Modelling,simulation, animation,and real-time control (MoSART) for a class of electromechanical systems: a system-theoretic approach

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of ‘cart-pendulum’ electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts through computer-aided analysis, design, graphical visualization, and 3D animation. Referred to as Cart-Pendulum Control3D-Lab1Control3D-Lab-short for control 3D animation laboratory. The author to whom correspondence should be addressed., the environment is based on Microsoft Windows/Visual C++/Direct-3D and MATLAB/Simulink2MATLAB and Simulant are trademarks of The Masterworks, Inc.. Pull-down menus provide access to systems/models/control laws, exogenous signals, parameters, animation models and visual indicators, a suite of (easy-to-modify) Simulant diagrams containing models and control laws, MATLAB m-files for detailed analysis and design, and detailed documentation for each of the above. Three blocks enable animation, joystick inputs, and real-time animation within Simulant. Examples are presented to illustrate the utility of the environment as a valuable tool for analysing/visualizing the above class of electromechanical systems and for enhancing mathematics instruction.     

The Saffman-Taylor problem for an extremely shear-thinning fluid

We consider a steady flow driven by pushing a finger of gasinto a highly shear-thinning power-law fluid, with exponentn, in a Hele-Shaw channel. We formulate the problem in termsof the streamfunction , which satisfies the p-Laplacian equation (with ), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit.We take a Legendre transform of the free-boundary problem for, which reduces it to a linear problem on a fixed domain. The solution to this problem is foundby using matched asymptotic expansions and the resulting shapeof the finger deduced (being, to leading order, a semi-infinitestrip). The nonlinear problem for the streamfunction is alsotreated using matched asymptotic expansion in the physical plane.The finger-width selection problem is briefly discussed in termsof our results.     

Structural anisotropy study by resonance Raman scattering in nematics with different dyes

Ionic liquid crystals based on congruent ion pairs composed of mesogenic cations and anions of similar shape provide an attractive tool for the tuning of mesophase properties. Here, the effect of the number and symmetry of lipophilic side chains and the type of head group on the phase type and thermal mesophase properties was probed by the synthesis and investigation of two series of novel guanidinium and imidazolium sulphonates and compared with the corresponding iodides. Their mesomorphic properties were examined via differential scanning calorimetry, optical polarising microscopy and X-ray diffraction. While derivatives bearing only one alkoxy chain in either cation or anion with up to three alkoxy chains in total within the ion pairs display smectic A mesophases, hexagonal columnar mesophases were observed for all other compounds with four or five alkoxy chains totally irrespective of the head group. However, with increasing steric bulk, i.e. with a total of six alkoxy chains, the symmetry of the aryl moiety in the anion as well as the type of head group becomes relevant, resulting in hexagonal columnar or plastic phases for guanidinium sulphonates with symmetrical anions, while those with unsymmetrical anions were non-mesomorphic. In contrast, the corresponding imidazolium sulphonates displayed cubic phases for the combinations of symmetrical cation/symmetrical anion and symmetrical cation/unsymmetrical anion. If both ions are unsymmetrically substituted, the imidazolium sulphonate displayed a hexagonal columnar phase. The results further demonstrate the utility of the congruent ion pairs for tailor-made ionic liquid crystals.     

HUMIC MACROMOLECULES IN NATURAL WATERS

Abstract

Humic substances are the major organic constituents of soils and sediments. They also occur in small concentrations in natural surface waters and groundwaters. They form through the breakdown of plant and animal tissues by chemical and biological processes that tend to produce complex chemical structures that are more stable than the original material from which they were derived. One of the more important characteristics of humic substances is their ability to form water-soluble and water-insoluble complexes with metal ions and hydrous oxides and to interact with clay minerals and various organic compounds such as alkanes, fatty acids, and toxic organic substances such as pesticides.