Nucleation Barriers for the Cubic‐to‐Tetragonal Phase Transformation

We are interested in the phase transformation from austenite to martensite. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic‐to‐tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like $\max \{ V^{2/3}, V^{9/11} \}$ in terms of the volume V. Moreover, our arguments illustrate the importance of self‐accommodation for achieving the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy. © 2012 Wiley Periodicals, Inc.     

Selective protein adsorption on a phase-separated solvent-cast polymer blend

Polymer-based biomedical devices are growing increasingly sophisticated as compositions evolve toward copolymers and blends in order to satisfy complex design criteria. Such polymers afford opportunities for both micro- and macrophase separation at nano- and micro-length scales and raise questions concerning the role of heterogeneous surface morphology on protein adsorption. Adsorbed protein layers play a critical role in mediating the interaction of cells with polymer surfaces, and both understanding and controlling protein adsorption is assuming greater significance in the development of surfaces with enhanced physiological compatibility. Here we study the short-time adsorption of ferritin, a model protein highly resistant to denaturation and easily imaged in the transmission electron microscope (TEM), onto a phase-separated homopolymer blend of polycaprolactone (PCL) and a polycarbonate derived from desaminotyrosyl-tyrosine dodecyl ester (PDTD). At physiological pH, ferritin selectively adsorbs onto the PDTD phase at a surface density approximately three times greater than that on the PCL phase. By decreasing the pH below ferritin's isoelectric point so its average charge becomes positive, the selective adsorption disappears and the surface density of adsorbed ferritin becomes independent of the phase separation. We attribute the selectivity to the electrostatic repulsion between ferritin and hydrolytically charged PCL, both of which will have a net negative charge at physiological pH. To perform these experiments, we solvent-cast ultrathin polymer films onto dissolvable salt substrates, and we characterize the morphology by TEM imaging and quantitative spatially resolved electron energy-loss spectroscopy (EELS). We find that the film morphology depends strongly on such processing-related variables as the solvent evaporation rate and the nature of the surface in contact with the polymer film during casting. The adsorption of ferritin depends on whether the film is phase-separated as well as to which surface of the film the protein solution is exposed, and these findings suggest that seemingly small variations in polymer processing that influence both the bulk and surface morphology can have a profound effect on the short-time protein adsorption.     

The equation on weakly pseudo-convex CR manifolds of dimension 3

Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of dimension 3, embedded in (N2), of codimension one or more, and endowed with the induced CR structure. Assuming that the tangential Cauchy-Riemann operator has closed range in L²(M) in order to rule out the Rossi example, we push regularity up to show has closed range in H^s(M) for all s>0. We then use the Szegö projection to show there is a smooth solution for the problem given smooth data. The results are obtained via microlocalization by piecing together estimates for functions and (0,1) forms that hold on different microlocal regions.     

Evaluating acoustic speaker normalization algorithms: evidence from longitudinal child data

Speaker vowel formant normalization, a technique that controls for variation introduced by physical differences between speakers, is necessary in variationist studies to compare speakers of different ages, genders, and physiological makeup in order to understand non-physiological variation patterns within populations. Many algorithms have been established to reduce variation introduced into vocalic data from physiological sources. The lack of real-time studies tracking the effectiveness of these normalization algorithms from childhood through adolescence inhibits exploration of child participation in vowel shifts. This analysis compares normalization techniques applied to data collected from ten African American children across five time points. Linear regressions compare the reduction in variation attributable to age and gender for each speaker for the vowels BEET, BAT, BOT, BUT, and BOAR. A normalization technique is successful if it maintains variation attributable to a reference sociolinguistic variable, while reducing variation attributable to age. Results indicate that normalization techniques which rely on both a measure of central tendency and range of the vowel space perform best at reducing variation attributable to age, although some variation attributable to age persists after normalization for some sections of the vowel space.     

Focusing femtosecond X‐ray free‐electron laser pulses by refractive lenses

The possibility of using a parabolic refractive lens with initial X‐ray free‐electron laser (XFEL) pulses, i.e. without a monochromator, is analysed. It is assumed that the measurement time is longer than 0.3 fs, which is the time duration of a coherent pulse (spike). In this case one has to calculate the propagation of a monochromatic wave and then perform an integration of the intensity over the radiation spectrum. Here a general algorithm for calculating the propagation of time‐dependent radiation in free space and through various objects is presented. Analytical formulae are derived describing the properties of the monochromatic beam focused by a system of one and two lenses. Computer simulations show that the European XFEL pulses can be focused with maximal efficiency, i.e. as for a monochromatic wave. This occurs even for nanofocusing lenses.     

Meta-control of an interacting-particle algorithm for global optimization

A common issue for stochastic global optimization algorithms is how to set the parameters of the sampling distribution (e.g. temperature, mutation/cross-over rates, selection rate, etc.) so that the samplings converge to the optimum effectively and efficiently. We consider an interacting-particle algorithm and develop a meta-control methodology which analytically guides the inverse temperature parameter of the algorithm to achieve desired performance characteristics (e.g. quality of the final outcome, algorithm running time, etc.). The main aspect of our meta-control methodology is to formulate an optimal control problem where the fractional change in the inverse temperature parameter is the control variable. The objectives of the optimal control problem are set according to the desired behavior of the interacting-particle algorithm. The control problem considers particles’ average behavior, rather than treating the behavior of individual particles. The solution to the control problem provides feedback on the inverse temperature parameter of the algorithm.     

Eine neue Gruppe substituierter Dioxindole

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