Collisionless hydrodynamics for 1D motion of inhomogeneous degenerate electron gases: equivalence of two recent descriptions

Recently I. Tokatly and O. Pankratov (''TP'', Phys. Rev. B 60, 15550 (1999)) used velocity moments of a semiclassical kinetic equation to derive a hydrodynamic description of electron motion in a degenerate electron gas. Independently, the present authors (Theochem 501-502, 327 (2000)) used considerations arising from the Harmonic Potential Theorem (Phys. Rev. Lett. 73, 2244 (1994)) to generate a new form of high-frequency hydrodynamics for inhomogeneous degenerate electron gases (HPT-N3 hydrodynamics). We show here that TP hydrodynamics yields HPT-N3 hydrodynamics when linearized about a Thomas-Fermi groundstate with one-dimensional spatial inhomnogeneity.Comment: 17p

Spin-resolved correlation kinetic energy of the spin-polarized electron gas

URL:http://link.aps.org/doi/10.1103/PhysRevB.70.205126 DOI:10.1103/PhysRevB.70.205126We give an exact formula, based on differentiation with respect to the electron mass, for the spin resolution of the kinetic energy (KE) of a general many-electron system, including the correlation KE. We evaluate the spin-resolved correlation KE for a uniform three dimensional electron gas of arbitrary spin polarization at metallic densities, using the Singwi-Tosi-Land-Sjolander formalism. We give a very accurate scaling relation for the data thus obtained. Our results are expected to be relevant in the analysis of spintronic systems.J.F.D. acknowledges support from an Australian Research Council Large Grant. G.V. acknowledges NSF Grant No. DMR-0313681. Computer time was provided by Research Computing Services at Griffith University

Determination of Clinical Outcome in Mitral Regurgitation With Cardiovascular Magnetic Resonance Quantification

Background—Surgery for severe mitral regurgitation is indicated if symptoms or left ventricular dilation or dysfunction occur. However, prognosis is already reduced by this stage, and earlier surgery on asymptomatic patients has been advocated if valve repair is likely, but identifying suitable patients for early surgery is difficult. Quantifying the regurgitation may help, but evidence for its link with outcome is limited. Cardiovascular magnetic resonance (CMR) can accurately quantify mitral regurgitation, and we examined whether this was associated with the future need for surgery. Methods and Results—One hundred nine asymptomatic patients with echocardiographic moderate or severe mitral regurgitation had baseline CMR scans and were followed up for up to 8 years (mean, 2.5±1.9 years). CMR quantification accurately identified patients who progressed to symptoms or other indications for surgery: 91% of subjects with regurgitant volume ≤55 mL survived to 5 years without surgery compared with only 21% with regurgitant volume >55 mL (P40%. CMR-derived end-diastolic volume index showed a weaker association with outcome (proportions surviving without surgery at 5 years, 90% for left ventricular end-diastolic volume index <100 mL/m2 versus 48% for ≥100 mL/m2) and added little to the discriminatory power of regurgitant fraction/volume alone. Conclusions—CMR quantification of mitral regurgitation was associated with the development of symptoms or other indications for surgery and showed better discriminatory ability than the reference-standard CMR-derived ventricular volumes. CMR may be able to identify appropriate patients for early surgery, with the potential to change clinical practice, although the clinical benefits of early surgery require confirmation in a clinical trial

Sampling-based path planning for multi-robot systems with co-safe linear temporal logic specifications

© 2017, Springer International Publishing AG. This paper addresses the problem of path planning for multiple robots under high-level specifications given as syntactically co-safe linear temporal logic formulae. Most of the existing solutions use the notion of abstraction to obtain a discrete transition system that simulates the dynamics of the robot. Nevertheless, these solutions have poor scalability with the dimension of the configuration space of the robots. For problems with a single robot, sampling-based methods have been presented as a solution to alleviate this limitation. The proposed solution extends the idea of sampling methods to the multiple robot case. The method samples the configuration space of the robots to incrementally constructs a transition system that models the motion of all the robots as a group. This transition system is then combined with a Büchi automaton, representing the specification, in a Cartesian product. The product is updated with each expansion of the transition system until a solution is found. We also present a new algorithm that improves the performance of the proposed method by guiding the expansion of the transition system. The method is demonstrated with examples considering different number of robots and specifications

The cutoff method for the numerical computation of nonnegative solutions of parabolic PDEs with application to anisotropic diffusion and lubrication-type equations

The cutoff method, which cuts off the values of a function less than a given number, is studied for the numerical computation of nonnegative solutions of parabolic partial differential equations. A convergence analysis is given for a broad class of finite difference methods combined with cutoff for linear parabolic equations. Two applications are investigated, linear anisotropic diffusion problems satisfying the setting of the convergence analysis and nonlinear lubrication-type equations for which it is unclear if the convergence analysis applies. The numerical results are shown to be consistent with the theory and in good agreement with existing results in the literature. The convergence analysis and applications demonstrate that the cutoff method is an effective tool for use in the computation of nonnegative solutions. Cutoff can also be used with other discretization methods such as collocation, finite volume, finite element, and spectral methods and for the computation of positive solutions.Comment: 19 pages, 41 figure

Ventricular longitudinal function is associated with microvascular obstruction and intramyocardial haemorrhage.

Microvascular obstruction (MVO) and intramyocardial haemorrhage (IMH) are associated with adverse prognosis, independently of infarct size after reperfused ST-elevation myocardial infarction (STEMI). Mitral annular plane systolic excursion (MAPSE) is a well-established parameter of longitudinal function on echocardiography.We aimed to investigate how acute MAPSE, assessed by a four-chamber cine-cardiovascular MR (CMR), is associated with MVO, IMH and convalescent left ventricular (LV) remodelling.54 consecutive patients underwent CMR at 3T (Intera CV, Philips Healthcare, Best, The Netherlands) within 3 days of reperfused STEMI. Cine, T2-weighted, T2* and late gadolinium enhancement (LGE) imaging were performed. Infarct and MVO extent were measured from LGE images. The presence of IMH was investigated by combined analysis of T2w and T2* images. Averaged-MAPSE (medial-MAPSE+lateral-MAPSE/2) was calculated from 4-chamber cine imaging.44 patients completed the baseline scan and 38 patients completed 3-month scans. 26 (59%) patients had MVO and 25 (57%) patients had IMH. Presence of MVO and IMH were associated with lower averaged-MAPSE (11.7±0.4 mm vs 9.3±0.3 mm; p<0.001 and 11.8±0.4 mm vs 9.2±0.3 mm; p<0.001, respectively). IMH (β=-0.655, p<0.001) and MVO (β=-0.567, p<0.001) demonstrated a stronger correlation to MAPSE than other demographic and infarct characteristics. MAPSE ≤10.6 mm demonstrated 89% sensitivity and 72% specificity for the detection of MVO and 92% sensitivity and 74% specificity for IMH. LV remodelling in convalescence was not associated with MAPSE (AUC 0.62, 95% CI 0.44 to 0.77, p=0.22).Postreperfused STEMI, LV longitudinal function assessed by MAPSE can independently predict the presence of MVO and IMH