Multifractality of the Feigenbaum attractor and fractional derivatives

It is shown that fractional derivatives of the (integrated) invariant measure of the Feigenbaum map at the onset of chaos have power-law tails in their cumulative distributions, whose exponents can be related to the spectrum of singularities $f(\alpha)$. This is a new way of characterizing multifractality in dynamical systems, so far applied only to multifractal random functions (Frisch and Matsumoto (J. Stat. Phys. 108:1181, 2002)). The relation between the thermodynamic approach (Vul, Sinai and Khanin (Russian Math. Surveys 39:1, 1984)) and that based on singularities of the invariant measures is also examined. The theory for fractional derivatives is developed from a heuristic point view and tested by very accurate simulations.Comment: 20 pages, 5 figures, J.Stat.Phys. in pres

Automated computation of materials properties

Materials informatics offers a promising pathway towards rational materials design, replacing the current trial-and-error approach and accelerating the development of new functional materials. Through the use of sophisticated data analysis techniques, underlying property trends can be identified, facilitating the formulation of new design rules. Such methods require large sets of consistently generated, programmatically accessible materials data. Computational materials design frameworks using standardized parameter sets are the ideal tools for producing such data. This work reviews the state-of-the-art in computational materials design, with a focus on these automated $\textit{ab-initio}$ frameworks. Features such as structural prototyping and automated error correction that enable rapid generation of large datasets are discussed, and the way in which integrated workflows can simplify the calculation of complex properties, such as thermal conductivity and mechanical stability, is demonstrated. The organization of large datasets composed of $\textit{ab-initio}$ calculations, and the tools that render them programmatically accessible for use in statistical learning applications, are also described. Finally, recent advances in leveraging existing data to predict novel functional materials, such as entropy stabilized ceramics, bulk metallic glasses, thermoelectrics, superalloys, and magnets, are surveyed.Comment: 25 pages, 7 figures, chapter in a boo

Near-threshold electron transfer in anion-nucleobase clusters : Does the identity of the anion matter?

Laser dissociation spectroscopy of I − ·adenine (I − ·A) and H 2 PO − 3 ·adenine (H 2 PO − 3 ·A) has been utilised for the first time to explore how the anion identity impacts on the excited states. Despite strong photodepletion, ionic photofragmentation is weak for both clusters, revealing that they decay predominantly by electron detachment. The spectra of I − ·A display a prominent dipole-bound excited state in the region of the detachment energy which relaxes to produce deprotonated adenine. In contrast, near-threshold photoexcitation of H 2 PO − 3 ·A does not access a dipole-bound state, but instead displays photofragmentation properties associated with ultrafast decay of an adenine-localised π→π* transition. Notably, the experimental electron detachment onset of H 2 PO − 3 ·A is around 4.7 eV, which is substantially lower than the expected detachment energy of an ion-dipole complex. The low value for H 2 PO − 3 ·A can be traced to initial ionisation of the adenine followed by significant geometric rearrangement on the neutral surface. We conclude that these dynamics quench access to a dipole-bound excited state for H 2 PO − 3 ·A and subsequent electron transfer. H 2 PO − 3 ·A represents an important new example of an ionic cluster where ionisation occurs from the neutral cluster component and where photodetachment initiates intra-molecular hydrogen atom transfer

Nuclear Resonance Vibrational Spectroscopy of Iron Sulfur Proteins

Nuclear inelastic scattering in conjunction with density functional theory (DFT) calculations has been applied for the identification of vibrational modes of the high-spin ferric and the high-spin ferrous iron-sulfur center of a rubredoxin-type protein from the thermophylic bacterium Pyrococcus abysii

Observation of Target Electron Momentum Effects in Single-Arm M\o ller Polarimetry

In 1992, L.G. Levchuk noted that the asymmetries measured in M\o ller scattering polarimeters could be significantly affected by the intrinsic momenta of the target electrons. This effect is largest in devices with very small acceptance or very high resolution in laboratory scattering angle. We use a high resolution polarimeter in the linac of the polarized SLAC Linear Collider to study this effect. We observe that the inclusion of the effect alters the measured beam polarization by -14% of itself and produces a result that is consistent with measurements from a Compton polarimeter. Additionally, the inclusion of the effect is necessary to correctly simulate the observed shape of the two-body elastic scattering peak.Comment: 29 pages, uuencoded gzip-compressed postscript (351 kb). Uncompressed postscript file (898 kb) available to DECNET users as SLC::USER_DISK_SLC1:[MORRIS]levpre.p

Fatty Acid Methyl Esters as Biosolvents of Epoxy Resins: A Physicochemical Study

The C8 to C18 fatty acid methyl esters (FAME) have been compared as solvents for two epoxy resin pre-polymers, bisphenol A diglycidyl ether (DGEBA) and triglycidyl paminophenol ether (TGPA). It was found that the solubilization limits vary according to the ester and that methyl caprylate is the best solvent of both resins. To explain these solubility performances, physical and chemical properties of FAME were studied, such as the Hansen parameters, viscosity, binary diffusion coefficient and vaporization enthalpy. Determination of the physicochemical parameters of FAME was carried out by laboratory experimentations and by calculation from bibliographic data. The Hansen parameters of FAME and epoxy resins pre-polymers were theoretically and experimentally determined. The FAME chain length showed a long dependence on the binary diffusion parameters and kinematic viscosity, which are mass and momentum transport properties. Moreover, the vaporization enthalpy of these compounds was directly correlated with the solubilization limits

Nonuniversal correlations in multiple scattering

We show that intensity of a wave created by a source embedded inside a three-dimensional disordered medium exhibits a non-universal space-time correlation which depends explicitly on the short-distance properties of disorder, source size, and dynamics of disorder in the immediate neighborhood of the source. This correlation has an infinite spatial range and is long-ranged in time. We suggest that a technique of "diffuse microscopy" might be developed employing spatially-selective sensitivity of the considered correlation to the disorder properties.Comment: 15 pages, 3 postscript figures, accepted to Phys. Rev.

Analytic solutions and Singularity formation for the Peakon b--Family equations

Using the Abstract Cauchy-Kowalewski Theorem we prove that the $b$-family equation admits, locally in time, a unique analytic solution. Moreover, if the initial data is real analytic and it belongs to $H^s$ with $s > 3/2$, and the momentum density $u_0 - u_{0,{xx}}$ does not change sign, we prove that the solution stays analytic globally in time, for $b\geq 1$. Using pseudospectral numerical methods, we study, also, the singularity formation for the $b$-family equations with the singularity tracking method. This method allows us to follow the process of the singularity formation in the complex plane as the singularity approaches the real axis, estimating the rate of decay of the Fourier spectrum