Abstract Random field models are mathematical structures used in the study of stochastic complex systems. In this paper, we compute shape operator Gaussian random manifolds using first and second fundamental forms (Fisher information matrices). Using Markov chain Monte Carlo techniques, simulate dynamics these fields Gaussian, mean principal curvatures parametric space, analyzing how quantities...

In this paper, we observe that the brane functional studied in [5] can be used to generalize some of the works that Schoen and I [4] did many years ago. The key idea is that if a three dimensional manifold M has a boundary with strongly positive mean curvature, the effect of this mean curvature can influence the internal geometry of M . For example, if the scalar curvature of M is greater than ...

Using molecular dynamics simulations, we examine the behavior of lipids whose preferred curvature can be systematically varied. This curvature is imposed by controlling the headgroup size of a coarse-grained lipid model recently developed by us. To validate this approach, we examine self-assembly of each individual lipid type and observe the complete range of expected bilayer and micelle phases...

We study the cosmology of the Randall-Sundrum brane-world where the Einstein-Hilbert action is modified by curvature correction terms: a four-dimensional scalar curvature from induced gravity on the brane, and a five-dimensional Gauss-Bonnet curvature term. The combined effect of these curvature corrections to the action removes the infinite-density big bang singularity, although the curvature ...