Cluster Growth Model Research Articles

Lead-free metal–halide perovskite nanocrystals: synthesis and optical properties [Review

Subject of study. Lead-free perovskite nanocrystals (LFPNCs), their main characteristics, synthesis methods, and optical properties are examined. Aim of study. The aim is to analyze the state-of-the-art research data on the synthesis methods and optical properties of LFPNCs. In addition, the formation processes of LFPNCs, their main synthesis methods, and the dependence of nanocrystal size and photoluminescence quantum yield (PLQY) on synthesis parameters (such as method, temperature, and ligand type) are determined. Main results. The formation of LFPNCs is analyzed based on the LaMer and cluster growth models. According to the research data, the primary methods for preparing these nanocrystals (NCs) are hot-injection and ligand-assisted reprecipitation (LARP). Evidently, the average size of LFPNCs increases with increasing reaction temperature. For NCs synthesized by LARP, increasing the reaction temperature to 100°C leads to a slight decrease in the quantum yield. However, for the NCs prepared by hot-injection, the PLQY remains independent of the temperature. Additionally, using oleic acid as a ligand results in a narrow size distribution of NCs, whereas using a mixture of ligands results in NCs exhibiting the highest PLQY. Practical significance. The literature analysis results show that the LARP method is the most promising for synthesizing LFPNCs owing to its ease of implementation, energy efficiency, and scalability. The LFPNCs produced using this method can be applied as active materials in sensor technologies, photovoltaics, and optoelectronic devices.

Computational Complexity of Biased Diffusion-Limited Aggregation

Diffusion-Limited Aggregation (DLA) is a cluster growth model that consists of a set of particles that are sequentially aggregated over a two-dimensional grid. In this paper, we introduce a biased version of the DLA model, in which particles are limited to move in a subset of possible directions. We denote $k$-DLA the model where the particles move only in $k$ possible directions. We study the biased DLA model from the perspective of Computational Complexity, defining two decision problems The first problem is Prediction, whose input is a site of the grid $c$ and a sequence $S$ of walks, representing the trajectories of a set of particles. The question is whether a particle stops at site $c$ when sequence $S$ is realized. The second problem is Realization, where the input is a set of positions of the grid, $P$. The question is whether there exists a sequence $S$ that realizes $P$, i.e. all particles of $S$ exactly occupy the positions in $P$. Our aim is to classify the Prediciton and Realization problems for the different versions of DLA. We first show that Prediction is P-Complete for 2-DLA (thus for 3-DLA). Later, we show that Prediction can be solved much more efficiently for 1DLA. In fact, we show that in that case, the problem is NL-Complete. With respect to Realization, we show that restricted to 2DLA the problem is in P, while for 1DLA is in L.

A Size-Perimeter Discrete Growth Model for Percolation Clusters

Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

A Study on the Coupling Mechanism between Horse Racing Technical Person Cluster and Economic Growth Model of Wuhan city

A Study on the Coupling Mechanism between Horse Racing Technical Person Cluster and Economic Growth Model of Wuhan city

Eden growth models for flat clathrin lattices with vacancies

Clathrin-mediated endocytosis is one of the major pathways by which cells internalise cargo molecules. Recently it has been shown that clathrin triskelia can first assemble as flat lattices before the membrane starts to bend. However, for fully assembled clathrin lattices high energetic and topological barriers exist for the flat-to-curved transition. Here we explore the possibility that flat clathrin lattices grow with vacancies that are not visible in traditional imaging techniques but would lower these barriers. We identify the Eden model for cluster growth as the most appropriate modeling framework and systematically derive the four possible variants that result from the specific architecture of the clathrin triskelion. Our computer simulations show that the different models lead to clear differences in the statistical distributions of cluster shapes and densities. Experimental results from electron microscopy and correlative light microscopy provide first indications for the model variants with a moderate level of lattice vacancies.

Kardar-Parisi-Zhang Interfaces with Curved Initial Shapes and Variational Formula.

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments with liquid-crystal turbulence, we determine the universal scaling functions that describe the height distribution and the spatial correlation of the interfaces growing outward from a ring. The scaling functions, controlled by a single dimensionless time parameter, show crossover from the statistical properties of the flat interfaces to those of the circular interfaces. Moreover, employing the KPZ variational formula to describe the case of the ring initial condition, we find that the formula, which we numerically evaluate, reproduces the numerical and experimental results precisely without adjustable parameters. This demonstrates that precise numerical evaluation of the variational formula is possible at all, and underlines the practical importance of the formula, which is able to predict the one-point distribution of KPZ interfaces for general initial conditions.

Prediction of HIV Transmission Cluster Growth With Statewide Surveillance Data.

Prediction of HIV transmission cluster growth may help guide public health action. We developed a predictive model for cluster growth in North Carolina (NC) using routine HIV surveillance data. We identified putative transmission clusters with ≥2 members through pairwise genetic distances ≤1.5% from HIV-1 pol sequences sampled November 2010-December 2017 in NC. Clusters established by a baseline of January 2015 with any sequences sampled within 2 years before baseline were assessed for growth (new diagnoses) over 18 months. We developed a predictive model for cluster growth incorporating demographic, clinical, temporal, and contact tracing characteristics of baseline cluster members. We internally and temporally externally validated the final model in the periods January 2015-June 2016 and July 2016-December 2017. Cluster growth was predicted by larger baseline cluster size, shorter time between diagnosis and HIV care entry, younger age, shorter time since the most recent HIV diagnosis, higher proportion with no named contacts, and higher proportion with HIV viremia. The model showed areas under the receiver-operating characteristic curves of 0.82 and 0.83 in the internal and temporal external validation samples. The predictive model developed and validated here is a novel means of identifying HIV transmission clusters that may benefit from targeted HIV control resources.

Transient Properties of Probability Distribution for a Markov Process with Size-dependent Additive Noise

This study considered a stochastic model for cluster growth in a Markov process with a cluster size dependent additive noise. According to this model, the probability distribution of the cluster size transiently becomes an exponential or a log-normal distribution depending on the initial condition of the growth. In this letter, a master equation is obtained for this model, and derivation of the distributions is discussed.

Reversible Cluster Aggregation and Growth Model for Graphene Suspensions

We present a reversible cluster aggregation model for 2‐D macromolecules represented by line segments in 2‐D; and, we use it to describe the aggregation process of functionalized graphene particles in an aqueous SDS surfactant solution. The model produces clusters with similar sizes and structures as a function of SDS concentration in agreement with experiments and predicts the existence of a critical surfactant concentration (Ccrit) beyond which thermodynamically stable graphene suspensions form. Around Ccrit, particles form dense clusters rapidly and sediment. At C ≪ Ccrit, a contiguous ramified network of graphene gel forms which also densifies, but at a slower rate, and sediments with time. The deaggregation–reaggregation mechanism of our model captures the restructuring of the large aggregates towards a graphite‐like structure for the low SDS concentrations. © 2017 American Institute of Chemical Engineers AIChE J, 63: 5462–5473, 2017

Optimising self-assembly through time-dependent interactions.

We demonstrate a simple method by which time-dependent interactions can be exploited to improve self-assembly in colloidal systems. We apply this method to two systems: a model colloid with a short-ranged attractive potential, which undergoes crystallisation, and a schematic model of cluster growth. The method is based on initially strong bonds between particles, to accelerate nucleation, followed by a stage with weaker bonds, to promote the growth of high-quality assembled structures. We track the growth of clusters during assembly, which reveals insight into effects of multiple nucleation events and of competition between the growth of clusters with different properties.

Computational growth model of breast microcalcification clusters in simulated mammographic environments

BackgroundWhen screening for breast cancer, the radiological interpretation of mammograms is a difficult task, particularly when classifying precancerous growth such as microcalcifications (MCs). Biophysical modeling of benign vs. malignant growth of MCs in simulated mammographic backgrounds may improve characterization of these structures MethodsA mathematical model based on crystal growth rules for calcium oxide (benign) and hydroxyapatite (malignant) was used in conjunction with simulated mammographic backgrounds, which were generated by fractional Brownian motion of varying roughness and quantified by the Hurst exponent to mimic tissue of varying density. Simulated MC clusters were compared by fractal dimension, average circularity of individual MCs, average number of MCs per cluster, and average cluster area. ResultsBenign and malignant clusters were distinguishable by average circularity, average number of MCs per cluster, and average cluster area with p<0.01 across all Hurst exponent values considered. Clusters were distinguishable by fractal dimension with p<0.05 in low Hurst exponent environments. As the Hurst exponent increased (tissue density increased) benign and malignant MCs became indistinguishable by fractal dimension. ConclusionsThe fractal dimension of MCs changes with breast tissue density, which suggests tissue environment plays a role in regulating MC growth. Benign and malignant MCs are distinguishable in all types of tissue by shape, size, and area, which is consistent with findings in the literature. These results may help to better understand the effects of the tissue environment on tumor progression, and improve classification of MCs in mammograms via computer-aided diagnosis.

Bimodal ensemble of nanoparticles on the surface of epitaxial lead telluride films under continuous laser radiation

We present the experimental and theoretical results of the study of laser modification of the solid phase of thin epitaxial films of lead telluride under continuous irradiation. An ensemble of nanoparticles with bimodal distribution depending on the laser power, beam diameter, and scanning rate of the surface is formed under laboratory conditions The process of the laser heating of a thin film is simulated, and the change in the temperature field, depending on the conditions of laser exposure, is described. The experimental results are interpreted based on the defect–deformation theory of the formation of a bimodal ensemble of nanoparticles under continuous laser irradiation. The diffusion model of cluster growth in the bulk and on the surface of a thin film demonstrates the possibility of forming a bimodal size distribution of clusters.

Impact of Aggregation on the Percolation Anisotropy on a Square Lattice in an Elongated Geometry

The Monte Carlo simulation is applied to study the impact of the aggregation on the percolation anisotropy on a square lattice in the elongated Lx × Ly geometry. An interactive cluster-growth model, in which the probability of occupying a site on a lattice fz is dependent on the number of occupied neighboring sites z is used. The value of fz is 1/r at z = 0 and is equal to 1 in other cases. The degree of the aggregation parameter r ≥ 1 controls the morphology of aggregates. The transition from r = 1 to r → ∞ corresponds to the transition from the ordinary random percolation to the percolation of compact Eden clusters. The effects of the lattice aspect ratio a = Lx/Ly (Lx &gt; Ly) on the finite-size scaling and the electrical conductivity are studied. The data evidence that the percolation threshold pc goes through the minimum, and the finite-size effects are enhanced with increase in r. The dependence of the electrical conductivity on the measuring direction (x or y) at different values of r and a is discussed.

Para-hydrogen and helium cluster size distributions in free jet expansions based on Smoluchowski theory with kernel scaling

The size distribution of para-H2 (pH2) clusters produced in free jet expansions at a source temperature of T0 = 29.5 K and pressures of P0 = 0.9-1.96 bars is reported and analyzed according to a cluster growth model based on the Smoluchowski theory with kernel scaling. Good overall agreement is found between the measured and predicted, Nk = A k(a) e(-bk), shape of the distribution. The fit yields values for A and b for values of a derived from simple collision models. The small remaining deviations between measured abundances and theory imply a (pH2)k magic number cluster of k = 13 as has been observed previously by Raman spectroscopy. The predicted linear dependence of b(-(a+1)) on source gas pressure was verified and used to determine the value of the basic effective agglomeration reaction rate constant. A comparison of the corresponding effective growth cross sections σ11 with results from a similar analysis of He cluster size distributions indicates that the latter are much larger by a factor 6-10. An analysis of the three body recombination rates, the geometric sizes and the fact that the He clusters are liquid independent of their size can explain the larger cross sections found for He.

Beyond the Young-Laplace model for cluster growth during dewetting of thin films: Effective coarsening exponents and the role of long range dewetting interactions

Long range dewetting forces acting across thin films, such as the fundamental van der Waals interactions, may drive the formation of large clusters (tall multilayer islands) and pits, observed in thin films of diverse materials such as polymers, liquid crystals, and metals. In this study we further develop the methodology of the nonequilibrium statistical mechanics of thin films coarsening within continuum interface dynamics model incorporating long range dewetting interactions. The theoretical test bench model considered here is a generalization of the classical Mullins model for the dynamics of solid film surfaces. By analytic arguments and simulations of the model, we study the coarsening growth laws of clusters formed in thin films due to the dewetting interactions. The ultimate cluster growth scaling laws at long times are strongly universal: Short and long range dewetting interactions yield the same coarsening exponents. However, long range dewetting interactions, such as the van der Waals forces, introduce a distinct long lasting early time scaling behavior characterized by a slow growth of the cluster height/lateral size aspect ratio (i.e., a time-dependent Young angle) and by effective coarsening exponents that depend on cluster size. In this study, we develop a theory capable of analytically calculating these effective size-dependent coarsening exponents characterizing the cluster growth in the early time regime. Such a pronounced early time scaling behavior has been indeed seen in experiments; however, its physical origin has remained elusive to this date. Our theory attributes these observed phenomena to ubiquitous long range dewetting interactions acting across thin solid and liquid films. Our results are also applicable to cluster growth in initially very thin fluid films, formed by depositing a few monolayers or by a submonolayer deposition. Under this condition, the dominant coarsening mechanism is diffusive intercluster mass transport while the cluster coalescence plays a minor role, both in solid and in fluid films.

Isotropic model for cluster growth on a regular lattice

There exists a plethora of mathematical models for cluster growth and/or aggregation on regular lattices. Almost all suffer from inherent anisotropy caused by the regular lattice upon which they are grown. We analyze the little-known model for stochastic cluster growth on a regular lattice first introduced by Ferreira Jr. and Alves [J. Stat. Mech. Theo. & Exp. (2006) P11007], which produces circular clusters with no discernible anisotropy. We demonstrate that even in the noise-reduced limit the clusters remain circular. We adapt the model by introducing a specific rearrangement algorithm so that, rather than adding elements to the cluster from the outside (corresponding to apical growth), our model uses mitosis-like cell splitting events to increase the cluster size. We analyze the surface scaling properties of our model and compare it to the behavior of more traditional models. In "1+1" dimensions we discover and explore a new, nonmonotonic surface thickness scaling relationship which differs significantly from the Family-Vicsek scaling relationship. This suggests that, for models whose clusters do not grow through particle additions which are solely dependent on surface considerations, the traditional classification into "universality classes" may not be appropriate.

Externalities, Transport Networks and the Economic Growth of Urban Clusters

This article uses network analysis tools and new economic geography theory to modify the neo-classical model of regional economic growth, establishes an economic growth model of urban clusters based on externalities and transport networks through a differentiation of transaction costs, and uses the 1990-2008 data of some Chinese cities and the VAR model to test the model. Our empirical study shows that under the influence of transport networks, central cities rely on factor agglomeration for growth, while peripheral cities catch up quickly; that improved transport networks expedite the factor agglomeration of central cities; and that when some newly-added factors are reserved, increasing the node clustering coefficient and reducing peripheral cities’ transport costs will promote these cities’ application of externalities, expedite their economic growth, and facilitate the coordinated growth of central and peripheral cities. Therefore, in building the transport infrastructure, equal emphasis should be placed on linking central cities with peripheral ones and on linking peripheral cities with each other.

From logarithmic to subdiffusive polynomial fluctuations for internal DLA and related growth models

We consider a cluster growth model on the d-dimensional lattice, called internal diffusion limited aggregation (internal DLA). In this model, random walks start at the origin, one at a time, and stop moving when reaching a site not occupied by previous walks. It is known that the asymptotic shape of the cluster is spherical. When dimension is 2 or more, we prove that fluctuations with respect to a sphere are at most a power of the logarithm of its radius in dimension d larger than or equal to 2. In so doing, we introduce a closely related cluster growth model, that we call the flashing process, whose fluctuations are controlled easily and accurately. This process is coupled to internal DLA to yield the desired bound. Part of our proof adapts the approach of Lawler, Bramson and Griffeath, on another space scale, and uses a sharp estimate (written by Blach\`ere in our Appendix) on the expected time spent by a random walk inside an annulus.

Sublogarithmic fluctuations for internal DLA

We consider internal diffusion limited aggregation in dimension larger than or equal to two. This is a random cluster growth model, where random walks start at the origin of the d-dimensional lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. It is known that the asymptotic shape of the cluster is a sphere. When the dimension is two or more, we have shown in a previous paper that the inner (resp., outer) fluctuations of its radius is at most of order $\log(\mathrm{radius})$ [resp., $\log^2(\mathrm{radius})$]. Using the same approach, we improve the upper bound on the inner fluctuation to $\sqrt{\log(\mathrm{radius})}$ when d is larger than or equal to three. The inner fluctuation is then used to obtain a similar upper bound on the outer fluctuation.

Lower bounds on fluctuations for internal DLA

We consider internal diffusion limited aggregation in dimension two or more. This is a random cluster growth model, where random walks start at the origin of the lattice, one at a time, and stop moving when reaching a site that is not occupied by previous walks. When \(n\) random walks are sent from the origin, we establish a lower bound for the inner and outer errors fluctuations of order square root of the logarithm of \(n\). When dimension is three or more, this lower bound matches the upper bound recently obtained in independent works of Asselah and Gaudilliere (Ann Prob arXiv:1011.4592, 2010) and Jerison et al. (Internal DLA and the Gaussian free field arXiv:1012.3453, 2010). Also, we produce as a corollary of our proof of Asselah and Gaudilliere (Ann Prob arXiv:1011.4592, 2010), an upper bound for the fluctuation of the inner error in a specified direction.