We propose a new algorithm for computing the Riemann mapping of the unit disk to a polygon, also known as the Schwarz–Christoffel transformation. The new algorithm, CRDT (for cross-ratios of the Delaunay triangulation), is based on cross-ratios of the prevertices, and also on cross-ratios of quadrilaterals in a Delaunay triangulation of the polygon. The CRDT algorithm produces an accurate repre...

The purpose of this paper is to study the discontinuous solutions to a shallow water wave equation with relaxation. The typical initial value problem of discontinuous solutions is the Riemann problem. Unlike the homogeneous hyperbolic conservation laws, due to the inhomogeneity of the system studied here, the solutions of the Riemann problem do not have a self-similar structure anymore. This pr...

We study the de Gennes free energy for smectic A liquid crystals over S2-valued vector fields to understand the chevron (zigzag) pattern formed in the presence of an applied magnetic field. We identify a small dimensionless parameter ε, and investigate the behaviors of the minimizers when the field strength is of order O(ε−1). In this regime, we show via Γ-convergence that a chevron structure w...

convergence hypothesis is one of the results of neoclassical growth model, which has been examined recently. this hypothesis has two forms of absolute and conditional beta-convergence and implies that regions with lower per capita output have higher per capita growth rates. since there is no data for regional gdp in iran, there has been n study to test convergence hypothesis in iran. our main c...

Assessing the convergence of a biomolecular simulation is an essential part of any computational investigation. This is because many important quantities (e.g., free energy differences) depend on the relative populations of different conformers; insufficient convergence translates into systematic errors. Here we present a simple method to selfconsistently assess the convergence of a simulation....

We present a simple method for utilizing experimental data to improve the efficiency of numerical calculations of free energy profiles from molecular dynamics simulations. The method involves umbrella sampling simulations with restraining potentials based on a known approximate estimate of the free energy profile derived solely from experimental data. The use of the experimental data results in...

Potential of mean force (PMF) calculations are used to characterize the free energy landscape of protein-lipid and protein-protein association within membranes. Coarse-grained simulations allow binding free energies to be determined with reasonable statistical error. This accuracy relies on defining a good collective variable to describe the binding and unbinding transitions, and upon criteria ...

In this paper we introduce a new notion of convergence of sparse graphs which we call Large Deviations or LD-convergence and which is based on the theory of large deviations. The notion is introduced by ”decorating” the nodes of the graph with random uniform i.i.d. weights and constructing random measures on [0, 1] and [0, 1]2 based on the decoration of nodes and edges. A graph sequence is defi...

Frictional convergence in an atmospheric boundary layer topped by a stable free troposphere is considered. In agreement with extensive previous work, we find that atmospheric stability reduces the vertical scale of the free tropospheric secondary circulation associated with frictional convergence. Associated with this reduction in vertical scale is a proportional reduction in the time scale for...

Central in a variational implicit-solvent description of biomolecular solvation is an effective free-energy functional of the solute atomic positions and the solute-solvent interface (i.e., the dielectric boundary). The free-energy functional couples together the solute molecular mechanical interaction energy, the solute-solvent interfacial energy, the solute-solvent van der Waals interaction e...