Noise load management at Amsterdam Airport Schiphol

Amsterdam Airport Schiphol is one of the five primary hub-airports in Europe. All flight movements are controlled by Air Traffic Control the Netherlands (LVNL), whose main objective is to guarantee safety, efficiency, and protection of the environment, that includes noise load. To this end, a number of enforcement points is located in the vicinity of Schiphol. Each aircraft movement contributes to the noise load at these points. If the cumulative load in an aviation year at an enforcement point exceeds its maximum, the civil aviation authority may impose severe sanctions, such as fines, or a reduction in the number of aircraft movements. The latter is a typical restriction for Schiphol.\ud Runway selection is carried out via the preference list, an ordered set of runway combinations such that the higher on the list a runway combination, the better this combination is for maintaining the noise load limit. The highest safe runway combination in the list will actually be used. This paper has formulated the preference list selection process in the mathematical framework of Stochastic Dynamic Programming that enables determining an optimal strategy for preference list selection taking into account future and unpredictable weather conditions, as well as safety and efficiency restrictions

Forward diffraction modelling : analysis and application to grating reconstruction

The semiconductor industry uses lithography machines for manufacturing complex integrated circuits (also called ICs) onto wafers. Because an IC is built up layer by layer and feature sizes get smaller and smaller, tight control of the lithography process is required to guarantee a fast production of working ICs. Typically a lot of information on the lithography process can be obtained by measuring test structures or gratings which are scattered over the wafer. These gratings are tiny periodic structures much smaller than ICs. First these gratings are illuminated and its response (a scattered intensity) is measured. For certain applications like overlay metrology the asymmetry in this measured signal (due to an offset between two gratings) can be used to align the lithographic process. For other applications like critical dimension (CD) metrology one is interested in the shape of the grating lines that produced the measured signal. Since this information is not directly available but encrypted in the measurement, a reconstruction algorithm is used to extract it. The reconstructed values like height, width and sidewall angle can then be related to machine settings like dose and focus which control the lithographic process. In particular the CD metrology application requires rigorous mathematical models that solve optical diffraction problems for periodic gratings in combination with advanced reconstruction algorithms. This thesis focuses on the optical diffraction problem for 1D periodic gratings. Starting from Maxwell's equations a reduced model is derived by simplifying both the grating and the incident electromagnetic field. The former is approximated with an infinitely periodic layered structure with isotropic non-magnetic materials. The latter is approximated with a time-harmonic incident plane wave. The reduced model is discretised using two different mode expansion methods, Bloch and the Rigorous Coupled-Wave Analysis (RCWA). Bloch expands the electromagnetic field in each layer in terms of the exact eigenfunctions whereas RCWA only uses approximate eigenfunctions. After truncation of the involved series a transmission problem is derived by matching the fields at the layer interfaces. Having solved the resulting linear system, the scattered field can be computed easily. Both mode expansion methods solve a similar linear system containing a large but sparse block-structured coefficient matrix. However, special care needs to be taken when solving this system stably and efficiently. Therefore a stable condensation algorithm is derived based on Riccati transformations that decouples the exponentially growing and decaying terms that are present in the solution. This separation or decoupling is the key feature explaining the stability which is not always clear in alternative condensation algorithms. Furthermore the algorithm is optimised for speed by using a two-stage approach. Finally it is shown that the resulting stable recursions are identical to those used in the 'enhanced transmittance matrix approach" (a frequently used condensation algorithm), thereby confirming its stability as well. This thesis also examines and extends both mode expansions methods. The Bloch method is generalised to deal with multiple material transitions inside a grating layer covering a wider range of applications. However, lossy or fully asymmetric gratings are still hard to solve. On the other hand the Fourier discretisation used in RCWA is much more exible but only approximates the more exact discretisation of Bloch. Therefore two RCWA modifications have been investigated to improve the accuracy while keeping its exibility and relatively straightforward implementation. Adaptive Spatial Resolution applies an additional layer specific coordinate transformation before Fourier discretising the problem again. A good transformation not only refines near a material interface but also does this in a smooth way. A significant improvement in accuracy is observed that approaches and sometimes outperforms the results obtained with the Bloch method. The second modification removes the Fourier discretisation completely and uses a finite difference approximation in the periodic direction. Although this approach allows for a better discretisation near a material interface, the sparsity of the resulting matrices could not be exploited to make a competitive implementation within the standard RCWA framework. Finally the integration of the forward diffraction model in the CD reconstruction application is discussed. Either a library based or real-time regressions approach can be used for this reconstruction. Both approaches rely heavily on having an accurate and fast forward model. By exploiting additional symmetries and smart reuse of information, acceptable library fill times and real-time reconstructions are now feasible

Polynomial cases of the tarification problem

We consider the problem of determining a set of optimal tariffs for an agent in a network, who owns a subset of the arcs of the network, and who wishes to maximize his revenues on this subset from a set of clients that make use of the network.The general variant of this problem is NP-hard, already with a single client. This paper introduces several new polynomially solvable special cases. An important case is the following.For multiple clients, if the number of tariff arcs is bounded from above, we can solve the problem by a polynomial number of linear programs (each of which is of polynomial size). Furthermore, we show that the parametric tarification problem and the single arc fixed charge tarification problem can be solved in polynomial time.Economics ;

Pricing Network Edges to Cross a River.

We consider a Stackelberg pricing problem in directed networks:Tariffs (prices) have to be defined by an operator, the leader, for a subset of the arcs. Clients, the followers, choose paths to route their demand through the network selfishly and independently of each other, on the basis of minimal total cost. The problem is to find tariffs such as to maximize the operator''s revenue. We consider the case where each client takes at most one tariff arc to route the demand.The problem, which we refer to as the river tarification problem, is a special case of problems studied previously in the literature.We prove that the problem is strongly NP-hard.Moreover, we show that the polynomially solvable case of uniform tarification yields an m--approximation algorithm, and this is tight. We suggest a new type of analysis that allows to improve the result to \bigO{\log m}, whenever the input data is polynomially bounded. We furthermore derive an \bigO{m^{1-\varepsilon}}--inapproximability result for problems where the operator must serve all clients, and we discuss some polynomial special cases. Finally, a computational study with instances from France Telecom suggests that uniform pricing performs better in practice than theory would suggest.operations research and management science;

Pricing bridges to cross a river.

We consider a Stackelberg pricing problem in directed, uncapacitated networks. Tariffs have to be defined by an operator, the leader, for a subset of m arcs, the tariff arcs. Costs of all other arcs are assumed to be given. There are n clients, the followers, that route their demand independent of each other on paths with minimal total cost. The problem is to find tariffs that maximize the operator's revenue. Motivated by problems in telecommunication networks, we consider a restricted version of this problem, assuming that each client utilizes at most one of the operator's tariff arcs. The problem is equivalent to pricing bridges that clients can use in order to cross a river. We prove that this problem is APX-hard. Moreover, we show that uniform pricing yields both an m–approximation, and a (1 + lnD)–approximation. Here, D is upper bounded by the total demand of all clients. We furthermore discuss some polynomially solvable special cases, and present a short computational study with instances from France Télécom. In addition, we consider the problem under the additional restriction that the operator must serve all clients. We prove that this problem does not admit approximation algorithms with any reasonable performance guarantee, unless NP = ZPP, and we prove the existence of an n–approximation algorithm.Pricing; Networks; Tariffs; Costs; Cost; Demand; Problems; Order; Yield; Studies; Approximation; Algorithms; Performance;

Surprising absence of association between flower surface microstructure and pollination system

The epidermal cells of flowers come in different shapes and have different functions, but how they evolved remains largely unknown. Floral micro-texture can provide tactile cues to insects, and increases in surface roughness by means of conical (papillose) epidermal cells may facilitate flower handling by landing insect pollinators. Whether flower microstructure correlates with pollination system remains unknown. Here, we investigate the floral epidermal microstructure in 29 (congeneric) species pairs with contrasting pollination system. We test whether flowers pollinated by bees and/or flies feature more structured, rougher surfaces than flowers pollinated by non-landing moths or birds and flowers that self-pollinate. In contrast with earlier studies, we find no correlation between epidermal microstructure and pollination system. The shape, cell height and roughness of floral epidermal cells varies among species, but is not correlated with pollinators at large. Intriguingly, however, we find that the upper (adaxial) flower surface that surrounds the reproductive organs and often constitutes the floral display is markedly more structured than the lower (abaxial) surface. We thus conclude that conical epidermal cells probably play a role in plant reproduction other than providing grip or tactile cues, such as increasing hydrophobicity or enhancing the visual signal

A Hamilton--Jacobi point of view on mean-field Gibbs-non-Gibbs transitions

We study the loss, recovery, and preservation of differentiability of time-dependent large deviation rate functions. This study is motivated by mean-field Gibbs-non-Gibbs transitions. The gradient of the rate-function evolves according to a Hamiltonian flow. This Hamiltonian flow is used to analyze the regularity of the time dependent rate function, both for Glauber dynamics for the Curie-Weiss model and Brownian dynamics in a potential. We hereby create a unifying framework for the treatment of mean-field Gibbs-non-Gibbs transitions, based on Hamiltonian dynamics and viscosity solutions of Hamilton-Jacobi equations