The response of a soap film to the continuous deformation of its wire boundary is considered, with particular attention to the topological transitions that can occur at critical stages of the deformation process. Two well-known examples that have been studied by both theory and experiment are the catenoid suspended between circular wires in parallel planes, and the Möbius-strip soap film spanni...

This paper proposes a robust algorithmic and computational framework to address the problem of modeling the volume obtained by sweeping a solid along a trajectory of rigid motions. The boundary representation (simply brep) of the input solid naturally induces a brep of the swept volume. We show that it is locally similar to the input brep and this serves as the basis of the framework. All the s...

In this paper the Immersed Boundary Method is presented, with some recent developments. The method is used to analyze fluid–structure interaction problems. Different aspects of the method are illustrated by applying it to blood flow in the heart and a flapping filament (flag-in-wind) problem.

We characterize lacunary series in mixed norm spaces on the unit ball B in C and on the unit polydisk D in C. Introduction and main results Let n be a positive integer. Two domains will be used in the paper: the open unit ball B in C, B = {z ∈ C : |z| < 1 }, and the open unit polydisk D in C, D = {z = (z1, ..., zn) ∈ C : |z1| < 1, ..., |zn| < 1 }. We write D = B = D. Denote by T the Shilov boun...

No abstract. Erratum After publication of the original article [1] it came to the Publisher's attention that the first author's name had been listed incorrectly. The list of authors has now been corrected. We apologise for any inconvenience this has caused. which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

We show that a minimal disk satisfying the free boundary condition in a constant curvature ball of any dimension is totally geodesic. We weaken the condition to parallel mean curvature vector in which case we show that the disk lies in a three dimensional constant curvature submanifold and is totally umbilic. These results extend to higher dimensions earlier three dimensional work of J. C. C. N...

In this note we present an immersed boundary (IB) method for restricted diffusion with permeable interfaces. These problems arise under a variety of circumstances, e.g., in thermal contact problems [7]. Diffusion in a medium consisting of two regimes separated by permeable boundaries is another example. It is well-known that cell boundaries in a living tissue are permeable to oxygen and water m...

In this paper we consider the one-parameter family of Bona-Smith systems, which belongs to the class of Boussinesq systems modelling two-way propagation of long waves of small amplitude on the surface of water in a channel. We study three initial-boundary-value problems for these systems, corresponding, respectively, to nonhomogeneous Dirichlet, reflection, and periodic boundary conditions pose...