An asymptotic preserving scheme for kinetic models with singular limit

We propose a new class of asymptotic preserving schemes to solve kinetic equations with mono-kinetic singular limit. The main idea to deal with the singularity is to transform the equations by appropriate scalings in velocity. In particular, we study two biologically related kinetic systems. We derive the scaling factors and prove that the rescaled solution does not have a singular limit, under appropriate spatial non-oscillatory assumptions, which can be verified numerically by a newly developed asymptotic preserving scheme. We set up a few numerical experiments to demonstrate the accuracy, stability, efficiency and asymptotic preserving property of the schemes.Comment: 24 pages, 6 figure

Non-invasive assessment of intracranial wall shear stress using high-resolution magnetic resonance imaging in combination with computational fluid dynamics technique

In vivo studies on association between wall shear stress (WSS) and intracranial plaque are deficient. Based on the three-dimensional T1-weighted high-resolution magnetic resonance imaging (3DT1 HR-MRI) data of patients with low-grade stenotic (<50%) atherosclerotic middle cerebral artery (MCA) and subjects with normal MCA, we built a three-dimensional reconstructed WSS model by computational fluid dynamics (CFD) technique. Three-dimensional registration of the CFD model to the HR-MRI was performed with projections based on the resolution and thickness of the images. The relationships between the WSS at each side of the vessel wall and plaque location were analyzed. A total of 94 MCA plaques from 43 patients and 50 normal MCAs were analyzed. In the normal MCAs, WSS was lower at the ventral-inferior wall than at the dorsal-superior wall (proximal segment, p < 0.001; middle segment, p < 0.001) and lower at the inner wall than at the outer wall of the MCA curve (p < 0.001). In atherosclerotic MCAs, similar low WSS regions were observed where plaques developed. The WSS ratio of the ventral-inferior wall to the dorsal-superior wall in atherosclerotic MCAs was lower than that in normal MCAs (p = 0.002). The WSSinner-outer ratio in atherosclerotic MCAs was lower than that in normal MCAs (p = 0.002). Low WSS was associated with MCA atherosclerosis formation and occurred mainly at the ventral-inferior wall, which was anatomically opposite the orifices of penetrating arteries, and at the inner wall of the MCA curve. Overall, the results were well consistent with the low WSS theory in atherosclerosis formation. The reconstructed WSS model is a promising novel method for assessing an individualized vascular profile once validated by further studies

Evidence for Ag participating the electrochemical migration of 96.5Sn-3Ag-0.5Cu alloy

Ag participating the electrochemical migration (ECM) of Sn-Ag based alloys is still controversial. In this work,Ag+concentration in electrolyte layer and Ag distribution in dendrites formed during the ECM of 96.5Sn-3Ag-0.5Cu alloy were investigated using Inductively Coupled Plasma Source Mass Spectrometer and ScanningTransmission Electron Microscopy, respectively. Results show that Ag+can only be detected when Ag can re-lease from Ag3Sn during the anodic polarization of 96.5Sn-3Ag-0.5Cu alloy. Under such a condition, Ag couldalso be found in dendrites. Therefore, it can be concluded that Ag participates the ECM of 96.5Sn-3Ag-0.5Cualloy, but it is potential-dependent

Simulation of fluid–particles flows: Heavy particles, flowing regime and AP–schemes

We are interested in an Eulerian–Lagrangian model describing particulate flows. The model under study consists of the Euler system and a Vlasov-Fokker-Planck equation coupled through momentum and energy exchanges. This problem contains asymptotic regimes that make the coupling terms stiff, and lead to a limiting model of purely hydrodynamic type. We design a numerical scheme which is able to capture this asymptotic behavior, without requiring prohibitive stability conditions. The construction of this Asymptotic Preserving scheme relies on an implicit discretization of the stiff terms which can be treated by efficient inversion methods. This method is a natural coupling of a kinetic solver for the particles with a kinetic scheme for the hydrodynamic Euler equations. Numerical experiments are conducted to study the performance of this scheme in various asymptotic regimes. Key words. Fluid–particles flows. Hydrodynamic regimes. Asymptotic Preserving schemes. Kinetic schemes. 2010 MSC Subject Classification. 82C80 82C40 35L65 35Q35 65M06 76N15 76M2