The role of zero-clusters in exchange-driven growth with and without input

The exchange-driven growth model describes the mean field kinetics of a population of composite particles (clusters) subject to pairwise exchange interactions. Exchange in this context means that upon interaction of two clusters, one loses a constituent unit (monomer) and the other gains this unit. Two variants of the exchange-driven growth model appear in applications. They differ in whether clusters of zero size are considered active or passive. In the active case, clusters of size zero can acquire a monomer from clusters of positive size. In the passive case they cannot, meaning that clusters reaching size zero are effectively removed from the system. The large time behaviour is very different for the two variants of the model. We first consider an isolated system. In the passive case, the cluster size distribution tends towards a self-similar evolution and the typical cluster size grows as a power of time. In the active case, we identify a broad class of kernels for which the the cluster size distribution tends to a non-trivial time-independent equilibrium in which the typical cluster size is finite. We next consider a non-isolated system in which monomers are input at a constant rate. In the passive case, the cluster size distribution again attains a self-similar profile in which the typical cluster size grows as a power of time. In the active case, a surprising new behavior is found: the cluster size distribution asymptotes to the same equilibrium profile found in the isolated case but with an amplitude that grows linearly in time

Identification and evaluation of linear damping models in beam vibrations

Sensitive method, identifying effective damping mechanisms, involves comparing experimentally determined ratio of first to second mode magnification factors related to common point on beam. Cluster size has little effect on frequencies of elements, magnification factor decreases with cluster size, and viscous and stress damping are dominant damping mechanisms

Cluster size dependence of high-order harmonic generation

We investigate high-order harmonic generation (HHG) from noble gas clusters in a supersonic gas jet. To identify the contribution of harmonic generation from clusters versus that from gas monomers, we measure the high-order harmonic output over a broad range of the total atomic number density in the jet (from 3*10^16 cm^{-3} to 3x10^18 cm{-3}) at two different reservoir temperatures (303 K and 363 K). For the firrst time in the evaluation of the harmonic yield in such measurements, the variation of the liquid mass fraction, g, versus pressure and temperature is taken into consideration, which we determine, reliably and consistently, to be below 20% within our range of experimental parameters. By comparing the measured harmonic yield from a thin jet with the calculated corresponding yield from monomers alone, we find an increased emission of the harmonics when the average cluster size is less than 3000. Using g, under the assumption that the emission from monomers and clusters add up coherently, we calculate the ratio of the average single-atom response of an atom within a cluster to that of a monomer and find an enhancement of around 10 for very small average cluster size (~200). We do not find any dependence of the cut-off frequency on the composition of the cluster jet. This implies that HHG in clusters is based on electrons that return to their parent ions and not to neighbouring ions in the cluster. To fully employ the enhanced average single-atom response found for small average cluster sizes (~200), the nozzle producing the cluster jet must provide a large liquid mass fraction at these small cluster sizes for increasing the harmonic yield. Moreover, cluster jets may allow for quasi-phase matching, as the higher mass of clusters allows for a higher density contrast in spatially structuring the nonlinear medium.Comment: 16 pages, 6 figure

Cluster size distributions in gas jets for different nozzle geometries

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.Comment: 7 pages, 6 figure

Evolution of scale-free random graphs: Potts model formulation

We study the bond percolation problem in random graphs of $N$ weighted vertices, where each vertex $i$ has a prescribed weight $P_i$ and an edge can connect vertices $i$ and $j$ with rate $P_iP_j$. The problem is solved by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous interactions for all pairs of spins. We apply this approach to the static model having $P_i\propto i^{-\mu} (0<\mu<1)$ so that the resulting graph is scale-free with the degree exponent $\lambda=1+1/\mu$. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density, and their associated critical exponents are also obtained. Finite-size scaling behaviors are derived using the largest cluster size in the critical regime, which is calculated from the cluster size distribution, and checked against numerical simulation results. We find that the process of forming the giant cluster is qualitatively different between the cases of $\lambda >3$ and $2 < \lambda <3$. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite $N$ shows double peaks.Comment: 34 pages, 9 figures, elsart.cls, final version appeared in NP

Cluster size distributions in particle systems with asymmetric dynamics

We present exact and asymptotic results for clusters in the one-dimensional totally asymmetric exclusion process (TASEP) with two different dynamics. The expected length of the largest cluster is shown to diverge logarithmically with increasing system size for ordinary TASEP dynamics and as a logarithm divided by a double logarithm for generalized dynamics, where the hopping probability of a particle depends on the size of the cluster it belongs to. The connection with the asymptotic theory of extreme order statistics is discussed in detail. We also consider a related model of interface growth, where the deposited particles are allowed to relax to the local gravitational minimum.Comment: 12 pages, 3 figures, RevTe

lntracluster rearrangement of protonated nitric acid: Infrared spectroscopic studies of H^+(HNO_3)(H_2O)_n

Infrared spectra of clusters of protonated nitric acid and water exhibit a marked change with cluster size, indicating that an intracluster reaction occurs with sufficient solvation. In small clusters, H_2O binds to a nitronium ion core, but at a critical cluster size the NO^+_2 reacts. A lower bound of 174 kcal/mol is found for the proton affinity of HNO_3

Long transients and cluster size in globally coupled maps

We analyze the asymptotic states in the partially ordered phase of a system of globally coupled logistic maps. We confirm that, regardless of initial conditions, these states consist of a few clusters, and they properly belong in the ordered phase of these systems. The transient times necessary to reach the asymptotic states can be very long, especially very near the transition line separating the ordered and the coherent phases. We find that, where two clusters form, the distribution of their sizes corresponds to windows of regular or narrow-band chaotic behavior in the bifurcation diagram of a system of two degrees of freedom that describes the motion of two clusters, where the size of one cluster acts as a bifurcation parameter.Comment: To appear in Europhysics Letter