Diffusion coefficient and shear viscosity of rigid water models

We report the diffusion coefficient and viscosity of popular rigid water models: two non-polarizable ones (SPC/E with three sites, and TIP4P/2005 with four sites) and a polarizable one (Dang-Chang, four sites). We exploit the dependence of the diffusion coefficient on the system size (Yeh and Hummer 2004 J. Phys. Chem. B 108 15873) to obtain the size-independent value. This also provides an estimate of the viscosity of all water models, which we compare to the Green-Kubo result. In all cases, a good agreement is found. The TIP4P/2005 model is in better agreement with the experimental data for both diffusion and viscosity. The SPC/E and Dang-Chang models overestimate the diffusion coefficient and underestimate the viscosity.     

Carotid plaque high-resolution MRI at 3 T: evaluation of a new imaging score for symptomatic plaque assessment

Purpose

To assess the sensitivity and specificity of intra-plaque hemorrhage (IPH), large lipid-rich necrotic core (LR-NC) and ulceration or cap rupture (UCR) for symptomatic carotid plaque characterization and to evaluate a new imaging score [Hemorrhage, Ulceration or cap rupture, Lipid-rich necrotic Core (HULC) score based on the sum of presence/absence of IPH, UCR and LR-NC; range 0–3] for assessment of recently symptomatic carotid plaques.

Material and methods

Twenty-seven recently symptomatic (< 8 weeks) and 36 asymptomatic patients with a carotid plaque thicker than 2 mm were prospectively imaged on a 3-T magnetic resonance (MR) system using high-resolution, multi-contrast MR sequences. Prior to analysis, all images were reviewed to assess image quality of each sequence. Sensitivity and specificity of IPH, LR-NC, UCR and HULC scores were calculated.

Results

Fifty-one patients were analyzed (26 symptomatic carotids and 67 asymptomatic carotids) after exclusion of studies with poor image quality. Sensitivity and specificity for symptomatic carotid plaque was, respectively, 46.1% and 97% for IPH, 84.6% and 73.1% for UCR and 80.7% and 76.1% for LR-NC. A HULC score of 2 or more showed a sensitivity of 73% and a specificity of 92.5%.

Conclusion

At 3 T, intra-plaque hemorrhage is the most specific criterion to characterize symptomatic carotid plaque. The HULC score offers the best compromise between sensitivity and specificity.     

Arithmetic partial differential equations, I

We develop an arithmetic analogue of linear partial differential equations in two independent “space-time” variables. The spatial derivative is a Fermat quotient operator, while the time derivative is the usual derivation. This allows us to “flow” integers or, more generally, points on algebraic groups with coordinates in rings with arithmetic flavor. In particular, we show that elliptic curves carry certain canonical “arithmetic flows” that are arithmetic analogues of the convection, heat, and wave equations, respectively. The same is true for the additive and the multiplicative group.     

On Blaschke products with derivatives in Bergman spaces with normal weights

We generalize a well-known sufficient condition for interpolating sequences for the Hilbert Bergman spaces to other Bergman spaces with normal weights (as defined by Shields and Williams) and obtain new results regarding the membership of the derivative of a Blaschke product or a general inner function in such spaces. We also apply duality techniques to obtain further results of this type and obtain new results about interpolating Blaschke products.     

On a multivariate Pareto distribution

A multivariate distribution possessing arbitrarily parameterized Pareto margins is formulated and studied. The distribution is believed to allow for an adequate modeling of dependent heavy tailed risks with a non-zero probability of simultaneous loss. Numerous links to certain existing probabilistic models, as well as seemingly useful characteristic results are proved. Expressions for, e.g., decumulative distribution functions, densities, (joint) moments and regressions are developed. An application to the classical pricing problem is considered, and some formulas are derived using the recently introduced economic weighted premium calculation principles.     

Geometric inequalities on Heisenberg groups

We establish geometric inequalities in the sub-Riemannian setting of the Heisenberg group \(\mathbb H^n\). Our results include a natural sub-Riemannian version of the celebrated curvature-dimension condition of Lott–Villani and Sturm and also a geodesic version of the Borell–Brascamp–Lieb inequality akin to the one obtained by Cordero-Erausquin, McCann and Schmuckenschläger. The latter statement implies sub-Riemannian versions of the geodesic Prékopa–Leindler and Brunn–Minkowski inequalities. The proofs are based on optimal mass transportation and Riemannian approximation of \(\mathbb H^n\) developed by Ambrosio and Rigot. These results refute a general point of view, according to which no geometric inequalities can be derived by optimal mass transportation on singular spaces.     

Vanishing Theorems on Holomorphic Lie Algebroids

The paper describes a Bochner-type study for holomorphic horizontal vector fields defined on a holomorphic Finsler algebroid E. We obtain in this setting a vanishing theorem for horizontal fields with compact support on E.     

A non-smooth three critical points theorem with applications in differential inclusions

We extend a recent result of Ricceri concerning the existence of three critical points of certain non-smooth functionals. Two applications are given, both in the theory of differential inclusions; the first one concerns a non-homogeneous Neumann boundary value problem, the second one treats a quasilinear elliptic inclusion problem in the whole \mathbb R^N{\mathbb R^N}.     

Active Control of Separating Boundary Layer

Flow control refers to the ability to alter flows with the aim of achieving a desired effect: examples include drag reduction, noise attenuation, improved mixing or increased combustion efficiency among many other industrial applications. The reduction and control of the viscous drag force exerted on bodies moving in a fluid is of great technical interest. Several active and passive methods to achieve a delay of separation in the boundary layer have been developed and are being developed. In this paper we present a new concept for boundary layer separation control that is based on the synthetic jet concept which converts acoustic oscillations into mean fluid motions. We use synthetic jets as methods for Coanda effect's amplification. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of Sound Radiated by Axisymmetric Vortex Ring

A theoretical and numerical study using the unsteady, 3D Navier-Stokes equations to generate axisymmetric vortex rings is reported. Increasing the vorticity, the vortex ring transition to a turbulent state are analyzed. After transition to a turbulent stage, the self-similarity of the temporal evolution of the flow is observed. Then we can compare sound radiated by the vortex ring to jet noise, at similar Reynolds number and low Mach number. The agreement between the simulation results and the simplified model is good. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)