A conditionally linearized Monte Carlo filter in non-linear structural dynamics

State and parameter estimations of non-linear dynamical systems, based on incomplete and noisy measurements, are considered using Monte Carlo simulations. Given the measurements, the proposed method obtains the marginalized posterior distribution of an appropriately chosen (ideally small) subset of the state vector using a particle filter. Samples (particles) of the marginalized states are then used to construct a family of conditionally linearized system of equations and thus obtain the posterior distribution of the states using a bank of Kalman filters. Discrete process equations for the marginalized states are derived through truncated Ito-Taylor expansions. Increased analyticity and reduced dispersion of weights computed over a smaller sample space of marginalized states are the key features of the filter that help achieve smaller sample variance of the estimates. Numerical illustrations are provided for state/parameter estimations of a Duffing oscillator and a 3-DOF non-linear oscillator. Performance of the filter in parameter estimation is also assessed using measurements obtained through experiments on simple models in the laboratory. Despite an added computational cost, the results verify that the proposed filter generally produces estimates with lower sample variance over the standard sequential importance sampling (SIS) filter.     

Coupled mode analysis of in-plane channel drop filters with resonant mirrors

A channel drop filter system that consists of two waveguides and three cavities is studied. One cavity couples with both waveguides, while the other two work as resonant mirrors to reflect the selected channel back into the system. The operation of this configuration is analyzed, using coupled mode theory. The conditions to achieve 100% in-plane channel transfer are derived. A method to suppress the side lobes of reflection and backward drop is also proposed. The direct coupling between the cavities is not required. The analysis is verified by two-dimensional finite difference time domain simulations in 2D hexagonal photonic crystals.     

紧支撑三元正交小波滤波器的参数化

高维小波分析是分析和处理多维数字信号的有力工具．非张量积多元小波被广泛地应用在模式识别、纹理分析和边缘检测等领域．本文给出方体域上三元正交滤波器的一种参数化构造算法,三元小波滤波器的这种构造方法使我们能更方便地研究非张量积的三元正交小波．最后给出数值算例．     

Geometry dependence of the elongation behavior of a polypropylene melt through a micro die

A series of rheological experiments was performed for a polypropylene (PP) melt to explore its elongation behavior through a capillary die. Using an advanced twin-bore capillary rheometer with dies measuring 1.0, 0.5, and 0.25 mm in diameter, the experiments were performed at 210, 220, and 230 °C. The results indicated that the temperature of the PP melt had a significant effect on its extensional viscosity. The different decreases in the extensional viscosity values in the tested dies revealed the geometry dependence of the extensional viscosity. In the case of PP in the 0.25 mm die at 210 °C, the extensional viscosity values under different extensional strain rates were much higher than those in the other dies. Only in the 1.0 mm die did the relationship between the extensional viscosity of PP and its temperature obey the Arrhenius equation due to the larger die size which related to a slight size effect on its elongation behavior. The calculated deviations of the extensional viscosity in the tested dies demonstrated that the increasing pressure applied to the PP melt in the micro channel was related to the geometry dependence of the elongation behavior of the PP melt. The change in the extensional viscosity eventually relied on the interaction of the die geometry, the temperature, and the extensional stress of the PP melt.     

Exploring Si/Mg composite supported Ziegler-Natta Ti-based catalysts for propylene polymerization

A series of(Si_O2/MgO/ID/MgCl_2)·TiClx Ziegler-Natta catalysts for propylene polymerization has been prepared with a new method. These catalysts were synthesized using soluble Mg-compounds as the Mg-source and the preparation progress was relatively simple. The catalyst could copy the spherical shape of the carrier very well. The propylene polymerization results showed that the catalyst revealed the best activity with 9,9-di(methoxymethyl)fluorene(BMMF) as internal donor at 50 °C with the optimal molar ratio Al/Ti = 5, which was much lower than what the industrial polypropylene catalyst used(at least molar ratio Al/Ti = 100), resulting in great cost saving. Additionally, the polymerization kinetics of the catalyst exhibited very stable property after achieving a relatively high value. These catalysts possessed rather high activity and good hydrogen response. The isotactic index(Ⅱ.) value of the PP products could be higher than 98% in the presence of both internal and external electron donors. Moreover, temperature rising elution fractionation method was used to understand the influence of donors and H2 on the properties of the PP products.     

The influence of gamma radiation on the dielectric relaxation behaviour of isotactic polypropylene: The α relaxation

The high-temperature α relaxation in gamma irradiated isotactic polypropylene (iPP) was studied over the temperature (298-406 K), frequency (10³-10⁶ Hz) and absorbed dose (0-700 kGy) ranges by means of dielectric spectroscopy. The multiple α relaxation was resolved from the β relaxation by curve fitting and its parameters were determined. Its position, intensity and activation energy were found to be strongly dependent on the changes in the structural and morphological parameters attributed to the exposure of the samples to radiation. Wide angle X-ray diffraction (WAXD) was used to investigate radiation-induced changes in the crystalline structure and degree of crystallinity, since this relaxation is connected with the crystal phase. Infrared (IR) spectroscopy and gel measurements were used to determine the changes in the oxidative degradation and the degree of network formation, respectively; the polar (carbonyl and/or hydroperoxide) groups that were introduced by irradiation were considered as tracer groups. Conclusions derived according to different methods were compared. The results reveal uncommon α relaxation behaviour with gamma radiation and confirm the multiple nature of this process, together with high dielectric and/or relaxation sensitivity of iPP to the radiation-induced changes.     

Control of degradation of polypropylene during its radical functionalisation with furan and thiophene derivatives

The traditional melt radical functionalisation of isotactic polypropylene (iPP) with maleic anhydride (MAH) and peroxide affords functionalized samples with a severe decrease of the average molecular weight (MW) due to the β-scission reaction. In this work new push-pull unsaturated molecules were investigated, consisting of a heterocyclic ring conjugated with a double bond bearing an electron attracting group. These molecules were specifically designed as MAH substitute able to limit the iPP degradation, while providing functionalisation through grafting. Butyl 3-(2-furanyl) propenoate (BFA) and butyl 3-(2-thienyl) propenoate (BTA) were comparatively tested. The analysis of the reaction products indicated that both molecules are able to graft onto the iPP backbone by prompt reaction with the macro-radicals formed through H-abstraction from iPP chains, thereby significantly limiting the MW decrease, as the functionalized macro-radicals are stabilized by resonance. Nonetheless, some of iPP macro-radicals can give a parallel chain scission before reacting with the new molecules. In the case of BFA, coupling reactions of the formed macro-radicals can lead to the formation of branched high MW architectures, whereas in the case of the thiophene derivative (BTA) only a partial retaining of polymer chain fragmentation was observed due to the reduction of β-scission.     

Carboxylate clays: A model study for polypropylene/clay nanocomposites

Sodium-montmorillonite was intercalated by carboxylate salts to prepare carboxylate clays. The intercalation of sodium acetate doubles the clay basal spacing and no degradation of the carboxylate clay is noticed in the extrusion temperature range. These carboxylate clays were used to synthesize polypropylene-graft-maleic anhydride (PP-g-MA)/clay nanocomposites. Nanocomposites were also produced by a one-pot process using in situ prepared carboxylate clay. The carboxylate salts within the clay layers partially neutralize the maleic anhydride groups of the PP-g-MA matrix, in situ during the melt compounding. The ionic groups of the partially neutralized polymer offer favourable interactions with the clay, hence reinforcing the interfacial bond between the polymer and the clay and improving the composite properties. The use of carboxylate clay clearly improves the clay dispersion into the PP-g-MA matrix and improves the nanocomposite’s thermal and rheological properties.