Convergence correction in colloid scattering

The error introduced in depolarisation measurements due to the convergence of the incident beam has been investigated theoretically as well as experimentally for the case of colloid scattering, where the particles are not small compared to the wavelength of light. Assuming the scattering particles to be anisotropic rods, it is shown that, when the incident unpolarised light is condensed by means of a lens with a circular aperture, the observed depolarisation ratio ϱ u is given by ϱ u = ϱ u0 + 5/3 θ2 where ϱ u0 is the true depolarisation for incident parallel light, and θ the semi-angle of convergence. Appropriate formulae are derived when the incident beam is polarised vertically and horizontally. Experiments performed on six typical colloids support the theoretical conclusions. Other immediate consequences of the theory are also discussed.

Ultrasound modulation of coherent light in a multiple-scattering medium: experimental verification of nonzero average phase carried by light

We demonstrate the phase fluctuation introduced by oscillation of scattering centers in the focal volume of an ultrasound transducer in an optical tomography experiment has a nonzero mean. The conditions to be met for the above are: (i) the frequency of the ultrasound should be in the vicinity of the most dominant natural frequency of vibration of the ultrasound focal volume, (ii) the corresponding acoustic wavelength should be much larger than l(n)*, a modified transport mean-free-path applicable for phase decorrelation and (iii) the focal volume of the ultrasound transducer should not be larger than 4 - 5 times (l(n)*)(3). We demonstrate through simulations that as the ratio of the ultrasound focal volume to (l(n)*)(3) increases, the average of the phase fluctuation decreases and becomes zero when the focal volume becomes greater than around 4(l(n)*)(3); and through simulations and experiments that as the acoustic frequency increases from 100 Hz to 1 MHz, the average phase decreases to zero. Through experiments done in chicken breast we show that the average phase increases from around 110 degrees to 130 degrees when the background medium is changed from water to glycerol, indicating that the average of the phase fluctuation can be used to sense changes in refractive index deep within tissue.

Penetrative phototactic bioconvection in an isotropic scattering suspension

Phototaxis is a directed swimming response dependent upon the light intensity sensed by micro-organisms. Positive (negative) phototaxis denotes the motion directed towards (away from) the source of light. Using the phototaxis model of Ghorai, Panda, and Hill ''Bioconvection in a suspension of isotropically scattering phototactic algae,'' Phys. Fluids 22, 071901 (2010)], we investigate two-dimensional phototactic bioconvection in an absorbing and isotropic scattering suspension in the nonlinear regime. The suspension is confined by a rigid bottom boundary, and stress-free top and lateral boundaries. The governing equations for phototactic bioconvection consist of Navier-Stokes equations for an incompressible fluid coupled with a conservation equation for micro-organisms and the radiative transfer equation for light transport. The governing system is solved efficiently using a semi-implicit second-order accurate conservative finite-difference method. The radiative transfer equation is solved by the finite volume method using a suitable step scheme. The resulting bioconvective patterns differ qualitatively from those found by Ghorai and Hill ''Penetrative phototactic bioconvection,'' Phys. Fluids 17, 074101 (2005)] at a higher critical wavelength due to the effects of scattering. The solutions show transition from steady state to periodic oscillations as the governing parameters are varied. Also, we notice the accumulation of micro-organisms in two horizontal layers at two different depths via their mean swimming orientation profile for some governing parameters at a higher scattering albedo. (C) 2013 AIP Publishing LLC.

Phonon anomalies, orbital-ordering and electronic raman scattering in iron-pnictide Ca(Fe0.97Co0.03)(2)As-2: temperature-dependent Raman study

We report inelastic light scattering studies on Ca(Fe0.97Co0.03)(2)As-2 in a wide spectral range of 120-5200 cm(-1) from 5 to 300 K, covering the tetragonal to orthorhombic structural transition as well as magnetic transition at T-sm similar to 160 K. The mode frequencies of two first-order Raman modes B-1g and E-g, both involving the displacement of Fe atoms, show a sharp increase below T-sm. Concomitantly, the linewidths of all the first-order Raman modes show anomalous broadening below T-sm, attributed to strong spin-phonon coupling. The high frequency modes observed between 400 and 1200 cm(-1) are attributed to electronic Raman scattering involving the crystal field levels of d-orbitals of Fe2+. The splitting between xz and yz d-orbital levels is shown to be similar to 25 meV, which increases as temperature decreases below T-sm. A broad Raman band observed at similar to 3200 cm(-1) is assigned to two-magnon excitation of the itinerant Fe 3d antiferromagnet.

A constitutive description of the inelastic response of ceramics

The objective of the article is to present a unified model for the dynamic mechanical response of ceramics under compressive stress states. The model incorporates three principal deformation mechanisms: (i) lattice plasticity due to dislocation glide or twinning; (ii) microcrack extension; and (iii) granular flow of densely packed comminuted particles. In addition to analytical descriptions of each mechanism, prescriptions are provided for their implementation into a finite element code as well as schemes for mechanism transitions. The utility of the code in addressing issues pertaining to deep penetration is demonstrated through a series of calculations of dynamic cavity expansion in an infinite medium. The results reveal two limiting behavioral regimes, dictated largely by the ratio of the cavity pressure p to the material yield strength σY. At low values of p/σY, cavity expansion occurs by lattice plasticity and hence its rate diminishes with increasing σY. In contrast, at high values, expansion occurs by microcracking followed by granular plasticity and is therefore independent of σY. In the intermediate regime, the cavity expansion rate is governed by the interplay between microcracking and lattice plasticity. That is, when lattice plasticity is activated ahead of the expanding cavity, the stress triaxiality decreases (toward more negative values) which, in turn, reduces the propensity for microcracking and the rate of granular flow. The implications for penetration resistance to high-velocity projectiles are discussed. Finally, the constitutive model is used to simulate the quasi-static and dynamic indentation response of a typical engineering ceramic (alumina) and the results compared to experimental measurements. Some of the pertinent observations are shown to be captured by the present model whereas others require alternative approaches (such as those based on fracture mechanics) for complete characterization. © 2011 The American Ceramic Society.

Deep tissue fluorescence imaging with time-reversed light

Advances in optical techniques have enabled many breakthroughs in biology and medicine. However, light scattering by biological tissues remains a great obstacle, restricting the use of optical methods to thin ex vivo sections or superficial layers in vivo. In this thesis, we present two related methods that overcome the optical depth limit—digital time reversal of ultrasound encoded light (digital TRUE) and time reversal of variance-encoded light (TROVE). These two techniques share the same principle of using acousto-optic beacons for time reversal optical focusing within highly scattering media, like biological tissues. Ultrasound, unlike light, is not significantly scattered in soft biological tissues, allowing for ultrasound focusing. In addition, a fraction of the scattered optical wavefront that passes through the ultrasound focus gets frequency-shifted via the acousto-optic effect, essentially creating a virtual source of frequency-shifted light within the tissue. The scattered ultrasound-tagged wavefront can be selectively measured outside the tissue and time-reversed to converge at the location of the ultrasound focus, enabling optical focusing within deep tissues. In digital TRUE, we time reverse ultrasound-tagged light with an optoelectronic time reversal device (the digital optical phase conjugate mirror, DOPC). The use of the DOPC enables high optical gain, allowing for high intensity optical focusing and focal fluorescence imaging in thick tissues at a lateral resolution of 36 µm by 52 µm. The resolution of the TRUE approach is fundamentally limited to that of the wavelength of ultrasound. The ultrasound focus (~ tens of microns wide) usually contains hundreds to thousands of optical modes, such that the scattered wavefront measured is a linear combination of the contributions of all these optical modes. In TROVE, we make use of our ability to digitally record, analyze and manipulate the scattered wavefront to demix the contributions of these spatial modes using variance encoding. In essence, we encode each spatial mode inside the scattering sample with a unique variance, allowing us to computationally derive the time reversal wavefront that corresponds to a single optical mode. In doing so, we uncouple the system resolution from the size of the ultrasound focus, demonstrating optical focusing and imaging between highly diffusing samples at an unprecedented, speckle-scale lateral resolution of ~ 5 µm. Our methods open up the possibility of fully exploiting the prowess and versatility of biomedical optics in deep tissues.

Reduced deep-tissue image degradation in three-dimensional multiphoton microscopy with concentric two-color two-photon fluorescence excitation

We theoretically demonstrate that enhanced penetration depth in three-dimensional multiphoton microscopy can be achieved using concentric two-color two-photon (C2C2P) fluorescence excitation in which the two excitation beams are separated in space before reaching their common focal spot. Monte Carlo simulation shows that, in comparison with the one-color two-photon excitation scheme, the C2C2P fluorescence microscopy provides a significantly greater penetration depth for imaging into a highly scattering medium. (C) 2008 Optical Society of America.

I. Application of multi-Regge theory to production processes. II. High energy model for proton-proton scattering

This dissertation consists of two parts. The first part presents an explicit procedure for applying multi-Regge theory to production processes. As an illustrative example, the case of three body final states is developed in detail, both with respect to kinematics and multi-Regge dynamics. Next, the experimental consistency of the multi-Regge hypothesis is tested in a specific high energy reaction; the hypothesis is shown to provide a good qualitative fit to the data. In addition, the results demonstrate a severe suppression of double Pomeranchon exchange, and show the coupling of two "Reggeons" to an external particle to be strongly damped as the particle's mass increases. Finally, with the use of two body Regge parameters, order of magnitude estimates of the multi-Regge cross section for various reactions are given.

The second part presents a diffraction model for high energy proton-proton scattering. This model developed by Chou and Yang assumes high energy elastic scattering results from absorption of the incident wave into the many available inelastic channels, with the absorption proportional to the amount of interpenetrating hadronic matter. The assumption that the hadronic matter distribution is proportional to the charge distribution relates the scattering amplitude for pp scattering to the proton form factor. The Chou-Yang model with the empirical proton form factor as input is then applied to calculate a high energy, fixed momentum transfer limit for the scattering cross section, This limiting cross section exhibits the same "dip" or "break" structure indicated in present experiments, but falls significantly below them in magnitude. Finally, possible spin dependence is introduced through a weak spin-orbit type term which gives rather good agreement with pp polarization data.

The autocorrelation of speckles in deep Fresnel diffraction region and characterizations of random self-affine fractal surfaces

This paper studies the correlation properties of the speckles in the deep Fresnel diffraction region produced by the scattering of rough self-affine fractal surfaces. The autocorrelation function of the speckle intensities is formulated by the combination of the light scattering theory of Kirchhoff approximation and the principles of speckle statistics. We propose a method for extracting the three surface parameters, i.e. the roughness w, the lateral correlation length xi and the roughness exponent alpha, from the autocorrelation functions of speckles. This method is verified by simulating the speckle intensities and calculating the speckle autocorrelation function. We also find the phenomenon that for rough surfaces with alpha = 1, the structure of the speckles resembles that of the surface heights, which results from the effect of the peak and the valley parts of the surface, acting as micro-lenses converging and diverging the light waves.

Time-dependent monoenergetic neutron transport in two adjacent semi-infinite media

An exact solution to the monoenergetic Boltzmann equation is obtained for the case of a plane isotropic burst of neutrons introduced at the interface separating two adjacent, dissimilar, semi-infinite media. The method of solution used is to remove the time dependence by a Laplace transformation, solve the transformed equation by the normal mode expansion method, and then invert to recover the time dependence.

The general result is expressed as a sum of definite, multiple integrals, one of which contains the uncollided wave of neutrons originating at the source plane. It is possible to obtain a simplified form for the solution at the interface, and certain numerical calculations are made there.

The interface flux in two adjacent moderators is calculated and plotted as a function of time for several moderator materials. For each case it is found that the flux decay curve has an asymptotic slope given accurately by diffusion theory. Furthermore, the interface current is observed to change directions when the scattering and absorption cross sections of the two moderator materials are related in a certain manner. More specifically, the reflection process in two adjacent moderators appears to depend initially on the scattering properties and for long times on the absorption properties of the media.

This analysis contains both the single infinite and semi-infinite medium problems as special cases. The results in these two special cases provide a check on the accuracy of the general solution since they agree with solutions of these problems obtained by separate analyses.

The influence of the NN* channel on elastic NN scattering

The problem of two channels NN and NN*, coupled through unitarity, is studied to see whether sizable peaks can be produced in elastic nucleon-nucleon scattering due to the opening of a strongly coupled inelastic channel. One-pion-exchange (OPE) interactions are calculated to estimate the NN*→NN* and NN→NN* amplitudes. The OPE production amplitudes are used as the sole dynamical input to drive the multichannel ND^-1 equations in the determinental approximation, and the effect on the J = 2+ (¹D₂) elastic NN scattering amplitude is studied as the width of the unstable N* and strength of coupling to the inelastic channel are varied. A cusp-type enhancement appears in the NN channel near the NN* threshold but for the known value of the N* width the cusp is so “wooly” that any resulting elastic peak is likely to be too broad and diminished in height to be experimentally prominent. A brief survey of current experimental knowledge of the real part of the ¹D₂ NN phase shift near the NN* threshold is given, and the values are found to be much smaller than the nearly “resonant” phase shifts predicted by the coupled channel model.

I. Quantum mechanics of one-dimensional two-particle models. II. A quantum mechanical treatment of inelastic collisions

Part I

Solutions of Schrödinger’s equation for system of two particles bound in various stationary one-dimensional potential wells and repelling each other with a Coulomb force are obtained by the method of finite differences. The general properties of such systems are worked out in detail for the case of two electrons in an infinite square well. For small well widths (1-10 a.u.) the energy levels lie above those of the noninteresting particle model by as much as a factor of 4, although excitation energies are only half again as great. The analytical form of the solutions is obtained and it is shown that every eigenstate is doubly degenerate due to the “pathological” nature of the one-dimensional Coulomb potential. This degeneracy is verified numerically by the finite-difference method. The properties of the square-well system are compared with those of the free-electron and hard-sphere models; perturbation and variational treatments are also carried out using the hard-sphere Hamiltonian as a zeroth-order approximation. The lowest several finite-difference eigenvalues converge from below with decreasing mesh size to energies below those of the “best” linear variational function consisting of hard-sphere eigenfunctions. The finite-difference solutions in general yield expectation values and matrix elements as accurate as those obtained using the “best” variational function.

The system of two electrons in a parabolic well is also treated by finite differences. In this system it is possible to separate the center-of-mass motion and hence to effect a considerable numerical simplification. It is shown that the pathological one-dimensional Coulomb potential gives rise to doubly degenerate eigenstates for the parabolic well in exactly the same manner as for the infinite square well.

Part II

A general method of treating inelastic collisions quantum mechanically is developed and applied to several one-dimensional models. The formalism is first developed for nonreactive “vibrational” excitations of a bound system by an incident free particle. It is then extended to treat simple exchange reactions of the form A + BC →AB + C. The method consists essentially of finding a set of linearly independent solutions of the Schrödinger equation such that each solution of the set satisfies a distinct, yet arbitrary boundary condition specified in the asymptotic region. These linearly independent solutions are then combined to form a total scattering wavefunction having the correct asymptotic form. The method of finite differences is used to determine the linearly independent functions.

The theory is applied to the impulsive collision of a free particle with a particle bound in (1) an infinite square well and (2) a parabolic well. Calculated transition probabilities agree well with previously obtained values.

Several models for the exchange reaction involving three identical particles are also treated: (1) infinite-square-well potential surface, in which all three particles interact as hard spheres and each two-particle subsystem (i.e. BC and AB) is bound by an attractive infinite-square-well potential; (2) truncated parabolic potential surface, in which the two-particle subsystems are bound by a harmonic oscillator potential which becomes infinite for interparticle separations greater than a certain value; (3) parabolic (untruncated) surface. Although there are no published values with which to compare our reaction probabilities, several independent checks on internal consistency indicate that the results are reliable.

Inelastic K+p reactions at incident momenta from 1.37 GeV/c to 2.17 GeV/c

A number of recent experiments have suggested the possibility of a highly inelastic resonance in K⁺p scattering. To study the inelastic K⁺p reactions, a 400 K exposure has been taken at the L.R.L. 25 inch bubble chamber. The data are spread over seven K⁺ momenta between 1.37 and 2.17 GeV/c.

Cross-sections have been measured for the reaction K⁺p → pK°π+ which is dominated by the quasi-two body channels K∆ and K*N. Both these channels are strongly peripheral, as at other momenta. The decay of the ∆ is in good agreement with the predictions of the rho-photon analogy of Stodolsky and Sakurai. The data on the K*p channel show evidence of both pseudo scalar and vector exchange.

Cross-sections for the final state pK⁺π+π- shows a strong contribution from the quasi-two body channel K*∆. This reaction is also very peripheral even at threshold. The decay angular distributions indicate the reaction is dominated as at higher momenta by a pion exchange mechanism. The data are also in good agreement with the quark model predictions of Bialas and Zalewski for the K* and ∆ decay.

Collective dynamics of glass-forming polymers at intermediate length scales: a synergetic combination of neutron scattering, atomistic simulations and theoretical modelling

Qens/wins 2014 - 11th International Conference on Quasielastic Neutron Scattering and 6th International Workshop on Inelastic Neutron Spectrometers / editado por:Frick, B; Koza, MM; Boehm, M; Mutka, H

Energy and momentum transfer in one-dimensional trapped gases by stimulated light scattering

In ultracold atoms settings, inelastic light scattering is a preeminent technique to reveal static and dynamic properties at nonzero momentum. In this work, we investigate an array of one-dimensional trapped Bose gases, by measuring both the energy and the momentum imparted to the system via light scattering experiments. The measurements are performed in the weak perturbation regime, where these two quantities-the energy and momentum transferred-are expected to be related to the dynamic structure factor of the system. We discuss this relation, with special attention to the role of in-trap dynamics on the transferred momentum.