Self-diffusion in remodeling and growth

Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture.     

Crux of the clock paradox

The central riddle or crux of the relativistic clock paradox is studied with methods that are familiar from thermodynamics and hamiltonian mechanics, but which are not usually used, as here, to relate theory to phenomenology in the context of relativistic chronometry. Contrasting ramifications of the special and general theory are considered.     

Kinetics and mechanism of the proton transfer to CpFe(dppe)H: absence of a direct protonation at the metal site

The reaction between CpFe(dppe)H and a number of different proton donors (2-fluoroethanol, MFE; 2,2,2-trifluoroethanol, TFE; hexafluoro-2-propanol, HFIP; perfluoro-tert-butyl alcohol, PFTB; and trifluoroacetic acid, TFA) has been investigated spectroscopically by variable-temperature infrared, UV-visible, and NMR spectroscopy, and has been measured kinetically by the stopped-flow technique with UV-visible detection. The low-temperature IR study shows the establishment of hydrogen-bonding interactions which involve the hydride ligand as the proton accepting site. This investigation quantifies the thermodynamics of the hydrogen-bonding interaction and the basicity factor (E(j)) of the hydride complex. All techniques agree in indicating an equilibration process, after the immediate hydrogen-bond formation, between the hydride complex and an intermediate dihydrogen complex, [CpFe(dppe)(H(2))](+). The equilibrium is shifted toward the dihydrogen complex to a greater extent for the stronger alcohols and for higher alcohol/Fe ratios. The observed equilibration rate constant is linearly dependent on the alcohol concentration, in agreement with the involvement of two alcohol molecules and the formation of a homoconjugate pair. The rate constant increases with the acidity of the proton donor (TFE < HFIP < PFTB < TFA). The rate of the subsequent irreversible isomerization leading to the classical dihydride complex, [CpFe(dppe)H(2)](+), is first order, and the rate constant does not depend on the proton donor nature. The reaction continues, if conducted in CH(2)Cl(2), with a third, slower step leading to the paramagnetic [CpFe(dppe)Cl](+) product. The kinetic data are in accord with an isomerization mechanism consisting of an intramolecular reorganization, leading in one step from the dihydrogen complex to the classical dihydride species, and disagree with the occurrence of a proton-transfer process at the metal site.     

An apparatus for continuous separation of macromolecules by combined electrophoresis and gel filtration

Summary An apparatus for continuous separation of soluble and particulate macromolecules, and of other electrically charged particles by combined electrophoresis and gel filtration, is described. The two principles, electrophoresis and gel filtration, which operate simultaneously at right angles, enable separation between the various macromelecules, depending upon differences in electric charge and molecular wight. The sample to be fractionated is fed continuously into the apparatus while the separated macromolecules reaching the distal end of the instrument are collected at the outlet ports. Data for a continuous fractionation of human plasma proteins using the instrument are given.     

Post-self-assembly cross-linking of molecular nanofibers for oscillatory hydrogels

After a polymerizable hydrogelator self-assembles in water to form molecular nanofibers, post-self-assembly cross-linking allows the catalyst of the Belousov-Zhabotinsky (BZ) reaction to be attached to the nanofibers, resulting in a hydrogel that exhibits concentration oscillations, spiral waves, and concentric waves. In addition to the first report of the observation of BZ spiral waves in a hydrogel that covalently integrates the catalyst, we suggest a new approach to developing active soft materials as chemical oscillators and for exploring the correlation between molecular structure and far-from-equilibrium dynamics.     

Existence and Properties of p-tupling Fixed Points

We prove the existence of fixed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity, univalence, behavior as r tends to infinity. Received: 10 April 2000 / Accepted: 7 July 2000     

Every minor-closed property of sparse graphs is testable

Suppose G is a graph of bounded degree d, and one needs to remove ?n of its edges in order to make it planar. We show that in this case the statistics of local neighborhoods around vertices of G is far from the statistics of local neighborhoods around vertices of any planar graph G^′. In fact, a similar result is proved for any minor-closed property of bounded degree graphs.The main motivation of the above result comes from theoretical computer-science. Using our main result we infer that for any minor-closed property P, there is a constant time algorithm for detecting if a graph is “far” from satisfying P. This, in particular, answers an open problem of Goldreich and Ron [STOC 1997] [20], who asked if such an algorithm exists when P is the graph property of being planar. The proof combines results from the theory of graph minors with results on convergent sequences of sparse graphs, which rely on martingale arguments.     

A note on a boundary condition for spouted beds

The boundary condition, zero solids pressure at the top of a particle bed of maximum spoutable height, Hm, is shown to eliminate any resort to empiricism in the derivation of the fluid velocity in the annulus of a spouted bed for which both viscous and inertial effects are taken into account. The same boundary condition fails when applied to a spouted bed for which the bed height H 〈 Hm, especially when H 〈 0.8Hm.     

Detection of monobasic phosphorus acid esters by conversion to cholinesterase inhibitors

Many monobasic acids of quinquevalent phosphorus form cholinesterase inhibitors when exposed to ketene. Based upon this finding, a sensitive test to detect the presence of these compounds on filter paper has been developed. Seventeen out of nineteen of these acids tested gave positive results. Negative results obtained with the remaining two are attributable to steric factors or to the high hydrolysis rate of the acetylated product. Only one of eighteen phosphorus compounds other than the monobasic acids examined, namely n-butylphosphonic acid, gave a positive test; an explanation is offered to account for this exception.     

Laser cooling of solids [Laser Photon. Rev. 3, No. 1–2, 67–84 (2009)]

Fig. 7b and Figs. 14a and b in the paper published in Laser Photon. Rev. 3 , 67–84 have not been referenced completely. Please find the correct figure captions here.