Reverse Approximation of Energetic Solutions to Rate-Independent Processes

Energetic solutions to rate-independent processes are usually constructed via time-incremental minimization problems. In this work we show that all energetic solutions can be approximated by such incremental problems if we allow for approximate minimizers, where the error in minimization has to be of the order of the time step. Moreover, we study sequences of problems where the energy functionals have a Γ-limit. Research partially supported by Deutsche Forschungsgemeinschaft via the MATHEON project C18.     

Modeling auditory evoked brainstem responses to transient stimuli

A quantitative model is presented that describes the formation of auditory brainstem responses (ABRs) to tone pulses, clicks, and rising chirps as a function of stimulation level. The model computes the convolution of the instantaneous discharge rates using the "humanized" nonlinear auditory-nerve model of Zilany and Bruce [J. Acoust. Soc. Am. 122, 402-417 (2007)] and an empirically derived unitary response function which is assumed to reflect contributions from different cell populations within the auditory brainstem, recorded at a given pair of electrodes on the scalp. It is shown that the model accounts for the decrease of tone-pulse evoked wave-V latency with frequency but underestimates the level dependency of the tone-pulse as well as click-evoked latency values. Furthermore, the model correctly predicts the nonlinear wave-V amplitude behavior in response to the chirp stimulation both as a function of chirp sweeping rate and level. Overall, the results support the hypothesis that the pattern of ABR generation is strongly affected by the nonlinear and dispersive processes in the cochlea.     

Graphs that admit right angle crossing drawings

We consider right angle crossing (RAC) drawings of graphs in which the edges are represented by polygonal arcs and any two edges can cross only at a right angle. We show that if a graph with n vertices admits a RAC drawing with at most 1 bend or 2 bends per edge, then the number of edges is at most 6.5n and 74.2n, respectively. This is a strengthening of a recent result of Didimo et al.     

Beyond Millikan: the dynamics of charging events on individual colloidal particles

By measuring the stable charge on oil drops in air, Millikan demonstrated the discrete nature of electric charge. We extend his approach to the charge on solid-liquid interfaces, and focus on the dynamics of the discrete fluctuations. Our measurements are accurate and fast enough to observe changes of one elementary charge. Experiments over thousands of seconds yield information about the fast dynamics of electrochemical reactions, relevant for physicochemical and biological systems. As an example, we study (dis)charging processes on colloidal particles in a nonpolar liquid.     

Facile One-Step Oxidation of N-Boc-Protected Diarylhydrazines to Diaryldiazenes with (Diacetoxyiodo)benzene under Mild Conditions

A study on the oxidation of N-Boc- and N,N'-bis-Boc-protected 1,2-diarylhydrazines with (diacetoxyiodo)benzene is reported. The reactions proceed quickly in acetic acid at slightly elevated temperatures, giving diaryldiazenes in good to excellent yields. Electron-donating and electron-withdrawing groups are well tolerated. This synthetic protocol also applies to synthesising (aryldiazenyl)pyridines and unsymmetrical 1,3,5-tris(arylazo)benzenes.     

One‐Pot Automated Synthesis of Quasi Triblock Copolymers for Self‐Healing Physically Crosslinked Hydrogels

The preparation of physically crosslinked hydrogels from quasi ABA‐triblock copolymers with a water‐soluble middle block and hydrophobic end groups is reported. The hydrophilic monomer N‐acryloylmorpholine is copolymerized with hydrophobic isobornyl acrylate via a one‐pot sequential monomer addition through reversible addition fragmentation chain‐transfer (RAFT) polymerization in an automated parallel synthesizer, allowing systematic variation of polymer chain length and hydrophobic–hydrophilic ratio. Hydrophobic interactions between the outer blocks cause them to phase‐separate into larger hydrophobic domains in water, forming physical crosslinks between the polymers. The resulting hydrogels are studied using rheology and their self‐healing ability after large strain damage is shown.

     

Polymer networks containing crystallizable poly(octadecyl vinyl ether) segments for shape‐memory materials

New polymer networks were prepared by free radical initiated copolymerization of crystallizable α,ω‐bismethacrylate‐terminated poly(octadecyl vinyl ether) (polyODVE) with butyl acrylate (BA). The polyODVE bismacromonomers were obtained by end‐capping the bifunctionally living cationic polymerization of ODVE with 2‐hydroxyethyl methacrylate (HEMA). The segmented networks show a high degree of phase separation over a wide range of compositions. The shape memory properties of a material containing 20 wt.‐% of polyODVE are reported.     

The sol-gel approach towards thermo-responsive poly(N-isopropyl acrylamide) hydrogels with improved mechanical properties

A new type of thermo-responsive hydrogels based on the polymer poly(N-isopropyl acrylamide) (PNIPAA) has been synthesized with the sol-gel technology. For the preparation of this type of nano-structured hydrogels, the inorganic silica phase was synthesized by the sol-gel process in the presence of an aqueous solution of high molecular weight PNIPAA. This combination of the organic and inorganic phases forms hybrid hydrogels with a semi-IPN morphology. The unique structure of these hydrogels improves the mechanical stability to a great extent as compared to conventional PNIPAA-hydrogels. This was shown by stress-strain experiments and the capability to absorb and desorb large amounts of water. The silica only slightly influences the transition temperature of the hydrogels but allows us to vary the thermo-responsive properties of the materials to a great extent.