A simulational and theoretical study of the spherical electrical double layer for a size-asymmetric electrolyte: the case of big coions

Monte Carlo simulations of a spherical macroion, surrounded by a size-asymmetric electrolyte in the primitive model, were performed. We considered 1:1 and 2:2 salts with a size ratio of 2 (i.e., with coions twice the size of counterions), for several surface charge densities of the macrosphere. The radial distribution functions, electrostatic potential at the Helmholtz surfaces, and integrated charge are reported. We compare these simulational data with original results obtained from the Ornstein-Zernike integral equation, supplemented by the hypernetted chain/hypernetted chain (HNC/HNC) and hypernetted chain/mean spherical approximation (HNC/MSA) closures, and with the corresponding calculations using the modified Gouy-Chapman and unequal-radius modified Gouy-Chapman theories. The HNC/HNC and HNC/MSA integral equations formalisms show good concordance with Monte Carlo "experiments", whereas the notable limitations of point-ion approaches are evidenced. Most importantly, the simulations confirm our previous theoretical predictions of the non-dominance of the counterions in the size-asymmetric spherical electrical double layer [J. Chem. Phys. 123, 034703 (2005)], the appearance of anomalous curvatures at the outer Helmholtz plane and the enhancement of charge reversal and screening at high colloidal surface charge densities due to the ionic size asymmetry.Comment: 11 pages, 7 figure

The electrical double layer for a fully asymmetric electrolyte around a spherical colloid: an integral equation study

The hypernetted chain/mean spherical approximation (HNC/MSA) integral equation is obtained and solved numerically for a totally asymmetric primitive model electrolyte around a spherical macroparticle. The ensuing radial distribution functions show a very good agreement when compared to our Monte Carlo and molecular dynamics simulations for spherical geometry and with respect to previous anisotropic reference HNC calculations in the planar limit. We report an analysis of the potential vs charge relationship, radial distribution functions, mean electrostatic potential and cumulative reduced charge for representative cases of 1:1 and 2:2 salts with a size asymmetry ratio of 2. Our results are collated with those of the Modified Gouy-Chapman (MGC) and unequal radius Modified Gouy-Chapman (URMGC) theories and with those of HNC/MSA in the restricted primitive model (RPM) to assess the importance of size asymmetry effects. One of the most striking characteristics found is that,\textit{contrary to the general belief}, away from the point of zero charge the properties of an asymmetric electrical double layer (EDL) are not those corresponding to a symmetric electrolyte with the size and charge of the counterion, i.e. \textit{counterions do not always dominate}. This behavior suggests the existence of a new phenomenology in the EDL that genuinely belongs to a more realistic size-asymmetric model where steric correlations are taken into account consistently. Such novel features can not be described by traditional mean field theories like MGC, URMGC or even by enhanced formalisms, like HNC/MSA, if they are based on the RPM.Comment: 29 pages, 13 figure

Missing and Quenched Gamow Teller Strength

Gamow-Teller strength functions in full $(pf)^{8}$ spaces are calculated with sufficient accuracy to ensure that all the states in the resonance region have been populated. Many of the resulting peaks are weak enough to become unobservable. The quenching factor necessary to bring into agreement the low lying observed states with shell model predictions is shown to be due to nuclear correlations. To within experimental uncertainties it is the same that is found in one particle transfer and (e,e') reactions. Perfect consistency between the observed $^{48}Ca(p,n)^{48}Sc$ peaks and the calculation is achieved by assuming an observation threshold of 0.75\% of the total strength, a value that seems typical in several experimentsComment: 11 pages, 6 figures avalaible upon request, RevTeX, FTUAM-94/0

An Anisotropic Ballistic Deposition Model with Links to the Ulam Problem and the Tracy-Widom Distribution

We compute exactly the asymptotic distribution of scaled height in a (1+1)--dimensional anisotropic ballistic deposition model by mapping it to the Ulam problem of finding the longest nondecreasing subsequence in a random sequence of integers. Using the known results for the Ulam problem, we show that the scaled height in our model has the Tracy-Widom distribution appearing in the theory of random matrices near the edges of the spectrum. Our result supports the hypothesis that various growth models in $(1+1)$ dimensions that belong to the Kardar-Parisi-Zhang universality class perhaps all share the same universal Tracy-Widom distribution for the suitably scaled height variables.Comment: 5 pages Revtex, 3 .eps figures included, new references adde

The Parallel Complexity of Growth Models

This paper investigates the parallel complexity of several non-equilibrium growth models. Invasion percolation, Eden growth, ballistic deposition and solid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale as $O(\log^2 N)$, where $N$ is the system size, and the number of processors required scale as a polynomial in $N$. The algorithms are based on fast parallel procedures for finding minimum weight paths; they illuminate the close connection between growth models and self-avoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such as diffusion-limited aggregation, for which fast parallel algorithms probably do not exist.Comment: 20 pages, latex, submitted to J. Stat. Phys., UNH-TR94-0

Integration of computational modeling for the Los Alamos National Laboratory low level radioactive waste disposal performance assessment

The preliminary Performance Assessment for the Los Alamos National Laboratory Low Level Radioactive Waste Disposal Facility at Area G is drawing to completion. The disposal site is located on the top of a finger mesa in the complex terrain of a semi-arid region which leads to considerable complications in the atmospheric and subsurface transport and in the requisite modeling. Infiltration and run-off are evaluated for the proposed disposal unit closure configuration. A new analytic source release model characterizes the disposal unit performance utilizing detailed source term characterization from the inventory data base. This analysis provides input to the subsurface modeling done by the sophisticated finite element transport code, FEHM, using realistic 2-D cross-sections of the geologic units stratigraphies and the disposal units. Subsurface transport via lateral flow to intermittent alluvial waters in adjacent canyons is evaluated in addition to the usual deep aquifer. Vapor phase flow has been treated separately and calibrated to field data for tritium migration. Atmospheric transport is based on Gaussian dispersion with a correction for complex canyon terrain evaluated from on-going 3-D atmospheric transport studies. Indications to date are that the Performance Assessment objectives are met for all migration pathways

Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions

A microscopic heterogeneous system under random influence is considered. The randomness enters the system at physical boundary of small scale obstacles as well as at the interior of the physical medium. This system is modeled by a stochastic partial differential equation defined on a domain perforated with small holes (obstacles or heterogeneities), together with random dynamical boundary conditions on the boundaries of these small holes. A homogenized macroscopic model for this microscopic heterogeneous stochastic system is derived. This homogenized effective model is a new stochastic partial differential equation defined on a unified domain without small holes, with static boundary condition only. In fact, the random dynamical boundary conditions are homogenized out, but the impact of random forces on the small holes' boundaries is quantified as an extra stochastic term in the homogenized stochastic partial differential equation. Moreover, the validity of the homogenized model is justified by showing that the solutions of the microscopic model converge to those of the effective macroscopic model in probability distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200

Model-Independent Global Constraints on New Physics

Using effective-lagrangian techniques we perform a systematic survey of the lowest-dimension effective interactions through which heavy physics might manifest itself in present experiments. We do not restrict ourselves to special classes of effective interactions (such as `oblique' corrections). We compute the effects of these operators on all currently well-measured electroweak observables, both at low energies and at the $Z$ resonance, and perform a global fit to their coefficients. Despite the fact that a great many operators arise in our survey, we find that most are quite strongly bounded by the current data. We use our survey to systematically identify those effective interactions which are {\it not} well-bounded by the data -- these could very well include large new-physics contributions. Our results may also be used to efficiently confront specific models for new physics with the data, as we illustrate with an example.Comment: plain TeX, 68 pages, 2 figures (postscript files appended), McGill-93/12, NEIPH-93-008, OCIP/C-93-6, UQAM-PHE-93/08, UdeM-LPN-TH-93-15

Enhanced T-odd P-odd Electromagnetic Moments in Reflection Asymmetric Nuclei

Collective P- and T- odd moments produced by parity and time invariance violating forces in reflection asymmetric nuclei are considered. The enhanced collective Schiff, electric dipole and octupole moments appear due to the mixing of rotational levels of opposite parity. These moments can exceed single-particle moments by more than two orders of magnitude. The enhancement is due to the collective nature of the intrinsic moments and the small energy separation between members of parity doublets. In turn these nuclear moments induce enhanced T- and P- odd effects in atoms and molecules. First a simple estimate is given and then a detailed theoretical treatment of the collective T-, P- odd electric moments in reflection asymmetric, odd-mass nuclei is presented and various corrections evaluated. Calculations are performed for octupole deformed long-lived odd-mass isotopes of Rn, Fr, Ra, Ac and Pa and the corresponding atoms. Experiments with such atoms may improve substantially the limits on time reversal violation.Comment: 28 pages, Revte