Bayesian model selection for time series using Markov chain Monte Carlo

We present a stochastic simulation technique for subset selection in time series models, based on the use of indicator variables with the Gibbs sampler within a hierarchical Bayesian framework. As an example, the method is applied to the selection of subset linear AR models, in which only significant lags are included. Joint sampling of the indicators and parameters is found to speed convergence. We discuss the possibility of model mixing where the model is not well determined by the data, and the extension of the approach to include non-linear model terms.

Linear gaussian computations for near-exact Bayesian Monte Carlo inference in skewed alpha-stable time series models

In this paper we study parameter estimation for time series with asymmetric α-stable innovations. The proposed methods use a Poisson sum series representation (PSSR) for the asymmetric α-stable noise to express the process in a conditionally Gaussian framework. That allows us to implement Bayesian parameter estimation using Markov chain Monte Carlo (MCMC) methods. We further enhance the series representation by introducing a novel approximation of the series residual terms in which we are able to characterise the mean and variance of the approximation. Simulations illustrate the proposed framework applied to linear time series, estimating the model parameter values and model order P for an autoregressive (AR(P)) model driven by asymmetric α-stable innovations. © 2012 IEEE.

The further understanding of chain topology effect on the properties of single polymer in good solvent: Special behaviors of single tadpole chain

Chain topology strongly affects the static and dynamic properties of polymer melts and polymers in dilute solution. For different chain architectures, such as ring and linear polymers, the molecular size and the diffusion behavior are different. To further understand the chain topology effect on the static and dynamic properties of polymers, we focus on the tadpole polymer which consists of a cyclic chain attached with one or more linear tails. It is found that both the number and the length of linear tails play important roles on the properties of the tadpole polymers in dilute solution. For the tadpole polymers with fixed linear tail length and number, with increasing the degree of polymerization of tadpole polymers, a transition from linear-like to ring-like behavior is observed for both the static and dynamic properties.

Influence of molecular topology on the static and dynamic properties of single polymer chain in solution

The influence of molecular topology on the structural and dynamic properties of polymer chain in solution with ring structure, three-arm branched structure, and linear structure are studied by molecular dynamics simulation. At the same degree of polymerization (N), the ring-shaped chain possesses the smallest size and largest diffusion coefficient. With increasing N, the difference of the radii of gyration between the three types of polymer chains increases, whereas the difference of the diffusion coefficients among them decreases. However, the influence of the molecular topology on the static and the dynamic scaling exponents is small. The static scaling exponents decrease slightly, and the dynamic scaling exponents increase slightly, when the topology of the polymer chain is changed from linear to ring-shaped or three-arm branched architecture. The dynamics of these three types of polymer chain in solution is Zimm-like according to the dynamic scaling exponents and the dynamic structure factors.

Chain propagation kinetics on melt grafting reaction

Graft copolymerization in the molten state is of fundamental importance as a probe of chemical modification and reactive compatibilization. However, few grafting kinetic studies on reactive extrusion have been carried out because of the inherent difficulties, as expected. In this work, we have studied chain propagation kinetics on melt grafting using pre-irradiated linear low density polyethylene (LLDPE) and three monomers, acrylic acid (AA), methacrylic acid (MAA), and methyl methacrylate (MMA), as the model system. We measured the apparent chain propagation rate coefficients of grafting (k(p,g)) and homopolymerization (k(p,h)) at an initial stage for the melt grafting by FT-IR spectroscopy and electron spin resonance spectroscopy. It was observed that the convective mixing affected the rate coefficients. The magnitude of k(p,h) and k(p,g) were in the same order, but k(p,h) was slightly larger than k(p,g) The k(p,g) of the three grafting systems increased in the order: LLDPE/MMA < LLDPE/MAA < LLDPE/AA. These results are explained in terms of phase separation, solubility, and inherent reactivity of the monomer.

Reversible addition-fragmentation chain transfer mediated radical polymerization of asymmetrical divinyl monomers targeting hyperbranched vinyl polymers

Reversible addition-fragmentation chain transfer (RAFT) mediated radical polymerizations of allyl methacrylate and undecenyl methacrylate, compounds containing two types of vinyl groups with different reactivities, were investigated to provide hyperbranched polymers. The RAFT agent benzyl dithiobenzoate was demonstrated to be an appropriate chain-transfer agent to inhibit crosslinking and obtain polymers with moderate-to-high conversions. The polymerization of allyl methacrylate led to a polymer without branches but with five- or six-membered rings. However, poly(undecenyl methacrylate) showed an indication of branching rather than intramolecular cycles. The hyperbranched structure of poly(undecenyl methacrylate) was confirmed by a combination of H-1, C-13, H-1-H-1 correlation spectroscopy, and distortionless enhancement by polarization transfer 135 NMR spectra. The branching topology of the polymers was controlled by the variation of the reaction temperature, chain-transfer-agent concentration, and monomer conversion. The significantly lower inherent viscosities of the resulting polymers, compared with those of linear analogues, demonstrated their compact structure,

Grafting of maleic anhydride onto linear polyethylene: A Monte Carlo study

Monte Carlo simulation was used to study the graft of maleic anhydride (MAH) onto linear polyethylene (PE-g-MAH) initiated by dicumyl peroxide (DCP). Simulation results revealed that major MAH monomers attached onto PE chains as branched graft at higher MAH content. However, at extremely low MAH content, the fraction of bridged graft was very close to that of branched graft. This conclusion was somewhat different from the conventional viewpoint, namely, the fraction of bridged graft was always much lower than that of branched graft under any condition. Moreover, the results indicated that the grafting degree increased almost linearly to MAH and DCP concentrations. On the other hand, it was found that the amount of grafted MAH dropped sharply with increasing the length of grafted MAH, indicating that MAH monomers were mainly attached onto the PE chain as single MAH groups or very short oligomers. With respect to the crosslink of PE, the results showed that the fraction of PE-(MAH)(n)-PE crosslink structure increased continuously, and hence the fraction of PE-PE crosslink decreased with increasing MAH concentration.

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.

Branched crystal morphology of linear polyethylene crystallized in a two-dimensional diffusion-controlled growth field

The branched crystal morphology of linear polyethylene formed at various temperatures from thin films has been studied by atomic-force microscopy (AFM), transmission electron microscopy (TEM), electron diffraction (ED) pattern and polymer decoration technique. Two types of branched patterns, i.e. dendrite and seaweed patterns, have been visualized. The fractal dimension d(f) = 1.65 of both dendrite and some of seaweed patterns was obtained by using the box-counting method, although most of the seaweed patterns are compact. Selected-area ED patterns indicate that the fold stems tilt about 34.5degrees around the b-axis and polymer decoration patterns show that the chain folding direction and regularity in two (200). regions are quite different from each other. Because of chain tilting, branched crystals show three striking features: 1) the lamella-like branches show two (200) regions with different thickness; 2) the crystals usually bend towards the thin region; 3) the thick region grows faster by developing branches, thus branches usually occur outside the thick region. The branched patterns show a characteristic width w, which gives a linear relationship with the crystallization temperature on a semilogarithmic plot.

Non-isothermal crystallization behavior and kinetics of metallocene short chain branched polyethylene

The non-isothermal crystallization behavior and kinetics of metallocene short chain branched polyethylene were investigated via DSC at cooling rates from 2.5 to 20 degreesC/min, and subsequent heating at rate of 10 degreesC/min. To verify the effect of molecular weight and branching content on crystallization, three group samples were chosen: (1) linear polyethylene with low molecular weight and high molecular weight; (2) low molecular weight polyethylene with low branching content and high branching content; (3) high molecular weight polyethylene with low branching content and high branching content. The results show that crystallization temperature, crystallinity, melting temperature and crystallization rate are highly branching content-dependent. Molecular weight effect is less important, compared to branching content. A dramatic decrease of crystallization temperature, crystallinity, crystallization rate and melting temperature was observed for branched samples. The non-isothermal kinetics was analyzed via the methods, developed by Gupta and Mo Zhi-shen, and good agreement was obtained.

Lateral habits of single crystals of metallocene-catalyzed low molecular weight short chain branched polyethylene from the melt

The lateral habits of low molecular weight short chain branched polyethylene single crystals from the melt were studied. Three crystallization temperatures (102, 104 and 106 degrees C) were selected for single crystal growth. It was found that the lateral habits of single crystals were asymmetric at all the crystallization temperatures selected. The electron diffraction patterns and tilting series experiments evidenced that there existed chain tilting in all the lamellae. It was the chain tilting that lead to the asymmetry of the growth rate and of lateral habits of the single crystals about the b-axis. The lateral habits substantially changed from the growth at 102 degrees C where the truncated lozenge single crystals formed with straight (110) faces to the growth at 104 degrees C where the lenticular single crystals appeared. This change occurred at 20 degrees C lower than that in a low molecular weight linear polyethylene with the same molecular weight. Furthermore, kinetics theory analysis evidenced that the change of lateral habits from truncated lozenge to lenticular shape resulted from the transition of growth regime. The results were the same as that of high molecular weight linear polyethylene but different to that of low molecular weight linear polyethylene. It may be attributed by the existence of short branched chains. (C) 2000 Elsevier Science Ltd. All rights reserved.

Influence of short chain branches on crystallization and melting behavior of low molecular weight polyethylenes

The crystallization and melting behavior of mellocene-catalized branched and linear polyethylenes of low molecular weight was studied. It was found that the crystalline lattice of branched polyethylene is larger than that of linear polyethylene because of the existence of branched chains. The melting behavior of branched polyethylene is similar to that of linear polyethylene since the branched chains can not enter the lattice. However, the crystalline behavior of low molecular weight branched polyethylene is the same as that of high molecular weight linear polyethylene, but different with that of low molecular weigh linear polyethylene. Kinetics theory analysis evidenced that the transition temperature of growth regime of the branched polyethylene is about 20 degreesC lower than that of linear polyethylene with the same molecular weight. It may be attributed to the existence of short branched chains.

Morphology, structure, and rheological property of linear low-density polyethylene grafted with acrylic acid

The chain structure, spherulite morphology, and theological property of LL-DPE-g-AA were studied by using electronspray mass spectroscopy, C-13-NMR, and rheometer. Experimental evidence proved that AA monomers grafted onto the LLDPE backbone formed multiunit AA branch chains. It was found that AA branch chains could hinder movement of the LLDPE main chain during crystallization. Spherulites of LLDPE became more anomalous because of the presence of AA branch chains. Rheological behavior showed that AA branch chains could act as an inner plasticizer at the temperature range of 170-200 degreesC, which made LLDPE-g-AA easy to further process. (C) 2001 John Wiley & Sons, Inc.

Study of the conductivity and side chain mobility of a comb-like polymer electrolyte using the dynamic mechanical method

Using poly(styrene-co-maleic anhydride) as a backbone and poly(ethylene glycol) methyl ether (PEGME) with different molecular weights as side chains, three comb-like polymers and their Li salt complexes were synthesized. The dynamic mechanical properties and conductivities were investigated. Results showed that the polymer electrolytes possess two glass transitions: alpha -transition and beta -transition, and the temperature dependence of the ionic conductivity shows WLF (Williams-Landel-Ferry) behavior. Based on the time-temperature equivalence principle, a master curve was constructed by selecting T-beta as reference temperature. The values of the WLF parameters (C-1 and C-2) were obtained and were found to be almost independent of the length of the PEGME side chain and the content of Li salt. By reference to T-0 = 50 degreesC. the relation between log tau (c) and c was found to be linear. The master curves are displaced progressively to higher frequencies as the molecular weight of the side chain is increased. The relation between log tau (n) and the molecular weight of the side chain is also linear. (C) 2001 Elsevier Science B.V. All rights reserved.

SYNTHESIS OF A POLYETHYLENE-GRAFT-POLYSTYRENE COPOLYMER AND ITS COMPATIBILIZATION FOR LINEAR LOW-DENSITY POLYETHYLENE/POLY(PHENYLENE OXIDE) BLENDS

Based on unsteady diffusion kinetics, polyethylene(PE)-graft-polystyrene (PS) copolymers were designed and synthesized with a heterogeneous high yield titanium-based catalyst by copolymerization of ethylene with a PS-macromonomer using 1-hexene as a short chain agent to promote the incorporation of the PS-macromonomer. The presence of 1-hexene facilitated the diffusion of the PS-macromonomer, giving rise to the significantly increased incorporation of the PS-macromonomer. Compatibilization of blends of linear low density polyethylene (LLDPE)/poly(phenylene oxide) (PPO) with the PE-g-PS copolymer were investigated using scanning electron microscopy (SEM) and dynamic mechanical analysis (DMA).