Is multiscaling an artifact in the stochastically forced Burgers equation?

We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum approximately 1/k, where k is the wave number. From very high-resolution numerical simulations, in the limit of vanishing viscosity, we find evidence for multiscaling of velocity structure functions which cannot be falsified by standard tests. We find a new artifact in which logarithmic corrections can appear disguised as anomalous scaling and conclude that bifractal scaling is likely.     

Singularities of Euler Flow? Not Out of the Blue!

Does three-dimensional incompressible Euler flow with smooth initial conditions develop a singularity with infinite vorticity after a finite time? This blowup problem is still open. After briefly reviewing what is known and pointing out some of the difficulties, we propose to tackle this issue for the class of flows having analytic initial data for which hypothetical real singularities are preceded by singularities at complex locations. We present some results concerning the nature of complex space singularities in two dimensions and propose a new strategy for the numerical investigation of blowup.     

Cryogenic Permanent Magnet Undulators

Cryogenic Permanent Magnet Undulators (CPMU) have been recently developed following the original concept proposed in 2004 [1 Hara, T. 2004. Phys. Rev. ST AB, 7: 050702 [Google Scholar]]. CPMUs are In-Vacuum Undulators (IVU) improved by means of permanent magnet materials operated at cryogenic temperatures. At low temperature, NdFeB-type materials have high remanence B_r together with high coercivity Hc_J. The remanence is directly linked to the field performance of the undulator while the coercivity is connected to the resistance to radiation-induced demagnetization. For the NdFeB material, a limitation is found at about 135 K due to a Spin Reorientation Transition (SRT). This effect sets a lower limit on the temperature of operation of NdFeB-based CPMUs but does not disqualify the NdFeB material. The PrFeB material is being currently evaluated as a possible alternative to NdFeB. The field measurements of a CPMU represent a substantial effort. The field integral and local field need to be accurately measured to evaluate the impact of cooling on the field quality. During the last three years, a number of full-scale CPMUs have been constructed in several facilities.     

Forced Burgers Equation in an Unbounded Domain

The inviscid Burgers equation with random and spatially smooth forcing is considered in the limit when the size of the system tends to infinity. For the one-dimensional problem, it is shown both theoretically and numerically that many of the features of the space-periodic case carry over to infinite domains as intermediate time asymptotics. In particular, for large time T we introduce the concept of T-global shocks replacing the notion of main shock which was considered earlier in the periodic case (1997, E et al., Phys. Rev. Lett. 78, 1904). In the case of spatially extended systems these objects are no anymore global. They can be defined only for a given time scale and their spatial density behaves as (T)T ^–2/3 for large T. The probability density function p(A) of the age A of shocks behaves asymptotically as A ^–5/3. We also suggest a simple statistical model for the dynamics and interaction of shocks and discuss an analogy with the problem of distribution of instability islands for a simple first-order stochastic differential equation.     

Geometry and violent events in turbulent pair dispersion

The statistics of Lagrangian pair dispersion in a homogeneous isotropic flow is investigated by means of direct numerical simulations. The focus is on deviations from the Richardson eddy-diffusivity model and in particular on the strong fluctuations experienced by tracers. Evidence is obtained that the distribution of distances attains an almost self-similar regime characterized by a very weak intermittency. The timescale of convergence to this behavior is found to be given by the kinetic energy dissipation time measured at the scale of the initial separation. Conversely the velocity differences between tracers are displaying a strongly anomalous behavior whose scaling properties are very close to that of Lagrangian structure functions. These violent fluctuations are interpreted geometrically and are shown to be responsible for a long-term memory of the initial separation. Despite this strong intermittency, it is found that the mixed moment defined by the ratio between the cube of the longitudinal velocity difference and the distance attains a statistically stationary regime on very short timescales. These results are brought together to address the question of violent events in the distribution of distances. It is found that distances much larger than the average are reached by pairs that have always separated faster since the initial time. They contribute a stretched exponential behavior in the large-value tail of the inter-tracer distance probability distribution. At large times this tail is found to be closer to a pure exponential than to the form obtained from the Richardson diffusive approach. At the same time, the distance distribution displays a time-dependent power-law behavior at very small values, which is interpreted in terms of fractal geometry. It is argued and demonstrated numerically that the exponent converges to one at large time, again in conflict with Richardson’s distribution.     

Chemical Characterization and Biological Activity of the Essential Oil from Araucaria brasiliensis Collected in Ecuador

The purpose of this study was to determine the chemical composition, physical properties, enantiomeric composition and cholinesterase inhibitory activity of the essential oil (EO) steam-distilled from the leaves of the plant Araucaria brasiliensis Loud. collected in Ecuador. The chemical composition was determined by gas chromatography coupled to mass spectrometry (GC-MS) analysis on two capillary GC columns (DB5-ms and HP-INNOWax). Thirty-three compounds were identified in the EO; the main compounds were beyerene (26.08%), kaurene (24.86%), myrcene (11.02%), α-pinene (9.99%) and 5,15-rosadiene (5.87%). Diterpene hydrocarbons (65.41%), followed by monoterpene hydrocarbons (21.11%), were the most representative components of the EO. Enantioselective analysis of the EO showed four pairs of enantiomeric compounds, α-pinene, camphene, γ-muurolene and δ-cadinene. In an in vitro assay, the EO showed moderate inhibitory activity towards the enzyme butyrylcholinesterase (BuChE) (95.7 µg/mL), while it was inactive towards acetylcholinesterase (AChE) (225.3 µg/mL). Further in vivo studies are needed to confirm the anticholinesterase potential of the EO.     

Stereospecific Grignard-Activated Solid Phase Synthesis of DNA Methylphosphonate Dimers

Stereoregular R(p) or S(p) DNA methylphosphonate dimers have been synthesized on a solid phase support. A deprotected 5'-hydroxyl-N(2)-isobutanoyldeoxyguanosine 3'-O-succinate coupled to high-loaded polyethylene glycol (PEG) coated polystyrene beads (HLP) was activated with a Grignard reagent, t-BuMgCl. After activation was complete, a pure diastereoisomer of 5'-(dimethoxytrityl) N-benzoyldeoxynucleoside 3'-(p-nitrophenyl methylphosphonate) p-nitrophenyl ester (R(p) or S(p)) was added. Coupling of the activated 5'-hydroxyl to the 3'-methylphosphonate ensued, releasing nitrophenol, yielding the R(p) or S(p) dimer, respectively. The dimers were then cleaved from the solid support, deprotected, and purified, yielding methylphosphonate DNA dimers of defined stereochemistry.     

DRUG SENSITIZATION: PHOTOBINDING OF SULFANILAMIDE TO BOVINE SERUM ALBUMIN

Abstract— Photobinding of sulfanilamide to bovine serum albumin (BSA) was investigated by irradiating BSA and buffered BSA/drug solutions with UV light (Λ= 300 nm) under anaerobic conditions. The protein solutions were then denatured and the unbound sulfanilamide removed. Marked differences in the UV and fluorescence spectra of the solutions before and after irradiation were observed, suggesting covalent binding of the drug to BSA. This was confirmed using [¹⁴C]labelled sulfanilamide. The extent of photobinding of sulfanilamide determined using the radiolabeled drug, was concentration dependent. The binding ratio varied from 3 mol drug per mol BSA for a 10^-4 M drug concentration, to 10 mol drug per mol BSA for 10^-2 M drug concentration.
The protein solutions were hydrolysed under acid conditions and the amino acids obtained were analysed by ion exchange chromatography. The hydrolysate of irradiated BSA (10^-4 M ) -sulfanilamide (10^-2 M ) mixture lost about 10 mol of cystine per mol of BSA. This loss was not observed after hydrolysis of irradiated alone or non-irradiated BSA. Irradiation of cystine with [¹⁴C]sulfanilamide in HC1 solutions produced the same compound as was found after hydrolysis of irradiated BSA/sulfanilamide mixtures. This was demonstrated by autoradiography of paper chromatograms. The same compound was also detected in an irradiated [³⁵S]cystine non-labelled sulfanilamide mixture. It was not detected, however, after irradiation of a mixture of all amino acids of BSA excluding cystine. These data suggest that cystine residues are involved in the photobinding of sulfanilamide (or its photoproducts) to BSA.