Comments on the Martingale Convergence Theorem Technical Report No. 21

Proofs of generality of martingale convergence theore

Spectroscopic studies on the denaturation of papain solubilized and triton X-100 - solubilized glucoamylase from rabbit small intestine

Intestinal brush border proteins consist of an enzymatically active hydrophilic moiety attached to a hydrophobic tail. Papain dissociates the hydrophilic part by cleaving off the hydrophobic tail, whereas the detergentTriton X-100 solubilizes the whole molecule. Denaturation by 8 M urea or 4 M guanidinium chloride does not alter the structure of the papain-solubilized enzyme. An appreciable alteration of the structure of detergent-solubilized enzyme was observed on denaturation. The difference spectra of Triton X-100 (1%)-solubilized enzyme and its urea denatured form shifts and intensifies, with increase in the concentration of the denaturant with an isobestic point at 252 nm. A new band at 280 nm also appears at 4 M urea concentration. Papain-solubilized glucoamylase has an ∝ -helical conformation in solution unlike the detergentsolubilized fraction. An elongated structure for the papain solubilized enzyme is inferred from the urea denaturation studies and from molecular weight determinations

Magnetoelastic effects in Jahn-Teller distorted CrF2_2 and CuF2_2 studied by neutron powder diffraction

We have studied the temperature dependence of crystal and magnetic structures of the Jahn-Teller distorted transition metal difluorides CrF$_2$ and CuF$_2$ by neutron powder diffraction in the temperature range 2-280 K. The lattice parameters and the unit cell volume show magnetoelastic effects below the N\'eel temperature. The lattice strain due to the magnetostriction effect couples with the square of the order parameter of the antiferromagnetic phase transition. We also investigated the temperature dependence of the Jahn-Teller distortion which does not show any significant effect at the antiferromagnetic phase transition but increases linearly with increasing temperature for CrF$_2$ and remains almost independent of temperature in CuF$_2$. The magnitude of magnetovolume effect seems to increase with the low temperature saturated magnetic moment of the transition metal ions but the correlation is not at all perfect

Combining Molecular Dynamics with Lattice-Boltzmann: A Hybrid Method for the Simulation of (Charged) Colloidal Systems

We present a hybrid method for the simulation of colloidal systems, that combines molecular dynamics (MD) with the Lattice-Boltzmann (LB) scheme. The LB method is used as a model for the solvent in order to take into account the hydrodynamic mass and momentum transport through the solvent. The colloidal particles are propagated via MD and they are coupled to the LB fluid by viscous forces. With respect to the LB fluid, the colloids are represented by uniformly distributed points on a sphere. Each such point (with a velocity V(r) at any off-lattice position r is interacting with the neighboring eight LB nodes by a frictional force F=\xi_0(V(r)-u(r)) with \xi_0 being a friction force and u(r) being the velocity of the fluid at the position r. Thermal fluctuations are introduced in the framework of fluctuating hydrodynamics. This coupling scheme has been proposed recently for polymer systems by Ahlrichs and D"unweg [J. Chem. Phys. 111, 8225 (1999)]. We investigate several properties of a single colloidal particle in a LB fluid, namely the effective Stokes friction and long time tails in the autocorrelation functions for the translational and rotational velocity. Moreover, a charged colloidal system is considered consisting of a macroion, counterions and coions that are coupled to a LB fluid. We study the behavior of the ions in a constant electric field. In particular, an estimate of the effective charge of the macroion is yielded from the number of counterions that move with the macroion in the direction of the electric field.Comment: 37 pages, 12 figure

Stability of Ca-montmorillonite hydrates: A computer simulation study

Classic simulations are used to study interlayer structure, swelling curves, and stability of Ca-montmorillonite hydrates. For this purpose, NPzzT$ and MuPzzT ensembles are sampled for ground level and given burial conditions. For ground level conditions, a double layer hydrate having 15.0 A of basal spacing is the predominant state for relative vapor pressures (p/po) ranging in 0.6-1.0. A triple hydrate counting on 17.9 A of interlaminar distance was also found stable for p/po=1.0. For low vapor pressures, the system may produce a less hydrated but still double layer state with 13.5 A or even a single layer hydrate with 12.2 A of interlaminar distance. This depends on the established initial conditions. On the other hand, the effect of burial conditions is two sided. It was found that it enhances dehydration for all vapor pressures except for saturation, where swelling is promoted.Comment: 8 pages, 9 figure

Antiferromagnetic Order in MnO Spherical Nanoparticles

We have performed unpolarized and polarized neutron diffraction experiments on monodisperse 8 nm and 13 nm antiferromagnetic MnO nanoparticles. For the 8 nm sample, the antiferromagnetic transition temperature $T_N$ (114 K) is suppressed compared to the bulk material (119 K) while for the 13 nm sample $T_N$ (120 K) is comparable to the bulk. The neutron diffraction data of the nanoparticles is well described using the bulk MnO magnetic structure but with a substantially reduced average magnetic moment of 4.2$\pm$0.3 $\mu_B$/Mn for the 8 nm sample and 3.9$\pm$0.2 $\mu_B$/Mn for the 13 nm sample. An analysis of the polarized neutron data on both samples shows that in an individual MnO nanoparticle about 80$$ of Mn ions order. These results can be explained by a structure in which the monodisperse nanoparticles studied here have a core that behaves similar to the bulk with a surface layer which does not contribute significantly to the magnetic order.Comment: 7 pages, 5 figure

Phonon spectra in CaFe2As2 and Ca0.6Na0.4Fe2As2: Measurement of the pressure and temperature dependence and comparison with ab-initio and shell model calculations

We report the pressure and temperature dependence of the phonon density-of-states in superconducting Ca0.6Na0.4Fe2As2 (Tc=21 K) and the parent compound CaFe2As2, using inelastic neutron scattering. We observe no significant change in the phonon spectrum for Ca0.6Na0.4Fe2As2 at 295 K up to pressures of 5 kbar. The phonon spectrum for CaFe2As2 shows softening of the low-energy modes by about 1 meV when decreasing the temperature from 300 K to 180 K. There is no appreciable change in the phonon density of states across the structural and anti-ferromagnetic phase transition at 172 K. These results, combined with our earlier temperature dependent phonon density of states measurements for Ca0.6Na0.4Fe2As2, indicate that the softening of low-energy phonon modes in these compounds may be due to the interaction of phonons with electron or short-range spin fluctuations in the normal state of the superconducting compound as well as in the parent compound. The phonon spectra are analyzed with ab-initio and empirical model calculations giving partial densities of states and dispersion relations.Comment: 14 pages, 6 figure