A constitutive theory for shape memory polymers. Part II: A linearized model for small deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modelling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

A constitutive theory for shape memory polymers. Part I: Large deformations

A constitutive theory is developed for shape memory polymers. It is to describe the thermomechanical properties of such materials under large deformations. The theory is based on the idea, which is developed in the work of Liu et al. [2006. Thermomechanics of shape memory polymers: uniaxial experiments and constitutive modeling. Int. J. Plasticity 22, 279-313], that the coexisting active and frozen phases of the polymer and the transitions between them provide the underlying mechanisms for strain storage and recovery during a shape memory cycle. General constitutive functions for nonlinear thermoelastic materials are used for the active and frozen phases. Also used is an internal state variable which describes the volume fraction of the frozen phase. The material behavior of history dependence in the frozen phase is captured by using the concept of frozen reference configuration. The relation between the overall deformation and the stress is derived by integration of the constitutive equations of the coexisting phases. As a special case of the nonlinear constitutive model, a neo-Hookean type constitutive function for each phase is considered. The material behaviors in a shape memory cycle under uniaxial loading are examined. A linear constitutive model is derived from the nonlinear theory by considering small deformations. The predictions of this model are compared with experimental measurements.     

A cationic 24-MC-8 manganese cluster with ring metals possessing three oxidation states [Mn(II)4Mn(III)6Mn(IV)2(mu4-O)2(mu3-O)4(mu3-OH)4(mu3-OCH3)2(pko)12](OH)(ClO4)3

Reaction of Mn(ClO4)2 with di-pyridyl ketone oxime, (2-py)2C=NOH, gives the novel cluster [Mn(II)4Mn(III)6Mn(IV)2(mu4-O)2(mu3-O)4(mu3-OH)4(mu3-OCH3)2(pko)12](OH)(ClO4)3 1. It is the only example of a 24-MC-8, and the first metallacrown with ring metal ions in three different oxidation states. Magnetic measurements show antiferromagnetic behavior.     

Bulk Free Radical Polymerization of Methyl Methacrylate and Vinyl Acetate: A Comparative Study

The model and methodology for estimating diffusion‐controlled rate coefficients for the methyl methacrylate (MMA) polymerization system is extended to the vinyl acetate (VAc) case. Comparison of the kinetic behavior and termination rate coefficients (k_t) of both monomers suggests that at low conversions the termination reaction is controlled by the chemical step, whereas at moderate and high conversions it is controlled by the diffusive step which in turn is determined by the segmental diffusion of the long radicals and not by the center of mass diffusion of short radicals. It is found that, for most of the conversion range, diffusion coefficient for VAc is lower than the one for MMA notwithstanding that k_tVAc > k_tMMA. An explanation of this apparent inconsistency on the base of the model results and in terms of segmental mobility is proposed.

     

Femtosecond time resolved fluorescence dynamics of a cationic water-soluble poly(fluorenevinylene-co-phenylenevinylene)

A recently synthesized cationic water-soluble poly(fluorenevinylene-co-phenylenevinylene) was studied by means of steady state and femtosecond time resolved upconversion spectroscopy in aqueous and EtOH solutions. Steady state spectroscopic measurements showed that the polymer emits at the blue-green spectral region and that aggregates are formed in concentrated polymer solutions. The fluorescence dynamics of the polymer in concentrated solutions, studied at a range of emission wavelengths, exhibited a wavelength dependent and multiexponential decay, indicating the existence of various decay mechanisms. Specifically, a rapid decay at short emission wavelengths and a slow rise at long wavelengths were observed. Both features reveal an energy transfer process from isolated to aggregated chains. The contribution of the energy transfer process as well as of the isolated chains and the aggregates on the overall fluorescence decay of the polymer was determined. The dependence of the energy transfer rate and efficiency on polymer concentration was also examined.     

Computational singular perturbation with non-parametric tabulation of slow manifolds for time integration of stiff chemical kinetics

This paper presents a novel tabulation strategy for the adaptive numerical integration of chemical kinetics using the computational singular perturbation (CSP) method. The strategy stores and reuses CSP quantities required to filter out fast dissipative processes, resulting in a non-stiff chemical source term. In particular, non-parametric regression on low-dimensional slow invariant manifolds (SIMs) in the chemical state space is used to approximate the CSP vectors spanning the fast chemical subspace and the associated fast chemical time-scales. The relevant manifold and its dimension varies depending on the local number of exhausted modes at every location in the chemical state space. Multiple manifolds are therefore tabulated, corresponding to different numbers of exhausted modes (dimensions) and associated radical species. Non-parametric representations are inherently adaptive, and rely on efficient approximate-nearest-neighbor queries. As the CSP information is only a function of the non-radical species in the system and has relatively small gradients in the chemical state space, tabulation occurs in a lower-dimensional state space and at a relatively coarse level, thereby improving scalability to larger chemical mechanisms. The approach is demonstrated on the simulation of homogeneous constant pressure H₂–air and CH₄–air ignition, over a range of initial conditions. For CH₄–air, results are shown that outperform direct implicit integration of the stiff chemical kinetics while maintaining good accuracy.     

Sample Size for Testing Homogeneity of Two a Priori Dependent Binomial Populations Using the Bayesian Approach

This paper establishes new methodology for calculating the optimal sample size when a hypothesis test between two binomial populations is performed. The problem is addressed from the Bayesian point of view, with prior information expressed through a Dirichlet distribution. The approach of this paper sets an upper bound for the posterior risk and then chooses as “optimum ”the combined sample size for which the likelihood of the data does not satisfy this bound. The combined sample size is divided equally between the two binomials. Numerical examples are discussed for which the two proportions are equal to either a fixed or to a random value.     

Photooxygenation of Furylalkylamines: Easy Access to Pyrrolizidine and Indolizidine Scaffolds

A highly adaptable method targeting the ubiquitous and very important pyrrolizidine and indolizidine scaffolds is presented. The general synthetic utility of the method is underscored by its application to the rapid and easy synthesis of five natural products starting from readily accessible alkylfuran precursors. These unprotected primary furylalkylamines are subjected to photooxygenation conditions, which initiate a complex cascade reaction sequence concluding with the production of high value motifs. This sequence can be tailored to need by varying the choice of both photosensitizer and base additive.     

Study of the 'teaching system' according to systems theory

The traditional triadic 'Teaching System' (the teacher, the student and mathematics) and the new quaternary version (the teacher, the student, mathematics and new technologies), are studied according to Systems Theory. Systems Theory is described and the model of the traditional 'Teaching System' and that of the new system are analysed with the aid of this theory; that is the structure of each system (elements, interactions) and its function are described. Finally, comments are made about the application of the new system on didactic, on the one hand, and the philosophical background of the incorporation of the fourth element (new technologies) in the traditional system, on the other.     

Sequential monitoring of a Bernoulli sequence when the pre-change parameter is unknown

The task of monitoring for a change in the mean of a sequence of Bernoulli random variables has been widely studied. However most existing approaches make at least one of the following assumptions, which may be violated in many real-world situations: (1) the pre-change value of the Bernoulli parameter is known in advance, (2) computational efficiency is not paramount, and (3) enough observations occur between change points to allow asymptotic approximations to be used. We develop a novel change detection method based on Fisher’s exact test which does not make any of these assumptions. We show that our method can be implemented in a computationally efficient manner, and is hence suited to sequential monitoring where new observations are constantly being received over time. We assess our method’s performance empirically via using simulated data, and find that it is comparable to the optimal CUSUM scheme which assumes both pre- and post-change values of the parameter to be known.