An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty

We present a robust optimization framework that is applicable to general nonlinear programs (NLP) with uncertain parameters. We focus on design problems with partial differential equations (PDE), which involve high computational cost. Our framework addresses the uncertainty with a deterministic worst-case approach. Since the resulting min–max problem is computationally intractable, we propose an approximate robust formulation that employs quadratic models of the involved functions that can be handled efficiently with standard NLP solvers. We outline numerical methods to build the quadratic models, compute their derivatives, and deal with high-dimensional uncertainties. We apply the presented approach to the parametrized shape optimization of systems that are governed by different kinds of PDE and present numerical results.     

Ultra-dense planar metallic nanowire arrays with extremely large anisotropic optical and magnetic properties

A nanofabrication method for the production of ultra-dense planar metallic nanowire arrays scalable to wafer-size is presented. The method is based on an efficient template deposition process to grow diverse metallic nanowire arrays with extreme regularity in only two steps. First, III–V semiconductor substrates are irradiated by a low-energy ion beam at an elevated temperature, forming a highly ordered nanogroove pattern by a “reverse epitaxy” process due to self-assembly of surface vacancies. Second, diverse metallic nanowire arrays (Au, Fe, Ni, Co, FeAl alloy) are fabricated on these III–V templates by deposition at a glancing incidence angle. This method allows for the fabrication of metallic nanowire arrays with periodicities down to 45 nm scaled up to wafer-size fabrication. As typical noble and magnetic metals, the Au and Fe nanowire arrays produced here exhibited large anisotropic optical and magnetic properties, respectively. The excitation of localized surface plasmon resonances (LSPRs) of the Au nanowire arrays resulted in a high electric field enhancement, which was used to detect phthalocyanine (CoPc) in surface-enhanced Raman scattering (SERS). Furthermore, the Fe nanowire arrays showed a very high in-plane magnetic anisotropy of approximately 412 mT, which may be the largest in-plane magnetic anisotropy field yet reported that is solely induced via shape anisotropy within the plane of a thin film.

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Investigation of charge carrier depletion in freestanding nanowires by a multi-probe scanning tunneling microscope

Profiling of the electrical properties of nanowires (NWs) and NW heterocontacts with high spatial resolution is a challenge for any application and advanced NW device development. For appropriate NW analysis, we have established a four-point prober, which is combined in vacuo with a state-of-the-art vapor-liquid-solid preparation, enabling contamination-free NW characterization with high spatial resolution. With this ultrahigh-vacuum-based multi-tip scanning tunneling microscopy (MT-STM), we obtained the resistance and doping profiles of freestanding NWs, along with surface-sensitive information. Our in-system 4-probe STM approach decreased the detection limit for low dopant concentrations to the depleted case in upright standing NWs, while increasing the spatial resolution and considering radial depletion regions, which may originate from surface changes. Accordingly, the surface potential of oxide-free GaAs NW {112} facets has been estimated to be lower than 20 mV, indicating a NW surface with very low surface state density.

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Toward a theory of managing creativity-intensive processes: a creative industries study

This paper reports the results of an exploratory, theory-building study on the impact of creativity on business processes, their management, and the use of information technology (IT) in particular. The empirical evidence was derived from organizations within the creative industries, specifically film and visual effects (VFX) production. An adapted grounded theory approach was employed in order to analyze the data. The study identifies the dynamics of business processes that can be described as highly dependent on creativity, intensively involving the client, complex, and interdependent. It explains the processes’ organizational context as well as strategies and IT systems that organizations use in order to manage these processes. The study suggests that creativity-intensive processes are characterized by high levels of uncertainty with regard to outcome, process structure, and required resources. Creative organizations pursue both creative and operational process performance while simultaneously mitigating creative and operational risk.     

Nested multigrid methods for time-periodic,parabolic optimal control problems

We present a nested multigrid method to optimize time-periodic, parabolic, partial differential equations (PDE). We consider a quadratic tracking objective with a linear parabolic PDE constraint. The first order optimality conditions, given by a coupled system of boundary value problems can be rewritten as an Fredholm integral equation of the second kind, which is solved by a multigrid of the second kind. The evaluation of the integral operator consists of solving sequentially a boundary value problem for respectively the state and the adjoints. Both problems are solved efficiently by a time-periodic space-time multigrid method.     

Non-standard bone simulation: interactive numerical analysis by computational steering

Numerous numerical methods have been developed in an effort to accurately predict stresses in bones. The largest group are variants of the h-version of the finite element method (h-FEM), where low order Ansatz functions are used. By contrast, we3 investigate a combination of high order FEM and a fictitious domain approach, the finite cell method (FCM). While the FCM has been verified and validated in previous publications, this article proposes methods on how the FCM can be made computationally efficient to the extent that it can be used for patient specific, interactive bone simulations. This approach is called computational steering and allows to change input parameters like the position of an implant, material or loads and leads to an almost instantaneous change in the output (stress lines, deformations). This direct feedback gives the user an immediate impression of the impact of his actions to an extent which, otherwise, is hard to obtain by the use of classical non interactive computations. Specifically, we investigate an application to pre-surgical planning of a total hip replacement where it is desirable to select an optimal implant for a specific patient. Herein, optimal is meant in the sense that the expected post-operative stress distribution in the bone closely resembles that before the operation.     

Optimization problems in contracted tensor networks

We discuss the calculus of variations in tensor representations with a special focus on tensor networks and apply it to functionals of practical interest. The survey provides all necessary ingredients for applying minimization methods in a general setting. The important cases of target functionals which are linear and quadratic with respect to the tensor product are discussed, and combinations of these functionals are presented in detail. As an example, we consider the representation rank compression in tensor networks. For the numerical treatment, we use the nonlinear block Gauss?CSeidel method. We demonstrate the rate of convergence in numerical tests.     

A Multidirectional Occlusion Shading Model for Direct Volume Rendering

In this paper, we present a novel technique which simulates directional light scattering for more realistic interactive visualization of volume data. Our method extends the recent directional occlusion shading model by enabling light source positioning with practically no performance penalty. Light transport is approximated using a tilted cone‐shaped function which leaves elliptic footprints in the opacity buffer during slice‐based volume rendering. We perform an incremental blurring operation on the opacity buffer for each slice in front‐to‐back order. This buffer is then used to define the degree of occlusion for the subsequent slice. Our method is capable of generating high‐quality soft shadowing effects, allows interactive modification of all illumination and rendering parameters, and requires no pre‐computation.     

Near-Entropy Hotlink Assignments

Consider a rooted tree T of arbitrary maximum degree d representing a collection of n web pages connected via a set of links, all reachable from a source home page represented by the root of T. Each web page i carries a probability p _i representative of the frequency with which it is visited. By adding hotlinks—shortcuts from a node to one of its descendents—we wish to minimize the expected number of steps l needed to visit pages from the home page, expressed as a function of the entropy H(p) of the access probabilities p. This paper introduces several new strategies for effectively assigning hotlinks in a tree. For assigning exactly one hotlink per node, our method guarantees an upper bound on l of 1.141H(p)+1 if d>2 and 1.08H(p)+2/3 if d=2. We also present the first efficient general methods for assigning at most k hotlinks per node in trees of arbitrary maximum degree, achieving bounds on l of at most \frac2H(p)log(k+1)+1\frac{2H(p)}{\log(k+1)}+1 and \fracH(p)log(k+d)-logd+1\frac{H(p)}{\log(k+d)-\log d}+1 , respectively. All our methods are strong, i.e., they provide the same guarantees on all subtrees after the assignment. We also present an algorithm implementing these methods in O(nlog n) time, an improvement over the previous O(n ²) time algorithms. Finally we prove a Ω(nlog n) lower bound on the running time of any strong method that guarantee an average access time strictly better than 2H(p).