Developments in the Theory of X-ray Absorption and Compton Scattering.

Thesis (Ph.D.)--University of Washington, 2016-06

Neutron-mapping polymer flow: Scattering, flow visualization, and molecular theory

Flows of complex fluids need to be understood at both macroscopic and molecular scales, because it is the macroscopic response that controls the fluid behavior, but the molecular scale that ultimately gives rise to rheological and solid-state properties. Here the flow field of an entangled polymer melt through an extended contraction, typical of many polymer processes, is imaged optically and by small-angle neutron scattering. The dual-probe technique samples both the macroscopic stress field in the flow and the microscopic configuration of the polymer molecules at selected points. The results are compared with a recent tube model molecular theory of entangled melt flow that is able to calculate both the stress and the single-chain structure factor from first principles. The combined action of the three fundamental entangled processes of reptation, contour length fluctuation, and convective constraint release is essential to account quantitatively for the rich rheological behavior. The multiscale approach unearths a new feature: Orientation at the length scale of the entire chain decays considerably more slowly than at the smaller entanglement length.

Dynamical properties of a strongly correlated model for quarter-filled layered organic molecular crystals

The dynamical properties of an extended Hubbard model, which is relevant to quarter-filled layered organic molecular crystals, are analyzed. We have computed the dynamical charge correlation function, spectral density, and optical conductivity using Lanczos diagonalization and large-N techniques. As the ratio of the nearest-neighbor Coulomb repulsion, V, to the hopping integral, t, increases there is a transition from a metallic phase to a charge-ordered phase. Dynamical properties close to the ordering transition are found to differ from the ones expected in a conventional metal. Large-N calculations display an enhancement of spectral weight at low frequencies as the system is driven closer to the charge-ordering transition in agreement with Lanczos calculations. As V is increased the charge correlation function displays a collective mode which, for wave vectors close to (pi,pi), increases in amplitude and softens as the charge-ordering transition is approached. We propose that inelastic x-ray scattering be used to detect this mode. Large-N calculations predict superconductivity with d(xy) symmetry close to the ordering transition. We find that this is consistent with Lanczos diagonalization calculations, on lattices of 20 sites, which find that the binding energy of two holes becomes negative close to the charge-ordering transition.

Scattering and tangential momentum accommodation at a 2D adsorbate-solid interface

We calculate tangential momentum coefficients for the exchange of momentum between molecules in transport and the internal surface of a membrane pore, modelled as a simple atomic structure. We introduce a local specular reflection (LSR) hypothesis, which states that impinging molecules undergo mirror-like reflection in a plane tangent to a surface atom at the point of impact. As a consequence, the components of the velocity, parallel to the direction of flow will (in general) change on impact. The overall effect is a loss of tangential momentum, since more is lost in the upstream direction than is gained in the downstream direction. The loss of tangential momentum is greater when the size ratio of fluid to solid atom is small, allowing more steeply inclined impact planes to become accessible to the fluid phase molecules. (c) 2005 Elsevier B.V. All rights reserved.

A Bethe ansatz solvable model for superpositions of Cooper pairs and condensed molecular bosons

We introduce a general Hamiltonian describing coherent superpositions of Cooper pairs and condensed molecular bosons. For particular choices of the coupling parameters, the model is integrable. One integrable manifold, as well as the Bethe ansatz solution, was found by Dukelsky et al. [J. Dukelsky, G.G. Dussel, C. Esebbag, S. Pittel, Phys. Rev. Lett. 93 (2004) 050403]. Here we show that there is a second integrable manifold, established using the boundary quantum inverse scattering method. In this manner we obtain the exact solution by means of the algebraic Bethe ansatz. In the case where the Cooper pair energies are degenerate we examine the relationship between the spectrum of these integrable Hamiltonians and the quasi-exactly solvable spectrum of particular Schrodinger operators. For the solution we derive here the potential of the Schrodinger operator is given in terms of hyperbolic functions. For the solution derived by Dukelsky et al., loc. cit. the potential is sextic and the wavefunctions obey PT-symmetric boundary conditions. This latter case provides a novel example of an integrable Hermitian Hamiltonian acting on a Fock space whose states map into a Hilbert space of PE-symmetric wavefunctions defined on a contour in the complex plane. (c) 2006 Elsevier B.V. All rights reserved.

Measuring and predicting the dynamics of linear monodisperse entangled polymers in rapid flow through an abrupt contraction. A small angle neutron scattering study

Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.

A simple electromagnetic model for understanding the operation of a MIMO system

Recent years have witnessed intense research in multiple input multiple output (MIMO) wireless communications systems, which use multiple element antennas (MEA) for signal transmission and reception. In this paper, we have described a novel electromagnetic model to investigate the effect of mutual coupling, inter-element spacing and array geometry on the capacity of MIMO systems. Simulation results have been presented illustrating the application of the proposed model. The presented model concept stems from a hollow waveguide analogue. Using this model other aspects such as richness of scattering environment (spacing and clustering), the effect of hard versus soft scatterers and pin hole effect can be investigated.

Simulation of optical fibre communication systems influenced by stimulated brillouin scattering

Boyd's SBS model which includes distributed thermal acoustic noise (DTAN) has been enhanced to enable the Stokes-spontaneous density depletion noise (SSDDN) component of the transmitted optical field to be simulated, probably for the first time, as well as the full transmitted field. SSDDN would not be generated from previous SBS models in which a Stokes seed replaces DTAN. SSDDN becomes the dominant form of transmitted SBS noise as model fibre length (MFL) is increased but its optical power spectrum remains independent of MFL. Simulations of the full transmitted field and SSDDN for different MFLs allow prediction of the optical power spectrum, or system performance parameters which depend on this, for typical communication link lengths which are too long for direct simulation. The SBS model has also been innovatively improved by allowing the Brillouin Shift Frequency (BS) to vary over the model fibre length, for the nonuniform fibre model (NFM) mode, or to remain constant, for the uniform fibre model (UFM) mode. The assumption of a Gaussian probability density function (pdf) for the BSF in the NFM has been confirmed by means of an analysis of reported Brillouin amplified power spectral measurements for the simple case of a nominally step-index single-mode pure silica core fibre. The BSF pdf could be modified to match the Brillouin gain spectra of other fibre types if required. For both models, simulated backscattered and output powers as functions of input power agree well with those from a reported experiment for fitting Brillouin gain coefficients close to theoretical. The NFM and UFM Brillouin gain spectra are then very similar from half to full maximum but diverge at lower values. Consequently, NFM and UFM transmitted SBS noise powers inferred for long MFLs differ by 1-2 dB over the input power range of 0.15 dBm. This difference could be significant for AM-VSB CATV links at some channel frequencies. The modelled characteristic of Carrier-to-Noise Ratio (CNR) as a function of input power for a single intensity modulated subcarrier is in good agreement with the characteristic reported for an experiment when either the UFM or NFM is used. The difference between the two modelled characteristics would have been more noticeable for a higher fibre length or a lower subcarrier frequency.

Elastic and inelastic scattering of fast neutrons in fusion reactor materials

In this work, the angular distributions for elastic and. inelastic scattering of fast neutrons in fusion .reactor materials have been studied. Lithium and lead material are likely to be common components of fusion reactor wall configuration design. The measurements were performed using an associated particle time-of- flight technique. The 14 and 14.44 Mev neutrons were produced by the T(d,n} 4He reaction with deuterons being accelerated in a 150kev SAMES type J accelerator at ASTON and in.the 3. Mev DYNAMITRON at the Joint Radiation Centre, Birmingham respectively. The associated alpha-particles and fast. neutrons were detected.by means of a plastic scintillator mounted on a fast focused photomultiplier tube. The samples used were extended flat plates of thicknesses up to 0.9 mean-free-path for Lithium and 1.562 mean-free-path for Lead. The differential elastic scattering cross-sections were measured for 14 Mev neutrons for various thicknesses of Lithium and Lead in the angular range from zero to; 90º. In addition, the angular distributions of elastically scattered 14,.44 Mev .neutrons from Lithium samples were studied in the same angular range. Inelastic scattering to the 4.63 Mev state in 7Li and the 2.6 Mev state, and 4.1 Mev state in 208Pb have:been :measured.The results are compared to ENDF/B-IV data files and to previous measurements. For the Lead samples the differential neutron scattering:cross-sections for discrete 3 Mev ranges and the angular distributions were measured. The increase in effective cross-section due to multiple scattering effects,as the sample thickness increased:was found to be predicted by the empirical .relation ....... A good fit to the exoerimental data was obtained using the universal constant............ The differential elastic scattering cross-section data for thin samples of Lithium and Lead were analyzed in terms of optical model calculations using the. computer code. RAROMP. Parameter search procedures produced good fits to the·cross-sections. For the case of thick samples of Lithium and Lead, the measured angular distributions of :the scattered neutrons were compared to the predictions of the continuous slowing down model.

A study of the scattering of fast neutrons in large samples

In the present work, the elastic scattering of fast neutrons from iron and concrete samples were studied at incident neutron energies of 14.0 and 14.4 Mev, using a neutron spectrometer based on the associated particle time-of-flight technique. These samples were chosen because of their importance in the design of fusion reactor shielding and construction. Using the S.A.M.E.S. accelerator and the 3 M v Dynamitron accelerator at the Radiation Centre, 14.0 and 14.4 Mev neutrons were produced by the T(d, n)4He reaction at incident deuteron energies of 140 keV and 900 keV mass III ions respectively. The time of origin of the neutron was determined by detecting the associated alpha particles. The samples used were extended flat plates of thicknesses up to 1.73 mean free paths for iron and 2.3 mean free paths for concrete. The associated alpha particles and fast neutrons were detected by means of a plastic scintillator mounted on a fast focused photomultiplier tube. The differential neutron elastic scattering cross-sections were measured for 14 Mev neutrons in various thicknesses of iron and concrete in the angular range from zero to 90°. In addition, the angular distributions of 14.4 Mev neutrons after passing through extended samples of iron were measured at several scattering angles in the same angular range. The measurements obtained for the thin sample of iron were compared with the results of Coon et al. The differential cross-sections for the thin iron sample were also analyzed on the optical model using the computer code RAROMP. For the concrete sample, the angular distribution of the thin sample was compared with the cross-sections calculated from the major constituent elements of concrete, and with the predicted values of the optical model for those elements. No published data could be found to compare with the results of the concrete differential cross-sections. In the case of thick samples of iron and concrete, the number of scattered neutrons were compared with a phenomological calculation based on the continuous slowing down model. The variation of measured cross-sections with sample thickness were found to follow the empirical relation σ = σ0 eαx. By using the universal constant "K", good fits were obtained to the experimental data. In parallel with the work at 14.0 and 14.4 Mev, an associated particle time-of-flight spectrometer was investigated which used the 2H(d,n)3He reaction for 3.02 Mev neutron energy at the incident deuteron energy of 1 Mev.

Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering

Results are reported from recent research on the use of the Brillouin gain/loss mechanism for distributed sensing. A theoretical model of the interaction of the pulsed and CW beams is described and compared with experiments. Results from a system with a 51 km sensing length are presented. We finally investigate issues related to the variation within the sensing fiber of the polarizations of the two beams.

Protein-protein interactions in ovalbumin solutions studied by small angle scattering: effect of ionic strength, and the chemical nature of cations

The influence of ionic strength and of the chemical nature of cations on the protein-protein interactions in ovalbumin solution was studied using small-angle X-ray and neutron scattering (SAXS/SANS). The globular protein ovalbumin is found in dimeric form in solutions as suggested by SANS/SAXS experiments. Due to the negative charge of the proteins at neutral pH, the protein-protein interactions without any salt addition are dominated by electrostatic repulsion. A structure factor related to screened Coulombic interactions together with an ellipsoid form factor was used to fit the scattering intensity. A monovalent salt (NaCl) and a trivalent salt (YCl3) were used to study the effect of the chemical nature of cations on the interaction in protein solutions. Upon addition of NaCl, with ionic strength below that of physiological conditions (150 mM), the effective interactions are still dominated by the surface charge of the proteins and the scattering data can be understood using the same model. When yttrium chloride was used, a reentrant condensation behavior, i.e., aggregation and subsequent redissolution of proteins with increasing salt concentration, was observed. SAXS measurements reveal a transition from effective repulsion to attraction with increasing salt concentration. The solutions in the reentrant regime become unstable after long times (several days). The results are discussed and compared with those from bovine serum albumin (BSA) in solutions.

Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering

Results are reported from recent research on the use of the Brillouin gain/loss mechanism for distributed sensing. A theoretical model of the interaction of the pulsed and CW beams is described and compared with experiments. Results from a system with a 51 km sensing length are presented. We finally investigate issues related to the variation within the sensing fiber of the polarizations of the two beams.

Experimental and theoretical studies on a distributed temperature sensor based on Brillouin scattering

Results are reported from recent research on the use of the Brillouin gain/loss mechanism for distributed sensing. A theoretical model of the interaction of the pulsed and CW beams is described and compared with experiments. Results from a system with a 51 km sensing length are presented. We finally investigate issues related to the variation within the sensing fiber of the polarizations of the two beams.

NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.