Scaling dynamics for solvable coagulation equations with dust and gel

We study limiting behavior of rescaled size distributions that evolve by Smoluchowski's rate equations for coagulation, with rate kernel K=2, x+y or xy. We find that the dynamics naturally extend to probability distributions on the half-line with zero and infinity appended, representing populations of clusters of zero and infinite size. The “scaling attractor” (set of subsequential limits) is compact and has a Levy-Khintchine-type representation that linearizes the dynamics and allows one to establish several signatures of chaos. In particular, for any given solution trajectory, there is a dense family of initial distributions (with the same initial tail) that yield scaling trajectories that shadow the given one for all time. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Short peptide-based cross-β amyloids exploit dual residues for phosphoesterase like activity

Herein, we report that short peptides are capable of exploiting their anti-parallel registry to access cross-β stacks to expose more than one catalytic residue, exhibiting the traits of advanced binding pockets of enzymes. Binding pockets decorated with more than one catalytic residue facilitate substrate binding and process kinetically unfavourable chemical transformations. The solvent-exposed guanidinium and imidazole moieties on the cross-β microphases synergistically bind to polarise and hydrolyse diverse kinetically stable model substrates of nucleases and phosphatase. Mutation of either histidine or arginine results in a drastic decline in the rate of hydrolysis. These results not only support the argument of short amyloid peptides as the earliest protein folds but also suggest their interactions with nucleic acid congeners, foreshadowing the mutualistic biopolymer relationships that fueled the chemical emergence of life.

Amyloid based short peptide assemblies use antiparallel registry to expose multiple catalytic residues to bind and cleave kinetically stable phosphoester bonds of nucleic acid congeners, foreshadowing interactions of protein folds with nucleic acids.     

Solubility products,thermodynamic functions and stability constants for the praseodymium and ytterbium fluoride — Water systems

The solubility products and thermodynamic functions for the praseodymium and ytterbium fluoride-water systems have been measured using different analytical techniques for comparison among the measured values as well as with values reported in literature. Although there is not much difference among our values obtained by potentiometric, conductometric and radiometric methods, the values for PrF₃ disagree with at least two of the reported values. The effects of precipitant, aging of the precipitate and pH of the saturated solutions on the solubility product were studied and found to be significant. The standard enthalpy and free energy changes for the dissolution of both fluorides were found to be positive although the enthalpy for YbF₃ is about twice as high as that for PrF₃. The standard entropy change for PrF₃ is negative, but that for YbF₃ is positive. The overall stability constants for the mono- and difluoride complexes of both Pr and Yb have also been measured potentiometrically using a simplified approach.     

Influence of iodine on the electrical properties of magnesium phthalocyanines thin film devices

The influence of iodine on the electrical properties of sandwich structures of magnesium phthalocyanine (Mg Pc) thin films with gold and aluminium electrodes has been investigated. The various electrical properties and different electrical parameters of the iodine-doped Mg Pc thin film devices have been estimated and compared with the values of normal Mg Pc devices from the analysis of the current-voltage characteristics. Generally samples showed an asymmetric conductivity both under forward and reverse bias. From our study we found that iodine doped Mg Pc films showed an enhanced electrical conductivity of nearly ten times that of typical Mg Pc. At low voltages the films showed an ohmic conduction with a hole concentration of P₀ = 6.34 × 10¹⁸ m⁻³ and hole mobility μ = 9.16 × 10⁻⁵ m ² V⁻¹ s⁻¹, whereas at higher voltage levels the conduction is dominated by space charged limited conduction (SCLC) with a discrete trapping level of 1.33 × 10²² m⁻³ at 0.63 eV above the valance band edge. The ratio of the free charges to trapped charges (trapping factor) for the doped samples was found to be 1.07 × 10⁻⁷. Furthermore the reverse conduction mechanisms have also been investigated. From the current limitations in the reverse condition a strong rectifying behaviour was evident which was attributed to Poole-Frankel emission with a field-lowering coefficient of value 2.24 × 10⁻⁵ eV m^1/2 V^−1/2.     

Universality Classes in Burgers Turbulence

We establish necessary and sufficient conditions for the shock statistics to approach self-similar form in Burgers turbulence with Lévy process initial data. The proof relies upon an elegant closure theorem of Bertoin and Carraro and Duchon that reduces the study of shock statistics to Smoluchowski’s coagulation equation with additive kernel, and upon our previous characterization of the domains of attraction of self-similar solutions for this equation.     

Approach to self‐similarity in Smoluchowski's coagulation equations

We consider the approach to self‐similarity (or dynamical scaling) in Smoluchowski's equations of coagulation for the solvable kernels K(x, y) = 2, x + y and xy. In addition to the known self‐similar solutions with exponential tails, there are one‐parameter families of solutions with algebraic decay, whose form is related to heavy‐tailed distributions well‐known in probability theory. For K = 2 the size distribution is Mittag‐Leffler, and for K = x + y and K = xy it is a power‐law rescaling of a maximally skewed α‐stable Lévy distribution. We characterize completely the domains of attraction of all self‐similar solutions under weak convergence of measures. Our results are analogous to the classical characterization of stable distributions in probability theory. The proofs are simple, relying on the Laplace transform and a fundamental rigidity lemma for scaling limits. © 2003 Wiley Periodicals, Inc.     

Studies on the electrical conductivity, optical absorption and x-ray diffraction in bismuth thin film

Spectroscopically pure bismuth is evaporated onto glass substrates at different substrate temperature using a Hind Hivac coating plant. The electrical conductivity of bismuth thin films, prepared at different substrate temperatures is measured and thermal activation energy is evaluated. From the recorded optical absorption spectrum in the ultraviolet and visible regions optical band gapE _g is determined. X-ray diffractograms are recorded and lattice parameters are determined.     

Small angle neutron scattering from micellar solutions of triton X-100

Micellar solutions of non-ionic surfactant triton X-100 (8% by weight) show phase separation at cloud pointT _cp ～ 335 K. This paper reports results of small angle neutron scattering (SANS) experiments from this solution as a function of temperature between 298 and 332 K. The range of wave-vector transferQ, covered in these experiments is from 0.02 to 0.15 Å^?1. It is seen that as one approachesT _cp, the neutron scattering cross section diverges in the region of lowQ (<0.06 Å^?1) while it is independent of temperature in region of largeQ(>0.06 Å^?1). We believe that the divergence of scattering at lowQ with an increase in temperature is because of changes in the structure factorS(Q) of the solution. The measured distributions have been analyzed using four different models for inter-micellar potential. The models used to calculate the structure factorS(Q) are (1) mean spherical approximation (MSA) with Yukawa tail for attractive potential, (2) MSA with an attractive square well potential, (3) random phase approximation (RPA) with an attractive square-well potential and (4) Sticky hard sphere model (attractive square-well potential with Percus-Yevick approximation). The strengths of the attractive potential required to fit the SANS data are (?6.6 to ? 14.4)/kt for model (1), (? 6.6 to ? 15.0)/kt for model (2), (? 3.8 to ? 7.3)/k _B T for model (3) and (?2 to ?2.7)/kt for model (4). On the basis of reasonableness of the derived strength of the potential near the phase separation temperature and its relative temperature dependence, it is concluded that present data favour the Sticky hard sphere model.