Exact Multifractal Spectra for Arbitrary Laplacian Random Walks

Iterated conformal mappings are used to obtain exact multifractal spectra of the harmonic measure for arbitrary Laplacian random walks in two dimensions. Separate spectra are found to describe scaling of the growth measure in time, of the measure near the growth tip, and of the measure away from the growth tip. The spectra away from the tip coincide with those of conformally invariant equilibrium systems with arbitrary central charge $c\leq 1$, with $c$ related to the particular walk chosen, while the scaling in time and near the tip cannot be obtained from the equilibrium properties.Comment: 4 pages, 3 figures; references added, minor correction

Advanced Fuel Cycle Initiative (AFCI) Repository Impact Evaluation FY-05 Progress Report

An important long-term objective of advanced nuclear fuel cycle (AFC) technologies is to provide improvement in the long-term management of radioactive waste. Compared to a once-thru fuel cycle, it is possible to generate far less waste, and potentially easier waste to manage, with advanced fuel cycles. However, the precise extent and value of these benefits are complex and difficult to quantify. This document presents a status report of efforts within AFCI Systems Analysis to define and quantify the AFC benefits to geologic disposal, development of cooperative efforts with the US repository program, and participation with international evaluations of AFC impacts on waste management. The primary analysis of repository benefits is conducted by ANL. This year repository impact evaluations have included: (1) Continued evaluation of LWR recycle benefits in support of scenario analysis. (2) Extension of repository analyses to consider long-term dose reductions. (3) Developing the opportunity for cooperation with the U.S. repository program. (4) International cooperation with OECD-NEA

Dynamics of electrostatically-driven granular media. Effects of Humidity

We performed experimental studies of the effect of humidity on the dynamics of electrostatically-driven granular materials. Both conducting and dielectric particles undergo a phase transition from an immobile state (granular solid) to a fluidized state (granular gas) with increasing applied field. Spontaneous precipitation of solid clusters from the gas phase occurs as the external driving is decreased. The clustering dynamics in conducting particles is primarily controlled by screening of the electric field but is aided by cohesion due to humidity. It is shown that humidity effects dominate the clustering process with dielectric particles.Comment: 4 pages, 4 fig

Relaxation of surface charge on rotating dielectric spheres: Implications on dynamic electrorheological effects

We have examined the effect of an oscillatory rotation of a polarized dielectric particle. The rotational motion leads to a re-distribution of the polarization charge on the surface of the particle. We show that the time averaged steady-state dipole moment is along the field direction, but its magnitude is reduced by a factor which depends on the angular velocity of rotation. As a result, the rotational motion of the particle reduces the electrorheological effect. We further assume that the relaxation of polarized charge is arised from a finite conductivity of the particle or host medium. We calculate the relaxation time based on the Maxwell-Wagner theory, suitably generalized to include the rotational motion. Analytic expressions for the reduction factor and the relaxation time are given and their dependence on the angular velocity of rotation will be discussed.Comment: Accepted for publications by Phys. Rev.

AFCI Storage & Disposal FY-06 Progress Report

AFCI Storage and Disposal participants at LLNL, ANL and INL provide assessment of how AFCI technology can optimize the future evolution of the fuel cycle, including optimization of waste management. Evaluation of material storage and repository disposal technical issues provides feedback on criteria and metrics for AFCI, and evaluation of AFCI waste streams provides technical alternatives for future repository optimization. LLNL coordinates this effort that includes repository analysis at ANL and incorporation of repository impacts into AFCI criteria at INL. Cooperative evaluation with YMP staff is pursued to provide a mutually agreed technical base. Cooperation with select international programs is supported

Intercalation-enhanced electric polarization and chain formation of nano-layered particles

Microscopy observations show that suspensions of synthetic and natural nano-layered smectite clay particles submitted to a strong external electric field undergo a fast and extended structuring. This structuring results from the interaction between induced electric dipoles, and is only possible for particles with suitable polarization properties. Smectite clay colloids are observed to be particularly suitable, in contrast to similar suspensions of a non-swelling clay. Synchrotron X-ray scattering experiments provide the orientation distributions for the particles. These distributions are understood in terms of competing (i) homogenizing entropy and (ii) interaction between the particles and the local electric field; they show that clay particles polarize along their silica sheet. Furthermore, a change in the platelet separation inside nano-layered particles occurs under application of the electric field, indicating that intercalated ions and water molecules play a role in their electric polarization. The resulting induced dipole is structurally attached to the particle, and this causes particles to reorient and interact, resulting in the observed macroscopic structuring. The macroscopic properties of these electro-rheological smectite suspensions may be tuned by controlling the nature and quantity of the intercalated species, at the nanoscale.Comment: 7 pages, 5 figure

Multifractality and percolation in the coupling space of perceptrons

The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated analytically using the replica formalism. The storage capacity and the generalization behaviour of the perceptron are shown to be related to properties of $f(\alpha)$ which are correctly described within the replica symmetric ansatz. Replica symmetry breaking is interpreted geometrically as a transition from percolating to non-percolating cells. The existence of empty cells gives rise to singularities in the multifractal spectrum. The analytical results for binary couplings are corroborated by numerical studies.Comment: 13 pages, revtex, 4 eps figures, version accepted for publication in Phys. Rev.

Granular packings with moving side walls

The effects of movement of the side walls of a confined granular packing are studied by discrete element, molecular dynamics simulations. The dynamical evolution of the stress is studied as a function of wall movement both in the direction of gravity as well as opposite to it. For all wall velocities explored, the stress in the final state of the system after wall movement is fundamentally different from the original state obtained by pouring particles into the container and letting them settle under the influence of gravity. The original packing possesses a hydrostatic-like region at the top of the container which crosses over to a depth-independent stress. As the walls are moved in the direction opposite to gravity, the saturation stress first reaches a minimum value independent of the wall velocity, then increases to a steady-state value dependent on the wall-velocity. After wall movement ceases and the packing reaches equilibrium, the stress profile fits the classic Janssen form for high wall velocities, while it has some deviations for low wall velocities. The wall movement greatly increases the number of particle-wall and particle-particle forces at the Coulomb criterion. Varying the wall velocity has only small effects on the particle structure of the final packing so long as the walls travel a similar distance.Comment: 11 pages, 10 figures, some figures in colo

Renormalization Theory of Stochastic Growth

An analytical renormalization group treatment is presented of a model which, for one value of parameters, is equivalent to diffusion limited aggregation. The fractal dimension of DLA is computed to be 2-1/2+1/5=1.7. Higher multifractal exponents are also calculated and found in agreement with numerical results. It may be possible to use this technique to describe the dielectric breakdown model as well, which is given by different parameter values.Comment: 39 pages, LaTeX, 11 figure

The 12 micron band of ethane: A spectral catalog from 765 cm(-1) to 900 cm(-1)

The high resolution laboratory absorption spectrum of the 12 micro band of ethane gas is studied. The data were obtained using the McMath Solar Telescope 1 meter Fourier Transform interferometer at Kitt Peak National Observatory and tunable diode laser spectrometers at the University of Tennessee and NASA/Goddard Space Flight Center. Over 200 individual vibration rotation transitions were analyzed taking into account many higher order effects including torsional splitting. Line positions were reproduced to better than 0.001/cm. Both ground and upper state molecular constants were determined in the analysis. The experimental details, the analysis procedures and the results are addressed. A list of ethane transitions occurring near (14)CO2 laser lines needed for heterodyne searches for C2H6 in extraterrestrial sources is also included. A spectral catalog of the ethane nu sub g fundamental from 765/cm to 900/cm is provided. A high dispersion (1/cm 12 in.) plot of both the Kitt Peak interferometric data and a simulated spectrum with Doppler limited resolution, a table of over 8500 calculated transitions listed quantum number assignments, frequencies and intensities are provided