High Order Upwind Schemes for Multidimensional Magnetohydrodynamics

A general method for constructing high order upwind schemes for multidimensional magnetohydrodynamics (MHD), having as a main built-in condition the divergence-free constraint \divb=0 for the magnetic field vector \bb, is proposed. The suggested procedure is based on {\em consistency} arguments, by taking into account the specific operator structure of MHD equations with respect to the reference Euler equations of gas-dynamics. This approach leads in a natural way to a staggered representation of the \bb field numerical data where the divergence-free condition in the cell-averaged form, corresponding to second order accurate numerical derivatives, is exactly fulfilled. To extend this property to higher order schemes, we then give general prescriptions to satisfy a $(r+1)^{th}$ order accurate \divb=0 relation for any numerical \bb field having a $r^{th}$ order interpolation accuracy. Consistency arguments lead also to a proper formulation of the upwind procedures needed to integrate the induction equations, assuring the exact conservation in time of the divergence-free condition and the related continuity properties for the \bb vector components. As an application, a third order code to simulate multidimensional MHD flows of astrophysical interest is developed using ENO-based reconstruction algorithms. Several test problems to illustrate and validate the proposed approach are finally presented.Comment: 34 pages, including 14 figure

A rarefaction-tracking method for hyperbolic conservation laws

We present a numerical method for scalar conservation laws in one space dimension. The solution is approximated by local similarity solutions. While many commonly used approaches are based on shocks, the presented method uses rarefaction and compression waves. The solution is represented by particles that carry function values and move according to the method of characteristics. Between two neighboring particles, an interpolation is defined by an analytical similarity solution of the conservation law. An interaction of particles represents a collision of characteristics. The resulting shock is resolved by merging particles so that the total area under the function is conserved. The method is variation diminishing, nevertheless, it has no numerical dissipation away from shocks. Although shocks are not explicitly tracked, they can be located accurately. We present numerical examples, and outline specific applications and extensions of the approach.Comment: 21 pages, 7 figures. Similarity 2008 conference proceeding

On the validity of mean-field amplitude equations for counterpropagating wavetrains

We rigorously establish the validity of the equations describing the evolution of one-dimensional long wavelength modulations of counterpropagating wavetrains for a hyperbolic model equation, namely the sine-Gordon equation. We consider both periodic amplitude functions and localized wavepackets. For the localized case, the wavetrains are completely decoupled at leading order, while in the periodic case the amplitude equations take the form of mean-field (nonlocal) Schr\"odinger equations rather than locally coupled partial differential equations. The origin of this weakened coupling is traced to a hidden translation symmetry in the linear problem, which is related to the existence of a characteristic frame traveling at the group velocity of each wavetrain. It is proved that solutions to the amplitude equations dominate the dynamics of the governing equations on asymptotically long time scales. While the details of the discussion are restricted to the class of model equations having a leading cubic nonlinearity, the results strongly indicate that mean-field evolution equations are generic for bimodal disturbances in dispersive systems with \O(1) group velocity.Comment: 16 pages, uuencoded, tar-compressed Postscript fil

Finite-Size Scaling in Two-Dimensional Superfluids

Using the $x-y$ model and a non-local updating scheme called cluster Monte Carlo, we calculate the superfluid density of a two dimensional superfluid on large-size square lattices $L \times L$ up to $400\times 400$. This technique allows us to approach temperatures close to the critical point, and by studying a wide range of $L$ values and applying finite-size scaling theory we are able to extract the critical properties of the system. We calculate the superfluid density and from that we extract the renormalization group beta function. We derive finite-size scaling expressions using the Kosterlitz-Thouless-Nelson Renormalization Group equations and show that they are in very good agreement with our numerical results. This allows us to extrapolate our results to the infinite-size limit. We also find that the universal discontinuity of the superfluid density at the critical temperature is in very good agreement with the Kosterlitz-Thouless-Nelson calculation and experiments.Comment: 13 pages, postscript fil

Untreated Type 2 Diabetes and Its Complications Are Associated With Subcortical Infarctions

OBJECTIVE - To investigate the association of type 2 diabetes with subcortical infarctions. RESEARCH DESIGN AND METHODS - We investigated this association in subjects with type 2 diabetes (case subjects; n = 93) and without type 2 diabetes (control subjects; n = 186), matched by age, sex, and years of education. Participants were a subset of the Mayo Clinic Study of Aging (median age 79 years) who had undergone magnetic resonance imaging. RESULTS - The frequency of subcortical infarctions was 39% in case subjects and 29% in control subjects (odds ratio 1.59 [95% CI 0.91-2.75]). The association was stronger in case subjects without treatment (2.60 [1.11- 6.08]) and in case subjects with diabetes-related complications (1.96 [1.02-3.74]) compared with control subjects. CONCLUSIONS - These findings suggest that untreated type 2 diabetes and type 2 diabetes with complications are associated with subcortical infarctions. © 2011 by the American Diabetes Association

Thinking inside the box:improving the lifestyle of inpatients with severe mental illness

BACKGROUND: An unhealthy lifestyle plays an important role in the substantially reduced life-expectancy of inpatients with severe mental illness (SMI). However, there is a lack of evidence on the long-term effectiveness and implementation of lifestyle improvements in inpatient mental healthcare.&lt;br/&gt; AIM: Increasing knowledge and understanding of (the implementation of) lifestyle changes in inpatients with SMI in longer-term clinical care.&lt;br/&gt; METHOD: Cross-sectional research followed by an observational study to evaluate a multidisciplinary lifestyle enhancing treatment (MULTI) for both changes in health-related outcomes after 18 months compared to treatment as usual (TAU), and the implementation barriers and facilitators.&lt;br/&gt; RESULTS: Patients were very sedentary and less physically active compared to people without SMI. After 18 months, MULTI showed significant improvements in total physical activity, cardiometabolic risk factors, psychosocial functioning and mediation use, compared to TAU. Physical health did not improve in TAU. The implementation of MULTI was hampered by organisational factors and facilitated by positive attitudes of healthcare professionals and patients towards MULTI and their own role in it.&lt;br/&gt; CONCLUSION: Using a multidisciplinary integrated approach, it is possible to improve the lifestyle, and thus the health status, of SMI inpatients, within the current context of routine mental healthcare.</p

Thinking inside the box:improving the lifestyle of inpatients with severe mental illness

BACKGROUND: An unhealthy lifestyle plays an important role in the substantially reduced life-expectancy of inpatients with severe mental illness (SMI). However, there is a lack of evidence on the long-term effectiveness and implementation of lifestyle improvements in inpatient mental healthcare.&lt;br/&gt; AIM: Increasing knowledge and understanding of (the implementation of) lifestyle changes in inpatients with SMI in longer-term clinical care.&lt;br/&gt; METHOD: Cross-sectional research followed by an observational study to evaluate a multidisciplinary lifestyle enhancing treatment (MULTI) for both changes in health-related outcomes after 18 months compared to treatment as usual (TAU), and the implementation barriers and facilitators.&lt;br/&gt; RESULTS: Patients were very sedentary and less physically active compared to people without SMI. After 18 months, MULTI showed significant improvements in total physical activity, cardiometabolic risk factors, psychosocial functioning and mediation use, compared to TAU. Physical health did not improve in TAU. The implementation of MULTI was hampered by organisational factors and facilitated by positive attitudes of healthcare professionals and patients towards MULTI and their own role in it.&lt;br/&gt; CONCLUSION: Using a multidisciplinary integrated approach, it is possible to improve the lifestyle, and thus the health status, of SMI inpatients, within the current context of routine mental healthcare.</p

A New Computational Fluid Dynamics Code I: Fyris Alpha

A new hydrodynamics code aimed at astrophysical applications has been developed. The new code and algorithms are presented along with a comprehensive suite of test problems in one, two, and three dimensions. The new code is shown to be robust and accurate, equalling or improving upon a set of comparison codes. Fyris Alpha will be made freely available to the scientific community.Comment: 59 pages, 27 figures For associated code see http://www.mso.anu.edu.au/fyri