PEG-POSS Star Molecules Blended in Polyurethane with Flexible Hard Segments: Morphology and Dynamics

A star polymer with a polyhedral oligomeric silsesquioxanne (POSS) core and poly(ethylene glycol) (PEG) vertex groups is incorporated in a polyurethane with flexible hard segments in-situ during the polymerization process. The blends are studied in terms of morphology, molecular dynamics, and charge mobility. The methods utilized for this purpose are scanning electron and atomic force microscopies (SEM, AFM), X-ray diffraction (XRD), differential scanning calorimetry (DSC), and to a larger extent dielectric relaxation spectroscopy (DRS). It is found that POSS reduces the degree of crystallinity of the hard segments. Contrary to what was observed in a similar system with POSS pendent along the main chain, soft phase calorimetric glass transition temperature drops as a result of plasticization, and homogenization of the soft phase by the star molecules. The dynamic glass transition though, remains practically unaffected, and a hypothesis is formed to resolve the discrepancy, based on the assumption of different thermal and dielectric responses of slow and fast modes of the system. A relaxation α′, slower than the bulky segmental α and common in polyurethanes, appears here too. A detailed analysis of dielectric spectra provides some evidence that this relaxation has cooperative character. An additional relaxation g, which is not commonly observed, accompanies the Maxwell Wagner Sillars interfacial polarization process, and has dynamics similar to it. POSS is found to introduce conductivity and possibly alter its mechanism. The study points out that different architectures of incorporation of POSS in polyurethane affect its physical properties by different mechanisms.     

Advanced MCMC methods for sampling on diffusion pathspace

The need to calibrate increasingly complex statistical models requires a persistent effort for further advances on available, computationally intensive Monte-Carlo methods. We study here an advanced version of familiar Markov-chain Monte-Carlo (MCMC) algorithms that sample from target distributions defined as change of measures from Gaussian laws on general Hilbert spaces. Such a model structure arises in several contexts: we focus here at the important class of statistical models driven by diffusion paths whence the Wiener process constitutes the reference Gaussian law. Particular emphasis is given on advanced Hybrid Monte-Carlo (HMC) which makes large, derivative-driven steps in the state space (in contrast with local-move Random-walk-type algorithms) with analytical and experimental results. We illustrate its computational advantages in various diffusion processes and observation regimes; examples include stochastic volatility and latent survival models. In contrast with their standard MCMC counterparts, the advanced versions have mesh-free mixing times, as these will not deteriorate upon refinement of the approximation of the inherently infinite-dimensional diffusion paths by finite-dimensional ones used in practice when applying the algorithms on a computer.     

Experiments and Simulations of <Emphasis Type="Italic">n</Emphasis>-Heptane Spray Auto-Ignition in a Closed Combustion Chamber at Diesel Engine Conditions

Auto-igniting n-heptane sprays have been studied experimentally in a high pressure, high temperature constant volume combustion chamber with optical access. Ignition delay and the total pressure increase due to combustion are highly repeatable whereas the ignition location shows substantial fluctuations. Simulations have subsequently been performed by means of a first-order fully elliptic Conditional Moment Closure (CMC) code. Overall, the simulations are in good agreement with the experiment in terms of spray evolution, ignition delay and the pressure development. The sensitivity of the predictions with respect to the measured initial conditions, the spray modelling options as well as the chemical mechanism employed have been analysed. Strong sensitivity on the chemical mechanism and to the initial temperature on the predicted ignition delay is reported. The primary atomisation model did not affect strongly the predicted auto-ignition time, but a strong influence was found on the ignition location prediction.     

On the singularities of a constrained (incompressible-like) tensegrity-cytoskeleton model under equitriaxial loading

Singularity theory is applied for the study of the characteristic three-dimensional tensegrity-cytoskeleton model after adopting an incompressibility constraint. The model comprises six elastic bars interconnected with 24 elastic string members. Previous studies have already been performed on non-constrained systems; however, the present one allows for general non-symmetric equilibrium configurations. Critical conditions for branching of the equilibrium are derived and post-critical behaviour is discussed. Classification of the simple and compound singularities of the total potential energy function is effected. The theory is implemented into the cusp catastrophe for the case of one-dimensional branching of the buckling-allowed tensegrity model, and an elliptic umbilic singularity for compound branching of a rigid-bar model. It is pointed out that singularity studies with constraints demand a quite different mathematical approach than those without constraints.     

Symmetry groups and similarity solutions for a free convective boundary-layer problem

The free convective boundary-layer problem due to the motion of an elastic surface into an electrically conducting fluid is studied with group-theoretical methods. The symmetry groups admitted by the corresponding boundary value problem are obtained. Particular attention is paid on the group of scaling which provides the similarity solution of the problem. Also, the admissible form of the data, in order to be conformed to the obtained symmetries, is provided. Finally, with the use of the entailed similarity solution the problem is transformed into a boundary value problem of ODEs and is solved numerically.     

Stochastic and Self-Organisation Patterns in a 17-Year PM10 Time Series in Athens,Greece

This paper utilises statistical and entropy methods for the investigation of a 17-year PM₁₀ time series recorded from five stations in Athens, Greece, in order to delineate existing stochastic and self-organisation trends. Stochastic patterns are analysed via lumping and sliding, in windows of various lengths. Decreasing trends are found between Windows 1 and 3500–4000, for all stations. Self-organisation is studied through Boltzmann and Tsallis entropy via sliding and symbolic dynamics in selected parts. Several values are below −2 (Boltzmann entropy) and 1.18 (Tsallis entropy) over the Boltzmann constant. A published method is utilised to locate areas for which the PM₁₀ system is out of stochastic behaviour and, simultaneously, exhibits critical self-organised tendencies. Sixty-six two-month windows are found for various dates. From these, nine are common to at least three different stations. Combining previous publications, two areas are non-stochastic and exhibit, simultaneously, fractal, long-memory and self-organisation patterns through a combination of 15 different fractal and SOC analysis techniques. In these areas, block-entropy (range 0.650–2.924) is significantly lower compared to the remaining areas of non-stochastic but self-organisation trends. It is the first time to utilise entropy analysis for PM₁₀ series and, importantly, in combination with results from previously published fractal methods.Data Set License: license under which the dataset is made available (CC0, CC-BY, CC-BY-SA, CC-BY-NC, etc.)