Reconstructing the knee joint mechanism from kinematic data

The interpretation of joint kinematics data in terms of displacements is a product of the type of movement, the measurement technique and the underlying model of the joint implemented in optimization procedures. Kinematic constraints reducing the number of degrees of freedom (DOFs) are expected to compensate for measurement errors and noise, thus, increasing the reproducibility of joint angles. One approach already successfully applied by several groups approximates the healthy human knee joint as a compound hinge joint with minimal varus/valgus rotation. Most of these optimizations involve an orthogonality constraint. This contribution compares the effect of a model with and without orthogonality constraint on the obtained joint rotation angles. For this purpose, knee joint motion is simulated to generate kinematic data without noise and with normally distributed noise of varying size. For small noise the unconstrained model provides more accurate results, whereas for larger noise this is the case for the constrained model. This can be attributed to the shape of the objective function of the unconstrained model near its minimum.     

Propagation of and Maxwellian weighted bounds for derivatives of solutions to the homogeneous elastic Boltzmann equation

We consider the n-dimensional space homogeneous Boltzmann equation for elastic collisions for variable hard potentials with Grad (angular) cutoff. We prove sharp moment inequalities, the propagation of L¹-Maxwellian weighted estimates, and consequently, the propagation L^∞-Maxwellian weighted estimates to all derivatives of the initial value problem associated to the afore mentioned equation. More specifically, we extend to all derivatives of the initial value problem associated to this class of Boltzmann equations corresponding sharp moment (Povzner) inequalities and time propagation of L¹-Maxwellian weighted estimates as originally developed Bobylev [A.V. Bobylev, Moment inequalities for the Boltzmann equation and applications to spatially homogeneous problems, J. Statist. Phys. 88 (1997) 1183–1214] in the case of hard spheres in 3 dimensions. To achieve this goal we implement the program presented in Bobylev–Gamba–Panferov [A.V. Bobylev, I.M. Gamba, V. Panferov, Moment inequalities and high-energy tails for Boltzmann equation with inelastic interactions, J. Statist. Phys. 116 (5–6) (2004) 1651–1682], which includes a full analysis of the moments by means of sharp moment inequalities and the control of L¹-exponential bounds, in the case of stationary states for different inelastic Boltzmann related problems with ‘heating’ sources where high energy tail decay rates depend on the inelasticity coefficient and the type of ‘heating’ source. More recently, this work was extended to variable hard potentials with angular cutoff by Gamba–Panferov–Villani [I.M. Gamba, V. Panferov, C. Villani, Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation, ARMA (2008), in press] in the elastic case collision case where the L¹-Maxwellian weighted norm was shown to propagate if initial states have such property. In addition, we also extend to all derivatives the propagation of L^∞-Maxwellian weighted estimates, proven in [I.M. Gamba, V. Panferov, C. Villani, Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation, ARMA (2008), in press], to solutions of the initial value problem to the Boltzmann equations for elastic collisions for variable hard potentials with Grad (angular) cutoff.     

Positive Solutions to Singular Second and Third Order Differential Equations for Quantum Fluids

We analyze a quantum trajectory model given by a steady-state hydrodynamic system for quantum fluids with positive constant temperature in bounded domains for arbitrary large data. The momentum equation can be written as a dispersive third-order equation for the particle density where viscous effects are incorporated. The phenomena that admit positivity of the solutions are studied. The cases, one space dimensional dispersive or non-dispersive, viscous or non-viscous, are thoroughly analyzed with respect to positivity and existence or non-existence of solutions, all depending on the constitutive relation for the pressure law. We distinguish between isothermal (linear) and isentropic (power law) pressure functions of the density. It is proved that in the dispersive, non-viscous model, a classical positive solution only exists for “small” (positive) particle current densities, both for the isentropic and isothermal case. Uniqueness is also shown in the isentropic subsonic case, when the pressure law is strictly convex. However, we prove that no weak isentropic solution can exist for “large” current densities. The dispersive, viscous problem admits a classical positive solution for all current densities, both for the isentropic and isothermal case, with an “ultra-diffusion” condition. The proofs are based on a reformulation of the equations as a singular elliptic second-order problem and on a variant of the Stampacchia truncation technique. Some of the results are extended to general third-order equations in any space dimension. Accepted July 1, 2000?Published online February 14, 2001     

On the existence of inequivalent quasideterministic domains

In the framework of the history approach to quantum mechanics and, in particular, of the formulation of Gell-Mann and Hartle, the question of the existence of inequivalent decoherent sets of histories is reconsidered. A simple but acceptably realistic model of the dynamics of the universe is proposed and a particular set of histories is shown to be decoherent. By suitable tranformations of this set, a family of sets of histories is then generated, such that the sets, first, are decoherent on the basis of the assumed dynamics of the universe and, secondly, arc certainly inequivalent, apart from trivial special cases. Finally, the original set of histories is refined to get a model of the usual quasiclassical domain and it is shown that, applying to it the previously considered transformations, a family of sets of histories is obtained which share typical properties of the usual quasiclassical domain.Supported in part by the Ministero dell'Università e della Ricerca Scientifica e Tecnologica and by the Istituto Nazionale di Fisica Nucleare.     

Side‐chain supramolecular polymers with induced supramolecular chirality through H‐bonding interactions

Side‐chain supramolecular polymers that show columnar mesomorphism have been prepared through H‐bonding interactions between a polyvinylpyridine polymer as H‐acceptor and different H‐donors derived from benzoic acid. These compounds have been designed according to a promesogenic structure, that is, either disk‐like or banana‐like, to promote stacking and therefore the formation of columnar arrangements. IR studies confirmed the formation of H‐bonds and demonstrated that the H‐bond intensity decreases upon increasing temperature. The mesophase organizations were studied by polarized optical microscopy, differential scanning calorimetry, and X‐ray diffraction. Associations containing poly‐3‐methyl‐4‐vinylpyridine showed supramolecular optical activity, as evidenced by circular dichroism studies on thin films. It is proposed that these supramolecular polymers adopt a helical structure that can be biased toward a given handedness by virtue of the configuration of the stereogenic centers in the peripheral tails of the acids. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 5528–5541, 2008     

Bioreduction of ionic mercury from wastewater in a fixed-bed bioreactor with activated carbon

Wide industrial use of mercury led to significant mercury pollution of the environment. It requires development of cleanup technologies which would allow treating large volumes of mercury contaminated water in a cost effective and environmentally friendly way. A novel bio-technology, developed from laboratory to industrial scale in Germany at HZI (former GBF), is based on enzymatic reduction of highly toxic Hg(II) to water-insoluble and relatively non-toxic Hg(0) using live mercury resistant bacteria immobilized on a porous carrier material in a fixed-bed bioreactor. Improvement of the original method was based on the use of activated carbon as a carrier for microorganisms and an adsorbent for mercury. Such integration of the process should increase the technology efficiency. In order to compare different carrier materials, activated carbon and pumice stones were used. The strain Pseudomonas putida was immobilized in bioreactors continuously fed with solutions of HgCl₂ enriched with nutrients. Simultaneously, experiments in two more reactors were run in the absence of microorganisms to investigate the influence of nutrients on the adsorption process. In the bioreactor with activated carbon, the outlet mercury concentration was approximately 50 % of that supplied with pumice. It may be concluded that the use of activated carbon in a fixed-bed bioreactor enables improvement of the technology by process integration. Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May 2007.