A geophysicist and a mathematician are having coffee. The mathematician queries, “what are you working on these days?” and the geophysicist responds, “I am studying the growth of ice.” The mathematician says, “I see, the Stefan Problem!”, to which his colleague says, “Oh, so you know about Stefan and Weyprecht?”...“Certainly, Stefan must be a mathematician, but Weyprecht–who is Weyprecht?” We a...

We study a nonlocal version of the one-phase Stefan problem which develops mushy regions, even if they were not present initially, a model which can be of interest at the mesoscopic scale. The equation involves a convolution with a compactly supported kernel. The created mushy regions have the size of the support of this kernel. If the kernel is suitably rescaled, such regions disappear and the...

1279 Retrospective Digital Image Fusion of Multidetector CT and 18F-FDG PET: Clinical Value in Pancreatic Lesions—A Prospective Study with 104 Patients Arne-Jörn Lemke, Stefan Markus Niehues, Norbert Hosten, Holger Amthauer, Michael Boehmig, Christian Stroszczynski, Torsten Rohlfing, Stefan Rosewicz, and Roland Felix 1287 The CT Motion Quantitation of Lung Lesions and Its Impact on PET-Measured...

Abstract. The phase transition between solid and liquid in an undercooled liquid leads to dendritic growth of the solid phase. The problem is modelled by the Stefan problem with a modified Gibbs-Thomson law, which includes the anisotropic mean curvature corresponding to a surface energy that depends on the direction of the interface normal. A finite element method for discretization of the Stef...

The introduction of the Rényi entropy allowed a generalization of the Shannon entropy and unified its notion with that of other entropies. However, so far there is no generally accepted conditional version of the Rényi entropy corresponding to the one of the Shannon entropy. Different definitions proposed so far in the literature lacked central and natural properties one way or another. In this...

37. E. Evans, Annu. Rev. Biophys. Biomol. Struct. 30, 105 (2001). 38. G. I. Bell, Science 200, 618 (1978). 39. For adhesive interactions important in soft tissues and organs of eukaryotic cell systems, the average times toff° reported for spontaneous dissociation of ligand/receptor bonds range from a fraction of a second to 100 s or more. 40. Because of thermal activation, the appropriate unit ...

In this present study, volume of fluid method in OpenFOAM open source CFD package will be extended to consider phase change phenomena with modified model due to condensation and boiling processes. This model is suitable for the case in which both unsaturated phase and saturated phase are present and for beginning boiling and condensation process needn't initial interface. Both phases (liquid-va...

we reduce the two phase stefan problem with kinetic to a system of nonlinear volterra integral equations of second kind and apply newton's method to linearize it. we found product integration solution of the linear form. sufficient conditions for convergence of the numerical method are given and their applicability is illustrated with an example.