1,721,176 research outputs found
Point processes and stochastic displacement fields
No full textThe effect of a stochastic displacement field on a statistically independent point process is analyzed. Stochastic displacement fields can be divided into two large classes: spatially correlated and uncorrelated. For both cases exact transformation equations for the two-point correlation function and the power spectrum of the point process are found, and a detailed study of them with important paradigmatic examples is done. The results are general and in any dimension. Particular attention is devoted to the kind of large-scale correlations that can be introduced by the displacement field and to the realizability of arbitrary "superhomogeneous" point processes
Visita 2004 CSIS (Center for Secure Information Systems) alla George Mason University, Fairfax, Virginia
No full text
Voronoi and void statistics for superhomogeneous point processes
No full textWe Study the Voronoi and void statistics of superhomogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Superhomogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluctuations and correlations of the associated Voronoi cells. We derive exact results for the complete joint statistics of the size of two Voronoi cells. We also provide a sum rule that the correlation matrix for the Voronoi cells must obey in any space dimension. In contrast to the conventional picture of superhomogeneous systems, we show that infinitely large Voronoi cells or voids can exist in superhomogeneous point processes in any dimension. We also present two heuristic conditions to identify and classify any superhomogeneous point process in terms of the asymptotic behavior of the void size distribution
Glass-like universe: Real-space correlation properties of standard cosmological models
No full textAfter reviewing the basic relevant properties of stationary stochastic processes (SSP), defining basic terms and quantities, we discuss the properties of the so-called Harrison-Zeldovich like spectra. These correlations, usually characterized exclusively in k space [i.e., in terms of power spectra P(k)], are a fundamental feature of all current standard cosmological models. Examining them in real space we note their characteristics to be a negative power law tail xi(r)similar to-r(-4), and a sub-Poissonian normalized variance in spheres sigma(2)(R)similar toR(-4)ln R. We note in particular that this latter behavior is at the limit of the most rapid decay (similar toR(-4)) of this quantity possible for any stochastic distribution (continuous or discrete). This very particular characteristic is usually obscured in cosmology by the use of Gaussian spheres. In a simple classification of all SSP into three categories, we highlight with the name "superhomogeneous" the properties of the class to which models such as this, with P(0)=0, belong. In statistical physics language they are well described as glass-like. They have neither "scale-invariant" features, in the sense of critical phenomena, nor fractal properties. We illustrate their properties with some simple examples, in particular that of a "shuffled" lattice
Field theory of self-organized fractal etching
No full textWe propose a phenomenological field theoretical approach to the chemical etching of a disordered solid. The theory is based on a recently proposed dynamical etching model. Through the introduction of a set of Langevin equations for the model evolution, we are able to map the problem into a field theory related to isotropic percolation. To the best of the author's knowledge, this constitutes the first application of field theory to a problem of chemical dynamics. By using this mapping, many of the etching process critical properties are seen to be describable in terms of the percolation renormalization group fixed point. The emerging field theory has the peculiarity of being self-organized in the sense that without any parameter fine tuning the system develops fractal properties up to a certain scale controlled solely by the volume V of the etching solution. In the limit V --> infinity the upper cutoff goes to infinity and the system becomes scale invariant. We present also a finite size scaling analysis and discuss the relation of this particular etching mechanism to gradient percolation. Finally, the possibility of considering this mechanism as a generic path to self-organized criticality is analyzed, with the characteristics of being closely related to a real physical system and therefore more directly accessible to experiments
Biasing in Gaussian Random Fields and Galaxy Correlations
No full textIn this Letter, we show that in a Gaussian random field, the correlation length-the typical size of correlated structures-does not change with biasing. We interpret the amplification of the correlation functions of subsets identified by different thresholds as being caused by the increasing sparseness of peaks over threshold. This clarifies a long-standing misconception in the literature. We also argue that this effect does not explain the observed increase of the amplitude of the correlation function xi(r) when galaxies of brighter luminosity or galaxy clusters of increasing richness are considered
Bio-Inspired Topology Maintenance Protocols for Secure Wireless Sensor Networks
No full textWe analyze the security vulnerabilities of some well-known topology maintenance protocols (TMPs) for wireless sensor networks. These protocols aim to increase the lifetime of the sensor network by only maintaining a subset of nodes in an active or awake state. The design of these protocols assumes that the sensor nodes will be deployed in a trusted, non-adversarial environment, and does not take into account the impact of attacks launched by malicious insider or outsider nodes. We describe three attacks against these protocols that may be used to reduce the lifetime of the sensor network, or to degrade the functionality of the sensor application by reducing the network connectivity and the sensing coverage that can be achieved. Further, we describe countermeasures, inspired by biological systems and processes, that can be taken to increase the security and fault-tolerance of the protocols. © 2008 Springer Berlin Heidelberg
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