Role of zero clusters in exchange-driven growth with and without input.

We demonstrate that the clustering statistics and the corresponding phase transition to non-equilibrium clustering found in many experiments and simulation studies with self-propelled particles (SPPs) with alignment can be obtained by a simple kinetic model. The key elements of this approach are the scaling of the cluster cross-section with cluster size—described by an exponent α—and the scaling of the cluster perimeter with cluster size—described by an exponent β. The analysis of the kinetic approach reveals that the SPPs exhibit two phases: (i) an individual phase, where the cluster size distribution (CSD) is dominated by an exponential tail that defines a characteristic cluster size, and (ii) a collective phase characterized by the presence of a non-monotonic CSD with a local maximum at large cluster sizes. Through a finite-size study of the kinetic model, we show that the critical point Pc that separates the two phases scales with the system size N as Pc∝N−ξ, while the CSD p(m), at the critical point Pc, is always a power law such that p(m)∝m−γ, where m is the cluster size. Our analysis shows that the critical exponents ξ and γ are a function of α and β, and even provides the relationship between them. Furthermore, the kinetic approach suggests that in the thermodynamic limit, a genuine clustering phase transition, in two and three dimensions, requires that α = β. Interestingly, the critical exponent γ is found to be in the range 0.8 < γ < 1.5 in line with the observations from experiments and simulations.

A comparison of quadrupole mass spectrometric (QMS) and transmission electron microscopic (TEM) characterization of silver nano‐cluster deposition produced by a nano‐cluster source consisting of a planar DC magnetron sputter source in a high pressure gas aggregation chamber is presented and discussed. Cluster sizes and size distributions detected by the two different techniques are compared and the differences are discussed. The effects of He to Ar ratio, gas flow and magnetron power on the cluster size distribution are evaluated. The influence of the target erosion and aging effects are mentioned, too (© 2012 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

We propose a simple irreversible multi-polymer coagulation model inwhich m polymers consist of multiple components bond spontaneously toform a larger cluster. We solve the generalized Smoluchowski rateequation with constant reaction rates to obtain the exact solution ofthe cluster size distribution. The results indicate that the evolutionbehaviour of the system depends crucially on the polymer number m ofthe coagulation reaction. The cluster concentrations decay as t-m/(m-1)2, and the typical size S(t) of the m-polymer coagulationsystem grows as t1/(m-1). On the other hand, the cluster sizedistribution may approach unusual scaling form in some cases.

The size distribution of geometrical spin clusters is exactly found for the onedimensional Ising model of finite extent. For the values of lattice constant β above some “critical value” βc the found size distribution demonstrates the non-monotonic behaviour with the peak corresponding to the size of the largest available cluster. In other words, for high values of the lattice constant there are two ways to fill the lattice: either to form a single largest cluster or to create many clusters of small sizes. This feature closely resembles the well-know bimodal size distribution of clusters which is usually interpreted as a robust signal of the first order liquid-gas phase transition in finite systems. It is remarkable that the bimodal size distribution of spin clusters appears in the one-dimensional Ising model of finite size, i.e. in the model which in thermodynamic limit has no phase transition at all.

Nanodosimetry is a methodology for quantifying the effects of ionising radiation on matter by determining the frequency distributions of the cluster size of ionisations in nanometric target volumes. In previous investigations with the Ion Counter nanodosimeter operated at PTB, significant deviations for large cluster sizes were found in the comparison between measured and simulated data of ionisation cluster size distributions. These deviations could be explained by a background of secondary ions, which are produced within the transport system of the ionised target molecules. In this paper, two different approaches were investigated to correct for the background of secondary ions in the measured data to obtain the “true” cluster size distribution to be used, e. g., in predictions of biological effectiveness. In the first approach, the correction of the background was treated as a minimising problem. In the second approach, an iterative unfolding algorithm using Bayes statistics was employed. In all cases where the convolution of the background-corrected results with the secondary ion background agrees well with the corresponding measured cluster size distribution, the background-correction led to an improved agreement between measurement and simulation. For the removal of a background of secondary ions from measured cluster size distributions, the unfolding algorithm using Bayes statistics is the preferred method as it proved to be the most effective and the least sensitive to boundary conditions. Moreover, it was considerably less time consuming.

Cluster size distribution is one of the most important factors in impact processes. In this study, cluster size distributions were studied with a time of flight (TOF) mass analyzer which has high mass resolution (M//spl Delta/M=500). The average and maximum cluster size increase with the increase of the source gas pressure. The detection of time of flight ions was performed with micro channel plate (MCP) and the detection probability of MCP decreased in proportion to the velocity of the ions. As the mass of a cluster is much higher than that of a monomer, the velocity of a cluster is much slower at the same acceleration energy. Therefore, higher acceleration energy is required for the detection of large cluster ions.

Size distributions of Pb, Bi, and Mo clusters produced by Xe ion bombardment have been measured by a deflection type mass spectrometer. In general, the ion intensity decreases with increasing cluster size n. Superimposed on this gradual decrease with n, some anomalies have been observed in the cases of Pb and Bi. No prominent anomaly for Mo clusters has been observed. A correlation is found between the size distribution of clusters produced by Xe ion bombardment and that produced by inert gas condensation method.

Cluster analysis (Jain &amp; Dubes, 1988) provides insight into the data by dividing the objects into groups (clusters), such that objects in a cluster are more similar to each other than objects in other clusters. Cluster analysis has long played an important role in a wide variety of fields, such as psychology, bioinformatics, pattern recognition, information retrieval, machine learning, and data mining. Many clustering algorithms, such as K-means and Unweighted Pair Group Method with Arithmetic Mean (UPGMA), have been wellestablished. A recent research focus on clustering analysis is to understand the strength and weakness of various clustering algorithms with respect to data factors. Indeed, people have identified some data characteristics that may strongly affect clustering analysis including high dimensionality and sparseness, the large size, noise, types of attributes and data sets, and scales of attributes (Tan, Steinbach, &amp; Kumar, 2005). However, further investigation is expected to reveal whether and how the data distributions can have the impact on the performance of clustering algorithms. Along this line, we study clustering algorithms by answering three questions: 1. What are the systematic differences between the distributions of the resultant clusters by different clustering algorithms? 2. How can the distribution of the “true” cluster sizes make impact on the performances of clustering algorithms? 3. How to choose an appropriate clustering algorithm in practice? The answers to these questions can guide us for the better understanding and the use of clustering methods. This is noteworthy, since 1) in theory, people seldom realized that there are strong relationships between the clustering algorithms and the cluster size distributions, and 2) in practice, how to choose an appropriate clustering algorithm is still a challenging task, especially after an algorithm boom in data mining area. This chapter thus tries to fill this void initially. To this end, we carefully select two widely used categories of clustering algorithms, i.e., K-means and Agglomerative Hierarchical Clustering (AHC), as the representative algorithms for illustration. In the chapter, we first show that K-means tends to generate the clusters with a relatively uniform distribution on the cluster sizes. Then we demonstrate that UPGMA, one of the robust AHC methods, acts in an opposite way to K-means; that is, UPGMA tends to generate the clusters with high variation on the cluster sizes. Indeed, the experimental results indicate that the variations of the resultant cluster sizes by K-means and UPGMA, measured by the Coefficient of Variation (CV), are in the specific intervals, say [0.3, 1.0] and [1.0, 2.5] respectively. Finally, we put together K-means and UPGMA for a further comparison, and propose some rules for the better choice of the clustering schemes from the data distribution point of view.

Periodical patterns of vegetation in an arid or semiarid ecosystem are described using statistical mechanics and Monte Carlo numerical simulation technique. Plants are characterized by the area that each individual occupies and a facilitation-competition pairwise interaction. Assuming that external resources (precipitation, solar radiation, nutrients, etc.) are available to the ecosystem, it is possible to obtain the persistent configurations of plants compatible with an equitable distribution of resources maximizing the Shannon entropy. Variation of vegetation patterns with density, critical cluster size, and facilitation distance are predicted. Morphological changes of clusters are shown to be a function of the external resources. As a final remark, it is proposed that an early warning of desertification could be detected from the coefficient of variation of the mean cluster size together with the distribution of cluster sizes.

Cluster size distributions were investigated in case of different nozzle geometries in argon and xenon using Rayleigh scattering diagnostics. Different nozzle geometries result in different behaviour, therefore both spatial- and temporal cluster size distributions were studied to obtain a well-characterized cluster target. It is shown that the generally used Hagena scaling can result in a significant deviation from the observed data and the behaviour cannot be described by a single material condensation parameter. The results along with the nanoplasma model applied to the data of previous high harmonic generation experiments allow the independent measurement of cluster size and cluster density.

Numerical evaluation of self-preserving spectra in smoluchowski's coagulation theory

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D f ≈ 1.2–1.4 at d ≈ 1.5 nm to D f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.

Transient dynamics leading to the synchrony of a type of pulse-coupled oscillators, so-called scrambler oscillators, has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the evolution of the cluster size distribution for general cluster sizes has not been fully understood yet. In this paper, we study the evolution of the cluster size distribution from the perspective of a percolation model by regarding the number of aggregations as the number of attached bonds. Specifically, we derive the scaling form of the cluster size distribution with specific values of the critical exponents using the property that the characteristic cluster size diverges as the percolation threshold is approached from below. Through simulation, it is confirmed that the scaling form well explains the evolution of the cluster size distribution. Based on the distribution behavior, we find that a giant cluster of all oscillators is formed discontinuously at the threshold and also that further aggregation does not occur like in a one-dimensional bond percolation model. Finally, we discuss the origin of the discontinuous formation of the giant cluster from the perspective of global suppression in explosive percolation models. For this, we approximate the aggregation process as a cluster-cluster aggregation with a given collision kernel. We believe that the theoretical approach presented in this paper can be used to understand the transient dynamics of a broad range of synchronizations.

MobiHoc 2010 Conference Best Paper Award

The vibrational dynamics of large Ar n clusters from n=30 to n=4500 is investigated by measuring the energy loss of He atoms in a high resolution scattering experiment. The clusters are generated by adiabatic expansion through conical nozzles and contain a distribution of cluster sizes. The He supersonic nozzle beam provides a resolution of better than 1 meV. The results are compared with calculated spectral density functions for single cluster sizes and bulk phonon spectra.