Degenerate Variational Integrators for Magnetic Field Line Flow and Guiding Center Trajectories

Symplectic integrators offer many advantages for the numerical solution of Hamiltonian differential equations, including bounded energy error and the preservation of invariant sets. Two of the central Hamiltonian systems encountered in plasma physics --- the flow of magnetic field lines and the guiding center motion of magnetized charged particles --- resist symplectic integration by conventional means because the dynamics are most naturally formulated in non-canonical coordinates, i.e., coordinates lacking the familiar $(q, p)$ partitioning. Recent efforts made progress toward non-canonical symplectic integration of these systems by appealing to the variational integration framework; however, those integrators were multistep methods and later found to be numerically unstable due to parasitic mode instabilities. This work eliminates the multistep character and, therefore, the parasitic mode instabilities via an adaptation of the variational integration formalism that we deem ``degenerate variational integration''. Both the magnetic field line and guiding center Lagrangians are degenerate in the sense that their resultant Euler-Lagrange equations are systems of first-order ODEs. We show that retaining the same degree of degeneracy when constructing a discrete Lagrangian yields one-step variational integrators preserving a non-canonical symplectic structure on the original Hamiltonian phase space. The advantages of the new algorithms are demonstrated via numerical examples, demonstrating superior stability compared to existing variational integrators for these systems and superior qualitative behavior compared to non-conservative algorithms

Ambulatory monitoring of activity levels of individuals in the sub-acute stage following stroke: a case series

<p>Abstract</p> <p>Background</p> <p>There is an important need to better understand the activities of individual patients with stroke outside of structured therapy since this activity is likely to have a profound influence on recovery. A case-study approach was used to examine the activity levels and associated physiological load of patients with stroke throughout a day.</p> <p>Methods</p> <p>Activities and physiologic measures were recorded during a continuous 8 hour period from 4 individuals in the sub-acute stage following stroke (ranging from 49 to 80 years old; 4 to 8 weeks post-stroke) in an in-patient rehabilitation hospital.</p> <p>Results</p> <p>Both heart rate (p = 0.0207) and ventilation rate (p < 0.0001) increased as intensity of activity increased. Results revealed individual differences in physiological response to daily activities, and large ranges in physiological response measures during 'moderately' and 'highly' therapeutic activities.</p> <p>Conclusion</p> <p>Activity levels of individuals with stroke during the day were generally low, though task-related changes in physiologic measures were observed. Large variability in the physiological response to even the activities deemed to be greatest intensity suggests that inclusion of such extended measurement of physiologic measures may improve understanding of physiological profile that could guide elements of the physical therapy prescription.</p

Effect of carbohydrate feeding on the bone metabolic response to running

Bone resorption is increased after running, with no change in bone formation. Feeding during exercise might attenuate this increase, preventing associated problems for bone. This study investigated the immediate and short-term bone metabolic responses to carbohydrate (CHO) feeding during treadmill running. Ten men completed two 7-day trials, once being fed CHO (8% glucose immediately before, every 20 min during, and immediately after exercise at a rate of 0.7 g CHO·kg body mass-1·h-1) and once being fed placebo (PBO). On day 4 of each trial, participants completed a 120-min treadmill run at 70% of maximal oxygen consumption (VO2 max). Blood was taken at baseline (BASE), immediately after exercise (EE), after 60 (R1) and 120 (R2) min of recovery, and on three follow-up days (FU1-FU3). Markers of bone resorption [COOH-terminal telopeptide region of collagen type 1 (β-CTX)] and formation [NH2-terminal propeptides of procollagen type 1 (P1NP)] were measured, along with osteocalcin (OC), parathyroid hormone (PTH), albumin-adjusted calcium (ACa), phosphate, glucagon-like peptide-2 (GLP-2), interleukin-6 (IL-6), insulin, cortisol, leptin, and osteoprotogerin (OPG). Area under the curve was calculated in terms of the immediate (BASE, EE, R1, and R2) and short-term (BASE, FU1, FU2, and FU3) responses to exercise. β-CTX, P1NP, and IL-6 responses to exercise were significantly lower in the immediate postexercise period with CHO feeding compared with PBO (β-CTX: P=0.028; P1NP: P=0.021; IL-6: P=0.036), although there was no difference in the short-term response (β-CTX: P=0.856; P1NP: P=0.721; IL-6: P=0.327). No other variable was significantly affected by CHO feeding during exercise. We conclude that CHO feeding during exercise attenuated the β-CTX and P1NP responses in the hours but not days following exercise, indicating an acute effect of CHO feeding on bone turnover

Scientific and Computational Challenges of the Fusion Simulation Program (FSP)

This paper highlights the scientific and computational challenges facing the Fusion Simulation Program (FSP) a major national initiative in the United States with the primary objective being to enable scientific discovery of important new plasma phenomena with associated understanding that emerges only upon integration. This requires developing a predictive integrated simulation capability for magnetically-confined fusion plasmas that are properly validated against experiments in regimes relevant for producing practical fusion energy. It is expected to provide a suite of advanced modeling tools for reliably predicting fusion device behavior with comprehensive and targeted science-based simulations of nonlinearly-coupled phenomena in the core plasma, edge plasma, and wall region on time and space scales required for fusion energy production. As such, it will strive to embody the most current theoretical and experimental understanding of magnetic fusion plasmas and to provide a living framework for the simulation of such plasmas as the associated physics understanding continues to advance over the next several decades. Substantive progress on answering the outstanding scientific questions in the field will drive the FSP toward its ultimate goal of developing the ability to predict the behavior of plasma discharges in toroidal magnetic fusion devices with high physics fidelity on all relevant time and space scales. From a computational perspective, this will demand computing resources in the petascale range and beyond together with the associated multi-core algorithmic formulation needed to address burning plasma issues relevant to ITER - a multibillion dollar collaborative experiment involving seven international partners representing over half the world's population. Even more powerful exascale platforms will be needed to meet the future challenges of designing a demonstration fusion reactor (DEMO). Analogous to other major applied physics modeling projects (e.g., Climate Modeling), the FSP will need to develop software in close collaboration with computers scientists and applied mathematicians and validated against experimental data from tokamaks around the world. Specific examples of expected advances needed to enable such a comprehensive integrated modeling capability and possible "co-design" approaches will be discussed. _________________________________________________

White Matter Deficits Assessed by Diffusion Tensor Imaging and Cognitive Dysfunction in Psychostimulant Users With Comorbid Human Immunodeficiency Virus Infection

Background Psychostimulant drug use is commonly associated with drug-related infection, including the human immunodeficiency virus (HIV). Both psychostimulant use and HIV infection are known to damage brain white matter and impair cognition. To date, no study has examined white matter integrity using magnetic resonance imaging (MRI) diffusion tensor imaging (DTI) in chronic psychostimulant users with comorbid HIV infection, and determined the relationship of white matter integrity to cognitive function. Methods Twenty-one subjects (mean age 37.5&nbsp;±&nbsp;9.0&nbsp;years) with a history of heavy psychostimulant use and HIV infection (8.7&nbsp;±&nbsp;4.3&nbsp;years) and 22 matched controls were scanned on a 3T MRI. Fractional anisotropy (FA) values were calculated with DTI software. Four regions of interest were manually segmented, including the genu of the corpus callosum, left and right anterior limbs of the internal capsule, and the anterior commissure. Subjects also completed a neurocognitive battery and questionnaires about physical and mental health. Results The psychostimulant using, HIV positive group displayed decreased white matter integrity, with significantly lower FA values for all white matter tracts (p&nbsp;&lt;&nbsp;0.05). This group also exhibited decreased cognitive performance on tasks that assessed cognitive set-shifting, fine motor speed and verbal memory. FA values for the white matter tracts correlated with cognitive performance on many of the neurocognitive tests. Conclusions White matter integrity was thus impaired in subjects with psychostimulant use and comorbid HIV infection, which predicted worsened cognitive performance on a range of tests. Further study on this medical comorbidity is required

Do functional walk tests reflect cardiorespiratory fitness in sub-acute stroke?

BACKGROUND AND PURPOSE: The Six-Minute Walk Test (6MWT) has been employed as a measure of functional capacity, but its relationship to cardiorespiratory fitness in stroke is not well established. Gait speed measured over short distances is commonly used as an index of walking competency following stroke. We evaluated the relationship between the 6MWT, aerobic fitness (VO(2)peak) and walking competency in sub-acute stroke. METHODS: Thirty-six individuals (mean age ± SD, 64.6 ± 14.4 years; time post-stroke 16.2 ± 13.3 days) were evaluated using the 6MWT (distance, speed, heart rate), a maximal exercise test (VO(2)peak, heart rate, exercise test duration), and walking competency using a five meter walk (speed, symmetry ratio). Correlation analyses were used to examine the relationships between these outcomes. RESULTS: There was a strong correlation between the 6MWT and five meter walk velocity for preferred (r = 0.79) and fast (r = 0.82) speed (p < 0.001). On average, the 6MWT speed was faster than the preferred gait speed (94.9 cm/s vs. 83.8 cm/s, p = 0.003), but slower than the fast-paced walk (115.1 cm/s, p < 0.001). There was significant though more moderate association between 6MWT distance and VO(2)peak (r = 0.56, p < 0.001) and exercise test duration (r = 0.60, p < 0.001). CONCLUSION: The speed selected during the 6MWT was strongly related to the velocities selected during the five meter walk distance (intermediate to the selected preferred and fast speeds). Although the 6MWT may be challenging to the cardiorespiratory system, it appears to be more strongly influenced by potential limits to walking speed rather than cardiorespiratory capacity. As a result, this test is not, by itself, an adequate measure of aerobic fitness early after stroke

Stresses in Proton Exchange Membranes Due to Hygro-Thermal Loading

Durability of the proton exchange membrane (PEM) is a major technical barrier to the commercial viability of polymer electrolyte membrane fuel cells (PEMFC) for stationary and transportation applications. In order to reach Department of Energy objectives for automotive PEMFCs, an operating design lifetime of at least 5000 h over a broad temperature range is required. Reaching these lifetimes is an extremely difficult technical challenge. Though good progress has been made in recent years, there are still issues that need to be addressed to assure successful, economically viable, long-term operation of PEM fuel cells. Fuel cell lifetime is currently limited by gradual degradation of both the chemical and hygro-thermomechanical properties of the membranes.Eventually the system fails due to a critical reduction of the voltage or mechanical damage. However, the hygro-thermomechanical loading of the membranes and how this effects the lifetime of thefuel cell is not understood. The long-term objective of the research is to establish a fundamental understanding of the mechanical processes in degradation and how they influence the lifetime of PEMFCs based on perfluorosulfuric acid membrane. In this paper, we discuss the finite element models developed to investigate the in situ stresses in polymer membranes

Stresses in Proton Exchange Membranes Due to Hygro-Thermal Loading

Durability of the proton exchange membrane (PEM) is a major technical barrier to the commercial viability of polymer electrolyte membrane fuel cells (PEMFC) for stationary and transportation applications. In order to reach Department of Energy objectives for automotive PEMFCs, an operating design lifetime of at least 5000 h over a broad temperature range is required. Reaching these lifetimes is an extremely difficult technical challenge. Though good progress has been made in recent years, there are still issues that need to be addressed to assure successful, economically viable, long-term operation of PEM fuel cells. Fuel cell lifetime is currently limited by gradual degradation of both the chemical and hygro-thermomechanical properties of the membranes.Eventually the system fails due to a critical reduction of the voltage or mechanical damage. However, the hygro-thermomechanical loading of the membranes and how this effects the lifetime of thefuel cell is not understood. The long-term objective of the research is to establish a fundamental understanding of the mechanical processes in degradation and how they influence the lifetime of PEMFCs based on perfluorosulfuric acid membrane. In this paper, we discuss the finite element models developed to investigate the in situ stresses in polymer membranes