Scalarizations for adaptively solving multi-objective optimization problems

In this paper several parameter dependent scalarization approaches for solving nonlinear multi-objective optimization problems are discussed. It is shown that they can be considered as special cases of a scalarization problem by Pascoletti and Serafini (or a modification of this problem). Based on these connections theoretical results as well as a new algorithm for adaptively controlling the choice of the parameters for generating almost equidistant approximations of the efficient set, lately developed for the Pascoletti-Serafini scalarization, can be applied to these problems. For instance for such well-known scalarizations as the ε-constraint or the normal boundary intersection problem algorithms for adaptively generating high quality approximations are derived.     

Advanced finite element formulations for modeling thin piezoelectric structures

This contribution is concerned with mixed finite element formulations for modeling piezoelectric beam and shell structures. Due to the electromechanical coupling, specific deformation modes are joined with electric field components. In bending dominated problems incompatible approximation functions of these fields cause incorrect results. These effects occur in standard finite element formulations, where interpolation functions of lowest order are used. A mixed variational approach is introduced to overcome these problems. The mixed formulation allows for a consistent approximation of the electromechanical coupled problem. It utilizes six independent fields and could be derived from a Hu-Washizu variational principle. Displacements, rotations and the electric potential are employed as nodal degrees of freedom. According to the Timoshenko theory (beam) and the Reissner-Mindlin theory (shell), the formulations account for constant transversal shear strains. To incorporate three dimensional constitutive relations all transversal components of the electric field and the strain field are enriched by mixed finite element interpolations. Thus the complete piezoelectric coupling is appropriately captured. The common assumption of vanishing transversal stress and dielectric displacement components is enforced in an integral sense. Some numerical examples will demonstrate the capability of the presented finite element formulation. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A finite element formulation of a viscoelastic model for dielectric elastomers

Smart materials by definition, are solids, fluids or gases which react independently on changing external conditions and modify one or more properties without external stimuli. Sensu lato an external energy can produce the reaction, such as stress, temperature, moisture, pH, magnetic or electric fields. The distinguishing characteristic for electroactive polymers (EAP) is, that they react with a deformation by the application of an electrical field. This contribution presents a nonlinear electro-viscoelastic model for dielectric elastomers and its finite element implementation. This type of smart materials belong to the group of EAP's and consists out of soft elastomer between compliant and conducting electrodes. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Influence of dynamic brake pad properties on automotive disk brake squeal

Comparing different methods of characterizing dynamic properties of brake pad materials clearly shows, that those properties strongly depend on the boundary conditions as well as on amplitude and frequency in the excitation. Actually simulations of brake squeal suffer on the missing of correct material parameters identified under conditions relevant for squeal. The present paper gives inside into a method for the measurement and identification of linear and nonlinear brake pad material parameters identified under correct boundary conditions. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Rational design of bacitracin A derivatives by incorporating natural product derived heterocycles

Heterocycles display common structural motifs in nonribosomally produced peptides with an enormous impact on their bioactivity. In the case of the branched cyclic Bacitracin A, the thiazoline moiety is manufactured during NRPS peptide chain elongation. Here we describe a method to selectively alter the heterocyclic metal binding subunit of Bacitracin A by the synthesis of heterocyclic building blocks that were successfully coupled to the linear decapeptide and subsequently cyclized using the excised bacitracin PCP-TE bidomain. Utilization of this cyclase allowed the first generation of branched cyclic bacitracin derivatives containing thiazole and oxazoles. The generated bacitracin derivatives showed bactericidal activity, indicating the possibility of altering the biological important heterocyclic subunit and overcoming existing limitations for the application of bacitracin.     

NMR distinction of single- and multiple-mode binding of small-molecule protein ligands

Identifying and characterizing small-molecule inhibitors of protein-protein interactions is of high interest for drug discovery and for chemical genetics studies of biological pathways. Very often, initial hits or first-generation compounds have low micromolar dissociation constants and cause line broadening in NMR spectra. It is very important for subsequent structure-based compound optimization to know if this line broadening is caused by intermediate exchange of the dissociation kinetics only or in addition by multiple binding modes. Here, we present an approach of how to distinguish these two situations and demonstrate its experimental application. Two very similar small-molecule ligands of Bcl-xL are considered that cause both severe line broadening of interface residues. We show that one compound exhibits single-mode binding, and broadening is just due to dissociation kinetics in the intermediate exchange regime, and the line broadening can be overcome by providing excess ligand. In the other case, line broadening is due to dissociation kinetics and exchange between multiple bound conformations, and broadening cannot be overcome by providing excess ligand. The procedures used are very general and can also be applied to characterizing protein-protein and protein-nucleic acid interactions.     

Infrared spectroscopy of hydrated sulfate dianions

We report the first infrared spectra of multiply-charged anions in the gas phase. The spectra of SO(4) (2-)(H(2)O)(n), with n=3-24, show four main bands assigned to two vibrations of the dianionic core, the water bending mode, and solvent libration. The triply degenerate SO(4) (2-) antisymmetric stretch vibration probes the local solvent symmetry, while the solvent librational band is sensitive to the hydrogen bonding network. The spectra and accompanying electronic structure calculations indicate a highly symmetric structure for the n=6 cluster and closure of the first solvation shell at n=12.     

Improved diffusion Monte Carlo propagators for bosonic systems using Itô calculus

The construction of importance sampled diffusion Monte Carlo (DMC) schemes accurate to second order in the time step is discussed. A central aspect in obtaining efficient second order schemes is the numerical solution of the stochastic differential equation (SDE) associated with the Fokker-Plank equation responsible for the importance sampling procedure. In this work, stochastic predictor-corrector schemes solving the SDE and consistent with It? calculus are used in DMC simulations of helium clusters. These schemes are numerically compared with alternative algorithms obtained by splitting the Fokker-Plank operator, an approach that we analyze using the analytical tools provided by Ito; calculus. The numerical results show that predictor-corrector methods are indeed accurate to second order in the time step and that they present a smaller time step bias and a better efficiency than second order split-operator derived schemes when computing ensemble averages for bosonic systems. The possible extension of the predictor-corrector methods to higher orders is also discussed.     

COAST: Controllable approximative stochastic reaction algorithm

We present an approximative algorithm for stochastic simulations of chemical reaction systems, called COAST, based on three different modeling levels: for small numbers of particles an exact stochastic model; for intermediate numbers an approximative, but computationally more efficient stochastic model based on discrete Gaussian distributions; and for large numbers the deterministic reaction kinetics. In every simulation time step, the subdivision of the reaction channels into the three different modeling levels is done automatically, where all approximations applied can be controlled by a single error parameter for which an appropriate value can easily be found. Test simulations show that the results of COAST simulations agree well with the outcomes of exact algorithms; however, the asymptotic run times of COAST are asymptotically proportional to smaller powers of the particle numbers than exact algorithms.