Fracture Spacing Variability and the Distribution of Fracture Patterns in Granitic Geothermal Reservoir: A Case Study in the Noble Hills Range (Death Valley, CA, USA)

Scanlines constitute a robust method to better understand in 3D the fracture network variability in naturally fractured geothermal reservoirs. This study aims to characterize the spacing variability and the distribution of fracture patterns in a fracture granitic reservoir, and the impact of the major faults on fracture distribution and fluid circulation. The analogue target named the Noble Hills (NH) range is located in Death Valley (DV, USA). It is considered as an analogue of the geothermal reservoir presently exploited in the Upper Rhine Graben (Soultz-sous-Forêts, eastern of France). The methodology undertaken is based on the analyze of 10 scanlines located in the central part of the NH from fieldwork and virtual (photogrammetric models) data. Our main results reveal: (1) NE/SW, E/W, and NW/SE fracture sets are the most recorded orientations along the virtual scanlines; (2) spacing distribution within NH shows that the clustering depends on fracture orientation; and (3) a strong clustering of the fracture system was highlighted in the highly deformed zones and close to the Southern Death Valley fault zone (SDVFZ) and thrust faults. Furthermore, the fracture patterns were controlled by the structural heritage. Two major components should be considered in reservoir modeling: the deformation gradient and the proximity to the regional major faults.

A Study on the Statistical Properties of the Prime Numbers Using the Classical and Superstatistical Random Matrix Theories

The prime numbers have attracted mathematicians and other researchers to study their interesting qualitative properties as it opens the door to some interesting questions to be answered. In this paper, the Random Matrix Theory (RMT) within superstatistics and the method of the Nearest Neighbor Spacing Distribution (NNSD) are used to investigate the statistical proprieties of the spacings between adjacent prime numbers. We used the inverse χ 2 distribution and the Brody distribution for investigating the regular-chaos mixed systems. The distributions are made up of sequences of prime numbers from one hundred to three hundred and fifty million prime numbers. The prime numbers are treated as eigenvalues of a quantum physical system. We found that the system of prime numbers may be considered regular-chaos mixed system and it becomes more regular as the value of the prime numbers largely increases with periodic behavior at logarithmic scale.

Weak integrability breaking and level spacing distribution

Recently it was suggested that certain perturbations of integrable spin chains lead to a weak breaking of integrability in the sense that integrability is preserved at the first order in the coupling. Here we examine this claim using level spacing distribution. We find that the volume dependent crossover between integrable and chaotic level spacing statistics {which marks the onset of quantum chaotic behaviour, is markedly different for weak vs. strong breaking of integrability. In particular}, for the gapless case we find that the crossover coupling as a function of the volume LL scales with a 1/L^{2}1/L2 law for weak breaking as opposed to the 1/L^{3}1/L3 law previously found for the strong case.

Nucleotide spacing distribution analysis for human genome

The distribution of nucleotides spacing in human genome was investigated. An analysis of the frequency of occurrence in the human genome of different sequence lengths flanked by one type of nucleotide was carried out showing that the distribution has no self-similar (fractal) structure. The results nevertheless revealed several characteristic features: (i) the distribution for short-range spacing is quite similar to the purely stochastic sequences; (ii) the distribution for long-range spacing essentially deviates from the random sequence distribution, showing strong long-range correlations; (iii) the differences between (A, T) and (C, G) nucleotides are quite significant; (iv) the spacing distribution displays tiny oscillations.

A Design Approach of Optical Phased Array with Low Side Lobe Level and Wide Angle Steering Range

In this paper, a new design approach of optical phased array (OPA) with low side lobe level (SLL) and wide angle steering range is proposed. This approach consists of two steps. Firstly, a nonuniform antenna array is designed by optimizing the antenna spacing distribution with particle swarm optimization (PSO). Secondly, on the basis of the optimized antenna spacing distribution, PSO is further used to optimize the phase distribution of the optical antennas when the beam steers for realizing lower SLL. Based on the approach we mentioned, we design a nonuniform OPA which has 1024 optical antennas to achieve the steering range of ±60°. When the beam steering angle is 0°, 20°, 30°, 45° and 60°, the SLL obtained by optimizing phase distribution is −21.35, −18.79, −17.91, −18.46 and −18.51 dB, respectively. This kind of OPA with low SLL and wide angle steering range has broad application prospects in laser communication and lidar system.

On a new robust workflow for the statistical and spatial analysis of fracture data collected with scanlines (or the importance of stationarity)

We present an innovative workflow for the statistical analysis of fracture data collected along scanlines, composed of two major stages, each one with alternative options. A prerequisite in our analysis is the assessment of stationarity of the dataset, which is motivated by statistical and geological considerations. Calculating statistics on non-stationary data can be statistically meaningless, and moreover the normalization and/or sub-setting approach that we discuss here can greatly improve our understanding of geological deformation processes. Our methodology is based on performing non-parametric statistical tests, which allow detecting important features of the spatial distribution of fractures, and on the analysis of the cumulative spacing function (CSF) and cumulative spacing derivative (CSD), which allows defining the boundaries of stationary domains in an objective way. Once stationarity has been analysed, other statistical methods already known in the literature can be applied. Here we discuss in detail methods aimed at understanding the degree of saturation of fracture systems based on the type of spacing distribution, and we evidence their limits in cases in which they are not supported by a proper spatial statistical analysis.

On a new robust workflow for the statistical and spatial analysis of fracture data collected with scanlines (or the importance of stationarity)

We present an innovative workflow for the statistical analysis of fracture data collected along scanlines, composed of two major stages, each one with alternative options. A prerequisite in our analysis is the assessment of stationarity of the dataset, that is motivated by statistical and geological motivations. Calculating statistics on non-stationary data can be statistically meaningless, and moreover the normalization and/or sub-setting approach that we discuss here can greatly improve our understanding of geological deformation processes. Our methodology is based on the analysis of the cumulative spacing function (CSF) and cumulative spacing derivative (CSD), that allows defining the boundaries of stationary domains in an objective way. Once stationarity has been analysed, other statistical methods already known in literature can be applied. Here we discuss in details methods aimed at understanding the degree of saturation of fracture systems based on the type of spacing distribution, and we evidence their limits in cases where they are not supported by a proper spatial statistics analysis.

The distribution of localization measures of chaotic eigenstates in the stadium billiard

The localization measures A (based on the information entropy) of localized chaotic eigenstates in the Poincaré-Husimi representation have a distribution on a compact interval [0;A0], which is well approximated by the beta distribution, based on our extensive numerical calculations. The system under study is the Bunimovich' stadium billiard, which is a classically ergodic system, also fully chaotic (positive Lyapunov exponent), but in the regime of a slightly distorted circle billiard (small shape parameter ") the diffusion in the momentum space is very slow. The parameter α = tH/tT , where tH and tT are the Heisenberg time and the classical transport time (diffusion time), respectively, is the important control parameter of the system, as in all quantum systems with the discrete energy spectrum. The measures A and their distributions have been calculated for a large number of ε and eigenenergies. The dependence of the standard deviation σ on α is analyzed, as well as on the spectral parameter β (level repulsion exponent of the relevant Brody level spacing distribution). The paper is a continuation of our recent paper (B. Batistić, Č. Lozej and M. Robnik, Nonlinear Phenomena in Complex Systems 21, 225 (2018)), where the spectral statistics and validity of the Brody level spacing distribution has been studied for the same system, namely the dependence of β and of the mean value < A > on α.

Spectral analysis for gene communities in cancer cells

We investigate gene interaction networks in various cancer cells by spectral analysis of the adjacency matrices. We observe the localization of the networks on hub genes, which have an extraordinary number of links. The eigenvector centralities take finite values only on special nodes when the hub degree exceeds the critical value $d_c \simeq 40$. The degree correlation function shows the disassortative behaviour in the large degrees, and the nodes whose degrees are $d \gtrsim 40$ have a tendency to link to small degree nodes. The communities of the gene networks centred at the hub genes are extracted based on the amount of node degree discrepancies between linked nodes. We verify the Wigner–Dyson distribution of the nearest neighbour eigenvalues spacing distribution $P(s)$ in the small degree discrepancy communities (the assortative communities), and the Poisson $P(s)$ in the communities of large degree discrepancies (the disassortative communities) including the hubs.