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Relativistic Space-Times Having Corresponding Geodesics Final Report

Pairs of Relativistic Space-Times are classified according to their Segre characteristics. Suitable bases consisting of pseudo-orthonormal tetrads are constructed and the condition that the spaces should have corresponding geodesics is imposed. contain spaces with corresponding geodesics. It is found that the [3, 1] and [(3, 1)] classes contain spaces with corresponding geodesics. Of these metrics, the vacuum ones are shown to be algebraically special, in the sense of the Petrov classification.

Segre characteristic↗

Glass/Jamming Transition in Colloidal Aggregation

We have studied colloidal aggregation in a model colloid plus polymer system with short-range attractive interactions. By varying the colloid concentration and the strength of the attraction, we explored regions where the equilibrium phase is expected to consist of colloidal crystallites in coexistance with colloidal gas (i.e. monomers). This occurs for moderate values of the potential depth, U approximately equal to 2-5 kT. Crystallization was not always observed. Rather, over an extended sub-region two new metastable phases appear, one fluid-like and one solid-like. These were examined in detail with light scattering and microscopy techniques. Both phases consist of a near uniform distribution of small irregular shaped clusters of colloidal particles. The dynamical and structural characteristics of the ergodic-nonergodic transition between the two phases share much in common with the colloidal hard sphere glass transition.

Segre, Philip N.↗

Entrapped Molecule‐Like Europium‐Oxide Clusters in Zinc Oxide with Nearly Unaffected Host Structure

Abstract Nanocrystalline ZnO sponges doped with 5 mol% EuO 1.5 are obtained by heating metal–salt complex based precursor pastes at 200–900 °C for 3 min. X‐ray diffraction, transmission electron microscopy, and extended X‐ray absorption fine structure (EXAFS) show that phase separation into ZnO:Eu and c ‐Eu 2 O 3 takes place upon heating at 700 °C or higher. The unit cell of the clean oxide made at 600 °C shows only ≈0.4% volume increase versus undoped ZnO, and EXAFS shows a ZnO local structure that is little affected by the Eu‐doping and an average Eu 3+ ion coordination number of ≈5.2. Comparisons of 23 density functional theory‐generated structures having differently sized Eu‐oxide clusters embedded in ZnO identify three structures with four or eight Eu atoms as the most energetically favorable. These clusters exhibit the smallest volume increase compared to undoped ZnO and Eu coordination numbers of 5.2–5.5, all in excellent agreement with experimental data. ZnO defect states are crucial for efficient Eu 3+ excitation, while c ‐Eu 2 O 3 phase separation results in loss of the characteristic Eu 3+ photoluminescence. The formation of molecule‐like Eu‐oxide clusters, entrapped in ZnO, proposed here, may help in understanding the nature of the unexpected high doping levels of lanthanide ions in ZnO that occur virtually without significant change in ZnO unit cell dimensions.

36 MATERIALS SCIENCE↗

Correlations and Gravitational Temperature in Settling Suspensions

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.05 less than phi less than 0.50. During sedimentation, velocity fluctuations are found to be organized into regions of characteristic size L approximately equal to 11 a phi(exp -1/3) and buoyant mass DELTA m given by the rms density fluctuations in a region of size L(exp 3) assuming random statistics. A simple model incorporating the suspension viscosity and excluded volume effects accurately predicts the magnitudes of the observed velocity fluctuations DELTA V. These lead to a universal relation for particle diffusion that can be written in a Stokes-Einstein type form as D approximately equal to (DELTA m gL)/(6 pi (eta)L).

Segre, Philip N.↗

Effective Gravitational Temperature in Sedimentation

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.05 less than phi less than 0.50. During sedimentation, velocity fluctuations are found to be organized into regions of characteristic size L approximately 11 a phi(exp-1/3) and buoyant mass DELTA m given by the rms density fluctuations in a region of size L(sup 3) assuming random statistics with excluded volume effects. A simple model accurately predicts the magnitudes of the velocity fluctuations DELTA V. Finally, we find a new universal relation for particle diffusion during sedimentation that can be written in a Stokes-Einstein type form as D approximately (DELTA mg L)/(6 pi eta L), where the effective temperature DELTA mg L is the gravitational potential energy of density fluctuations.

Segre, Philip N.↗

Origin of Stability in Particle Sedimentation

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.0001 less than phi less than 0.50. During sedimentation, particle velocity fluctuations are found to be organized into regions of characteristic size xi approximately 11 a phi (exp -1/3). A simple model, based upon buoyant mass fluctuations DELTAm given by random density fluctuations in a region of size xi, accurately predicts the magnitudes of the velocity fluctuations DELTAV. We also find a new universal relation for particle diffusion during sedimentation. It can be written in a Stokes-Einstein form as Dapproximately(DELTAmxi)/(6pietaxi), where the effective temperature DELTAmgxi is the gravitational potential energy of density fluctuations. In addition related experiments examining inertial effects and transient states, that are aimed at uncovering the origin of the new lengthscale xi, will also be given.

Segre, Philip N.↗

Effective Gravitational Temperature in Sedimentation

Particle Image Velocimetry (PIV) is used to study the slow settling motions of spheres in suspensions ranging from dilute to highly concentrated, 0.0001 less than phi less than 0.50. During sedimentation, particle velocity fluctuations are found to be organized into regions of characteristic size xi approx. parallel to (alpha)phi(sup -1/3). A simple model, based upon buoyant mass fluctuations (Delta)m given by random density fluctuations in a region of size xi, accurately predicts the magnitudes of the velocity fluctuations (Delta)V. We also find a new universal relation for particle diffusion during sedimentation. It can be written in a Stokes-Einstein form as D approx. (Delta m g xi)/(6pi eta xi), where the effective temperature Delta m g xi is the gravitational potential energy of density fluctuations. In addition related experiments examining inertial effects and transient states, that are aimed at uncovering the origin of the new length-scale xi, will also be given.

Segre, Philip N.↗

Physics of Colloids in Space-2 (PCS-2)

The Physics of Colloids-2 (PCS-2) experiment is aimed at investigating the basic physical properties of several types of colloidal suspensions. The three broad classes of colloidal systems of interest are binary colloids, colloid-polymer mixtures, and fractal gels. The objective is to understand their phase behavior as well as the kinetics of the phase transitions in the absence of gravity. The nucleation, growth, and morphology characteristics of the crystals and gels that form would be studied using confocal microscopy. These will be observed directly with excellent time resolution, and therefore extensive information about the different phases and their growth mechanisms will be gained. With the laser tweezers, it will be possible to measure the strength of these structures and to modify them in a controlled way, and the spectrophotometer will provide the possibility to probe their optical properties. We believe that this experiment will provide the basis for future 'colloid engineering' in which complicated structures with novel properties (e.g., photonic crystals) will be grown by controlled self-assembly.

Sankaran, Subramanian↗