Oscillations, SE(2)-snakes and motion control: a study of the Roller Racer

This paper is concerned with the problem of motion generation via cyclic variations in selected degrees of freedom (usually referred to as shape variables) in mechanical systems subject to non-holonomic constraints (here the classical system of a disc rolling without sliding on a flat surface). In earlier work, we identified an interesting class of such problems arising in the setting of Lie groups, and investigated these under a hypothesis on constraints, that naturally led to a purely kinematic approach. In the present work, the hypothesis on constraints does not hold, and as a consequence, it is necessary to take into account certain dynamical phenomena. Specifically we concern ourselves with the group SE (2) of rigid motions in the plane and a concrete mechanical realization dubbed the 2-node, 1-module SE (2)snake. In a restricted version, it is also known as the Roller Racer (a patented ride/ toy). Based on the work of Bloch, Krishnaprasad, Marsden and Murray, one recognizes in the example of this paper a balance law called the momentum equation, which is a direct consequence of the interaction of the SE (2)-symmetry of the problem with the constraints. The systematic use of this type of balance law results in certain structures in the example of this paper. We exploit these structures to demonstrate that the single shape freedom in this problem can be cyclically varied to produce a rich variety of motions of the SE (2)-snake. In their study of the snakeboard, a patented modification of the skateboard that also admits the group SE (2) as a symmetry group, Lewis, Ostrowski, Burdick and Murray exploited the same type of balance law as that discussed here to generate motions. A key difference, however, is that, in the present paper, we have only one control variable and thus controllability considerations become somewhat more delicate. In the present paper, we give a self-contained treatment of the geometry, mechanics and motion control of the Roller Racer.     

Banded and tapered estimates for autocovariance matrices and the linear process bootstrap

We address the problem of estimating the autocovariance matrix of a stationary process. Under short range dependence assumptions, convergence rates are established for a gradually tapered version of the sample autocovariance matrix and for its inverse. The proposed estimator is formed by leaving the main diagonals of the sample autocovariance matrix intact while gradually down‐weighting off‐diagonal entries towards zero. In addition, we show the same convergence rates hold for a positive definite version of the estimator, and we introduce a new approach for selecting the banding parameter. The new matrix estimator is shown to perform well theoretically and in simulation studies. As an application, we introduce a new resampling scheme for stationary processes termed the linear process bootstrap (LPB). The LPB is shown to be asymptotically valid for the sample mean and related statistics. The effectiveness of the proposed methods are demonstrated in a simulation study.     

Hydrolytic Depolymerization of PET in a Microwave Reactor

Recycling of PET was examined using hydrolytic depolymerization in an alkaline solution under microwave irradiation. The reaction was carried out in a sealed microwave reactor in which the pressure and temperature were controlled and recorded. The main products were the monomers TPA and EG. The effect of reaction temperature, time, amount of PET and alkaline concentration on the degree of PET depolymerization and TPA recovery was investigated. Microwave irradiation was found to reduce the time needed to achieve a specific degradation of PET significantly, with almost complete depolymerization occurring in 30 min at 180 °C and only 46 W of microwave power. Using a phase transfer catalyst (TOMAB) resulted in the same amount of unreacted PET but at significantly lower depolymerization temperatures.

     

Removal of some organic pollutants in water employing ceramic membranes impregnated with cross-linked silylated dendritic and cyclodextrin polymers

Triethoxysilylated derivatives of poly(propylene imine) dendrimer, polyethylene imine and polyglycerol hyperbranched polymers and beta-cyclodextrin have been synthesized and characterized. These compounds impregnated ceramic membranes made from Al(2)O(3), SiC and TiO(2) and subsequently sol-gel reaction led to their polymerization and chemical bond formation with the ceramic substrates. The resulting organic-inorganic filters were tested for the removal of a variety of organic pollutants from water. They were found to remove of polycyclic aromatic hydrocarbons (up to 99%), of monocyclic aromatic hydrocarbons (up to 93%), trihalogen methanes (up to 81%), pesticides (up to 43%) and methyl-tert-butyl ether (up to 46%).     

Evaluation of the antiradical and reducing properties of selected Greek white wines: correlation with polyphenolic composition

The total hydroxycinnamate (THC) and total flavanol (TF) contents were determined in 26 selected Greek white wines of ‘Appellation of Origin of High Quality’ using well‐established spectrophotometric methodology. Furthermore, two parameters related to the antioxidant capacity of wines, the antiradical activity (A_AR) and the reducing power (P_R), were also determined using the stable DPPH· radical and a ferric reducing power assay respectively. THC content varied from 64.4 to 197.1 mg l^?1 chlorogenic acid equivalents (CGAE), whereas TF content exhibited larger variation, ranging from 3.3 to 205.3 mg l^?1 catechin equivalents (CTE). A_AR and P_R were found to range from 0.47 to 0.60 mM Trolox equivalents (TRE) and from 0.32 to 2.05 mM quercetin equivalents (QE) respectively. Regression analysis at 95% significance level indicated that reducing effects are likely to be exerted by the flavanol fraction (SF < 0.05), as opposed to antiradical efficiency which is primarily affected by the sum of THC and TF contents (SF < 0.05), suggesting that synergistic phenomena account for the overall antioxidant status of white wines. © 2002 Society of Chemical Industry     

Development of a comprehensive mathematical model for free radical suspension polymerization of methyl methacrylate

In this work a detailed mathematical model for free radical suspension polymerization of methyl methacrylate (MMA) in water is developed. This model is based on sound principles such as the free volume theory to account for the diffusion limited reactions in suspension polymerization. Additionally, the complex polymerization kinetics process of the aqueous suspension polymerization of MMA is studied as a one‐dimensional numerical experiment. For this purpose, the polymerization process is modeled as a moving boundary mass transfer problem coupled with polymerization reactions. The Galerkin finite element method is used to simultaneously solve the nonlinear governing equations. The model predictions for conversion and average molecular weights vs. time were found to be in close agreement with laboratory data. It is believed that this work, as it provides fundamental understanding of the process, it might contribute to a more rational design of polymerization reactors. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers     

Mode of action of a minor xylanase from Thermoascus aurantiacus on polysaccharides and model substrates

The mode of action of a minor xylanase on a variety of polysaccharides and model substrates was investigated. The enzyme was excreted by Thermoascus aurantiacus grown in solid state fermentation (SSF). The purified enzyme had a molecular mass of 33,000. Thin layer chromatography analysis showed that the endoxylanase liberated short fragments from polysaccharides. The enzyme hydrolysed aryl-β- -cellobioside and the chromogenic (fluorogenic) 4-methylumbelliferyl-β-glycosides of xylobiose (MeUmbXyl₂) and xylotriose (MeUmbXyl₃) at the agluconic linkage. The results suggested that the endoxylanase belonged to family 10.     

On composite likelihood estimation of a multivariate INAR(1) model

In several circumstances the collected data are counts observed in different time points, while the counts at each time point are correlated. Current models are able to account for serial correlation but usually fail to account for cross‐correlation. Motivated by the lack of appropriate tools for handling such type of data, we define a multivariate integer‐valued autoregressive process of order 1 (MINAR(1)) and examine its basic statistical properties. Apart from the general specification of the MINAR(1) process, we also study two specific parametric cases that arise under the assumptions of a multivariate Poisson and a multivariate negative binomial distribution for the innovations of the process. To overcome the computational difficulties of the maximum likelihood approach we suggest the method of composite likelihood. The performance of the two methods of estimation, that is, maximum likelihood and composite likelihood, is compared through a small simulation experiment. Extensions of the time‐invariant model to a regression model are also discussed. The proposed model is applied to a trivariate data series related to daily traffic accidents in three areas in the Netherlands.