Relaxation dynamics in glycerol-water mixtures: I. Glycerol-rich mixtures

We discuss the relaxation dynamics of glycerol-water mixtures, as studied by dielectric spectroscopy in the frequency range from 1 Hz to 250 MHz and at temperatures between 173 and 323 K. The experimental results obtained for the glycerol-rich mixtures suggest that the main dielectric relaxation process, as well as the so-called high-frequency "excess wing" (EW) and dc conductivity, follow the same temperature dependence. This result indicates that all of these processes are induced by the same molecular origin. A new phenomenological function is proposed to describe the whole dielectric spectrum in the covered frequency range, and some possible mechanisms of dielectric behaviors through the dc conductivity, the main relaxation process, and the EW are discussed.     

Dynamic mechanism of photochemical induction of turing superlattices in the chlorine dioxide-iodine-malonic acid reaction-diffusion system

We study the mechanism of development of superlattice Turing structures from photochemically generated hexagonal patterns of spots with wavelengths several times larger than the characteristic wavelength of the Turing patterns that spontaneously develop in the nonilluminated system. Comparison of the experiment with numerical simulations shows that interaction of the photochemical periodic forcing with the Turing instability results in generation of multiple resonant triplets of wave vectors, which are harmonics of the external forcing. Some of these harmonics are situated within the Turing instability band and are therefore able to maintain their amplitude as the system evolves and after illumination ceases, while photochemically generated harmonics outside the Turing band tend to decay.     

Radiation damage and annealing in Sb implanted diamond

The predicted, but as yet unobserved, intradonor absorption spectrum of the hydrogenic-like donors in CdF₂ crystals is presented. The role of phonon coupling in these spectra is discussed. From the data on the insulator-semiconductor transition in CdPbF₂ it is concluded that the dominant factor in convertibility of CdF₂ to a semiconducting state is its electron affinity, the largest among the fluorites (x≈4 eV).     

Superlattice Turing structures in a photosensitive reaction-diffusion system

Families of complex superlattice structures, consisting of combinations of basic hexagonal or square patterns, are found in a photosensitive reaction-diffusion system. The structures are induced by simple illumination patterns whose wavelengths are appropriately related to that of the system's intrinsic Turing pattern. Computer simulations agree with the structures and their stability. The technique offers a general approach to generating superlattices for use in information storage and other applications.     

Improved lower bounds on the total variation distance for the Poisson approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen–Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is addressed.     

Anomalies in supercooled NaCl aqueous solutions: a microscopic perspective

In this work we studied the effect of NaCl on the thermodynamic and dynamic properties of supercooled water, for salt concentrations between 0.19 and 1.33 mol?kg(-1), using molecular dynamic simulations for TIP5P∕E water model and ion parameters specially designed to be used in combination with this potential. We studied the isobaric heat capacity (C(p)) temperature dependence and observed a maximum in C(p), occurring at T(m), that moves to lower temperature values with increasing salt concentration. Many characteristic changes were observed at scaled temperature T∕T(m) ～ 0.96, namely a minimum in the density of the system, a reduction of the slope of the number of hydrogen bonds vs. temperature, and a crossover from Vogel-Tamman-Fulcher to Arrhenius dynamics. Finally, at low temperatures we observed that water dynamics become heterogeneous with an apparently common relationship between the fraction of immobile molecules and T/T(m) for all studied systems.     

Shell model description of interacting bosons

The interacting boson model, describing collective states of even-even nuclei, is introduced as a drastic truncation of large scale shell model calculations. The shell model hamiltonian can be diagonalized by using a correspondence, or mapping, of the nucleon states in the truncated space into states obtained by coupling proton and neutron s- and d-bosons. The equivalent boson hamiltonian in a simple case is obtained and diagonalized. Eigenstates with definite proton-neutron symmetry (good F-spin) emerge for certain values of proton and neutron numbers. In general the situation is more complex but the results obtained follow closely the experimental data.     

Laser-microprobe elemental determinations with an optical multichannel detection system

The results obtained when a laser microprobe is adapted to imaging detectors for multiwavelength detection are described. Detectors evaluated are a silicon-intensified target vidicon and a second-generation photodiode array. Data are presented to illustrate how the combined system can be used to monitor both surface and depth profiles of elemental content of a variety of sample types including a ruby rod and ceramic material with blemishes, electrical capacitors, integrated circuits, and surface-coated electrical conductors. It is also shown how the gating capability of the intensified vidicon can be used to monitor time-dependent changes in the several nanosecond range during the laser microprobe excitation process. Detection limits obtained with both detectors are in the range 2–500 ppm depending on the element, the wavelength used, the matrix, and other variables. The uncertainty associated with the measurement step can be improved by a factor of 2–3 by using ratios of spectral lines. Principal limitations of the laser microprobe method are the nonlinear response of intensity vs. concentration and the resulting need for reference materials with matrices similar to samples for calibration purposes.     

Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.