James A. Given

Comment on: Fluid distributions in two‐phase random media: Arbitrary matrices

It is pointed out that the Ornstein–Zernike equations recently used by Madden in treating quenched‐annealed mixtures are approximate. The exact equations are given and briefly discussed.

On the thermodynamics of fluids adsorbed in porous media

We develop thermodynamics for partly quenched systems, i.e., systems in which some of the particles are quenched, or frozen in place, and some of which are annealed, or allowed to equilibrate. In particular, we focus on a class of models for fluids adsorbed in microporous media, in which the quenched particles constitute a microporous matrix, while the annealed particles constitute a fluid adsorbed in that matrix. The replica method is used to relate the matrix‐averaged quantities describing such a model to the thermodynamic quantities of a corresponding fully equilibrated model, called the replicated model. For these models, we present averaging methods that give the matrix‐averaged thermodynamic quantities of the fluid. We show that there are two natural definitions for the average pressure and three natural definitions for the chemical potential of these systems. We provide both operational definitions and Mayer expansions of these quantities. We establish the Gibbs–Duhem relations for these quantities...

Generalized ISAR-part II: interferometric techniques for three-dimensional location of scatterers

This paper is the second part of a study dedicated to optimizing diagnostic inverse synthetic aperture radar (ISAR) studies of large naval vessels. The method developed here provides accurate determination of the position of important radio-frequency scatterers by combining accurate knowledge of ship position and orientation with specialized signal processing. The method allows for the simultaneous presence of substantial Doppler returns from both change of roll angle and change of aspect angle by introducing generalized ISAR ates. The first paper provides two modes of interpreting ISAR plots, one valid when roll Doppler is dominant, the other valid when the aspect angle Doppler is dominant. Here, we provide, for each type of ISAR plot technique, a corresponding interferometric ISAR (InSAR) technique. The former, aspect-angle dominated InSAR, is a generalization of standard InSAR; the latter, roll-angle dominated InSAR, seems to be new to this work. Both methods are shown to be efficient at identifying localized scatterers under simulation conditions.

Comparison of analytic and numerical results for the mean cluster density in continuum percolation

Recently a number of techniques have been developed for bounding and approximating the important quantities in a description of continuum percolation models, such as 〈nc〉/ρ, the mean number of clusters per particle. These techniques include Kirkwood–Salsburg bounds, and approximations from cluster enumeration series of Mayer–Montroll type, and the scaled‐particle theory of percolation. In this paper, we test all of these bounds and approximations numerically by conducting the first systematic simulations of 〈nc〉/ρ for continuum percolation. The rigorous Kirkwood–Salsburg bounds are confirmed numerically in both two and three dimensions. Although this class of bounds seems not to converge rapidly for higher densities, averaging an upper bound with the corresponding lower bound gives an exceptionally good estimate at all densities. The scaled‐particle theory of percolation is shown to give extremely good estimates for the density of clusters in both two and three dimensions at all densities below the perc...

On the rapid estimation of permeability for porous media using Brownian motion paths

We describe two efficient methods of estimating the fluid permeability of standard models of porous media by using the statistics of continuous Brownian motion paths that initiate outside a sample and terminate on contacting the porous sample. The first method associates the ‘‘penetration depth’’ with a specific property of the Brownian paths, then uses the standard relation between penetration depth and permeability to calculate the latter. The second method uses Brownian paths to calculate an effective capacitance for the sample, then relates the capacitance, via angle-averaging theorems, to the translational hydrodynamic friction of the sample. Finally, a result of Felderhof is used to relate the latter quantity to the permeability of the sample. We find that the penetration depth method is highly accurate in predicting permeability of porous material.

Generalized ISAR - part I: an optimal method for imaging large naval vessels

We describe a generalized inverse synthetic aperture radar (ISAR) process that performs well under a wide variety of conditions common to the naval ISAR tests of large vessels. In particular, the generalized ISAR process performs well in the presence of moderate intensity ship roll. The process maps localized scatterers onto peaks on the ISAR plot. However, in a generalized ISAR plot, each of the two coordinates of a peak is a fixed linear combination of the three ship coordinates of the scatterer causing the peak. Combining this process with interferometry will then provide high-accuracy three-dimensional location of the important scatterers on a ship. We show that ISAR can be performed in the presence of simultaneous roll and aspect change, provided the two Doppler rates are not too close in magnitude. We derive the equations needed for generalized ISAR, both roll driven and aspect driven, and test them against simulations performed in a variety of conditions, including large roll amplitudes.

Liquid-State Theory for Some Non-Equilibrium Processes

Recent advances in liquid-state theory permit the calculation of thermodynamic quantities and correlation functions for systems in which some of the degrees of freedom are quenched, or frozen in place, while the rest are annealed. Basic examples include models for porous media, crystals containing quenched impurities, and spin glasses. We further extend these methods to treat materials constructed in layers, each layer being added to the system and allowed to equilibrated, then frozen in place before the next layer is added. We discuss sequentially adsorbed systems as an important class of examples.

Liquid-state methods for random media. II: Spin glasses

The continuum replica method allows one to use equilibrium liquid‐state theory to treat those nonequilibrium systems in which the quenched and annealed degrees of freedom correspond to distinct subsets of the particles in the system. In this paper, we provide a new generalization of the replica method that applies to a much larger class of continuum models. This involves using methods from the theory of chemical association to represent a particle as a bound state of pseudoparticles of different types or ‘‘species,’’ each of which carries some of the degrees of freedom of the particle. We use this method to study a realistic continuum spin glass. In particular, we show how to construct thermodynamic perturbation theory for the correlation functions of the system. We also show in detail how to apply association methods to study models of growth and aggregation treating, in particular, the Eden model and self‐avoiding walks (SAWs).

Diffusion‐controlled reactions in a polydisperse medium of reactive sinks

We study diffusion‐controlled reactions in which a reactive solute diffuses through a medium containing static, reactive, spherical traps of many different sizes. We focus on the cases of impenetrable, i.e., nonoverlapping traps, and of randomly overlapping traps. Bounds for the trapping rate are derived using trial functions of the kind developed by Doi, and by Weissberg and Prager. It is shown that the bounds for trapping rate are relatively insensitive to dispersivity of trap size when they are plotted against the proper scaling variable. The trap volume fraction is the proper scaling variable for randomly overlapping traps. The mean density of traps ρ〈a〉 is shown to be the proper scaling variable for nonoverlapping traps. It is shown that the low‐density limits of both the Doi and the Weissberg–Prager bounds fail to reproduce the radius‐averaged single‐trap solution of Smoluchowski. We give a generalization of these classes of bounds that has the proper behavior. In evaluating trapping bounds for impe...

Scaled‐particle theory and the short distance behavior of continuum percolation

In this paper, we use results from geometric probability theory to constrain the behavior of continuum percolation models. Specifically, we consider the random percolation of spheres, in which particles are distributed at random with density ρ, each pair being considered connected if its separation is less than a distance a. For this model we prove a zero‐separation theorem, which gives the first three terms in a Taylor series expansion around zero separation of the two‐point connectedness function. These expressions are then used in a closure for the Born–Green equations of percolation. The result is an approximate equation of state, or formula for the mean number of clusters 〈nc〉 as a function of density, which is quite accurate at moderate densities. Using the relation between continuum percolation and the continuum Potts model, we develop two different forms of scaled particle theory for continuum percolation. These theories are then combined with the zero‐separation theorems to give several approxim...