A bound on the strain energy for the traction problem in finite elasticity with localized non-zero surface data

For the boundary value problem in finite elasticity in which nonzero tractions are given on a connected subdomain of the boundary, the rest of the boundary is stress-free, and there are no body forces, a bound is obtained for the strain energy in terms of the L ₂ integral norm of the surface tractions with the constant involved depending only upon and the material constants.The result is obtained in the context of finite elasticity under the assumptions that the unstressed body occupies a convex domain and the displacement gradients are sufficiently small. In the context of the linear theory, the same result is obtained without these assumptions.

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Zusammenfassung Wir betrachten ein Randwertproblem in der nichtlinearen Elastizität in dem nur ein zusammenhängendes Teilgebiet der Randfläche belastet ist, sonst aber keine Randbelastung oder Körperkräfte vorhanden sind. Eine Schranke für die Verzerrungsenergie wird mittels der L ₂ Integralnorme der Randbelastung hergeleitet, wobei die auftretende Konstante nur von dem Teilgebiet und von den Eigenschaften des Materials abhängig ist.Das Ergebnis gilt für die nichtlinearen Elastizität, unter den Vorraussetzungen dass das unbelastete Material ein konvexes Gebiet besetzt und dass die Verschiebungsgradiente hinreichend klein sind. Das gleiche Ergebnis gilt in der linearen Elastizität ohne diese Vorraussetzungen.

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The second author was a visitor at Georgia Institute of Technology, School of Mathematics, at the time that the revised version was prepared.     

Desulfurization of mercaptans to hydrocarbons by carbon monoxide and water in the presence of cobalt carbonyl

Benzylic mercaptans and thiophenols undergo desulfurization when exposed to carbon monoxide and water, with cobalt carbonyl as the catalyst; carbonyl sulfide is evolved in these reactions.     

Comment on isospin mixing in nuclei

The central collisions of 70 GeV/c protons with Ag, Br and Pb nuclei have been studied, with the help of BR-2 photoemulsion and emulsion of the same constitution loaded with Pb nuclei. It is shown that the average multiplicity of produced particles (s-particles) increases slowly with increasing the atomic weight of the target nucleus. The ratio of the average multiplicity for these particles to the average charged particle multiplicity for protonproton interactions equals 3.2 forp-Ag, Br and 3.5 forp-Pb. The average multiplicities of particles from nuclear disintegration with energies for protons from 26 up to 400 MeV (g-particles) are 14.2±0.8 forp-Ag, Br and 23.0±1.0 forp-Pb corresponding to the emission of about half of all nucleons from the nucleus at the first rapid stage of interaction. The difference of thes-particle pseudorapidity distributions forp-Ag, Br, Pb andp-p interactions at pseudorapidities larger than 4.2 can be explained by successive interactions of the incident proton with nucleus nucleons.     

Establishment and implications of a characterization method for magnetic nanoparticle using cell tracking velocimetry and magnetic susceptibility modified solutions

Magnetic micro and nanoparticles conjugated to affinity labels have become a significant, commercial reagent. It has been demonstrated that the performance of cell separation systems using magnetic labels is a function of the magnitude of the magnetic force that can be generated through labeling. This magnetic force is proportional to the number of magnetic particles bound to the cell, the magnetic energy gradient, and the particle-field interaction parameter. This particle-field interaction parameter, which is the product of the relative volumetric, magnetic susceptibility and the volume of the micro or nanoparticle, is a fundamental parameter which can be used to characterize the magnetic particles. An experimental technique is presented which measures the volumetric magnetic susceptibility of particles through the use of susceptibility modified solutions and an experimental instrument, Cell Tracking Velocimetry, CTV. Experimental studies were conducted on polystyrene microspheres alone and those bound to four different magnetic nanoparticles. The experimentally determined values of the magnetic susceptibility of the polystyrene microspheres are consistent with values found from literature. Consequently, magnetic susceptibility measurements of these polystyrene microspheres bound with the magnetic nanoparticles combined with particle size measurements using commercial dynamic light scattering instrument allowed estimates of the particle-field interaction parameter to be made for four commercial, magnetic nanoparticles. The value found for MACS beads is close to what is reported from an independent study. The values for MACS beads and Imag beads are found to agree with what is observed from experiments. Finally, an experimental demonstration of the impact that differences in this field interaction parameter has on the labeling of human lymphocytes is presented.     

Fluctuation and synchronization of gait intervals and gait force profiles distinguish stages of Parkinson's disease

We study the effects of Parkinson's disease (PD) on the long-term fluctuation and phase synchronization properties of gait timing (series of interstride intervals) as well as gait force profiles (series characterizing the morphological changes between the steps). We find that the fluctuations in the gait timing are significantly larger for PD patients and early PD patients, who were not treated yet with medication, compared to age-matched healthy controls. Simultaneously, the long-term correlations and the phase synchronization of right and left leg are significantly reduced in both types of PD patients. Surprisingly, long-term correlations of the gait force profiles are relatively weak for treated PD patients and healthy controls, while they are significantly larger for early PD patients. The results support the idea that timing and morphology of recordings obtained from a complex system can contain complementary information.     

Surface instability of a nuclear fermi liquid drop

A mechanical instability of an incompressible Fermi liquid drop with respect to surface distortions is considered. It is shown that the Fermi surface distortion (FSD) reduces the instability-growth rate for surface fluctuations due to its effects on both the viscosity and the increase in the stiffness coefficient. The dependence of the limiting temperature T_lim on the mass number and the multipolarity of the nuclear-surface distortion is calculated. It is shown that T_lim is not influenced by the FSD effect.     

Scale-free networks on lattices

We suggest a method for embedding scale-free networks, with degree distribution Pk approximately k(-lambda), in regular Euclidean lattices accounting for geographical properties. The embedding is driven by a natural constraint of minimization of the total length of the links in the system. We find that all networks with lambda>2 can be successfully embedded up to a (Euclidean) distance xi which can be made as large as desired upon the changing of an external parameter. Clusters of successive chemical shells are found to be compact (the fractal dimension is df=d), while the dimension of the shortest path between any two sites is smaller than 1: dmin=(lambda-2)/(lambda-1-1/d), contrary to all other known examples of fractals and disordered lattices.