Multidisciplinary Design of Transonic Fans for Civil Aeroengines

For current state-of-the-art turbofan engines the bypass section of the fan stage alone provides the majority of the total thrust in cruise and the size of the fan has a considerable effect on overall engine weight and nacelle drag. Thrust requirements in different parts of the flight envelope must also be satisfied together with sufficient margins towards stall. A complex set of system requirements and objectives, combined with component technology of high maturity level, demands performance predictions with higher accuracy that are sensitive to more detailed design features at an early conceptual design phase. Failing to meet these demands may result in a sub-optimal choice of aircraft-engine system architecture.The emphasise of this thesis work is on fan-stage design and performance prediction in terms of aerodynamic efficiency and stability. The aspect of accuracy when it comes to establishing engine cycle performance for existing state-of-the-art technology based on open literature data is undertaken in the first paper. In the second paper a strategy to expand the parameter interdependencies of a fan-stage performance model with a multidisciplinary perspective is explored. The resulting model is integrated into an engine systems model and coupled with a simplified weight model to investigate the trade-off between weight and specifc fuel consumption. Results implied that being able to predict the rotor solidity required to maintain a given average blade loading - in addition to stage efficiency - is of high importance

Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups

In the Heisenberg group of dimension 2n+1, we consider the sub-Laplacian witha drift in the horizontal coordinates. There is a related measure for whichthis operator is symmetric.The corresponding Riesz transforms are known to be L^p boundedwith respect to this measure.We prove that the Riesz transforms of order 1 are also of weak type (1,1),and that this is false for order 3 and above. Further, we consider the relatedmaximal Littlewood-Paley-Stein operators and prove the weak type (1,1) forthose of order 1 and disprove it for higher orders

Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space.

Let $v \ne 0$ be a vector in $\R^n$. Consider the Laplacian on $\R^n$ with drift $\Delta_{v} = \Delta + 2v\cdot \nabla$ and the measure $d\mu(x) = e^{2 \langle v, x \rangle} dx$, with respect to which $\Delta_{v}$ is self-adjoint. %Let $d$ and $\nabla$ denote the Euclidean distance and the gradient operator on $\R^n$. Consider the space $(\R^n, d,d\mu)$, which has the property of exponential volume growth. This measure has exponential growth with respect to the Euclidean distance. We study weak type $(1, 1)$ and other sharp endpoint estimates for the Riesz transforms of any order, and also for the vertical and horizontal Littlewood-Paley-Stein functions associated with the heat and the Poisson semigroups

Riesz transforms of a general Ornstein--Uhlenbeck semigroup

We consider Riesz transforms of any order associated to an Ornstein--Uhlenbeck operator \ue238, with covariance Q given by a real, symmetric and positive definite matrix, and with drift B given by a real matrix whose eigenvalues have negative real parts. In this general Gaussian context, we prove that a Riesz transform is of weak type (1,1) with respect to the invariant measure if and only if its order is at most 2

On the variation operator for the Ornstein–Uhlenbeck semigroup in dimension one

Consider the variation seminorm of the Ornstein–Uhlenbeck semigroup Ht in dimension one, taken with respect to t. We show that this seminorm defines an operator of weak type (1,\ua01) for the relevant Gaussian measure. The analogous Lp estimates for 1 < p< ∞ were already known

On the maximal operator of a general Ornstein–Uhlenbeck semigroup

If Q is a real, symmetric and positive definite n 7 n matrix, and B a real n 7 n matrix whose eigenvalues have negative real parts, we consider the Ornstein–Uhlenbeck semigroup on Rn with covariance Q and drift matrix B. Our main result says that the associated maximal operator is of weak type (1,\ua01) with respect to the invariant measure. The proof has a geometric gist and hinges on the “forbidden zones method” previously introduced by the third author

On non-centered maximal operators related to a non-doubling and non-radial exponential measure

We investigate mapping properties of non-centered Hardy–Littlewood maximal operators related to the exponential measure dμ(x) = exp (- | x1| - ⋯ - | xd|) dx in Rd. The mean values are taken over Euclidean balls or cubes (ℓ∞ balls) or diamonds (ℓ1 balls). Assuming that d≥ 2 , in the cases of cubes and diamonds we prove the Lp-boundedness for p> 1 and disprove the weak type (1,\ua01) estimate. The same is proved in the case of Euclidean balls, under the restriction d≤ 4 for the positive part

Weighted Analysis of Microarray Experiments

DNA microarrays are strikingly efficient tools for analysing gene expression for large sets of genes simultaneously. The aim is often to identify genes which are differentially expressed between some studied conditions, thereby gaining insight into which cellular mechanisms are differently active between the conditions. In the measurement process, several steps exist that risk going partly or entirely wrong and quality control is therefore crucial.In Paper I-III, a novel method is developed which integrates quality control quantitatively into the analysis of microarray experiments. The noise structure for each gene is modelled by (i) a global covariance structure matrix catching decreased quality by array-wise variances and catching shared sources of variation by correlations, and (ii) gene-wise variance scales having a prior distribution with parameters estimated from the data of all genes in an empirical Bayes manner. The variances and correlations are entirely estimated from the data. In the estimates and tests for differential expression, arrays with lower precision or arrays sharing sources of variation are downweighted. Thus, the sharp decision of entirely excluding arrays is avoided. The method is called Weighted Analysis of Microarray Experiments (WAME).Current methods for microarray analysis generally disregard the quality variations. Simulations based on real data show that this often results in severely invalid p-values. Trusting such p-values therefore risks resulting in false biological conclusions. WAME gives increased power and valid p-values when few genes are differentially expressed and conservative p-values otherwise. Similar results are seen on simulations according to the model.In Paper IV, WAME is used to identify genes which are differentially expressed between small and large human fat cells. WAME here successfully downweights one array that was suspected of decreased quality on biological grounds.The WAME method is freely available as a add-on package for the R language