Scaling and the Smoluchowski Equations

The Smoluchowski equations, which describe coalescence growth, take into account combination reactions between a j-mer and a k-mer to form a (j+k)-mer, but not breakup of larger clusters to smaller ones. All combination reactions are assumed to be second order, with rate constants K jk. The K jk are said to scale if K λj,γk =λ μγ μK jk for j ≤ k. It can then be shown that, for large k, the number density or population of k-mers is given by Ak ae -bk, where A is a normalization constant (a function of a, b, and time), a=-(μ+ ν), and b μ+ν-1 depends linearly on time. We prove this in a simple, transparent manner. We also discuss the origin of odd-even population oscillations for small k. A common scaling arises from the ballistic model, which assumes that the velocity of a k-mer is proportional to 1/ √m k (Maxwell distribution), i.e., thermal equilibrium. This does not hold for the nascent distribution of clusters produced from monomers by reactive collisions. By direct calculation, invoking conservation of momentum in collisions, we show that, for this distribution, velocities are proportional to m k -0-.577. This leads to μ+ν=0.090, intermediate between the ballistic (0.167) and diffusive (0.000) results. These results are discussed in light of the existence of systems in the experimental literature which apparently correspond to very negative values of μ+ν

Application of Scaling and Kinetic Equations to Helium Cluster Size Distributions: Homogeneous Nucleation of a Nearly Ideal Gas

A previously published model of homogeneous nucleation [Villarica et al., J. Chem. Phys. 98, 4610 (1993)] based on the Smoluchowski [Phys. Z. 17, 557 (1916)] equations is used to simulate the experimentally measured size distributions of 4He clusters produced in free jet expansions. The model includes only binary collisions and does not consider evaporative effects, so that binary reactive collisions are rate limiting for formation of all cluster sizes despite the need for stabilization of nascent clusters. The model represents these data very well, accounting in some cases for nearly four orders of magnitude in variation in abundance over cluster sizes ranging up to nearly 100 atoms. The success of the model may be due to particularities of 4He clusters, i.e., their very low coalescence exothermicity, and to the low temperature of 6.7 K at which the data were collected

Structural and Electronic Properties of Amorphous and Polycrystalline In2Se3 Films

Structural and electronic properties of amorphous and single-phase polycrystalline films of gamma- and kappa-In2Se3 have been measured. The stable gamma phase nucleates homogeneously in the film bulk and has a high resistivity, while the metastable kappa phase nucleates at the film surface and has a moderate resistivity. The microstructures of hot-deposited and post-annealed cold-deposited gamma films are quite different but the electronic properties are similar. The increase in the resistivity of amorphous In2Se3 films upon annealing is interpreted in terms of the replacement of In-In bonds with In-Se bonds during crystallization. Great care must be taken in the preparation of In2Se3 films for electrical measurements as the presence of excess chalcogen or surface oxidation may greatly affect the film properties.Comment: 23 pages and 12 figure

Transmission Electron Study of Heteroepitaxial Growth in the BiSrCaCuO System

Films of Bi$\rm _2$Sr$\rm _2$CaCu$\rm _2$O$\rm _8$ and Bi$\rm _2$Sr$\rm _2$CuO$\rm _6$ have been grown using Atomic-Layer-by-Layer Molecular Beam Epitaxy (ALL-MBE) on lattice-matched substrates. These materials have been combined with layers of closely-related metastable compounds like Bi$\rm _2$Sr$\rm _2$Ca$\rm _7$Cu$\rm _8$O$\rm _{20}$ (2278) and rare-earth-doped compounds like Bi$\rm _2$Sr$\rm _2$Dy$\rm _x$Ca$\rm _{1-x}$Cu$\rm _2$O$\rm _8$ (Dy:2212) to form heterostructures with unique superconducting properties, including superconductor/insulator multilayers and tunnel junctions. Transmission electron microscopy (TEM) has been used to study the morphology and microstructure of these heterostructures. These TEM studies shed light on the physical properties of the films, and give insight into the growth mode of highly anisotropic solids like Bi$\rm _2$Sr$\rm _2$CaCu$\rm _2$O$\rm _8$.Comment: 17 pages, submitted to J. Materials Research. Email to [email protected] if you want to receive copies of the figure

Selective self-categorization: Meaningful categorization and the in-group persuasion effect

Research stemming from self-categorization theory (Turner et al., 1987) has demonstrated that individuals are typically more persuaded by messages from their in-group than by messages from the out-group. The present research investigated the role of issue relevance in moderating these effects. In particular, it was predicted that in-groups would only be more persuasive when the dimension on which group membership was defined was meaningful or relevant to the attitude issue. In two studies, participants were presented with persuasive arguments from either an in-group source or an out-group source, where the basis of the in-group/out-group distinction was either relevant or irrelevant to the attitude issue. Participants' attitudes toward the issue were then measured. The results supported the predictions: Participants were more persuaded by in-group sources than out-group sources when the basis for defining the group was relevant to the attitude issue. However, when the defining characteristic of the group was irrelevant to the attitude issue, participants were equally persuaded by in-group and out-group sources. These results support the hypothesis that the fit between group membership and domain is an important moderator of self-categorization effects

Thermal state entanglement in harmonic lattices

We investigate the entanglement properties of thermal states of the harmonic lattice in one, two and three dimensions. We establish the value of the critical temperature for entanglement between neighbouring sites and give physical reasons. Further sites are shown to be entangled only due to boundary effects. Other forms of entanglement are addressed in the second part of the paper by using the energy as witness of entanglement. We close with a comprehensive diagram showing the different phases of entanglement versus complete separability and propose techniques to swap and tune entanglement experimentally.Comment: 9 pages, 4 figure

Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.Comment: to be published in J. Phys.

Noninvasive, In-Vivo, Tissue Modulated Near Infrared Spectroscopy of Fingertips: Resonance Raman Spectrum of Human Hemoglobin

Tissue modulation refers to using external stimuli such as mechanical pressure and temperature to produce various spatiotemporal distributions of blood and conceivably other fluids in tissues. Having the capacity to execute tissue modulation1 allows forms of difference spectroscopy to be used to isolate spectroscopic signals from specific components of the tissues noninvasively and in vivo. In the case of human fingertips we can think of the tissues present in the probed volume as being static tissue, plasma and red blood cells (RBCs). Static tissues deform under mechanical pressure based tissue modulation and the only possible fluid motions2 involve plasma and RBCs. Figure 1 shows the difference spectrum produced, negative modulated fluorescence and positive modulated Raman, when simultaneously a small amount of RBCs move into and some plasma is move out of the probed volume. We present spectra for all limiting forms of tissue modulation and show prototypical spectra that include fluorescence Rayleigh/Mie and Raman scattering

Simultaneous, noninvasive observation of elastic scattering, fluorescence and inelastic scattering as a monitor of blood flow and hematocrit in human fingertip capillary beds

We report simultaneous observation of elastic scattering, fluorescence, and inelastic scattering from in vivo near-infrared probing of human skin. Careful control of the mechanical force needed to obtain reliable registration of in vivo tissue with an appropriate optical system allows reproducible observation of blood flow in capillary beds of human volar side fingertips. The time dependence of the elastically scattered light is highly correlated with that of the combined fluorescence and Raman scattered light. We interpret this in terms of turbidity (the impeding effect of red blood cells on optical propagation to and from the scattering centers) and the changes in the volume percentages of the tissues in the irradiated volume with normal homeostatic processes. By fitting to a model, these measurements may be used to determine volume fractions of plasma and RBCs