Limiting problems for a nonstandard viscous Cahn--Hilliard system with dynamic boundary conditions

This note is concerned with a nonlinear diffusion problem of phase-field type, consisting of a parabolic system of two partial differential equations, complemented by boundary and initial conditions. The system arises from a model of two-species phase segregation on an atomic lattice and was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp.105--118. The two unknowns are the phase parameter and the chemical potential. In contrast to previous investigations about this PDE system, we consider here a dynamic boundary condition for the phase variable that involves the Laplace-Beltrami operator and models an additional nonconserving phase transition occurring on the surface of the domain. We are interested to some asymptotic analysis and first discuss the asymptotic limit of the system as the viscosity coefficient of the order parameter equation tends to 0: the convergence of solutions to the corresponding solutions for the limit problem is proven. Then, we study the long-time behavior of the system for both problems, with positive or zero viscosity coefficient, and characterize the omega-limit set in both cases

Global existence for a nonstandard viscous Cahn--Hilliard system with dynamic boundary condition

In this paper, we study a model for phase segregation taking place in a spatial domain that was introduced by Podio-Guidugli in Ric. Mat. 55 (2006), pp. 105-118. The model consists of a strongly coupled system of nonlinear parabolic differential equations, in which products between the unknown functions and their time derivatives occur that are difficult to handle analytically. In contrast to the existing literature about this PDE system, we consider here a dynamic boundary condition involving the Laplace-Beltrami operator for the order parameter. This boundary condition models an additional nonconserving phase transition occurring on the surface of the domain. Different well-posedness results are shown, depending on the smoothness properties of the involved bulk and surface free energies

Possible Subclinical Leaflet Thrombosis in Bioprosthetic Aortic Valves

To the Editor: Makkar et al. (Nov. 19 issue)(1) report possible subclinical leaflet thrombosis in up to 40% of patients involved in a clinical trial of transcatheter aortic-valve replacement (TAVR). In contrast, we found a relatively low incidence (7%) of possible subclinical valve leaflet thrombosis among patients in our series in which 255 patients underwent TAVR with the use of a CoreValve prosthesis. A retrospective review of our series (unpublished data) showed that in 104 patients, cardiac computed tomography (CT) at a median of 7 days after implantation (range, 3 to 87) (in 51 patients), transesophageal echocardiography at a median . . 

Weak formulation for singular diffusion equation with dynamic boundary condition

In this paper, we propose a weak formulation of the singular diffusion equation subject to the dynamic boundary condition. The weak formulation is based on a reformulation method by an evolution equation including the subdifferential of a governing convex energy. Under suitable assumptions, the principal results of this study are stated in forms of Main Theorems A and B, which are respectively to verify: the adequacy of the weak formulation; the common property between the weak solutions and those in regular problems of standard PDEs.Comment: 23 page

On the aggregation of wind/snow data when using a transfer function to account for wind-induced errors

Since solid precipitation records, and the associated wind speed data, are commonly stored with a quite coarse resolution in time (30 or 60 minutes), we investigated the impact of the aggregation scale on the accuracy of data corrected by using the transfer functions. We used data from the WMO SPICE (Solid Precipitation Intercomparison Experiment) field campaign, observed at the Marshall field test site (Colorado, USA) during the winter seasons from 2013 to 2015. The snowfall rates were recorded by three Geonor weighing gauges with different configurations: unshielded (UN), SA shielded and a DFIR to serve as the reference. Both precipitation and wind speed data are quality controlled and provided with the time resolution of 1 minute

Coming to America: Multiple Origins of New World Geckos

Geckos in the Western Hemisphere provide an excellent model to study faunal assembly at a continental scale. We generated a time-calibrated phylogeny, including exemplars of all New World gecko genera, to produce a biogeographic scenario for the New World geckos. Patterns of New World gecko origins are consistent with almost every biogeographic scenario utilized by a terrestrial vertebrate with different New World lineages showing evidence of vicariance, dispersal via temporary land bridge, overseas dispersal, or anthropogenic introductions. We also recovered a strong relationship between clade age and species diversity, with older New World lineages having more species than more recently arrived lineages. Our data provide the first phylogenetic hypothesis for all New World geckos and highlight the intricate origins and ongoing organization of continental faunas. The phylogenetic and biogeographical hypotheses presented here provide an historical framework to further pursue research on the diversification and assembly of the New World herpetofauna