Flexible multibody dynamics — An object-oriented approach

An approach to the computer aided analysis of flexible multibody systems using object-oriented programming methods is presented. The aim is to support the rapid generation of specialized programs by providing an open, extensible C++ toolkit. This toolkit contains modules (C++ classes) which allow the declaration and manipulation of multibody components such as joints, bodies and actuators in an intuitive manner. New components (e.g., new finite elements) are easily introduced to extend the toolkit. The equations of motion for a multibody system consisting of these components are formulated by direct application of the principle of virtual work using symbolic techniques. It is possible to use absolute as well as relative coordinates in a problem-dependent manner.The author is now working for the Institut für Mechatronik, IMECH GmbH, Bergwerkstraße, 47445 Moers, Germany     

The microwave heating of three-dimensional blocks: semi-analytical solutions

The microwave heating of three-dimensional blocks, by the transversemagnetic waveguide mode TM₁₁, is considered in a long rectangularwaveguide. The governing equations are the forced heat equationand a steady-state version of Maxwell's equations, while theboundary conditions take into account both convective and radiativeheat loss. Semi-analytical solutions, valid for small thermalabsorptivity, are found using the Galerkin method. The electricalconductivity and the thermal absorptivity are assumed to betemperature dependent, while both the electrical permittivityand magnetic permeability are taken to be constant. Both a quadraticrelation and an Arrhenius-type law are used for the temperaturedependency. As the Arrhenius-type law is not amenable analytically,it is approximated by a rational–cubic function. A multivaluedsteady-state temperature versus power relationship is foundto be possible for both types of temperature dependency. Atthe critical power level thermal runaway occurs when the temperaturejumps from the lower (cool) temperature branch to the upper(hot) temperature branch of the solution. The semi-analyticalsolutions are compared with numerical solutions of the governingequations for various special cases such as the limits of smalland large heat loss at the edges of the block. An excellentcomparison is obtained between the semi-analytical and numericalsolutions, on both temperature branches for the Arrhenius-typelaw. For the quadratic temperature dependency the comparisonis excellent on the low branch but the semi-analytical theorysignificantly underpredicts the temperature on the upper solutionbranch.     

On asymmetry of some convex bodies

We determine Minkowski's measure of asymmetry for convex hulls of a point and some sets for which the asymmetry is known. Some properties of the asymmetry measure are found which may indicate some interesting properties of convex bodies. Received March 1, 2001, and in revised form June 29, 2001. Online publication December 17, 2001.     

Solubilization and Refolding with Simultaneous Purification of Recombinant Human Stem Cell Factor

Recombinant human stem cell factor (rhSCF) was solubilized and renatured from inclusion bodies expressed in Escherichia coli. The effect of both pH and urea on the solubilization of rhSCF inclusion bodies was investigated; the results indicate that the solubilization of rhSCF inclusion bodies was significantly influenced by the pH of the solution employed, and low concentration of urea can drastically improve the solubilization of rhSCF when solubilized by high pH solution. The solubilized rhSCF can be easily refolded with simultaneous purification by ion exchange chromatography (IEC), with a specific activity of 7.8 × 10⁵ IU·mg⁻¹, a purity of 96.3%, and a mass recovery of 43.0%. The presented experimental results show that rhSCF solubilized by high pH solution containing low concentration of urea is easier to be renatured than that solubilized by high concentration of urea, and the IEC refolding method was more efficient than dilution refolding and dialysis refolding for rhSCF. It may have a great potential for large-scale production of rhSCF.     

Generalized intersection bodies are not equivalent

In [A. Koldobsky, A functional analytic approach to intersection bodies, Geom. Funct. Anal. 10 (2000) 1507-1526], A. Koldobsky asked whether two types of generalizations of the notion of an intersection body are in fact equivalent. The structures of these two types of generalized intersection bodies have been studied by the author in [E. Milman, Generalized intersection bodies, J. Funct. Anal. 240 (2) (2006) 530-567], providing substantial evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprising negative answer to this question in a strong sense. This implies the existence of non-trivial non-negative functions in the range of the spherical Radon transform, and the existence of non-trivial spaces which embed in Lp for certain negative values of p.     

Ultrasound for the remediation of contaminated waters with persistent organic pollutants: A short review

The rising amount of persistent organic contaminants released into water reservoirs in the last years became a cause of concern for the industry, academy, and public administration, due to their bioaccumulation, mutagenicity, and photosynthesis reduction. Therefore, the search for processes that efficiently remove such contaminants became of primary importance. In this context, ultrasound (US) is one of the most promising and economically viable alternatives to degrade organic pollutants in varied environments. Whereas the use of other advanced oxidation processes (AOPs), such as Fenton and photocatalysis, has been widely reported for this purpose, only a few papers deal with ultrasound application as a possible AOP. In this review, a general overview of ultrasound is provided, covering the last twenty years. It includes fundamental aspects of ultrasound and applications, individually or combined with other AOPs, to deplete organic pollutants from various classes in an aqueous environment. Finally, the review concludes by indicating that additional research should be conducted worldwide to explore the full potential of ultrasound as a useful AOP.     

A note on subgaussian estimates for linear functionals on convex bodies

We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If is a convex body in with volume one and center of mass at the origin, there exists such that

for all , where is an absolute constant. The proof is based on the study of the -centroid bodies of . Analogous results hold true for general log-concave measures.

     

Features of the turbulent flow around symmetric elongated bluff bodies

The flow fields around three elongated bluff bodies with the same chord-to-thickness ratios but distinct leading and trailing edge details were measured at a Reynolds number of 3×10⁴. These models each represent a case where: leading edge shedding dominates, trailing edge shedding dominates and a case where there is a balance between the two. The results show that the vortex street parameters vary between the models, and in particular, the shedding frequencies are significantly altered by the geometry. However, contrary to the current understanding for shorter bluff bodies, the scale of the recirculation region is found to be similar for each model, even though the shedding frequency changes within the range from 0.15 to 0.24. Also, the base pressure does not follow trends with shedding frequency expected from shorter bluff bodies. A force balance of the recirculation region shows that the near wake of each body is significantly affected by the Reynolds shear stress distribution and the resultant force due to the pressure field in the mean recirculation region. These differences infer that the distinct vortex formation characteristics depend on the state of the trailing edge shear layers. The boundary layers at the trailing edge have been quantified, as have the leading edge separation bubbles, and the marked differences in the wake details are shown to depend on the leading edge separation.     

Stability in the Busemann–Petty and Shephard problems

A comparison problem for volumes of convex bodies asks whether inequalities fK(ξ)?fL(ξ) for all ξ∈Sn−1 imply that Voln(K)?Voln(L), where K, L are convex bodies in Rn, and fK is a certain geometric characteristic of K. By linear stability in comparison problems we mean that there exists a constant c such that for every ε>0, the inequalities fK(ξ)?fL(ξ)+ε for all ξ∈Sn−1 imply that .We prove such results in the settings of the Busemann–Petty and Shephard problems and their generalizations. We consider the section function fK(ξ)=SK(ξ)=Voln−1(K∩ξ^⊥) and the projection function fK(ξ)=PK(ξ)=Voln−1(K|ξ^⊥), where ξ^⊥ is the central hyperplane perpendicular to ξ, and K|ξ^⊥ is the orthogonal projection of K to ξ^⊥. In these two cases we prove linear stability under additional conditions that K is an intersection body or L is a projection body, respectively. Then we consider other functions fK, which allow to remove the additional conditions on the bodies in higher dimensions.