Banana in Middle American economy

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A posteriori error analysis for the mean curvature flow of graphs

We study the equation describing the motion of a nonparametric surface according to its mean curvature flow. This is a nonlinear nonuniformly parabolic PDE that can be discretized in space via a finite element method. We conduct an aposteriori error analysis of the spatial discretization and derive upper bounds on the error in terms of computable estimators based on local residual indicators. The reliability of the estimators is illustrated with two numerical simulations, one of which treats the case of a singular solution

Estimating the Collapse Pressure of an Inflatable Aerodynamic Decelerator

The collapse pressure of an inflatable membrane is the minimum differential pressure which will sustain a specific desired shape under an applied load. In this paper, we present a method for estimating the collapse pressure of a tension-cone inflatable aerodynamic decelerator (IAD) that is subject to a static aerodynamic load. The IAD surface is modeled as an elastic membrane. For a given aerodynamic load and sufficiently high torus differential pressure, the IAD assumes a stable axisymmetric equilibrium shape. When the torus pressure is reduced sufficiently, the symmetric equilibrium state becomes unstable and we define this instance to be the critical pressure Pcr. In this paper, we will compare our predicted critical torus pressure with the corresponding observed torus collapse pressure (OTCP) for fifteen tests that were conducted by the third author and his collaborators at the NASA Glenn Research Center 10x10 Supersonic Wind Tunnel in April 2008. One of the difficulties with these types of comparisons is establishing the instance of torus collapse and determining the OTCP from quantities measured during the experiment. In many cases, torus collapse is gradual and the OTCP is not well-defined. However, in eight of the fifteen wind tunnel tests where the OTCP is well-defined, we find that the average of the relative differences (Pcr - OTCP/Pcr) was 8.9%. For completeness, we will also discuss the seven tests where the observed torus collapse pressure is not well-defined

Influence of magnetic field on the orientation of anisotropic magnetic particles at liquid interfaces

We study theoretically the influence of an external magnetic field on the orientation of an ellipsoidal magnetic particle adsorbed at a liquid interface. Using the finite element program Surface Evolver, we calculate the equilibrium meniscus shape around the ellipsoidal particle and its equilibrium tilt angle with respect to the undeformed interface θt when a magnetic field B is applied perpendicular to the interface. We find that as we increase field strength, θt increases and at a critical magnetic field Bc1 and tilt angle θc1, the particle undergoes a discontinuous transition to the ‘perpendicular’ orientation (θt = 90°). Our results agree qualitatively with the simplified theory of Bresme and Faraudo [F. Bresme and J. Faraudo, J. Phys.: Condens. Matter, 2007, 19, 375110] which assumes that the liquid interface is flat, while they agree quantitatively with recent lattice-Boltzmann simulations of Davies et al. [G. Davies et al., Soft Matter, 2014, 10, 6742] which account for the deformation of the liquid meniscus. We also show for the first time that upon reducing the external magnetic field, at a critical magnetic field Bc2 < Bc1, the particle undergoes a second discontinuous transition from the perpendicular orientation to a finite tilt angle θc2 < θc1. In other words, for micron-sized particles where the thermal energy kBT is negligible compared to the interfacial energy, the tilt angle vs. magnetic field curve exhibits hysteresis behaviour. Due to the higher degree of accuracy of the Surface Evolver method, we are able to analyse the behaviour of the particles near these orientational transitions accurately and study how the critical quantities Bc1, Bc2, θc1 and θc2 vary with particle aspect ratio and contact angle

Stereology of dihedral angles

summary:The paper presents a short survey of stereological problems concerning dihedral angles, their solutions and applications, and introduces a graph for determining the distribution functions of planar angles under the hypothesis that dihedral angles in $\mathbb{R}^3$ are of the same size and create a random field