We consider a one-phase free boundary problem involving a fractional Laplacian (−∆), 0 < α < 1, and we prove that “flat free boundaries” are C . We thus extend the known result for the case α = 1/2.

We investigate the regularity of a free boundary near contact points with a fixed boundary, with C boundary data, for an obstacle-like free boundary problem. We will show that under certain assumptions on the solution, and the boundary function, the free boundary is uniformly C up to the fixed boundary. We will also construct some examples of irregular free boundaries.

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surfa...

We present the theory of the multi-α-solutions of the variational problem for the upper bounds on the convective heat transport in a heated from below horizontal fluid layer with rigid lower boundary and stress-free upper boundary. A sequence of upper bounds on the convective heat transport is obtained. The highest bound Nu = 1+(1/6)R is between the bounds Nu = 1+0.152R for the case of a fluid ...

holds for all (x, t)sQ. The (t(t) are called the free boundaries of the respective solutions. It is known that they are C smooth functions (Caffarelli and Friedmann first showed that they are C \ and using this Aronson and Vazquez, Kreis and Hollig, and the author proved independently and by different means that the boundaries are indeed C°°). Under special circumstances the free boundary may e...

Recent years have seen great advances in our ability to predict crystal structures from first principles. However, previous algorithms have focused on the prediction of bulk crystal structures, where the global minimum is the target. Here, we present a general atomistic approach to simulate in multicomponent systems the structures and free energies of grain boundaries and heterophase interfaces...

Adoption of the hyperbolic Cattaneo-Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent t...

We evaluate the phase diagram of the "BKS" potential [Phys. Rev. Lett. 64, 1955 (1990)]], a model of silica widely used in molecular dynamics (MD) simulations. We conduct MD simulations of the liquid, and three crystals ( beta -quartz, coesite, and stishovite) over wide ranges of temperature and density, and evaluate the total Gibbs free energy of each phase. The phase boundaries are determined...

The relationship between crystal quality and the properties of indium phosphide nanowires grown on silicon (111) has been studied by transmission electron microscopy, photoluminescence spectroscopy, and photoelectrochemistry. Wires with no defects and with {111} twin boundaries parallel and perpendicular to the growth direction were obtained by metalorganic vapor-phase epitaxy using liquid indi...

Many statistical physics models are defined on an infinite lattice by taking appropriate limits of finite lattice regions, where a key consideration is how the boundaries are defined. For several models on planar lattices, such as 3-colorings and lozenge tilings, efficient sampling algorithms are known for regions with fixed boundary conditions, where the colors or tiles around the boundary are...