The survival probability of critical and subcritical branching processes in finite state space Markovian environment

Let ${\left(Z_n\right)}_{n\ge 0}$ be a branching process in a random environment defined by a Markov chain ${\left(X_n\right)}_{n\ge 0}$ with values in a finite state space $\mathbb{X}$. Let ${\mathbb{P}}_i$ be the probability law generated by the trajectories of ${\left(X_n\right)}_{n\ge 0}$ starting at $X_0=i\in \mathbb{X}.$ We study the asymptotic behaviour of the joint survival probability ${\mathbb{P}}_i\left(Z_n>0,X_n=j\right)$, $j\in \mathbb{X}$ as $n\to +\infty$ in the critical and strongly, intermediate and weakly subcritical cases.     

Orientational correlations in molecular liquids by neutron scattering Carbon tetrachloride and germanium tetrabromide

Neutron diffraction structure factors for liquid carbon tetrachloride and germanium tetrabromide have been measured and are analysed to determine the molecular centre positional correlation function allowing for molecular angular correlation. The analysis shows quite unequivocally that appreciable molecular orientational correlations must exist in these liquids but that it may only extend to nearest neighbours. This is thought to cause the pair distribution function for the molecular liquids to be markedly different from that for atomic liquids such as argon and the difference is discussed.     

Water-annealing regulated protein-based magnetic nanofiber materials: tuning silk structure and properties to enhance cell response under magnetic fields

In this study, flexible silk fibroin protein and biocompatible barium hexaferrite (BaM) nanoparticles were combined and electrospun into nanofibers, and their physical properties could be tuned through the mixing ratios and a water annealing process. Structural analysis indicates that the protein structure of the materials is fully controllable by the annealing process. The mechanical properties of the electrospun composites can be significantly improved by annealing, while the magnetic properties of barium hexaferrite are maintained in the composite. Notably, in the absence of a magnetic field, cell growth increased slightly with increasing BaM content. Application of an external magnetic field during in vitro cell biocompatibility study of the materials demonstrated significantly larger cell growth. We propose a mechanism to explain the effects of water annealing and magnetic field on cell growth. This study indicates that these composite electrospun fibers may be widely used in the biomedical field for controllable cell response through applying different external magnetic fields.     

Mesoscopic phase statistics of diffuse ultrasound in dynamic matter

Temporal fluctuations in the phase of waves transmitted through a dynamic, strongly scattering, mesoscopic sample are investigated using ultrasonic waves, and compared with theoretical predictions based on circular Gaussian statistics. The fundamental role of phase in diffusing acoustic wave spectroscopy is revealed, and phase statistics are also shown to provide a sensitive and accurate way to probe scatterer motions at both short and long time scales.