Relaxing mixed integer optimal control problems using a time transformation

Mixed integer control systems are used to model dynamical behavior that can change instantly, for example a driving car with different gears. Changing a gear corresponds to an instant change of the differential equation what is achieved in the model by changing the value of the integer control function. The optimal control of a mixed integer control system by a discretize-then-optimize approach leads to a mixed integer optimization problem that is not differentiable with respect to the integer variables, such that gradient based optimization methods can not be applied. In this work, differentiability with respect to all optimization variables is achieved by reformulating the mixed integer optimal control problem (MIOCP). A fixed integer control function and a time transformation are introduced. The combination of both allows to change the sequence of active differential equations by partially deactivating the fixed integer control function. In contrast to other works, here different fixed integer control functions are taken into account. Advantages of so called control consistent (CC) fixed integer control functions are discussed and confirmed on a numerical example. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Parallel solution of volume-coupled multi-field problems using an Abaqus-PANDAS software interface

Numerical simulations have proven to be a powerful tool in several engineering disciplines, such as mechanical, civil and biomechanical engineering, and are thus widely used. However, the reliability of the simulations strongly relies on the governing material model. These models are usually developed in academic or industrial research projects and are implemented into dedicated software packages to proof their concepts. A transfer of these models from the research into a production-related environment is often time consuming and prone to failures, and therefore a costly task. The present work introduces a general interface between the research code PANDAS, which is a dedicated multi-field finite-element solver based on a monolithic solution strategy, and the commercial finite-element package Abaqus. The coupling is based on the user-defined element subroutine (UEL) of Abaqus. This procedure, on the one hand, allows for a straight-forward embedding of the PANDAS material models into Abaqus. On the other hand, it provides, in comparison to the native UEL subroutine of Abaqus, a user-friendly programming environment for user-defined material models with an extended number of degrees of freedom. Furthermore, the coupling also supports the parallel-analysis capabilities for large-scale problems on high-performance computing clusters. The Abaqus-PANDAS linkage can be applied to various coupled multi-field problems. However, the present contribution addresses, in particular, volume-coupled multi-field problems as they arise when proceeding from the Theory of Porous Media (TPM) as a modelling framework. For instance, it can be used to model partially or fully saturated soils, or chemically or electro-chemically driven swelling phenomena as they appear, for example, within hydrogels. Additionally, discontinuities, such as cracks, can be described for instance via phase-field models or by the extended finite-element method (XFEM). (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stable and Storable N(CF3)2 Transfer Reagents

Fluorinated groups are essential for drug design, agrochemicals, and materials science. The bis(trifluoromethyl)amino group is an example of a stable group that has a high potential. While the number of molecules containing perfluoroalkyl, perfluoroalkoxy, and other fluorinated groups is steadily increasing, examples with the N(CF₃)₂ group are rare. One reason is that transfer reagents are scarce and metal-based storable reagents are unknown. Herein, a set of Cu^I and Ag^I bis(trifluoromethyl)amido complexes stabilized by N- and P-donor ligands with unprecedented stability are presented. The complexes are stable solids that can even be manipulated in air for a short time. They are bis(trifluoromethyl)amination reagents as shown by nucleophilic substitution and Sandmeyer reactions. In addition to a series of benzylbis(trifluoromethyl)amines, 2-bis(trifluoromethyl)amino acetate was obtained, which, upon hydrolysis, gives the fluorinated amino acid N,N-bis(trifluoromethyl)glycine.     

Pentafluoroethylaluminates: A Combined Synthetic,Spectroscopic, and Structural Study

Salts of the tetrakis(pentafluoroethyl)aluminate anion [Al(C₂F₅)₄]⁻ were obtained from AlCl₃ and LiC₂F₅. They were isolated with different counter-cations and characterized by NMR and vibrational spectroscopy and mass spectrometry. Degradation of the [Al(C₂F₅)₄]⁻ ion was found to proceed via 1,2-fluorine shifts and stepwise loss of CF(CF₃) under formation of [(C₂F₅)_4−nAlF_n]⁻ (n=1–4) as assessed by NMR spectroscopy and mass spectrometry and supported by results of DFT calculations. In addition, the [(C₂F₅)AlF₃]⁻ ion was structurally characterized.     

An Iterative Divergent Approach to Conjugated Starburst Borane Dendrimers

Using a new divergent approach, conjugated triarylborane dendrimers were synthesized up to the 2^nd generation. The synthetic strategy consists of three steps: 1) functionalization, via iridium catalyzed C−H borylation; 2) activation, via fluorination of the generated boronate ester with K[HF₂] or [N(nBu₄)][HF₂]; and 3) expansion, via reaction of the trifluoroborate salts with aryl Grignard reagents. The concept was also shown to be viable for a convergent approach. All but one of the conjugated borane dendrimers exhibit multiple, distinct and reversible reduction potentials, making them potentially interesting materials for applications in molecular accumulators. Based on their photophysical properties, the 1^st generation dendrimers exhibit good conjugation over the whole system. However, the conjugation does not increase further upon expansion to the 2^nd generation, but the molar extinction coefficients increase linearly with the number of triarylborane subunits, suggesting a potential application as photonic antennas.     

Boron: Its Role in Energy‐Related Processes and Applications

Boron's unique position in the Periodic Table, that is, at the apex of the line separating metals and nonmetals, makes it highly versatile in chemical reactions and applications. Contemporary demand for renewable and clean energy as well as energy‐efficient products has seen boron playing key roles in energy‐related research, such as 1) activating and synthesizing energy‐rich small molecules, 2) storing chemical and electrical energy, and 3) converting electrical energy into light. These applications are fundamentally associated with boron's unique characteristics, such as its electron‐deficiency and the availability of an unoccupied p orbital, which allow the formation of a myriad of compounds with a wide range of chemical and physical properties. For example, boron's ability to achieve a full octet of electrons with four covalent bonds and a negative charge has led to the synthesis of a wide variety of borate anions of high chemical and electrochemical stability—in particular, weakly coordinating anions. This Review summarizes recent advances in the study of boron compounds for energy‐related processes and applications.     

Analyzing sub-100-μm samples with transmission terahertz time domain spectroscopy

The authors propose a method for the extraction of material parameter and thickness information from sub-100-μm thin samples using non-differential transmission terahertz time domain spectroscopy. The approach relies on an additional Fourier transform of the frequency dependent material parameters to a quasi space regime. In this quasi space, periodic Fabry-Perot oscillations from the frequency domain, which originate from multiple reflections inside the sample, correspond to discrete peaks. By iterative minimization of these peaks, the highly precise thickness information along with the refractive index and absorption coefficient of the sample can be determined. Experimental verification of the approach is also provided.     

Consistent density deconvolution under partially known error distribution

We estimate the distribution of a real-valued random variable from contaminated observations. The additive error is supposed to be normally distributed, but with an unknown variance. The distribution is identifiable from the observations if we restrict the class of considered distributions by a simple condition in the time domain. A minimum distance estimator is shown to be consistent imposing only a slightly stronger assumption than the identification condition.     

Micro-fabricated metal nozzle plates used for water-in-oil and oil-in-water emulsification

In this paper the fabrication and use of micro-structured metal nozzle plates as emulsification devices is investigated and discussed. These structured metal nozzle plates were fabricated via two distinct routes. Laser ablation, performed with a femtosecond laser, was used to drill micrometer-sized holes into stainless steel and aluminum foils. Also a conventional steel mesh with an average pore size of 2.4 μm fabricated by weaving and roll compaction of micrometer-sized steel wires was investigated. The perforated metal nozzle plates were used for oil-in-water and after hydrophobization with alkylchlorosilanes for water-in-oil emulsification as well. In both cases, two types of drop formation processes were observed. The first one is the shear-induced drop formation well known for cross-flow membrane emulsification. The second is the spontaneous drop formation known from microchannel emulsification.