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)     

A comparative study of CE-SDS,SDS-PAGE,and Simple Western: Influences of sample preparation on molecular weight determination of proteins

The development of capillary electrophoresis, especially CE-SDS devices, has led CE-SDS to become an established tool in a wide range of applications in the analysis of biopharmaceuticals and is increasingly replacing its method of origin, SDS-PAGE. The goal of this study was to evaluate the comparability of molecular weight (MW) determination especially by CE-SDS and SDS-PAGE. For ensuring comparability, model proteins that have little or no posttranslational modifications and an IgG antibody were used. Only a minor influence of sample preparation conditions, including sample buffer, temperature conditions, and different reducing agents on the MW determination were found. In contrast, the selection of the MW marker plays a decisive role in determining the accurate apparent MW of a protein. When using different MW markers, the deviation in MW determination can exceed 10%. Interestingly, CE-SDS and 10% SDS-PAGE hardly differ in their trueness of MW determination. The trueness in relation to the reference MW for each protein was calculated. Although the trueness values for the model proteins considered range between 1.00 and 1.11 using CE-SDS, they range between 0.93 and 1.03 on SDS-PAGE, depending on the experimental conditions chosen.     

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.     

Third Generation ATP Sensor with Enzymatic Analyte Recycling

For the first time the direct electron transfer of an enzyme ‐ cellobiose dehydrogenase, CDH ‐ has been coupled with the hexokinase catalyzed competition for glucose in a sensor for ATP. To enhance the signal output for ATP, pyruvate kinase was coimmobilized to recycle ADP by the phosphoenolpyruvate driven reaction. The new sensor overcomes the limit of 1 : 1 stoichiometry of the sequential or competitive conversion of ATP by effective enzymatic recycling of the analyte. The anodic oxidation of the glucose converting CDH proceeds at electrode potentials below 0 mV vs. Ag|AgCl thus potentially interfering substances like ascorbic acid or catecholamines do not influence the measuring signal. The combination of direct electron transfer of CDH with the enzymatic recycling results in an interference‐free and oxygen‐independent measurement of ATP in the lower µmolar concentration range with a lower limit of detection of 63.3 nM (S/N=3).     

Physicochemical properties of SARS-CoV-2 for drug targeting,virus inactivation and attenuation,vaccine formulation and quality control

The material properties of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and its proteins are discussed. We review the viral structure, size, rigidity, lipophilicity, isoelectric point, buoyant density and centrifugation conditions, stability against pH, temperature, UV light, gamma radiation, and susceptibility to various chemical agents including solvents and detergents. Possible inactivation, downstream, and formulation conditions are given including suitable buffers and some first ideas for quality-control methods. This information supports vaccine development and discussion with competent authorities during vaccine approval and is certainly related to drug-targeting strategies and hygienics. Several instructive tables are given, including the pI and grand average of hydropathicity (GRAVY) of SARS-CoV-1 and -2 proteins in comparison. SARS-CoV-1 and SARS-CoV-2 are similar in many regards, so information can often be derived. Both are unusually stable, but sensitive at their lipophilic membranes. However, since seemingly small differences can have strong effects, for example, on immunologically relevant epitope settings, unevaluated knowledge transfer from SARS-CoV-1 to SARS-CoV-2 cannot be advised. Published knowledge regarding downstream processes, formulations and quality assuring methods is, as yet, limited. However, standard approaches employed for other viruses and vaccines seem to be feasible including virus inactivation, centrifugation conditions, and the use of adjuvants.     

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.