Theory of viscous and thermal attenuation of sound by small spheres

The problem is to calculate the attenuation of plane sound waves passing through a viscous, heat-conducting fluid containing small spherical inhomogeneities. The attenuation is calculated by evaluating the rate of increase of entropy caused by two irreversible processes: (1) the mechanical work done by the viscous stresses in the presence of velocity gradients, and (2) the flow of heat down the thermal gradients. The method is first applied to a homogeneous fluid with no spheres and shown to give the classical Stokes-Kirchhoff expressions. The method is then used to calculate the additional viscous and thermal attenuation when small spheres are present. The viscous attenuation agrees with Epstein's result obtained in 1941 for a non-heat-conducting fluid. The thermal attenuation is found to be similar in form to the viscous attenuation and, for gases, of comparable magnitude. The general results are applied to the case of water drops in air and air bubbles in water.

For water drops in air the viscous and thermal attenuations are camparable; the thermal losses occur almost entirely in the air, the thermal dissipation in the water being negligible. The theoretical values are compared with Knudsen's experimental data for fogs and found to agree in order of magnitude and dependence on frequency. For air bubbles in water the viscous losses are negligible and the calculated attenuation is almost completely due to thermal losses occurring in the air inside the bubbles, the thermal dissipation in the water being relatively small. (These results apply only to non-resonant bubbles whose radius changes but slightly during the acoustic cycle.)

Relativistic mean field theory: methods and applications

We develop a method for performing one-loop calculations in finite systems that is based on using the WKB approximation for the high energy states. This approximation allows us to absorb all the counterterms analytically and thereby avoids the need for extreme numerical precision that was required by previous methods. In addition, the local approximation makes this method well suited for self-consistent calculations. We then discuss the application of relativistic mean field methods to the atomic nucleus. Self-consistent, one loop calculations in the Walecka model are performed and the role of the vacuum in this model is analyzed. This model predicts that vacuum polarization effects are responsible for up to five percent of the local nucleon density. Within this framework the possible role of strangeness degrees of freedom is studied. We find that strangeness polarization can increase the kaon-nucleus scattering cross section by ten percent. By introducing a cutoff into the model, the dependence of the model on short-distance physics, where its validity is doubtful, is calculated. The model is very sensitive to cutoffs around one GeV.

Analysis of dispersion compensation for position-dependence in externally modulated CATV lightwave systems by using chirped fiber grating

The dispersion compensation characteristics of the chirped fiber grating (CFG) for different dispersion compensation positions are analyzed in externally modulated cable television (CATV) lightwave system and the analytic expression of the composite second order (CSO) distortion is derived. The analyses give a reasonable explanation for the position-dependent effect of CFG dispersion compensator, which was found in practical systems. Moreover, the theoretical result is also verified by an experiment. It is believed that the theory will be helpful in designing optical CATV fiber links with nodes at proper positions both for intensity amplification and dispersion compensation.

Current dependence of the energy gap in superconductors : a direct measurement

From the tunneling characteristics of a tin-tin oxide-lead junction, a direct measurement has been made of the energy-gap variation for a superconductor carrying a current in a compensated geometry. Throughout the region investigated – several temperatures near T_c and down to a reduced temperature t = 0.8 –the observed current dependence agrees quite well with predictions based on the Ginzburg-Landau-Gor’kov theory. Near T_c the predicted temperature dependence is also well verified, though deviations are observed at lower temperatures; even for the latter, the data are internally consistent with the temperature dependence of the experimental critical current. At the lowest temperature investigated, t = 0.8, a small “Josephson” tunneling current allowed further a direct measurement of the electron drift velocity at low current densities. From this, a preliminary experimental value of the critical velocity, believed to be the first reported, can be inferred in the basis of Ginzburg-Landau theory. For tin at t = 0.8, we find v_c = 87 m/sec. This value does not appear fully consistent with those predicted by recent theories for superconductors with short electronic mean-free-paths.

1. Ultrasonic studies of binary liquid structure in the critical region. Theory and experiment for the 2,6-lutidine/water system. 2. Hartree-Fock calculations of electric polarizabilities of some simple atoms and molecules, and their practicality. 3. Calculation of vibrational transition probabilities in collinear atom-diatom and diatom-diatom collisions with Lennard-Jones interaction

Part 1. Many interesting visual and mechanical phenomena occur in the critical region of fluids, both for the gas-liquid and liquid-liquid transitions. The precise thermodynamic and transport behavior here has some broad consequences for the molecular theory of liquids. Previous studies in this laboratory on a liquid-liquid critical mixture via ultrasonics supported a basically classical analysis of fluid behavior by M. Fixman (e. g., the free energy is assumed analytic in intensive variables in the thermodynamics)--at least when the fluid is not too close to critical. A breakdown in classical concepts is evidenced close to critical, in some well-defined ways. We have studied herein a liquid-liquid critical system of complementary nature (possessing a lower critical mixing or consolute temperature) to all previous mixtures, to look for new qualitative critical behavior. We did not find such new behavior in the ultrasonic absorption ascribable to the critical fluctuations, but we did find extra absorption due to chemical processes (yet these are related to the mixing behavior generating the lower consolute point). We rederived, corrected, and extended Fixman's analysis to interpret our experimental results in these more complex circumstances. The entire account of theory and experiment is prefaced by an extensive introduction recounting the general status of liquid state theory. The introduction provides a context for our present work, and also points out problems deserving attention. Interest in these problems was stimulated by this work but also by work in Part 3.

Part 2. Among variational theories of electronic structure, the Hartree-Fock theory has proved particularly valuable for a practical understanding of such properties as chemical binding, electric multipole moments, and X-ray scattering intensity. It also provides the most tractable method of calculating first-order properties under external or internal one-electron perturbations, either developed explicitly in orders of perturbation theory or in the fully self-consistent method. The accuracy and consistency of first-order properties are poorer than those of zero-order properties, but this is most often due to the use of explicit approximations in solving the perturbed equations, or to inadequacy of the variational basis in size or composition. We have calculated the electric polarizabilities of H₂, He, Li, Be, LiH, and N₂ by Hartree-Fock theory, using exact perturbation theory or the fully self-consistent method, as dictated by convenience. By careful studies on total basis set composition, we obtained good approximations to limiting Hartree-Fock values of polarizabilities with bases of reasonable size. The values for all species, and for each direction in the molecular cases, are within 8% of experiment, or of best theoretical values in the absence of the former. Our results support the use of unadorned Hartree-Pock theory for static polarizabilities needed in interpreting electron-molecule scattering data, collision-induced light scattering experiments, and other phenomena involving experimentally inaccessible polarizabilities.

Part 3. Numerical integration of the close-coupled scattering equations has been carried out to obtain vibrational transition probabilities for some models of the electronically adiabatic H₂-H₂ collision. All the models use a Lennard-Jones interaction potential between nearest atoms in the collision partners. We have analyzed the results for some insight into the vibrational excitation process in its dependence on the energy of collision, the nature of the vibrational binding potential, and other factors. We conclude also that replacement of earlier, simpler models of the interaction potential by the Lennard-Jones form adds very little realism for all the complication it introduces. A brief introduction precedes the presentation of our work and places it in the context of attempts to understand the collisional activation process in chemical reactions as well as some other chemical dynamics.

From organism to population: the role of life-history theory

The role of life-history theory in population and evolutionary analyses is outlined. In both cases general life histories can be analysed, but simpler life histories need fewer parameters for their description. The simplest case, of semelparous (breed-once-then-die) organisms, needs only three parameters: somatic growth rate, mortality rate and fecundity. This case is analysed in detail. If fecundity is fixed, population growth rate can be calculated direct from mortality rate and somatic growth rate, and isoclines on which population growth rate is constant can be drawn in a ”state space” with axes for mortality rate and somatic growth rate. In this space density-dependence is likely to result in a population trajectory from low density, when mortality rate is low and somatic growth rate is high and the population increases (positive population growth rate) to high density, after which the process reverses to return to low density. Possible effects of pollution on this system are discussed. The state-space approach allows direct population analysis of the twin effects of pollution and density on population growth rate. Evolutionary analysis uses related methods to identify likely evolutionary outcomes when an organism's genetic options are subject to trade-offs. The trade-off considered here is between somatic growth rate and mortality rate. Such a trade-off could arise because of an energy allocation trade-off if resources spent on personal defence (reducing mortality rate) are not available for somatic growth rate. The evolutionary implications of pollution acting on such a trade-off are outlined.

Selected topics in financial engineering: first-exit times and dependence structures of Marshall-Olkin Kind

146 p.

Theoretical analysis of optical properties of dielectric coatings dependence on substrate subsurface defects

A model for refractive index of stratified dielectric substrate was put forward according to theories of inhomogeneous coatings. The substrate was divided into surface layer, subsurface layer and bulk layer along the normal direction of its surface. Both the surface layer (separated into N-1 sublayers of uniform thickness) and subsurface layer (separated into N-2 sublayers of uniform thickness), whose refractive indices have different statistical distributions, are equivalent to inhomogeneous coatings, respectively. And theoretical deduction was carried Out by employing characteristic matrix method of optical coatings. An example of mathematical calculation for optical properties of dielectric coatings had been presented. The computing results indicate that substrate subsurface defects can bring about additional bulk scattering and change propagation characteristic in thin film and Substrate. Therefore, reflectance, reflective phase shift and phase difference of an assembly of coatings and substrate deviate from ideal conditions. The model will provide some beneficial theory directions for improving optical properties of dielectric coatings via substrate surface modification. (c) 2005 Elsevier B.V. All rights reserved.

Angular dependence of domain wall resistivity in artificial magnetic domain structures.

We exploit the ability to precisely control the magnetic domain structure of perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial domain wall arrays and study their transport properties. The scaling behavior of this model system confirms the intrinsic domain wall origin of the magnetoresistance, and systematic studies using domains patterned at various angles to the current flow are excellently described by an angular-dependent resistivity tensor containing perpendicular and parallel domain wall resistivities. We find that the latter are fully consistent with Levy-Zhang theory, which allows us to estimate the ratio of minority to majority spin carrier resistivities, rho downward arrow/rho upward arrow approximately 5.5, in good agreement with thin film band structure calculations.

Dependence of dye regeneration and charge collection on the pore-filling fraction in solid-state dye-sensitized solar cells

Solid-state dye-sensitized solar cells rely on effective infiltration of a solid-state hole-transporting material into the pores of a nanoporous TiO 2 network to allow for dye regeneration and hole extraction. Using microsecond transient absorption spectroscopy and femtosecond photoluminescence upconversion spectroscopy, the hole-transfer yield from the dye to the hole-transporting material 2,2′,7,7′-tetrakis(N,N-di-p- methoxyphenylamine)-9,9'-spirobifluorene (spiro-OMeTAD) is shown to rise rapidly with higher pore-filling fractions as the dye-coated pore surface is increasingly covered with hole-transporting material. Once a pore-filling fraction of ≈30% is reached, further increases do not significantly change the hole-transfer yield. Using simple models of infiltration of spiro-OMeTAD into the TiO2 porous network, it is shown that this pore-filling fraction is less than the amount required to cover the dye surface with at least a single layer of hole-transporting material, suggesting that charge diffusion through the dye monolayer network precedes transfer to the hole-transporting material. Comparison of these results with device parameters shows that improvements of the power-conversion efficiency beyond ≈30% pore filling are not caused by a higher hole-transfer yield, but by a higher charge-collection efficiency, which is found to occur in steps. The observed sharp onsets in photocurrent and power-conversion efficiencies with increasing pore-filling fraction correlate well with percolation theory, predicting the points of cohesive pathway formation in successive spiro-OMeTAD layers adhered to the pore walls. From percolation theory it is predicted that, for standard mesoporous TiO2 with 20 nm pore size, the photocurrent should show no further improvement beyond an ≈83% pore-filling fraction. Solid-state dye-sensitized solar cells capable of complete hole transfer with pore-filling fractions as low as ∼30% are demonstrated. Improvements of device efficiencies beyond ∼30% are explained by a stepwise increase in charge-collection efficiency in agreement with percolation theory. Furthermore, it is predicted that, for a 20 nm pore size, the photocurrent reaches a maximum at ∼83% pore-filling fraction. © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Pressure dependence of Mn2+ luminescence in differently sized ZnS : Mn nanoparticles

The pressure behavior of Mn2+ emission in the 10-, 4.5-, 3.5-, 3-, and 1-nm-sized ZnS:Mn2+ nanoparticles is investigated. The emission shifts to lower energies with increasing pressure, and the shift rate (the absolute value of the pressure coefficient) is larger in the ZnS:Mn2+ nanoparticles than in bulk. The pressure coefficient increases with the decrease in particle size with the 1-nm-sized particles as an exception. Pressure coefficient calculations based on the crystal field theory are in agreement with the experimental results. The pressure dependence of the emission intensity is also size dependent. For nanoparticles 1 and 3 nm in size, the luminescence intensity of Mn2+ decreases dramatically with increasing pressure, while, for bulk and particles with average sizes of 3.5, 4.5, and 10 nm, the luminescence intensity of Mn2+ is virtually unchanged at different pressures. The bandwidth increases faster with increasing pressure for smaller particles. This is perhaps due to the fact that there are more Mn2+ ions at the near-surface sites and because the phonon frequency is greater for smaller particles. These new phenomena provide some insight into the luminescence behavior of Mn2+ in ZnS:Mn2+ nanoparticles.

Theory and experiment of two-photon 'direct' interference for type-II spontaneous parametric down-conversion with an ultrafast pulse laser pump

Fourth-order spatial interference of entangled photon pairs generated in the process of spontaneous parametric down-conversion pumped by a femtosecond pulse laser has been performed for the first time. In theory, it takes into account the transverse correlation between the two photons and is used to calculate the dependence of the visibility of the interference pattern obtained in Young's double-slit experiment. In this experiment, a short focal length tens and two narrow band interference filters were adopted to eliminate the effects of the broadband pump laser and improve the visibility of the interference pattern under the condition of nearly collinear light and degenerate phase matching.

A partially incoherent rate theory of long-range charge transfer in deoxyribose nucleic acid

A quantum chemistry based Green's function formulation of long-range charge transfer in deoxyribose nucleic acid (DNA) double helix is proposed. The theory takes into account the effects of DNA's electronic structure and its incoherent interaction with aqueous surroundings. In the implementation, the electronic tight-binding parameters for unsolvated DNA molecules are determined at the HF/6-31G* level, while those for individual nucleobase-water couplings are at a semiempirical level by fitting with experimental redox potentials. Numerical results include that: (i) the oxidative charge initially at the donor guanine site does hop sequentially over all guanine sites; however, the revealed rates can be of a much weaker distance dependence than that described by the ordinary Ohm's law; (ii) the aqueous surroundings-induced partial incoherences in thymine/adenine bridge bases lead them to deviate substantially from the superexchange regime; (iii) the time scale of the partially incoherent hole transport through the thymine/adenine pi stack in DNA is about 5 ps. (C) 2002 American Institute of Physics.

Impact of polarization on quasi-two-dimensional exciton and barrier-width dependence of the exciton associated transition in wurtzite III-V nitride quantum wells

Excitonic states in AlxGa1-xN/GaN quantum wells (QWs) are studied within the framework of effective-mass theory. Spontaneous and piezoelectric polarizations are included and their impact on the excitonic states and optical properties are studied. We witnessed a significant blue shift in transition energy when the barrier width decreases and we attributed this to the redistribution of the built-in electric field between well layers and barrier layers. For the exciton the binding energies, we found in narrow QWs that there exists a critical value for barrier width, which demarcates the borderline for quantum confinement effect and the quantum confined Stark effect. Exciton and free carrier radiative lifetimes are estimated by simple argumentation. The calculated results suggest that there are efficient non-radiative mechanisms in narrow barrier QWs. (C) 2002 Elsevier Science Ltd. All rights reserved.

Pressure dependence of Mn2+ fluorescence in ZnS : Mn2+ nanoparticles

The photoluminescence of Mn2+ in ZnS:Mn2+ nanoparticles with an average size of 4.5 nm has been measured under hydrostatic pressure from 0 to 6 GPa. The emission position is red-shifted at a rate of -33.3+/-0.6meV/GPa, which is in good agreement with the calculated value of -30.4meV/GPa using the crystal field theory. (C) 2000 Elsevier Science B.V. All rights reserved.