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)     

Mapping Multivalency and Differential Affinities within Large Intrinsically Disordered Protein Complexes with Segmental Motion Analysis

Intrinsically disordered proteins (IDPs) can bind to multiple interaction partners. Numerous binding regions in the IDP that act in concert through complex cooperative effects facilitate such interactions, but complicate studying IDP complexes. To address this challenge we developed a combined fluorescence correlation and time‐resolved polarization spectroscopy approach to study the binding properties of the IDP nucleoporin153 (Nup153) to nuclear transport receptors (NTRs). The detection of segmental backbone mobility of Nup153 within the unperturbed complex provided a readout of local, region‐specific binding properties that are usually masked in measurements of the whole IDP. The binding affinities of functionally and structurally diverse NTRs to distinct regions of Nup153 can differ by orders of magnitudes—a result with implications for the diversity of transport routes in nucleocytoplasmic transport.     

Molar mass determination by end group analysis - amino group determination in aliphatic and partially aromatic polyamides with 1-fluoro-2,4-dinitrobenzene in benzyl alcohol

End group analysis is the most important absolute method of obtaining number-average molar mass values for polymers of the step-growth polymerization type. A great number of methods are available which primarily differ in the detection of the end group concerned. Special chemical methods based on the formation of covalent derivatives of the end groups (e.g. introduction of UV/VIS chromophores) are important if there is a need to demonstrate, with the aid of gel permeation chromatography, that damage to the polymer (e.g. onset of cross-linking) has occurred. In the case of fibre-forming polycondensation products, the applicability of end group analysis is often restricted by the lack of suitable reagents and solvents. This is also true of the determination of amino end groups in polyamides by means of 1-fluoro-2,4-dinitrobenzene, as is already contained in the German Standards specification (DIN 54 274) - albeit only for polyamide 6 and 6,6. This contribution describes a modified version of the 1-fluoro-2,4-dinitrobenzene method. The analytical principle and practical procedure correspond to those of DIN 54 274, but the solvent used for the reaction with the reagent is benzyl alcohol, and that for the photometric evaluation is 1,1,1,3,3,3-hexafluoro-2-propanol. The scope of the method is thus increased. Examples of applications for this method are commercial products based on aliphatic polyamides (6; 11; 12; 6,6; 6, 12), partially aromatic polyamides (2,4,4-trimethylhexamethylenediamine, terephthalic acid; copolyamides with bis-(4-aminocyclohexyl)propane(2), isophthalic acid, ω-aminododecanoic acid) and multicomponent systems with the abovementioned polyamides (bicomponent fibres, blends). It is shown that large differences may arise between the value determined by titration and the actual amino end group content. In addition, the presence of secondary amino groups can be demonstrated in polyamides of the Trogamid T type.     

Die Verteilung von Molybdänsäure-Brenzcatechin-Komplexen zwischen wäßrigen Lösungen und organischen Lösungsmitteln

Molybdic-acid catechol complexes can be extracted from acidic aqueous solutions by organic solvents, if organic basic compounds are added. Results with tetraphenyl arsonium chloride were especially favourable.     

Direkte elektrometrische Bestimmung des Fluorid-Ions

Zusammenfassung Die Arbeitsweise einer Fluoridionen-empfindlichen Elektrode wurde geprüft und der Einfluß von Fremdsubstanzen auf die Potentiale untersucht. Die Störungen können durch Maskierung, Pufferung oder durch eine Auswertmethode vermindert werden.

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Summary The working characteristics of a fluoride-sensitive electrode and the influence of foreign substances on the fluoride potentials were tested. Changes in potential can be diminished by masking or buffering. Furthermore, a special addition technique can be applied.

     

Configuration interaction calculations for the ground and excited states of ozone and its positive ion: Energy locations and transition probabilities

Large-scale configuration interaction calculations (including energy extrapolation) are reported for the various states of ozone and its positive ion. The first four dipole-forbidden electronic transitions in the O₃ spectrum are calculated to occur at 1.20, 1.44, 1.59, and 1.72 eV, respectively, while the corresponding low-energy-allowed species known as the Chappuis, Huggins, and Hartley bands are predicted to possess vertical excitation energies of 1.95, 3.60, and 4.97 eV, respectively. These results all appear to fit in quite well with the observed location of the pertinent spectral features, with respect to both energy and intensity. The 5- to 8-eV region of the ozone spectrum is found to be characterized by a series of double-excitation transitions out of the highest three occupied orbitals to the lowest unoccupied 2b₁(π^*) species. The strong features observed at 9.3 and 10.2 eV are thereupon calculated to result primarily from transitions into the 7a₁ (σ^*) MO (calculated 9.29 and 10.05 eV) and in the former case also from the 3s members of the various O₃ Rydberg series (calculated 9.21 and 9.38 eV). Finally the order of the first three ip's is found to be 6a₁, 4b₂, and 1a₂, while the feature in the neighborhood of 16 eV is attributed to a shake-up state of ²B₁ symmetry.     

Ab initio MRD-CI study of ethane: The 14–25 eV PES region and Rydberg states of positive ions

Ab initio calculations of the MRD-CI type are reported for various states of the C₂H₆⁺ ion in two different nuclear geometries and the results are compared with the experimentally observed ethane PES in the 14–25 eV region. The calculated vertical IP values for ionization out of the 1e_u, 2a_2u and 2a_1g MO's respectively agree well with the locations of the three ionization maxima in this spectral range. The analogous findings for excitation out of the relaxed ionic ground state find several relatively low-lying species which occupy a 2pσ* MO in addition to states resulting from simple ionization of the neutral molecule. A number of Rydberg states are also calculated at the relaxed-ion geometry, from which results it is determined that the quantum defects for such species are from 0.40–0.45 units smaller than for their counterparts in neutral systems; these findings are clearly consistent with a decrease in the core penetrability of the Rydberg electron as the effective charge is increased to Z = 2.     

An approach to developing a force field for molecular simulation of martensitic phase transitions between phases with subtle differences in energy and structure

d,l-Norleucine is one of only a few molecules whose crystals exhibit a martensitic or displacive-type phase transformation where the emerging phase shows a topotaxial relationship with the parent phase. The molecular mechanism for such phase transformations, particularly in molecular crystals, is not well understood. Crystalline phases that exhibit displacive phase transitions tend to be very similar in structure and energy. Consequently, the development of a force field for such phases is challenging as the phase behavior is determined by subtle differences in their lattice energies and entropies. We report an approach for developing a force field for such phases with an application to d,l-norleucine. The proposed procedure includes calculation of the phase diagram of the crystalline phases as a function of temperature to identify the best force field. d,l-Norleucine also presents an additional problem since in the solid state it exists as a zwitterion that is unstable in vacuo and therefore cannot be characterized using high-level ab initio calculations in the gas phase. However, a stable zwitterion could be obtained using Onsager's reaction-field continuum model for a solvent (SCRF) using both Hartree-Fock and density functional theory. A number of force fields and the various sets of partial charges obtained from the SCRF calculations were screened for their ability to reproduce the crystal structures of the two known phases, alpha and beta, of d,l-norleucine. Selected parameter sets were then employed in free energy minimizations to identify the best set on the basis of a correct prediction of the alpha-beta phase transition. The Williams' nonbonded parameters combined with partial charges from SCRF-Polarized Continuum Model calculation were found to reproduce the structures of the phases accurately and also maintained their stability in extended molecular dynamics simulations in the Parrinello-Rahman constant stress ensemble. Moreover, we were also able to successfully simulate the phase transformation of the beta- to the alpha-phase. The identified force field should enable detailed studies of the phase transformations exhibited by crystals of d,l-norleucine and hence enhance our understanding of martensitic-type transformations in molecular crystals.