Surrogate-Based Optimization Using Multifidelity Models with Variable Parameterization and Corrected Space Mapping

Surrogate-based-optimization methods provide a means to achieve high-fidelity design optimization at reduced computational cost by using a high-fidelity model in combination with lower-fidelity models that are less expensive to evaluate. This paper presents a provably convergent trust-region model-management methodology for variableparameterization design models: that is, models for which the design parameters are defined over different spaces. Corrected space mapping is introduced as a method to map between the variable-parameterization design spaces. It is then used with a sequential-quadratic-programming-like trust-region method for two aerospace-related design optimization problems. Results for a wing design problem and a flapping-flight problem show that the method outperforms direct optimization in the high-fidelity space. On the wing design problem, the new method achieves 76% savings in high-fidelity function calls. On a bat-flight design problem, it achieves approximately 45% time savings, although it converges to a different local minimum than did the benchmark.

Semiclassical treatment of Wannier's theory when the exponent diverges

We consider a non-standard application of the Wannier model. A physical example is the single ionization of a hydrogenic beryllium ion with a fully stripped beryllium ion, where the ratio of the charge of the third particle to the charges of the escaping particles is 1/4; we investigate the single ionization by an electron of an atom comprising an electron and a nucleus of charge 1/4. An infinite exponent is obtained suggesting that this process is not tractable within the Wannier model. A modified version of Crothers' uniform semiclassical wavefunction for the outgoing particles has been adopted, since the Wannier exponents and are infinite for an effective charge of Z = 1/4. We use Bessel functions to describe the Peterkop functions u and u and derive a new turning point ?. Since u is well behaved at infinity, there exists only the singularity in u at infinity, thus we employ a one- (rather than two-) dimensional change of dependent variable, ensuring that a uniform solution is obtained that avoids semiclassical breakdown on the Wannier ridge. The regularized final-state asymptotic wavefunction is employed, along with a continuum-distorted-wave approximation for the initial-state wavefunction to obtain total cross sections on an absolute scale. © 2006 IOP Publishing Ltd.

Accumulation of entanglement in a continuous variable memory

We study entanglement accumulation in a memory built out of two continuous variable systems interacting with a qubit that mediates their indirect coupling. We show that, in contrast with the case of bidimensional Hilbert spaces, entanglement superior to one ebit can be accumulated in the memory, even though no entangled resource is used. The protocol is immediately implementable and we assess the role of the main imperfections.

Formulation of Locally Reacting Surfaces in FDTD/K-DWM Modelling of Acoustic Spaces

In this paper, we present new methods for constructing and analysing formulations of locally reacting surfaces that can be used in finite difference time domain (FDTD) simulations of acoustic spaces. Novel FDTD formulations of frequency-independent and simple frequency-dependent impedance boundaries are proposed for 2D and 3D acoustic systems, including a full treatment of corners and boundary edges. The proposed boundary formulations are designed for virtual acoustics applications using the standard leapfrog scheme based on a rectilinear grid, and apply to FDTD as well as Kirchhoff variable digital waveguide mesh (K-DWM) methods. In addition, new analytic evaluation methods that accurately predict the reflectance of numerical boundary formulations are proposed. numerical experiments and numerical boundary analysis (NBA) are analysed in time and frequency domains in terms of the pressure wave reflectance for different angles of incidence and various impedances. The results show that the proposed boundary formulations structurally adhere well to the theoretical reflectance. In particular, both reflectance magnitude and phase are closely approximated even at high angles of incidence and low impedances. Furthermore, excellent agreement was found between the numerical boundary analysis and the experimental results, validating both as tools for researching FDTD boundary formulations.

Infinite Dimensional Banach spaces of functions with nonlinear properties

The aim of this paper is to show that there exist infinite dimensional Banach spaces of functions that, except for 0, satisfy properties that apparently should be destroyed by the linear combination of two of them. Three of these spaces are: a Banach space of differentiable functions on Rn failing the Denjoy-Clarkson property; a Banach space of non Riemann integrable bounded functions, but with antiderivative at each point of an interval; a Banach space of infinitely differentiable functions that vanish at infinity and are not the Fourier transform of any Lebesgue integrable function.

An Investigation of the Flow Field through a Variable Geometry Turbine Stator with Vane Endwall Clearance

Variable geometry turbines provide an extra degree of flexibility in air management in turbocharged engines. The pivoting stator vanes used to achieve the variable turbine geometry necessitate the inclusion of stator vane endwall clearances. The consequent leakage flow through the endwall clearances impacts the flow in the stator vane passages and an understanding of the impact of the leakage flow on stator loss is required. A numerical model of a typical variable geometry turbine was developed using the commercial CFX-10 computational fluid dynamics software, and validated using laser doppler velocimetry and static pressure measurements from a variable geometry turbine with stator vane endwall clearance. Two different stator vane positions were investigated, each at three different operating conditions representing different vane loadings. The vane endwall leakage was found to have a significant impact on the stator loss and on the uniformity of flow entering the turbine rotor. The leakage flow changed considerably at different vane positions and flow incidence at vane inlet was found to have a significant impact.