Bulk effects on topological conduction on the surface of 3-D topological insulators

The surface states of a topological insulator in a fine-tuned magnetic field are ideal candidates for realizing a topological metal which is protected against disorder. Its signatures are (1) a conductance plateau in long wires in a finely tuned longitudinal magnetic field and (2) a conductivity which always increases with sample size, and both are independent of disorder strength. We numerically study how these experimental transport signatures are affected by bulk physics in the interior of the topological insulator sample. We show that both signatures of the topological metal are robust against bulk effects. However the bulk does substantially accelerate the metal's decay in a magnetic field and alter its response to surface disorder. When the disorder strength is tuned to resonance with the bulk band the conductivity follows the predictions of scaling theory, indicating that conduction is diffusive. At other disorder strengths the bulk reduces the effects of surface disorder and scaling theory is systematically violated, signaling that conduction is not fully diffusive. These effects will change the magnitude of the surface conductivity and the magnetoconductivity

On the Uniqueness of Global Multiple SLEs

This article focuses on the characterization of global multiple Schramm-Loewner evolutions (SLE). The chordal SLE process describes the scaling limit of a single interface in various critical lattice models with Dobrushin boundary conditions, and similarly, global multiple SLEs describe scaling limits of collections of interfaces in critical lattice models with alternating boundary conditions. In this article, we give a minimal amount of characterizing properties for the global multiple SLEs: we prove that there exists a unique probability measure on collections of pairwise disjoint continuous simple curves with a certain conditional law property. As a consequence, we obtain the convergence of multiple interfaces in the critical Ising and FK-Ising models.Comment: 30 pages, 4 figure

Asymptotic shallow water models for internal waves in a two-fluid system with a free surface

In this paper, we derive asymptotic models for the propagation of two and three-dimensional gravity waves at the free surface and the interface between two layers of immiscible fluids of different densities, over an uneven bottom. We assume the thickness of the upper and lower fluids to be of comparable size, and small compared to the characteristic wavelength of the system (shallow water regimes). Following a method introduced by Bona, Lannes and Saut based on the expansion of the involved Dirichlet-to-Neumann operators, we are able to give a rigorous justification of classical models for weakly and strongly nonlinear waves, as well as interesting new ones. In particular, we derive linearly well-posed systems in the so called Boussinesq/Boussinesq regime. Furthermore, we establish the consistency of the full Euler system with these models, and deduce the convergence of the solutions.Comment: 32 pages, 4 figure

Flash Point Measurements and Modeling for Ternary Partially Miscible Aqueous­Organic Mixtures

Flash point is the most important variable used to characterize the fire and explosion hazard of liquids. This paper presents the first partially miscible aqueousorganic mixtures flash point measurements and modeling for the ternary type-I mixtures, water + ethanol + 1-butanol, water + ethanol + 2-butanol, and the type-II mixture, water + 1-butanol + 2-butanol. Results reveal that the flash points are constant in each tie line. Handling the non-ideality of the liquid phase through the use of activity coefficient models, the general flash-point model of Liaw et al. extended to partially miscible mixtures predicts the experimental data well when using literature LLE and the VLE activity coefficient model binary parameters to estimate sequentially the span and flash point in each tie line and the flash point in the mutual solubility region, respectively. The constant flash-point behavior in a tie line is also observed and predicted, in agreement with the VLLE tie line property that a single vapor is in equilibrium with all liquid composition on a tie line. For the aqueousorganic mixtures here studied, a deviation between prediction and measurements is observed, arising from the failure of the constant lower flammable limit assumption in the mutual solubility inert-rich region. Potential application for the model concerns the assessment of fire and explosion hazards and the development of inherently safer designs for chemical processes containing partially miscible aqueousorganic mixtures

On Patchworks and Hierarchies

Motivated by questions in biological classification, we discuss some elementary combinatorial and computational properties of certain set systems that generalize hierarchies, namely, 'patchworks', 'weak patchworks', 'ample patchworks' and 'saturated patchworks' and also outline how these concepts relate to an apparently new 'duality theory' for cluster systems that is based on the fundamental concept of 'compatibility' of clusters.Comment: 17 pages, 2 figure