical applications of these magnetized flow solutions with or without MHD shocks.Comment: 21 pages, 7 figures, accepted for publication in APS

Massive stars as thermonuclear reactors and their explosions following core collapse

Nuclear reactions transform atomic nuclei inside stars. This is the process of stellar nucleosynthesis. The basic concepts of determining nuclear reaction rates inside stars are reviewed. How stars manage to burn their fuel so slowly most of the time are also considered. Stellar thermonuclear reactions involving protons in hydrostatic burning are discussed first. Then I discuss triple alpha reactions in the helium burning stage. Carbon and oxygen survive in red giant stars because of the nuclear structure of oxygen and neon. Further nuclear burning of carbon, neon, oxygen and silicon in quiescent conditions are discussed next. In the subsequent core-collapse phase, neutronization due to electron capture from the top of the Fermi sea in a degenerate core takes place. The expected signal of neutrinos from a nearby supernova is calculated. The supernova often explodes inside a dense circumstellar medium, which is established due to the progenitor star losing its outermost envelope in a stellar wind or mass transfer in a binary system. The nature of the circumstellar medium and the ejecta of the supernova and their dynamics are revealed by observations in the optical, IR, radio, and X-ray bands, and I discuss some of these observations and their interpretations.Comment: To be published in " Principles and Perspectives in Cosmochemistry" Lecture Notes on Kodai School on Synthesis of Elements in Stars; ed. by Aruna Goswami & Eswar Reddy, Springer Verlag, 2009. Contains 21 figure

Hemophagocytosis causes a consumptive anemia of inflammation

IFN-γ stimulates blood-eating macrophages (hemophagocytes) by acting directly on macrophages to promote phagocytosis and uptake of blood cells

Absence of diabetic retinopathy in a patient who has had diabetes mellitus for 69 years, and inadequate glycemic control: case presentation

The main risk factors for the development and progression of diabetic retinopathy (DR) are chronic hyperglycemia, disease duration and systemic blood pressure. So far chronic hyperglycemia is the strongest evidence concerning the risk of developing DR. However there are some patients with poor metabolic control who never develop this diabetic complication. We present a case of a 73-year-old woman with type 1 diabetes mellitus, diagnosed 69 years ago. The patient is 73 years old, with no evidence of DR, despite poor glycemic control and several risk factors for DR. This case suggests the presence of a possible protection factor, which could be genetic

Three-dimensional Hydrodynamic Instabilities in Stellar Core Collapses

A spherically symmetric hydrodynamic stellar core collapse under gravity is time-dependent and may become unstable once disturbed. Specifically for a homologously collapse of stellar core characterized by a polytropic exponent \Gamma=4/3, we examine oscillations and/or instabilities of three dimensional (3D) general polytropic perturbations. For compressible 3D perturbations, the polytropic index \gamma of perturbations can differ from \Gamma=4/3 of the general polytropic hydrodynamic background flow. Our model formulation here is more general and allows the existence of internal gravity g(-)-modes and/or g(+)-modes. Eigenvalues and eigen-functions of various oscillatory and unstable perturbation modes are computed. As studied in several specialized cases of Goldreich & Weber and of Cao & Lou, we further confirm that acoustic p-modes and surface f-modes remain stable in the current more general situations. In comparison, g(-)-modes and sufficiently high radial order g(+)-modes are unstable, leading to inevitable convective motions within the collapsing stellar interior. Unstable growths of 3D g-mode disturbances are governed dominantly by the angular momentum conservation and modified by the gas pressure restoring force. We note in particular that unstable temporal growths of 3D vortical perturbations exist even when the specific entropy distribution becomes uniform and \gamma=\Gamma=4/3. Conceptually, unstable g-modes might bear conceivable physical consequences on supernova explosions, the initial kicks of nascent proto-neutron stars (PNSs) and break-ups of the collapsing core, while unstable growths of vortical perturbations can lead to fast spins of compact objects and other relevant results.Comment: 16 pages, MNRAS(to be published

Web-based guided insulin self-titration in patients with type 2 diabetes: the Di@log study. Design of a cluster randomised controlled trial [TC1316]

<p>Abstract</p> <p>Background</p> <p>Many patients with type 2 diabetes (T2DM) are not able to reach the glycaemic target level of HbA1c < 7.0%, and therefore are at increased risk of developing severe complications. Transition to insulin therapy is one of the obstacles in diabetes management, because of barriers of both patient and health care providers. Patient empowerment, a patient-centred approach, is vital for improving diabetes management. We developed a web-based self-management programme for insulin titration in T2DM patients. The aim of our study is to investigate if this internet programme helps to improve glycaemic control more effectively than usual care.</p> <p>Methods/Design</p> <p>T2DM patients (n = 248), aged 35–75 years, with an HbA1c ≥ 7.0%, eligible for treatment with insulin and able to use the internet will be selected from general practices in two different regions in the Netherlands. Cluster randomisation will be performed at the level of general practices. Patients in the intervention group will use a self-developed internet programme to assist them in self-titrating insulin. The control group will receive usual care.</p> <p>Primary outcome is the difference in change in HbA1c between intervention and control group. Secondary outcome measures are quality of life, treatment satisfaction, diabetes self-efficacy and frequency of hypoglycaemic episodes. Results will be analysed according to the intention-to-treat principle.</p> <p>Discussion</p> <p>An internet intervention supporting self-titration of insulin therapy in T2DM patients is an innovative patient-centred intervention. The programme provides guided self-monitoring and evaluation of health and self-care behaviours through tailored feedback on input of glucose values. This is expected to result in a better performance of self-titration of insulin and consequently in the improvement of glycaemic control. The patient will be enabled to 'discover and use his or her own ability to gain mastery over his/her diabetes' and therefore patient empowerment will increase. Based on the self-regulation theory of Leventhal, we hypothesize that additional benefits will be achieved in terms of increases in treatment satisfaction, quality of life and self-efficacy.</p> <p>Trial registration</p> <p>Dutch Trial Register TC1316.</p