Stiffening while drying

We present two models for the drying of waterborne paints, which consist of non-volatile latex particles suspended in water. One model considers the water and latex density in a layer as a function of time. Water evaporation at the surface represents the drying. This model results in a one-dimensional free boundary problem, which is solved numerically. Extensions to the model are given that describe the stiffening of the paint. A second model is a particle based dynamical simulation where latex particles form a network through which water particles move. A thin slab of the suspension in a three-dimensional box is studied. Water particles escaping the slab at the surface represent the drying, progressing network formation the stiffening of the paint. Both models allow for validation with material properties as determined experimentally on real coatings

Thruster Allocation for Dynamical Positioning

Positioning a vessel at a fixed position in deep water is of great importance when working offshore. In recent years a Dynamical Positioning (DP) system was developed at Marin [2]. After the measurement of the current position and external forces (like waves, wind etc.), each thruster of the vessel is actively controlled to hold the desired location. In this paper we focus on the allocation process to determine the settings for each thruster that results in the minimal total power and thus fuel consumption. The mathematical formulation of this situation leads to a nonlinear optimization problem with equality and inequality constraints, which can be solved by applying Lagrange multipliers. We give three approaches: first of all, the full problem was solved using the MATLAB fmincon routine with the solution from the linearised problem as a starting point. This implementation, with robust handling of the situations where the thrusters are overloaded, lead to promising results: an average reduction in fuel consumption of approximately two percent. However, further analysis proved useful. A second approach changes the set of variables and so reduces the number of equations. The third and last approach solves the Lagrange equations with an iterative method on the linearized Lagrange problem

Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions

In this paper we develop a symmetry preserving method for the rigorous computation of stationary states of the Ohta-Kawasaki partial differential equation in three space dimensions. By preserving the relevant symmetries we achieve an enormous reduction in computational cost. This makes it feasible to construct computer-assisted proofs of complex three-dimensional structures. In particular, we provide the first existence proofs for both the double gyroid and body centered cubic packed sphere solutions to this problem

Validated Numerical Approximation of Stable Manifolds for Parabolic Partial Differential Equations

This paper develops validated computational methods for studying infinite dimensional stable manifolds at equilibrium solutions of parabolic PDEs, synthesizing disparate errors resulting from numerical approximation. To construct our approximation, we decompose the stable manifold into three components: a finite dimensional slow component, a fast-but-finite dimensional component, and a strongly contracting infinite dimensional “tail”. We employ the parameterization method in a finite dimensional projection to approximate the slow-stable manifold, as well as the attached finite dimensional invariant vector bundles. This approximation provides a change of coordinates which largely removes the nonlinear terms in the slow stable directions. In this adapted coordinate system we apply the Lyapunov-Perron method, resulting in mathematically rigorous bounds on the approximation errors. As a result, we obtain significantly sharper bounds than would be obtained using only the linear approximation given by the eigendirections. As a concrete example we illustrate the technique for a 1D Swift-Hohenberg equation.</p

Non-imaging Optics for LED-Lighting

In this report, several methods are investigated to rapidly compute the light intensity function, either in the far field or on a finite-distance screen, of light emanating from a light fixture with a given shape. Different shapes are considered, namely polygonal and (piecewise) smooth. In the first case, analytic methods are sought to circumvent the use of Monte Carlo methods and ray-tracing with large sample size. In the second case, refinements of the Monte Carlo method (notably using a bootstrap procedure) are devised to minimize the number of samples needed for a good approximation of the intensity function

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD

Recruitment Strategies and Colony Size in Ants

Ants use a great variety of recruitment methods to forage for food or find new nests, including tandem running, group recruitment and scent trails. It has been known for some time that there is a loose correlation across many taxa between species-specific mature colony size and recruitment method. Very small colonies tend to use solitary foraging; small to medium sized colonies use tandem running or group recruitment whereas larger colonies use pheromone recruitment trails. Until now, explanations for this correlation have focused on the ants' ecology, such as food resource distribution. However, many species have colonies with a single queen and workforces that grow over several orders of magnitude, and little is known about how a colony's organization, including recruitment methods, may change during its growth. After all, recruitment involves interactions between ants, and hence the size of the colony itself may influence which recruitment method is used—even if the ants' behavioural repertoire remains unchanged. Here we show using mathematical models that the observed correlation can also be explained by recognizing that failure rates in recruitment depend differently on colony size in various recruitment strategies. Our models focus on the build up of recruiter numbers inside colonies and are not based on optimality arguments, such as maximizing food yield. We predict that ant colonies of a certain size should use only one recruitment method (and always the same one) rather than a mix of two or more. These results highlight the importance of the organization of recruitment and how it is affected by colony size. Hence these results should also expand our understanding of ant ecology