Nearest-neighbor Distribution Research Articles

Statistical analysis of excitation energies in actinide and rare-earth nuclei

Statistical analysis of distributions of the collective states in actinide and rare-earth nuclei is performed in terms of the nearest-neighbor spacing distribution (NNSD). Several approximations, such as the linear approach to the level repulsion density and that suggested by Brody to the NNSDs were applied for the analysis. We found an intermediate character of the experimental spectra between the order and the chaos for a number of rare-earth and actinide nuclei. The spectra are closer to the Wigner distribution for energies limited by 3 MeV, and to the Poisson distribution for data including higher excitation energies and higher spins. The latter result is in agreement with the theoretical calculations. These features are confirmed by the cumulative distributions, where the Wigner contribution dominates at smaller spacings while the Poisson one is more important at larger spacings, and our linear approach improves the comparison with experimental data at all desired spacings.

Local box-counting dimensions of discrete quantum eigenvalue spectra: Analytical connection to quantum spectral statistics.

Two decades ago, Wang and Ong, [Phys. Rev. A 55, 1522 (1997)]10.1103/PhysRevA.55.1522 hypothesized that the local box-counting dimension of a discrete quantum spectrum should depend exclusively on the nearest-neighbor spacing distribution (NNSD) of the spectrum. In this Rapid Communication, we validate their hypothesis by deriving an explicit formula for the local box-counting dimension of a countably-infinite discrete quantum spectrum. This formula expresses the local box-counting dimension of a spectrum in terms of single and double integrals of the NNSD of the spectrum. As applications, we derive an analytical formula for Poisson spectra and closed-form approximations to the local box-counting dimension for spectra having Gaussian orthogonal ensemble (GOE), Gaussian unitary ensemble (GUE), and Gaussian symplectic ensemble (GSE) spacing statistics. In the Poisson and GOE cases, we compare our theoretical formulas with the published numerical data of Wang and Ong and observe excellent agreement between their data and our theory. We also study numerically the local box-counting dimensions of the Riemann zeta function zeros and the alternate levels of GOE spectra, which are often used as numerical models of spectra possessing GUE and GSE spacing statistics, respectively. In each case, the corresponding theoretical formula is found to accurately describe the numerically computed local box-counting dimension.

Experimental evidence of chaos in the bound states of 208Pb

Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states at higher excitation energy, in regions of high level density. However, it had not been possible up to now to observe chaos in the experimental bound energy levels of any single nucleus. In this paper we study the spectral fluctuations of the 208Pb nucleus using the complete experimental spectrum of 151 states up to excitation energies of 6.20 MeV. For natural parity states the results are very close to the predictions of Random Matrix Theory (RMT) for the nearest-neighbor spacing distribution. By contrast, the results for unnatural parity states are far from RMT behavior. We interpret these results as a consequence of the strength of the residual interaction in 208Pb, which, according to experimental data, is much stronger for natural than for unnatural parity states. In addition our results show that chaotic and non-chaotic nuclear states coexist in the same energy region of the spectrum.

Temporal evolution of the degree distribution of alters in growing networks

AbstractThe degree distribution of the neighbors of nodes in a network is a theoretically important tool that is invoked in diverse studies in network science, such as epidemics, network resilience, network search and observability, network synchronization, random walks, opinion dynamics, and other dynamical systems on networks. Many real networks grow, and their properties pertaining to the said phenomena evolve. There is a paucity of theoretical research on how the evolution of these properties depend upon time and upon the structure of the initial network. This paper addresses this problem by providing the first theoretical study of the temporal evolution of the nearest-neighbor degree distribution for arbitrary networks (with any size) in arbitrary times. The posited results enable the analysis of the structural properties of growing networks in the short-time and intermediary time regimes, which are typically ignored in favor of the steady state. We corroborate the solutions via Monte Carlo simulations on various topologies. As a byproduct of the obtained solutions, we also demonstrate that the existing result in the literature on the asymptotic behavior of the Pearson coefficient of growing networks under the preferential attachment mechanism is incorrect, and we present the correct solution.

Nearest Neighborhood Characteristics of a Tropical Mixed Broadleaved Forest Stand

Structural complexity and local biodiversity of species-rich tropical forests can be characterized by their spatial patterns, which contribute to species intra- and interspecific interactions. Aiming to describe spatial patterns of species at fine spatial scales, we applied the quantitative analyses based on the relationships of nearest neighbors of conspecific and heterospecific trees. In a two-hectare plot of a tropical broadleaved forest stand in central Vietnam with minimal human influence, all tree individuals with diameter at breast height ≥ 2.5 cm were mapped and their characteristics were recorded. We applied two different types of analyses: (1) Intraspecific structural characteristics using nearest neighbor statistics; (2) overall interspecific associations through a classification scheme based on bivariate nearest neighbor distribution function D12(r) and Ripley’s K function K12(r). The findings showed that: (1) Most of studied species in the forest were highly mixed with other species, while conspecifics were regular to aggregated distribution at small spatial scales. Tree individuals with different diameter values were surrounded by heterospecific trees; (2) The majority of 306 species-species pairs showed spatial independence (66.7%), whereas 29.8% of all species showed an overall positive association and negative association consisted only a small percentage (3.5%) up to spatial scales of 50 m. We found significant evidences of the main ecological theories such as dispersal limitation, Neutral theory, Janzen-Connell hypothesis, and other effects like the stochastic dilution. We suggest using both the bivariate distribution of the structural parameters and the spatial point pattern analysis based on nearest neighbor distance as advantageous approaches for further understanding of population structure, as well as discovering and protecting biodiversity in the future.

Nanoscopy of Single Charge Carrier Jumps in a Conjugated Polymer Nanoparticle

We present super-resolution (∼2 nm spatial resolution per frame, 1 ms time resolution) tracking of single charge carriers in nanoparticles of the conjugated polymer PFBT. The motion of the charge carrier is determined from fluctuations in the centroid position of the particle fluorescence spot arising from fluorescence quenching by the polaron. A single polaron is observed to hop between a few sites, consistent with dispersive charge transport in a disordered energy landscape. In some shorter segments of the trajectory, there is repeated hopping between two sites, whereas for longer segments and full trajectories, random walk-like behavior consistent with multiple sites is observed. The hopping times range from a few milliseconds to seconds, following a power law distribution, while the hopping distances range from 2 to 5 nm, roughly following an exponential distribution. From the polaron hopping time distribution, we estimate a barrier height of 430–570 meV, with a nearest-neighbor distribution ranging f...

Spatial distribution of nuclei in progressive nucleation: Modeling and application

Phase transformations ruled by non-simultaneous nucleation and growth do not lead to random distribution of nuclei. Since nucleation is only allowed in the untransformed portion of space, positions of nuclei are correlated. In this article an analytical approach is presented for computing pair-correlation function of nuclei in progressive nucleation. This quantity is further employed for characterizing the spatial distribution of nuclei through the nearest neighbor distribution function. The modeling is developed for nucleation in 2D space with power growth law and it is applied to describe electrochemical nucleation where correlation effects are significant. Comparison with both computer simulations and experimental data lends support to the model which gives insights into the transition from Poissonian to correlated nearest neighbor probability density.

Nearest-Neighbor and Contact Distance Distributions for Matérn Cluster Process

In this letter, we derive the cumulative density function of the nearest neighbor and contact distance distributions of the Matern cluster process (MCP) in $\mathbb {R}^{2}$ . These results will be useful in the performance analysis of many real-world wireless networks that exhibit inter-node attraction. Using these results, we concretely demonstrate that the contact distance of the MCP stochastically dominates its nearest-neighbor distance as well as the contact distance of the homogenous Poisson point process with the same density.

One-Dimensional Fluids with Second Nearest–Neighbor Interactions

As is well known, one-dimensional systems with interactions restricted to first nearest neighbors admit a full analytically exact statistical-mechanical solution. This is essentially due to the fact that the knowledge of the first nearest-neighbor probability distribution function, $p_1(r)$, is enough to determine the structural and thermodynamic properties of the system. On the other hand, if the interaction between second nearest-neighbor particles is turned on, the analytically exact solution is lost. Not only the knowledge of $p_1(r)$ is not sufficient anymore, but even its determination becomes a complex many-body problem. In this work we systematically explore different approximate solutions for one-dimensional second nearest-neighbor fluid models. We apply those approximations to the square-well and the attractive two-step pair potentials and compare them with Monte Carlo simulations, finding an excellent agreement.

Effects of Short-Range Order on the Magnetic and Mechanical Properties of FeCoNi(AlSi)x High Entropy Alloys

The properties of a material are sensitive to chemically-ordered structure in multi-element alloys. Understanding the effects of chemical short-range order (SRO) on magnetic and mechanical properties is important. In this work, we use the Monte Carlo method in combination with density functional theory to investigate atomic nearest neighbor distribution, magnetic moment and elastic modulus in FeCoNi (AlSi)x alloys. It is found that the prominent feature of the FeCoNi (AlSi)x alloys is the change of SRO parameters: the SRO parameters are positive between Al-Al, Al-Si, Si-Si pairs and negative between Ni-Al, Co-Si, Fe-Co, Ni-Si and Fe-Si pairs. The Al and Si elements tend to bond with Fe, Co, Ni elements to form an SRO structure. The change of the atomic nearest neighbor environment leads to a reduction in the atomic magnetic moments of magnetic elements. The calculated saturation magnetizations by considering the effect of SRO are in good accord with the experimental values. We further show that SRO leads to an increase of the elastic modulus, by sacrificing ductility and isotropy. In the study of the structure and properties of high entropy alloys, the effect of SRO should not be ignored.

Weighted random-geometric and random-rectangular graphs: spectral and eigenfunction properties of the adjacency matrix

Within a random-matrix-theory approach, we use the nearest-neighbor energy level spacing distribution $P(s)$ and the entropic eigenfunction localization length $\ell$ to study spectral and eigenfunction properties (of adjacency matrices) of weighted random--geometric and random--rectangular graphs. A random--geometric graph (RGG) considers a set of vertices uniformly and independently distributed on the unit square, while for a random--rectangular graph (RRG) the embedding geometry is a rectangle. The RRG model depends on three parameters: The rectangle side lengths $a$ and $1/a$, the connection radius $r$, and the number of vertices $N$. We then study in detail the case $a=1$ which corresponds to weighted RGGs and explore weighted RRGs characterized by $a\sim 1$, i.e.~two-dimensional geometries, but also approach the limit of quasi-one-dimensional wires when $a\gg1$. In general we look for the scaling properties of $P(s)$ and $\ell$ as a function of $a$, $r$ and $N$. We find that the ratio $r/N^\gamma$, with $\gamma(a)\approx -1/2$, fixes the properties of both RGGs and RRGs. Moreover, when $a\ge 10$ we show that spectral and eigenfunction properties of weighted RRGs are universal for the fixed ratio $r/{\cal C}N^\gamma$, with ${\cal C}\approx a$.

Inhomogeneity of local packing density and atomic bonding of Ni67Zr33 amorphous alloy

Pulsed neutron diffraction and synchrotron X-ray diffraction measurements were performed on a melt-quenching Ni67Zr33 amorphous alloy sample. The Ni-Ni, Ni-Zr and Zr-Zr nearest neighbour distributions were obtained from differences in the scattering intensities between the two probes in conjunction with the Gaussian fitting. The results demonstrate that the Ni-Zr and Zr-Zr nearest neighbour distributions are respectively represented by single Gaussian peaks but the Ni-Ni one is an asymmetric shape. Three-dimensional structure models were constructed by using reverse Monte Carlo (RMC) modelling method with fitting to the neutron and X-ray diffraction data sets. The Voronoi-Delaunay method was used on the RMC configurations to investigate the local packing properties of each coordination cluster. With reference to the macroscopic packing fraction, inhomogeneous structural feature arising from dense and loose packing domains is observed in the structure of Ni67Zr33 amorphous alloy.

Nearest-neighbour distribution of distances in crystals from extended X-ray absorption fine structure.

Extended X-ray absorption fine structure (EXAFS) is a powerful probe of the distribution of nearest-neighbour distances around selected atomic species. We consider here the effect of vibrational disorder in crystals. The potential of EXAFS for the accurate evaluation of the coefficient of bond thermal expansion and its temperature dependence is discussed, with the aim of stimulating and facilitating the comparison with the results from total scattering experiments. The meaning of the distribution asymmetry in crystals and its connection with the effective potential anharmonicity and the bond expansion is quantitatively explored by comparing the results for a number of different systems. The extent of the relative atomic vibrations perpendicular to the bond direction and the perpendicular to parallel anisotropy are correlated with the extent of lattice negative thermal expansion as well as with the ionic mobility in superionic crystals.

Statistical behavior of time dynamics evolution of HIV infection

We use the tools of the random matrix theory (RMT) to investigate the statistical behavior of the evolution of human immunodeficiency virus (HIV) infection. By means of the nearest-neighbor spacing distribution we have identified four distinct regimes of the evolution of HIV infection. We verified that at the beginning of the so-called clinical latency phase the concentration of infected cells grows slowly and evolves in a correlated way. This regime is followed by another one in which the correlation is lost and that in turn leads the system to a regime in which the increase of infected cells is faster and correlated. In the final phase, the one in which acquired immunodeficiency syndrome (AIDS) is stablished, the system presents maximum correlation as demonstrated by GOE distribution.

Robust nonparametric quantification of clustering density of molecules in single-molecule localization microscopy.

We report a robust nonparametric descriptor, J′(r), for quantifying the density of clustering molecules in single-molecule localization microscopy. J′(r), based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that J′(r) displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. Most importantly, the position of the J′(r) valley () depends exclusively on the density of clustering molecules (ρc). Therefore, it is ideal for direct estimation of the clustering density of molecules in single-molecule localization microscopy. As an example, this descriptor was applied to estimate the clustering density of ptsG mRNA in E. coli bacteria.

GOE-GUE-Poisson transitions in the nearest-neighbor spacing distribution of magnetoexcitons.

Recent investigations on the Hamiltonian of excitons by Schweiner et al.. [Phys. Rev. Lett. 118, 046401 (2017)]PRLTAO0031-900710.1103/PhysRevLett.118.046401 revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest-neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE), or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulas for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.

Excited-state quantum phase transitions in a two-fluid Lipkin model

Background: Composed systems have became of great interest in the framework of the ground state quantum phase transitions (QPTs) and many of their properties have been studied in detail. However, in these systems the study of the so called excited-state quantum phase transitions (ESQPTs) have not received so much attention. Purpose: A quantum analysis of the ESQPTs in the two-fluid Lipkin model is presented in this work. The study is performed through the Hamiltonian diagonalization for selected values of the control parameters in order to cover the most interesting regions of the system phase diagram. [Method:] A Hamiltonian that resembles the consistent-Q Hamiltonian of the interacting boson model (IBM) is diagonalized for selected values of the parameters and properties such as the density of states, the Peres lattices, the nearest-neighbor spacing distribution, and the participation ratio are analyzed. Results: An overview of the spectrum of the two-fluid Lipkin model for selected positions in the phase diagram has been obtained. The location of the excited-state quantum phase transition can be easily singled out with the Peres lattice, with the nearest-neighbor spacing distribution, with Poincar\'e sections or with the participation ratio. Conclusions: This study completes the analysis of QPTs for the two-fluid Lipkin model, extending the previous study to excited states. The ESQPT signatures in composed systems behave in the same way as in single ones, although the evidences of their presence can be sometimes blurred. The Peres lattice turns out to be a convenient tool to look into the position of the ESQPT and to define the concept of phase in the excited states realm.

The Wigner distribution and 2D classical maps

The Wigner spacing distribution has a long and illustrious history in nuclear physics and in the quantum mechanics of classically chaotic systems. In this paper, a novel connection between the Wigner distribution and 2D classical mechanics is introduced. Based on a well-known correspondence between the Wigner distribution and the 2D Poisson point process, the hypothesis that typical pseudo-trajectories of a 2D ergodic map have a Wignerian nearest-neighbor spacing distribution (NNSD) is put forward and numerically tested. The standard Euclidean metric is used to compute the interpoint spacings. In all test cases, the hypothesis is upheld, and the range of validity of the hypothesis appears to be robust in the sense that it is not affected by the presence or absence of: (i) mixing; (ii) time-reversal symmetry; and/or (iii) dissipation.

Competitive interactions of Persian oak coppice trees (Quercus brantii var. persica) in a pure dry woodland revealed through point pattern analysis

Understanding intraspecific interactions among Persian oaks is essential to predict the responses of Zagros dry woodlands purely covered by these coppice trees to environmental changes (such as drought) that have direct effects on the sustainability of these woodlands. This investigation attempted to explore the scale-dependent competition among Persian oaks and highlight the impacts of competitive interactions on their biophysical properties (i.e. tree height, diameter at root collar and crown attributes) via point pattern analysis. Structurally different summary statistics were implemented to analyse the spatial pattern of Persian oaks in a pure 9-ha study plot. Nearest neighbour distribution function D(r) indicated that these coppice trees had no nearest neighbours up to the spatial scale of 2 m, and they all had a nearest neighbour at distances shorter than 12 m. Furthermore, pair correlation function g(r) showed the significant dispersion of Persian oaks up to the scale of 5 m, which may be the outcome of intraspecific competition for resources such as soil nutrients and water. As explored by mark variograms γ m (r), Persian oaks of the same size had significant spatial correlations that illustrated the competitive (not facilitative) interactions of these coppice trees in the study plot. Mark correlation function k mm (r) additionally revealed negative correlations of height and radial growth up to large spatial scales. Consequently, the outcome of this study highlighted the significant effects of competitive intraspecific interactions among Persian oak coppice trees on their spatial pattern and biophysical properties.

Robust Nonparametric Descriptors for Clustering Quantification in Single-Molecule Localization Microscopy

Single-molecule localization microscopy (SMLM) has been utilized broadly in imaging biological molecules in various biological systems, allowing quantitative analyses on the spatial organizations and patterns of these molecules. However, parameters are needed in many of the currently available methods or algorithms, likely introducing subjective bias in the analyses. Here, we report a robust nonparametric descriptor, J'(r) , for quantifying the spatial organization of molecules in single-molecule localization microscopy. J'(r) , based on nearest neighbor distribution functions, does not require any parameter as an input for analyzing point patterns. We show that it displays a valley shape in the presence of clusters of molecules, and the characteristics of the valley reliably report the clustering features in the data. More importantly, the position of the J'(r) valley (rJ'm) depends exclusively on the density of clustering molecules. Therefore, it is ideal for direct measurements of clustering density of molecules in single-molecule localization microscopy.