Cluster Size Distribution Function Research Articles

Numerical study of collective motion of microswimmers in Giesekus viscoelastic fluids

Few simulations currently explore the dynamics of microswimmers swimming through viscoelastic environments. In this study, we employ a direct-forcing fictitious domain method to investigate the collective behavior of spherical squirmers within viscoelastic fluids at low Reynolds numbers. Our findings reveal clear differences between pusher and puller swimmers: puller swimmers exhibit a tendency to aggregate into clusters, particularly noticeable in suspensions with high concentrations, which increases the average speed of the swimmers. Through an analysis of the cluster-size distribution function, we observe the larger-scale clusters of puller swimmers with increasing concentration. Moreover, the presence of fluid elasticity significantly reduces both the average swimming speed of squirmers and the fluid’s kinetic energy.

Unravelling the structural and dynamical properties of concentrated aqueous ammonium nitrate solutions: MD simulation studies

ABSTRACT In this work, we present, the concentration-dependent solvation structure and dynamics of an ammonium nitrate (AN) ion pair in aqueous media by means of classical molecular dynamics simulations. Structural properties were investigated by computing the potentials of mean force (PMFs), radial distribution functions (RDFs), cluster size distribution functions, and hydrogen bond dynamics. The change in the depth of the contact ion pair (CIP) and solvent-separated ion pair minima (SSIP) is marginal, whereas for the solvent-assisted ion pair (SAIP) is more stable at lower salt concentrations. The marginal difference in the depth of the CIP minimum of the PMF is explained based on cluster size distribution and hydrogen bonding. The solvation structure of the ions is not affected by the salt concentration. Ab-initio and classical molecular dynamics simulations (both constrained and unconstrained) give similar results for the solvation structure around the cation and the anion. The spatial density distribution functions of the anions around the cations show that the anions occupy the space around the ammonium hydrogen atoms. Profound differences in dynamical properties are found in the case of concentrated solutions as compared to dilute solutions.

Size distribution of clusters and nucleation preference of trimers during SiC (0001) surface epitaxial growth under low coverage

In order to better understand the microscopic nucleation behavior during the epitaxial growth of a SiC crystal, a lattice kinetic Monte Carlo model is developed, in which Si and C particles are set as the basic elements. The events list is built up to implement group search and binary search, which can improve the efficiency of the algorithm. In addition, the Hoshen–Kopelman algorithm is also used to calculate the statistics of the properties of clusters. Then, the cluster size distribution function and the nucleation preference of trimers are analyzed. The results show that the cluster size distribution function obeys the Gauss distribution, and the proportion of crystal nuclei close to the average size gradually increases. Moreover, the growth temperature mainly affects the trapping rate of adatoms by dimers, and the C/Si ratio affects the formation of different types of dimers and the concentration of adatoms.

On modeling of the kinetics of aggregation in low-polar C60 solutions

Based on some recent experimental evidence, kinetics of cluster growth in a fullerene C60 low-polar solution are considered within a model based on oxides C60Ox as aggregation initializers. A system of equations for the time-evolution of the cluster-size distribution function is developed. First stage of clusters growth consists in formation of packed small C60 clusters around separate fullerene oxides. For this stage analytical solutions of equations were obtained and compared with numerical results. During the next stages, cluster-cluster aggregation events start to play a role. First numerical results for stage II are obtained and discussed. The results are compared with experimental study of clusters growth in the saturated C60/benzene solution by dynamic light scattering.

Evolution of New Phase Clusters at the Initial Stages of Binary Alloy Decomposition Described in Terms of a Modified Theory of Nucleation

The work considers the thermodynamics and the kinetics of initial decomposition stages in a supersaturated binary solid solution inthe framework of the modified nucleation theory. The specific surface energy is considered as a function of intensive state parameters of both the cluster and the matrix, which allows one to uniformly describe clusters of critical, subcritical, and supercritical size. The analysis was performed in two stages. On the first one, the optimal size dependences of the compositions of new phase clusters were determined by analyzing the macroscopic equations of growth of nuclei. On the second stage, we solved akinetic equation to describe the evolution of the size distribution function of new-phase clusters along this optimal composition line.The effect of various kinetic factors on the behavior of the distribution function and characteristics of new-phase clusters was studied. The obtained distributions demonstrate a possibility of the existence of bimodal size distributions of new-phase clusters.

Kinetics of cluster formation in active suspension: Coarsening regime.

The active suspension has an amazing property to undergo a phase transition into dense and dilute gas phases, even in the absence of the interparticle forces of attraction. In this work, the phase transition in active suspension is considered within a minimal model, in which self-propelled particles are moving with a constant speed, while their direction of propagation is governed by mutual collisions. The final stage of cluster formation in active suspension is studied when the larger clusters grow by consuming the smaller ones. The analysis of kinetic equation for the evolution of the number of particles in a cluster and conservation of particles law in active suspension shows that the number of clusters decreases with time according to a power of minus three fifths and the average number of particles in a cluster depends on their speed and time in the power of three fifths. The size distribution function of clusters is obtained, which is found to be asymmetric with respect to the average number of particles in clusters.

Off-stoichiometry effects on crystal nucleation and growth kinetics in soda-lime-silicate glasses. The combeite (Na2O•2CaO•3SiO2) – devitrite (Na2O•3CaO•6SiO2) joint

To the present date, the vast majority of fundamental studies on glass crystallization has been carried out using stoichiometric compositions, whereas by far, the most common cases in glass technology are off-stoichiometric. In this work, we performed a comprehensive study on the nucleation and growth kinetics of combeite crystals in non-stoichiometric glasses of the combeite (Na2O•2CaO•3SiO2) – devitrite (Na2O•3CaO•6SiO2) system. Using cluster-size distribution functions based on a previously developed kinetic model of nucleation, we constructed the dependencies of the number N(T) of nucleated and grown crystals on the nucleation time, t, and estimated the nucleation rates, I(T)=dN(T)/dt. We then cross-checked the theoretical calculations versus experimental data. In these calculations, the critical nucleus-supercooled liquid specific interfacial energy, σ, and the effective diffusion coefficient,D, were left as fitting parameters for the best possible description of experimental data. We show that as the precursor glass composition shifts from combeite to devitrite, and thus the difference of composition between the initial glass and the precipitated crystals increases, the interfacial energy increases, and the maximum steady-state nucleation rate, Ist(Tmax), of combeite strongly drops. On the other hand, as a consequence of the composition shift, depending on the glass-forming system, the diffusion coefficient may increase or decrease. We also show a significant difference between D estimated from the nucleation experiments and Du calculated from the growth rates. These results corroborate our previous studies on other systems and are relevant to elucidate the complex mechanisms of crystallization of non-stoichiometric glasses.

Modeling of the Evolution of Cluster-Size Distribution Functions in Polar Fullerene C60 Solutions

We propose a method for calculating the evolution of the cluster-size distribution functions of fullerene C60 aggregates in polar solutions within the previously developed limited growth model. This method allows calculation of the distribution function f(r,t) at arbitrary moments of time for the given parameters of the system. As an example, we calculate the evolution of the mean cluster size, concentrations of monomers, and f(r,t) for a model polar solution of fullerenes. Small-angle neutron scattering curves at different times from the onset of C60 aggregation in the solution are obtained.

Cell aggregation in monolayer culture: Clues to a universal kinetics

Aggregation of animal cells in culture comprises a series of motility, collision and adhesion processes of basic relevance for tissue engineering, bioseparations, oncology research and in vitro drug testing. In the present paper, we characterize the aggregation kinetics of normal and cancer cells in culture by determining their cluster size distribution functions. Our experiments reveal that the complementary cumulative distributions for eight cell lines from epithelial and mesenchymal origins are described by stretched exponential functions. Also, we find that as time evolves and the cell density increases, a dynamical phase transition occurs from an aggregation regime described by monotonically decreasing cluster size distributions to another one in which these distributions are nonmonotonic, exhibiting local maxima at large cluster sizes. Subtly, the universality of the stretched exponential distributions admits distinct cluster growth processes controlled by motility and adhesion traits of the cells.

Analytical Solution of Smoluchowski Equations in Aggregation–Fragmentation Processes

The z-transform technique is used to analyze Smoluchowski equations of aggregation–fragmentation processes where the selection of aggregation clusters, a decomposed cluster and a generated cluster is entirely random and independent of cluster size. An analytic form of asymptotic behavior for a cluster size distribution function is derived on the basis of approximation where lower-order terms in the average cluster size are neglected. The obtained results agree well with numerical ones.

A 2D suspension of active agents: the role of fluid mediated interactions

Taking into account both the Vicsek short-range ordering and the far-field hydrodynamic interactions mediated by the ambient fluid, we investigate the role of long-range interactions in the ordering phenomena in a quasi 2-dimensional active suspension. By studying the number fluctuations, the velocity correlation functions and cluster size distribution function, we show that depending on the number density of swimmers and the strength of noise, the hydrodynamic interactions can have significant effects in a suspension. For a fixed value of noise, at larger density of particles, long-range interactions enhance the particle pairing and cluster formation in the system.

Grouping techniques for large-scale cluster dynamics simulations of reaction diffusion processes

Cluster dynamics is a powerful, high fidelity, mesoscale method for modeling the kinetic evolution of point defects, impurities, and their clusters in materials and is commonly used in studying radiation damage. These methods excel at modeling nucleation, but often require too many equations to successfully model the long term growth and coarsening that govern microstructural evolution. One solution to this problem is to group equations into a coarser approximation of the cluster size distribution function which can reduce the cost of solution by many orders of magnitude. While such grouping methods have been advanced for a limited class of problems, no reliable method currently exists for the general case. This paper advances a framework for grouping arbitrary cluster dynamics problems, and develops several competing schemes based on that framework. These schemes are each evaluated against a variety of test problems designed to assess their accuracy, robustness, and efficiency.

Mathematical models of water nucleation process for the Direct Simulation Monte Carlo method

Two models of the nucleation process are developed on the basis of (a) size corrected classical nucleation theory and (b) kinetic approach within the Direct Simulation Monte Carlo method. Expressions for probabilities of cluster formation/decomposition reactions are proposed using the models for corresponding rate constants. Both models are employed for the direct simulation of stationary nucleation process in a spatially homogeneous water vapor, where the monomer parameters are kept constant. The relaxation of size distribution function of water clusters is computed for moderate supersaturation values and temperature of 320 K. Numerical analysis shows sufficient difference in results obtained within above mentioned models. The difference arises due to the incorrect description of the internal cluster temperatures caused by the limitation of the classical nucleation theory consisting in one-temperature approximation, which does not describe the details of the energy relaxation. The impact of the dimer formation mechanism (by triple and binary collisions) on cluster size distribution is also analyzed.

Universality class of site and bond percolation on multifractal scale-free planar stochastic lattice.

In this article, we investigate both site and bond percolation on a weighted planar stochastic lattice (WPSL), which is a multifractal and whose dual is a scale-free network. The characteristic property of percolation is that it exhibits threshold phenomena as we find sudden or abrupt jump in spanning probability across p_{c} accompanied by the divergence of some other observable quantities, which is reminiscent of a continuous phase transition. Indeed, percolation is characterized by the critical behavior of percolation strength P(p)∼(p_{c}-p)^{β}, mean cluster size S∼(p_{c}-p)^{-γ}, and the system size L∼(p_{c}-p)^{-ν}, which are known as the equivalent counterpart of the order parameter, susceptibility, and correlation length, respectively. Moreover, the cluster size distribution function n_{s}(p_{c})∼s^{-τ} and the mass-length relation M∼L^{d_{f}} of the spanning cluster also provide useful characterization of the percolation process. We numerically obtain a value for p_{c} and for all the exponents such as β,ν,γ,τ, and d_{f}. We find that, except for p_{c}, all the exponents are exactly the same in both bond and site percolation despite the significant difference in the definition of cluster and other quantities. Our results suggest that the percolation on WPSL belongs to a new universality class, as its exponents do not share the same value as for all the existing planar lattices. Besides, like all other cases, its site and bond type belong to the same universality class.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ГАЗОФАЗНОЙ КОНДЕНСАЦИИ МЕТАЛЛИЧЕСКИХ НАНОЧАСТИЦ В КАМЕРЕ С ДУГОВЫМ РАЗРЯДОМ

Numerical simulation of the metallic nanoparticles synthesis in a chamber with an arc discharge were elaborated. The efficiency of the vapor phase condensation of metallic nanoclusters and nanopowders was determined by setting optimum process parameters, the possibilities of experimental estimation of which is limited. Mathematical and physical models were developed to perform computer analysis of the vapor phase condensation to describe the macroscopic characteristics of the process (temperature regime, gas mixture dynamics, diffusion and convective transport of clusters) with allowance for the properties of the components on a microscopic level. The classical Becker-Doring‑Folmer‑Weber thermodynamic nucleation theory was used for the description of the probability of atom-cluster aggregation. The distributions of macroscopic (temperature, pressure, velocity field) and microscopic (cluster size distribution) values in the chamber were obtained. It is found that the size distribution function of clusters deposited on the chamber walls has two peaks, the first – in the region of small clusters (1–50 atoms) and the second – for the clusters containing more than 10 4 atoms. Based on the results of numerical calculations the assumptions are made about the relationship between the type of size distribution function and characteristics of the process.

Percolation on a multifractal scale-free planar stochastic lattice and its universality class.

We investigate site percolation on a weighted planar stochastic lattice (WPSL), which is a multifractal and whose dual is a scale-free network. Percolation is typically characterized by a threshold value p(c) at which a transition occurs and by a set of critical exponents β, γ, ν which describe the critical behavior of the percolation probability P(p), mean cluster size S(p), and the correlation length ξ. Besides, the exponent τ characterizes the cluster size distribution function n(s)(p(c)) and the fractal dimension d(f) characterizes the spanning cluster. We numerically obtain the value of p(c) and of all the exponents. These results suggest that the percolation on WPSL belong to a separate universality class than on all other planar lattices.

Calculation of the cluster size distribution functions and small-angle neutron scattering data for C60/N-methylpyrrolidone

The aggregate growth in a C60/N-methylpyrrolidone (NMP) solution has been considered in the framework of the approach developed earlier for describing the cluster growth kinetics in fullerene polar solutions. The final cluster size distribution functions in model solutions have been estimated for two fullerene aggregation models including the influence of complex formation on the cluster growth using extrapolations of the characteristics of the cluster state and distribution parameters. Based on the obtained results, the model curves of small-angle neutron scattering have been calculated for a C60/NMP solution at various values of the model parameters.

Pore-scale micro-computed-tomography imaging: Nonwetting-phase cluster-size distribution during drainage and imbibition

We investigated the cluster-size distribution of the residual nonwetting phase in a sintered glass-bead porous medium at two-phase flow conditions, by means of micro-computed-tomography (μCT) imaging with pore-scale resolution. Cluster-size distribution functions and cluster volumes were obtained by image analysis for a range of injected pore volumes under both imbibition and drainage conditions; the field of view was larger than the porosity-based representative elementary volume (REV). We did not attempt to make a definition for a two-phase REV but used the nonwetting-phase cluster-size distribution as an indicator. Most of the nonwetting-phase total volume was found to be contained in clusters that were one to two orders of magnitude larger than the porosity-based REV. The largest observed clusters in fact ranged in volume from 65% to 99% of the entire nonwetting phase in the field of view. As a consequence, the largest clusters observed were statistically not represented and were found to be smaller than the estimated maximum cluster length. The results indicate that the two-phase REV is larger than the field of view attainable by μCT scanning, at a resolution which allows for the accurate determination of cluster connectivity.

Pore-Scale Micro-CT Imaging: Cluster Size Distribution During Drainage and Imbibition

In the present study we investigate the size and volume distribution of n-decane clusters in a brine saturated porous glass sample by means of micro-CT imaging with pore-scale resolution. Cluster size distribution functions and cluster volumes were obtained by image analysis for a range of injected pore volumes under both imbibition and drainage conditions, and with a field of view larger than the porosity-based representative elementary volume (REV). n-decane clusters were found to be distributed in sizes greater than that of the REV, with the largest one containing between 65 and 99% of the entire non-wetting phase. The results indicate that the two-phase REV may be substantially larger than for single-phase flow and larger than the attainable field of view.

Modeling of cluster formation and growth under atomic vapor condensation

A model is presented of cluster formation and growth in supersaturated vapor of the clustering material. The model is based on numerical analysis of evolution of the cluster size distribution function. The calculations are performed on the basis of the presented model under cluster plasma parameters specific to the magnetron method of cluster generation. A comparison is made of the numerical experiment results with the estimates made by other authors. The results are presented of the numerical experiment with allowance for coalescence. The results are shown to be in agreement with those of calculations on the basis of the approximate analytical models within the domain of applicability of the latter.