This paper studies Frequency-Difference-of-Arrival (FDOA) curves for the 2-dimensional, 2-sensor case. The primary focus of this paper is to give a description of curves associated to the FDOA problem from the algebro-geometric point of view. To be more precise, the complex projective picture of the family of FDOA curves for all possible relative velocities is described.

First‐passage and last‐passage Monte Carlo algorithms have been used for computing charge distribution on a conducting object. First‐passage algorithms are used for an overall charge distribution on a conducting object and Given–Hwang's last‐passage algorithms are used for a charge density at a specific point on a flat or spherical surface of a conductor. In this paper, a last‐passage algorithm for computing charge distribution over a finite region of a conducting object is presented.

Many state-of-the-art methods in source localization require large numbers of sensors and perform poorly or require additional sensors when emitters of interest transmit highly correlated waveforms. We present a new source localization technique which employs a cross correlation measure of the time difference of arrival (TDOA) for signals recorded at two separate platforms, at least one of which is in motion. This data is backprojected through a process of synthetic aperture source localization (SASL) to form an image of the locations of the emitters in a region of interest (ROI) This method has the advantage of not requiring anya prioriknowledge of the number of emitters in the scene. Nor does it rest on an ability to identify regions of the data which come from individual emitters, though if this capability is present it may improve image quality. We demonstrate that this method is capable of localizing emitters which transmit highly correlated waveforms, though complications arise when several such emitters are present in the scene. We discuss these complications and strategies to mitigate them.

In this paper we establish a general framework for deriving two-channel detectors for passively detecting sources of acoustic or electromagnetic radiation. The framework is based on a first-order model for multivariate normal measurements at two spatially separated arrays, each consisting of L sensors that record M snapshots. The question to be answered is whether or not these measurements contain a signal common to both sensor arrays, indicating the existence of a radiating source. Generalized likelihood ratios (GLRs) aim to maximize the output signal-to-noise ratio (SNR) of a two-channel receiver. Quite generally, the GLRs are maximum eigenvalues of variance-normalized covariance matrices constructed from spacetime measurements at the two arrays. So, while the underlying measurement model is a first-order model, the resulting GLR statistics are decidedly nonlinear functions of the measurements.

This paper develops a mathematical method for determining the locations of multiple transmitters from passive measurements of the signals at two or more receivers. The method applies to the case of emitters transmitting either wideband or narrowband signals.

We develop and test the last-passage diffusion algorithm, a charge-based Monte Carlo algorithm, for the mutual capacitance of a system of conductors. The first-passage algorithm is highly efficient because it is charge based and incorporates importance sampling; it averages over the properties of Brownian paths that initiate outside the conductor and terminate on its surface. However, this algorithm does not seem to generalize to mutual capacitance problems. The last-passage algorithm, in a sense, is the time reversal of the first-passage algorithm; it involves averages over particles that initiate on an absorbing surface, leave that surface, and diffuse away to infinity. To validate this algorithm, we calculate the mutual capacitance matrix of the circular-disk parallel-plate capacitor and compare with the known numerical results. Good agreement is obtained.

We prove rigorous inequalities for the hydrodynamic translational friction and mobility matrices ζ and μO of an arbitrarily shaped rigid particle in terms of the electrostatic capacitance C of a conducting particle of identical shape. Specifically, we derive the scalar and matrix inequalities 13trζ−1⩽13trμO⩽C−1 and 23ζ−1⩽C−1I, where all quantities are normalized by the corresponding values for a sphere, and the mobility matrix is evaluated in the center-of-mobility reference frame. These bounds are obtained using a variational approach with the energy dissipation functional expressed in terms of the induced force distribution on the surface of the particle. To relate the hydrodynamic problem to the solution of the corresponding electrostatic problem, the trial force field is expressed in terms of the charge distribution on the equipotential particle surface. This procedure yields the first rigorous bounds on hydrodynamic friction that apply to bodies with translation-rotation coupling. We demonstrate that the error of the Hubbard–Douglas approximation 13trζ−1≈C−1, corresponding to our scalar bound, is quadratic in the deviation of the trial induced-force field from the exact form—which explains why this relation is highly accurate for many particle shapes. Our numerical results confirm that the Hubbard–Douglas approximation is accurate for a variety of objects, including helices with translational–rotational coupling. In addition, we establish a rigorous, sharp bound on the effective (scalar) Brownian diffusion coefficient of an arbitrarily shaped particle.

In our previous study, [8], we described two efficient methods of estimating the fluid permeability of a porous medium as a function of the medium's porosity. These methods use the statistics of Brownian particles diffusing near a sample of the medium. The Brownian trajectories are constructed by using the Green's function first-passage method. These trajectories are built up as a series of discrete jumps, each jump leaving the center of a first-passage domain.and landing at a point on its first-passage surface. Using transition probabilities that are sampled from the Laplacian Green's function for the geometry of the first-passage domain, each landing position is determined. This is an exact sampling method that is an acceleration of the walk on spheres method. The first of these two firstpassage methods estimates permeability in terms of the fluid-dynamic penetration depth, identifying the latter with a penetration property of Brownian paths. The second method computes the effective electrostatic capacitance of the sample and relates it, via angleaveraging theorems, to the translational hydrodynamic friction, and then uses a mean-field approximation to equate the latter quantity to the permeability of the porous medium. For the sampling of porous media, we exploited our "sharp-boundary" sampling method. We improve on our previous permeability estimates using a refinement of the sharp-boundary sampling algorithm. In our new algorithm, we decrease the number of jumps required to simulate a complete Brownian path. This is accomplished by starting the paths directly on the spherical sharp boundary of the porous medium sample. This is mathematically equivalent to the old method, but both much faster and more numerically precise. In fact, our new method is about three times faster, and the new method provides better permeability estimates at low porosities. The new method produces trajectories with many fewer jumps on average. Since the computational cost of these methods is roughly proportional to number of jumps, this explains the speed up. Moreover, our improvements in precision and execution time are most dramatic when simulating low porosity sample. With our previous method, the low porosity case was the most demanding. In several of the cases studied here, our permeability results are identical to those obtained from detailed deterministic solution of the Stokes equations, to within statistical error. Finally, the reduction in the average number of jumps reduces the effective dimensionality of the problem. This opens the possibility of further acceleration though the use of quasirandom numbers, [2j. "Department of Computer Science, Florida State University, 203 Love Building, Tallahassee, FL 32306-4530, USA, E-mail: chwangOcs.fsu.edu tDepartment of Computer Science, Florida State University, 203 Love Building, Tallahassee, FL 32306-4530, USA, E-mail: mascagniOcs.fsu.edu, URL: http://vtfv.cs.fsu.edu/~mascagni *Angie Inc., 7406 Alban Station Court, Suite A112, Springfield, VA 22150 USA, E-mail: giveno angle inc. com 214 Chi-Ok Hwang, Michael Mascagni and James A. Given

We use the methods of continuum percolation theory to develop a consistent, essentially analytic theory for the properties of the restricted primitive model (RPM) of electrolytes. Contributions to the thermodynamic properties of this system are divided into two types; those from pairs of ions in the same cluster, and those from pairs in different clusters (we call these IN and OUT contributions, respectively, for brevity). We give exact expressions for the IN contributions as weighted integrals over the ionic pair connectedness functions. We give an exact analytic solution for these functions in the generalized mean-spherical approximation. The OUT contributions are calculated by replacing the system of ionic clusters by a system of charged hard spheres having the same statistics, and using the analytic results available for the latter system. Because the method requires no input from simulations, it can be readily adapted to treat many different electrolyte systems. Our method closely models simulation data for the thermodynamic quantities of the RPM. An earlier note [J. Chem. Phys. 96, 9233 (1992)] sketched our theory and compared our results to electrolyte data. Here we present in detail the analytic basis for our method. In future papers we expect to present detailed numerical results.

MD simulations, currently the most detailed description of the dynamic evolution of proteins, are based on the repeated solution of a set of differential equations implementing Newton's second law. Many such systems are known to exhibit chaotic behavior, i.e., very small changes in initial conditions are amplified exponentially and lead to vastly different, inherently unpredictable behavior. We have investigated the response of a protein fragment in an explicit solvent environment to very small perturbations of the atomic positions (10(-3)-10(-9) A). Independent of the starting conformation (native-like, compact, extended), perturbed dynamics trajectories deviated rapidly, leading to conformations that differ by approximately 1 A RMSD within 1-2 ps. Furthermore, introducing the perturbation more than 1-2 ps before a significant conformational transition leads to a loss of the transition in the perturbed trajectories. We present evidence that the observed chaotic behavior reflects physical properties of the system rather than numerical instabilities of the calculation and discuss the implications for models of protein folding and the use of MD as a tool to analyze protein folding pathways.

Many important properties of a macromolecule can be expressed in terms of averages over the trajectories of diffusing particles that begin in the medium surrounding the molecule and terminate at its surface. These properties include its translational hydrodynamic friction coefficient and the Smoluchowski rate constant for diffusion-limited reactions. In this paper we introduce a first-passage algorithm (FPA) for calculating such quantities. This algorithm uses certain exact Green’s functions, or propagators, for the Laplace equation to eliminate the need to construct explicitly those portions of a diffusing particle’s trajectory that are not near an absorbing object. The algorithm is especially efficient for studying objects that contain large voids or have very irregular surfaces, such as macromolecules. Diffusion algorithms were previously shown to give accurate results for the quantities we study. In this paper, we show that first-passage methods make these algorithms more accurate and efficient. In future work, we expect to present systematic results for the properties of globular proteins.

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. We also present new exact relations that express the thermodynamic quantities of partly quenched media in terms of the correlation functions in such media. These include a set of compressibility relations and a virial relation.

Publisher Summary This chapter outlines the connection with continuum percolation provided by the continuum Potts model. It explains how this connection helps provide computationally useful formulas for the quantities that describe clustering. Concepts of clustering are important in many branches of engineering and all of the physical sciences. Over the past few years, a detailed statistical theory of clustering in disordered materials has been developed by adapting from the molecular theory of liquids notions of association and correlation and powerful approximation techniques. The chapter presents some of these results. It discusses in particular a way to extend a theory of the percolation transition to obtain a general method for calculating the cluster-size distribution. The method includes a scaled-particle theory for the quantity n c ( p ), the mean number density of clusters. Adding an external ghost field allows one to further calculate the cluster-size distribution function. The chapter discusses ongoing development of a theory of ionic clustering in electrolytes based on percolation theory.

In this paper we solve the replica Ornstein-Zernike (ROZ) equations in the hypernetted-chain (HNC), Percus-Yevick (PY), and reference Percus-Yevick (RPY) approximations for partly quenched systems. The ROZ equations, which apply to the general class of partly quenched systems, are here applied to a class of models for porous media. These models involve two species of particles: an annealed or equilibrated species, which is used to model the fluid phase, and a quenched or frozen species, whose excluded-volume interactions constitute the matrix in which the fluid is adsorbed. We study two models for the quenched species of particles: a hard-sphere matrix, for which the fluid-fluid, matrix-matrix, axid matrix-fluid sphere diameters sigma11, sigma00, and sigma01 are additive, and a matrix of randomly overlapping particles (which still interact with the fluid particle as hard spheres) that gives a ''random'' matrix with interconnected pore structure. For the random-matrix case we study a ratio sigma01/sigma11 of 2.5, which is a demanding one for the theories. The HNC and RPY results represent significant improvements over the PY result when compared with the Monte Carlo simulations we have generated for this study, with the HNC result yielding the best results overall among those studied. A phenomenological percolating-fluid approximation is also found to be of comparable accuracy to the HNC results over a significant range of matrix and fluid densities. In the hard-sphere matrix case, the RPY is the best of the theories that we have considered.

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.

We develop a method for calculating the physical and geometric properties of atomic clusters in a very general aggregation model. Our method accommodates an arbitrary interparticle potential. It also allows the use of a very wide range of pairing criteria for specifying which configuations are considerd to form clusters. We develop an exact differential equation satisfied by the generating function for the quantities {n(c)(k)}, where n(c)(k) is the mean number per unit volume of clusters containing exactly k atoms. We discuss economic methods of solving this equation; a second paper is planned to discuss numerical solutions in detail. We show that the analog, for continuum percolation, of the virial theorem is an exact rate equation of Smoluchowski type for the cluster densities, in which the time is replaced by the total particle density. In this equation, the rate constants are given by contact values of connectedness functions. Applications of this rate equation are discussed. We also give an exact equation for the generating function for cluster volumes. Extensions of the method to calculate cluster free energies economically are described.

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).