Jauch-Piron system of imprimitivities for phonons. I. Localizability in discrete space

This paper is devoted to a discussion of the notion of localizability for phonons, i.e., quasiparticles arising from the harmonic vibrations of a system ofn atoms bound to one another by elastic forces. The natural tools for the analysis of localizability are the projection operatorsÊ() acting on the Hilbert space of one-phonon states, where is an arbitrary subset of the set that consists ofn vectors specifying the equilibrium positions ofn atoms. The expectation value ofÊ() is the probability that the phonon belongs to the atoms whose equilibrium positions are characterized by the elements of . For a strongly localizable phonon all of the projection operatorsÊ() commute with one another, whereas in the case of a weakly localizable phonon the operatorsÊ(₁) andÊ(₂) do not commute when ₁ and ₂ overlap. With the aid of the Jauch-Piron quantum theory of localization in space, the present paper describes the method of obtainingÊ() and also shows that if in the system ofn atoms there exist normal modes of zero frequency, then the phonon is only weakly localizable. Given the explicit expression forÊ(), one can define the number-of-phonons operator as well as the quasiparticle analogue (given in a companion paper) of the Wigner distribution function.     

Asymmetric decompositions of abelian groups

A subsetA of an Abelian groupG is said to be asymmetric ifg+S⊄A for any elementg∈G and any infinite symmetric subsetS⊂G (S=−S). The minimal cardinality of a decomposition of the groupG into asymmetric sets is denoted by ν(G). for any Abelian groupG, the cardinal number ν(G is expressed via the following cardinal invariants: the free rank, the 2-rank, and the cardinality of the group. In particular, . Translated fromMatematicheskie Zametki, Vol. 66, No. 1, pp. 10–19, July, 1999.     

Alpha,omega-bis(thioacetyl)oligophenylenevinylene chromophores from thioanisol precursors

The selective cleavage of arylmethyl thioethers provides a convenient protocol for the synthesis of all-E isomers of alpha, omega-bis(thioacetyl)oligophenyenevinylene molecules (OPVs). The S-methyl group is tolerant of Wittig-type and Heck-type reactions for forming OPV structures and can be converted to the S-acetyl group by treatment with sodium thiomethoxide and acetyl chloride. The thermal conditions of the deprotection/reprotection step concurrently isomerize the conjugated chromophore to the all-E isomer, regardless of the stereochemistry of the starting olefins. This approach is demonstrated for a variety of linear and [2.2]paracyclophane containing OPVs, which have been characterized by electrochemical and spectroscopic techniques. Additionally, these S-acetyl-terminated OPVs self-assemble on gold surfaces. Monolayers containing these molecules were characterized by water contact angle measurements, ellipsometry, and X-ray photoelectron spectroscopy.     

A multifaceted approach to hydrogen storage

The widespread adoption of hydrogen as an energy carrier could bring significant benefits, but only if a number of currently intractable problems can be overcome. Not the least of these is the problem of storage, particularly when aimed at use onboard light-vehicles. The aim of this overview is to look in depth at a number of areas linked by the recently concluded HYDROGEN research network, representing an intentionally multi-faceted selection with the goal of advancing the field on a number of fronts simultaneously. For the general reader we provide a concise outline of the main approaches to storing hydrogen before moving on to detailed reviews of recent research in the solid chemical storage of hydrogen, and so provide an entry point for the interested reader on these diverse topics. The subjects covered include: the mechanisms of Ti catalysis in alanates; the kinetics of the borohydrides and the resulting limitations; novel transition metal catalysts for use with complex hydrides; less common borohydrides; protic-hydridic stores; metal ammines and novel approaches to nano-confined metal hydrides.     

On the balance laws of extended thermodynamics (ET) for non-ideal gases

The conservation laws of mass and momentum and the equations of balance of momentum flux and energy flux as well as the higher order balance laws are derived by means of the modified Klimontovich kinetic equation for non-ideal gases. The effect of the body forces and inertial forces during the persistence of a collision is taken into account in order to have the balance laws valid for general frames of reference. The sequence of macroscopic quantities appearing in the balance equations is decomposed into convective and non-convective parts and this decomposition is explained on the basis of statistical mechanics. A problem of symmetry or non-symmetry of tensors associated with the presence of interactions between microscopic particles is discussed from a molecular point of view. Explicit expressions for the energy density, the pressure, the pressure tensor, the heat flux and the other expressions characteristic for ET are given in terms of microscopic variables.     

Relaxation of polymer thin films in isothermal temperature‐jump measurements

The dynamic behavior of thin polymer films is of interest in the fabrication of microelectronics and optoelectronics and in the coatings industry. It is known that polymer relaxation is affected by film thickness and the particular substrate/polymer pair. We previously used a spectroscopic ellipsometer to investigate the glass transition in thin films. In addition to information on the modification of thermal transitions such as the glass‐transition temperature, the speed of data acquisition in an automated, spectroscopic ellipsometer, operated at a single wavelength of 780 nm, allows for the direct observation of the isothermal dimensions of a thin polymer film as a function of time after a rapid temperature change. In this article, we discuss recent results from the observation of the time dependence of film‐normal thickness and normalized, in‐plane, lateral dimension as well as simple fits to this relaxation behavior in terms of a normalized viscosity and relaxation time. The results support a highly asymmetric initial thermal expansion normal to the film followed by close to isotropic relaxation and anisotropic “flow” (the flow in response to the vanishingly small shears of thermal expansion). These features may clarify issues involving the observation of chain confinement in thin polymer films in terms of potential differences between equilibrium and dynamic measurements. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2929–2936, 2000     

Dispersion relation in the limit of high frequency for a hyperbolic system with multiple eigenvalues

The results of a previous paper (Muracchini et al., 1992) are generalized by considering a hyperbolic system in one space dimension with multiple eigenvalues. The dispersion relation for linear plane waves in the high-frequency limit is analyzed and the recurrence formulas for the phase velocity and the attenuation factor are derived in terms of the coefficients of a formal series expansion in powers of the reciprocal of frequency. In the case of multiple eigenvalues, it is also verified that linear stability implies λ$\lambda$-stability for the waves of weak discontinuity. Moreover, for the linearized system, the relationship between entropy and stability is studied. When the nonzero eigenvalue is simple, the results of the paper mentioned above are recovered. In order to illustrate the procedure, an example of the linear hyperbolic system is presented in which, depending on the values of parameters, the multiplicity of nonzero eigenvalues is either one or two. This example describes the dynamics of a mixture of two interacting phonon gases.     

Co-Localization of Copper, Zinc and Lead with Calcium in Their Accumulation Sites in the Housefly’s Abdomen by Micro-PIXE

Our previous study showed that treatment of Musca domestica larvae with semi-lethal doses of Cu, Zn or Pb leads to their accumulation in the adult fly’s abdomen. Now we report that the distribution pattern of heavy metals is similar to that of Ca. The housefly’s larvae were reared on media contaminated with semi-lethal doses of Cu (800 ppm), Zn (2000 ppm) or Pb (10,000 ppm) and on control medium. Ten days after eclosion, adult houseflies were prepared for X-ray microanalysis. Analyses were performed on the whole freeze-dried abdomen specimens using a nuclear microprobe (PIXE and RBS) at iThemba LABS, South Africa. GeoPIXE II software was used to obtain quantitative elemental maps by the Dynamic Analysis method. On the basis of Cu, Zn and Pb accumulation sites, the concentrations of these elements were correlated with the concentration of Ca. There was a clear relationship between Ca and all heavy metals examined, indicating Ca co-localization in their deposition sites. In the control animals, Zn and Ca deposition sites were significantly correlated. Association of heavy metals with Ca in their accretion sites suggests the presence of metal-accumulating granules, the so-called “concretions” probably in the Malpighian tubules, midgut epithelium or in the fat body.     

On a cardinal group invariant related to decompositions of Abelian groups

For each Abelian groupG, a cardinal invariant χ(G) is introduced and its properties are studied. In the special caseG = ? ⁿ , the cardinalχ(? ⁿ ) is equal to the minimal cardinality of an essential subset of ? ⁿ , i.e., a of a subsetA ? ? ⁿ such that, for any coloring of the group ? ⁿ inn colors, there exists an infinite one-color subset that is symmetric with respect to some pointα ofA. The estimaten( ^{n +} l)/2 ≤χ(? ⁿ ) < 2n is proved for alln and the relationχ(? ⁿ ) =n(n + 1)/2 forn ≤ 3. The structure of essential subsets of cardinalityχ(? ⁿ ) in ? ⁿ is completely described forn ≤ 3.