Cluster Size Distribution Research Articles

Morphogenesis of Biofilms in Porous Media and Control on Hydrodynamics.

The functioning of natural and engineered porous media, like soils and filters, depends in many cases on the interplay between biochemical processes and hydrodynamics. In such complex environments, microorganisms often form surface-attached communities known as biofilms. Biofilms can take the shape of clusters, which alter the distribution of fluid flow velocities within the porous medium, subsequently influencing biofilm growth. Despite numerous experimental and numerical efforts, the control of the biofilm clustering process and the resulting heterogeneity in biofilm permeability is not well understood, limiting our predictive abilities for biofilm-porous medium systems. Here, we use a quasi-2D experimental model of a porous medium to characterize biofilm growth dynamics for different pore sizes and flow rates. We present a method to obtain the time-resolved biofilm permeability field from experimental images and use the obtained permeability field to compute the flow field through a numerical model. We observe a biofilm cluster size distribution characterized by a spectrum slope evolving in time between -2 and -1, a fundamental measure that can be used to create spatio-temporal distributions of biofilm clusters for upscaled models. We find a previously undescribed biofilm permeability distribution, which can be used to stochastically generate permeability fields within biofilms. An increase in velocity variance for a decrease in physical heterogeneity shows that the bioclogged porous medium behaves differently than expected from studies on heterogeneity in abiotic porous media.

Patchy colloidal gels under the influence of gravity.

In this contribution, gravitational effects in gel-forming patchy colloidal systems are studied. We focus on how the gel structure is modified by gravity. Through Monte Carlo computer simulations of gel-like states recently identified by the rigidity percolation criterion [J. A. S. Gallegos et al., Phys. Rev. E 104, 064606 (2021)], the influence of the gravitational field, characterized by the gravitational Péclet number, Pe, on patchy colloids is studied in terms of the patchy coverage, χ. Our findings point out that there exists a threshold Péclet number, Peg, that depends on χ above which the gravitational field enhances the particle bonding and, in consequence, promotes the aggregation or clustering of particles; the smaller the χ value, the higher the Peg. Interestingly, when χ ∼ 1 (near the isotropic limit), our results are consistent with an experimentally determined threshold Pe value where gravity affects the gel formation in short-range attractive colloids. In addition, our results show that the cluster size distribution and the density profile undergo variations that lead to changes in the percolating cluster, i.e., gravity is able to modify the structure of the gel-like states. These changes have an important impact on the structural rigidity of the patchy colloidal dispersion; the percolating cluster goes from a uniform spatially network to a heterogeneous percolated structure, where an interesting structural scenario emerges, namely, depending on the Pe value, the new heterogeneous gel-like states can coexist with both diluted and dense phases or they simply reach a crystalline-like state. In the isotropic case, the increase in the Pe number can shift the critical temperature to higher temperatures; however, when Pe > 0.01, the binodal disappears and the particles fully sediment at the bottom of the sample cell. Furthermore, gravity moves the rigidity percolation threshold to lower densities. Finally, we also note that within the values of the Péclet number here explored, the cluster morphology is barely altered.

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.

Percolation critical exponents in cluster kinetics of pulse-coupled oscillators.

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.

Revisiting the Impact of Tungsten on the Catalytic Properties of Ammonia-SCR V2O5-WO3/TiO2 Catalysts: Geometric vs. Electronic Effects

The SCR performance of V2O5-WO3/TiO2 SCR-catalysts characterized by different surface W density (2.1W/nm2 and 9.5W/nm2) and different surface V density varying in the range 1–8V/nm2 has been investigated in order to clarify existing controversies on the preferential involvement of electronic and geometric effects in the catalytic properties. It was found that tungsten has a weak effect on the VOx cluster size distribution through contraction of dilution effect. In contrast, the optimal interaction between W and V, when both reach their highest composition, appears to be a relevant parameter that can enhance their acidic properties and improve the catalytic efficiency in dry conditions. On the other hand, an absence of significant interaction leads to discontinuity due to deactivation. In the presence of steam, acidic properties are averaged, lowering the impact of the V to W ratio. Finally, the critical importance of acidic properties which outperform redox properties in the definition of active site is pointed out in the light of this study.

Mutual independence of water and n-nonane nucleation at low temperatures.

The interaction of water with different substances in the earth's atmosphere lies at the heart of many processes that influence our climate. However, it is still unclear how different species interact with water on the molecular level and in which ways this interaction contributes to the water vapor phase transition. Here, we report the first measurements of water-nonane binary nucleation in the 50-110K temperature range, along with unary nucleation data of both. The time-dependent cluster size distribution in a uniform post-nozzle flow was measured by time-of-flight mass spectrometry coupled with single-photon ionization. From these data, we extract experimental rates and rate constants for both nucleation and cluster growth. The observed mass spectra of water/nonane clusters are not or only slightly affected by the introduction of the other vapor, and the formation of mixed clusters was not observed during nucleation of the mixed vapor. Additionally, the nucleation rate of either substance is not much affected by the presence (or absence) of the other species, i.e., the nucleation of water and nonane proceeds independently, indicating that hetero-molecular clusters do not play a role during nucleation. Only at the lowest temperature of our experiment (i.e., 51K) do the measurements suggest that interspecies interaction slows water cluster growth. The findings here are in contrast to our earlier work in which we showed that vapor components in other mixtures, e.g., CO2 and toluene/H2O, can interact to promote nucleation and cluster growth in a similar temperature range.

A novel method for the 3D inhomogeneous percolation on the Lattice with its application

This article anticipates the puzzle of acquiring a three-dimensional inhomogeneous site percolation on an irregular Bethe Lattice (TDIBL). In this work, we explore a TDIBL with the intent to realize the right tradeoff among different percolating variates, namely, cluster size distribution (CSD), critical occupation probability (COP), percolating probability (PP), and mean cluster size (MCS). The variates results are acquired using the generating function (GF) and generalized recursive approaches (GRA). The findings revealed that, for inhomogeneous site percolation (ISP) on the proposed model, the high fraction of probabilities (occupation and distribution probabilities) boosts the intensity of the process, which will enlarge the mean degree of the system in the percolation process. Moreover, numerical simulation and sensitivity analysis will also enhance our understanding of the percolating process via 2D and 3D. Their corresponding shape profiles of earned findings are drawn to perceive their dynamics amongst the options of entailed parameters. Furthermore, exhausting the above scheme, we discuss the transmission behavior of the novel corona-virus 2019 (COVID-19) and present particular disease-control schemes courtesy of groups with numerous infection probabilities and find the effect according to the age distribution. We recognize that this endeavor is timely, that it will be about curiosity, and that it will include scientists working with diverse percolation approaches.

Kinetics of Precipitation Processes at Non-Zero Input Fluxes of Segregating Particles

We consider the process of formation and growth of clusters of a new phase in segregation processes in solid or liquid solutions in an open system when segregating particles are added continuously to it with a given rate of input fluxes, Φ. As shown here, the value of the input flux significantly affects the number of supercritical clusters formed, their growth kinetics, and, in particular, the coarsening behavior in the late stages of the process. The detailed specification of the respective dependencies is the aim of the present analysis, which combines numerical computations with an analytical treatment of the obtained results. In particular, a treatment of the coarsening kinetics is developed, allowing a description of the development of the number of clusters and their average sizes in the late stages of the segregation processes in open systems, which goes beyond the scope of the classical Lifshitz, Slezov and Wagner theory. As is also shown, in its basic ingredients, this approach supplies us with a general tool for the theoretical description of Ostwald ripening in open systems, or systems where the boundary conditions, like temperature or pressure, vary with time. Having this method at one's disposal supplies us with the possibility that conditions can be theoretically tested, leading to cluster size distributions that are most appropriate for desired applications.

Calcium oscillation on homogeneous and heterogeneous networks of ryanodine receptor.

Calcium oscillation is an important calcium homeostasis, imbalance of which is the key mechanism of initiation and progression of many major diseases. The formation and maintenance of calcium homeostasis are closely related to the spatial distribution of calcium channels on endoplasmic reticulum, whose complex structure was unveiled by recent observations with superresolution imaging techniques. In the current paper, a theoretical framework is established by abstracting the spatial distribution of the calcium channels as a nonlinear biological complex network with calcium channels as nodes and Ca^{2+} as edges. A dynamical model for a ryanodine receptor (RyR) is adopted to investigate the effect of spatial distribution on calcium oscillation. The mean-field model can be well reproduced from the complete graph and dense Erdös-Rényi network. The synchronization of RyRs is found important to generate a global calcium oscillation. Below a critical density of the Erdös-Rényi or BaraBási-Albert network, the amplitude and interspike interval decrease rapidly with the end of disappearance of oscillation due to the desynchronization. The clique graph with a cluster structure cannot produce a global oscillation due to the failure of synchronization between clusters. A more realistic geometric network is constructed in a two-dimensional plane based on the experimental information about the RyR arrangement of clusters and the frequency distribution of cluster sizes. Different from the clique graph, the global oscillation can be generated with reasonable parameters on the geometric network. The simulation also suggests that existence of small clusters and rogue RyRs plays an important role in the maintenance of global calcium oscillation through keeping synchronization between large clusters. Such results support the heterogeneous distribution of RyRs with different-size clusters, which is helpful to understand recent observations with superresolution nanoscale imaging techniques. The current theoretical framework can also be extent to investigate other phenomena in calcium signal transduction.

Radial growth rate of near-critical crystal nuclei in poly(l-lactic acid) (PLLA) in Tammann's two-stage development method.

The specific features of crystal nucleation widely determine the morphology of the evolving crystalline material. Crystal nucleation is, as a rule, not accessible by direct observation of the nuclei, which develop with time. This limitation is caused by the small size (nanometer scale) of the critical nuclei and the stochastic nature of their formation. We describe an experimental approach to the determination of specific features of the cluster size distribution employing fast scanning calorimetry at scanning rates up to 10 000Ks-1. The surviving cluster fraction is determined by selectively melting/dissolving clusters smaller than the critical size corresponding to the highest temperature of a short spike positioned between the nucleation and the development stage in Tammann's two-stage method. This approach allows for estimating the time evolution of the radius of the largest detectable clusters in the distribution. Knowing this radius as a function of nucleation time allows for determining a radial growth rate. In the example of poly(l-lactic acid) (PLLA), the order of magnitude estimate of radial growth rates of clusters of about 2-5nm yields values between 10-5 and 10-3nms-1. The radial growth rate of micrometer-sized spherulites is available from optical microscopy. The corresponding values are about three orders of magnitude higher than the values for the nanometer-sized clusters. This difference is explainable by stochastic effects, transient features, and the size dependence of the growth processes on the nanometer scale. The experimental and (order of magnitude) classical nucleation theory estimates agree well.

Modeling contractility kit-mediated cytoskeletal network assembly.

The proper function of the cytoskeleton enables mechanoresponsiveness, the ability of cells to sense and respond to mechanical cues. Myosin II, cortexillin I and IQGAP proteins preassemble in the cytoplasm of Dictyostelium cells into contractility kits (CKs). These CKs are thought to play a pivotal role in the regulation and delivery of contractile proteins to sites of mechanical stress. The IQGAPs complementarily regulate the mechanoresponsiveness of cortexillin I-myosin II elements within CKs. Whereas cells that have only IQGAP2 are highly mechanoresponsive, those that have only IQGAP1 are not. Moreover, double mutants lacking both IQGAPs are also mechanoresponsive, suggesting that IQGAP1 serves as an inhibitor of cortexillin I and myosin II, and part of the role of IQGAP2 is to alleviate IQGAP1's inhibition. To investigate the mechanism of CK self-assembly and the possible molecular means for IQGAP regulation, we developed in SpringSaLaD a coarse-grained excluded-volume molecular model in which all protein polymers are represented by nm-sized spheres connected by spring-like links. The model is parameterized using experimentally measured values acquired through fluorescence cross-correlation spectroscopy (FCCS) and fluorescence correlation spectroscopy (FCS), which describe the interaction affinities and diffusion coefficients for individual molecular components. Simulations of the model provided cluster diffusion coefficients, distributions of cluster sizes, cluster component distributions, and IQGAP ratios in the clusters. Simulations of wild-type and null-mutant conditions revealed that the temporal order of assembly of these kits is dominated by myosin II dimer formation and that IQGAP proteins mediate cluster growth. Additionally, our simulations predicted, and FCCS experiments confirmed, the existence of CKs that incorporate both IQGAP1 and IQGAP2. This molecular model serves to describe the formation of CKs and how their assembly enables and regulates mechanoresponsiveness.

Characterizing Experimental Monoclonal Antibody Interactions and Clustering Using a Coarse-Grained Simulation Library and a Viscosity Model.

Attractive protein-protein interactions in concentrated monoclonal antibody (mAb) solutions may lead to the formation of clusters that increase viscosity. Here, we propose an analytical model that relates mAb solution viscosity to clustering by accounting for the contributions of suboptimal mAb packing within a cluster and cluster fractal dimension. The influence of short-range, anisotropic attractions and long-range Coulombic repulsion on cluster properties is investigated by analyzing the cluster-size distributions, cluster fractal dimensions, radial distribution functions, and static structure factors from a library of coarse-grained molecular dynamics simulations. The library spans a vast range of mAb charges and attractive interactions in solutions of varying ionic strength. We present a framework for combining the viscosity model and simulation library to successfully characterize the attraction, repulsion, and clustering of an experimental mAb in three different pH and cosolute conditions by fitting the measured viscosity or structure factor from small-angle X-ray scattering. At low ionic strength, the cluster-size distribution is impacted by strong charges, and both the viscosity and net charge or structure factor and net charge must be considered to deconvolute the effects of short-range attraction and long-range repulsion.

Interatomic Coulombic decay in small helium clusters.

Interatomic Coulombic decay (ICD) is an ultrafast non-radiative electronic decay process wherein an excited atom transfers its excess energy to a neighboring species leading to the ionization of the latter. In helium clusters, ICD can take place, for example, after simultaneous ionization and excitation of one helium atom within the cluster. After ICD, two helium ions are created and the system undergoes a Coulomb explosion. In this work, we investigate theoretically ICD in small helium clusters containing between two and seven atoms and compare our findings to two sets of coincidence measurements on clusters of different mean sizes. We provide a prediction on the lifetime of the excited dimer and show that ICD is faster for larger clusters. This is due to (i) the increased number of neighboring atoms (and therefore the number of decay channels) and (ii) the substantial decrease of the interatomic distances. In order to provide more details on the decay dynamics, we report on the kinetic-energy distributions of the helium ions. These distributions clearly show that the ions may undergo charge exchange with the neutral atoms within the cluster, such process is known as frustrated Coulomb explosion. The probability for these charge-exchange processes increases with the size of the clusters and is reflected in our calculated and measured kinetic-energy distributions. These distributions are therefore characteristics of the size distribution of small helium clusters.

Clustering-Based Energy Efficient Task Offloading for Sustainable Fog Computing

Delay and energy efficient task offloading from device to fog nodes involves decision making challenges wherein an integrated optimal scheme for preserving sustainability of the terminal nodes (TNs) and fog nodes (FNs) is extremely important. In this paper, we propose a novel clustering based delay aware energy efficient task offloading scheme in a Software-Defined Networking (SDN) based fog architecture. A bi-objective problem is formulated for optimum clustering of TNs with respect to FNs, selection of offloading parameters and, joint delay and energy minimization. It is then tranformed to a scalarized single objective problem which has a nested structure with the two problems: 1) optimal clustering and 2) optimal offloading for a given set of clusters. Based on this, Optimal Clustering and Offloading Parameters (OCOP) algorithm is designed which has lesser time complexity than the usual quadratic case. Through extensive simulations, we have shown that the use of explicit clustering in the proposed algorithm improves FN participation and reduces activity time and energy levels thereby increasing sustainability of the FNs and TNs as compared with the random case and a similar task offloading algorithm. Moreover, even cluster size distribution lowers our algorithm’s running time than the quadratic case.

Revealing the governing factors for long-term radiation damage evolution in multi-principal elemental alloys through atomistically-informed cluster dynamics

Multi-principal elemental alloys (MPEAs) exhibit unusual mechanical properties and irradiation resistance. It has been reported that the irradiation tolerance of MPEAs originates from the long-term defect evolution stage rather than the ballistic collision phase. However, understanding the long-term evolution of MPEAs is exceptionally challenging due to intrinsic chemical disorder. In this work, we apply atomistically-informed cluster dynamics to study defect evolution in MPEAs for the first time, which enables us to elucidate the critical features responsible for the irradiation performance of MPEAs. With suitable irradiation parameters, our obtained cluster size distributions are in good agreement with experiments. We further discuss the influences of defect migration energy heterogeneity, cluster geometry, and temperature on the produced defect cluster forms. Our results suggest that the small clusters during the collision phase in MPEAs suppress the formation of large-sized defect clusters in the long term. Contrary to the common belief, a broader migration energy distribution due to chemical disorder cannot reduce the maximal defect cluster size but increase the proportion of small clusters. Our results thus reveal that the major role of chemical complexity in MPEAs is to modify the growth mechanism of clusters by promoting small cluster formation and suppressing overall defect diffusivities.

Particle identification with the cluster counting technique for the IDEA drift chamber

IDEA (Innovative Detector for an Electron–positron Accelerator) is a general-purpose detector concept, designed to study electron–positron collisions in a wide energy range in a very large circular leptonic collider. Its drift chamber is designed to provide an efficient tracking, a high precision momentum measurement and an excellent particle identification by exploiting the application of the cluster counting technique. To investigate the potential of the cluster counting techniques on physics events, a simulation of the ionization cluster generation is needed, therefore we developed an algorithm which can use the energy deposit information provided by the Geant4 toolkit to reproduce, in a fast and convenient way, the cluster number and cluster size distributions. The results obtained confirm that the cluster counting technique allows to reach a resolution two times better than the traditional dE/dx method. A beam test has been performed during November 2021 at CERN on the H8 beam line to validate the simulations results, to define the limiting effects for a fully efficient cluster counting and to count the number of electron clusters released by an ionizing track at a fixed βγ as a function of the track angle. The simulation and the beam test results will be described briefly in this issue.

Comparison of Solute Nanoclusters in Fe–Cr–N Tempered Martensite Observed by Different Atom Probe Instruments

AbstractThe solute clustering behaviors in Fe-1.0mass%Cr-0.3mass%N tempered martensite were comparatively studied by using three atom probe instruments, i.e. LEAP 4000 HR, 5000 XR, and 5000 XS. The microstructural features of nanoclusters were measured under the same conditions in voltage pulse mode, while statistical analysis including nearest neighbor distribution, radial distribution, frequency distribution, and cluster size distribution of Cr atoms were performed on the reconstructed datasets. The results revealed the superior capability of the LEAP 5000 XR to detect Cr nanoclusters in tempered martensite compared with the LEAP 4000 HR as a result of the improvement in detection efficiency and hit detection performance, whereas the high level of background in the mass-to-charge spectrum measured by the LEAP 5000 XS in voltage pulse mode limits its application in the detection of solute nanoclusters.

COVID-19 outbreaks analysis in the Valencian Region of Spain in the prelude of the third wave.

The COVID-19 pandemic has led to unprecedented social and mobility restrictions on a global scale. Since its start in the spring of 2020, numerous scientific papers have been published on the characteristics of the virus, and the healthcare, economic and social consequences of the pandemic. However, in-depth analyses of the evolution of single coronavirus outbreaks have been rarely reported. In this paper, we analyze the main properties of all the tracked COVID-19 outbreaks in the Valencian Region between September and December of 2020. Our analysis includes the evaluation of the origin, dynamic evolution, duration, and spatial distribution of the outbreaks. We find that the duration of the outbreaks follows a power-law distribution: most outbreaks are controlled within 2 weeks of their onset, and only a few last more than 2 months. We do not identify any significant differences in the outbreak properties with respect to the geographical location across the entire region. Finally, we also determine the cluster size distribution of each infection origin through a Bayesian statistical model. We hope that our work will assist in optimizing and planning the resource assignment for future pandemic tracking efforts.

Statistics of vacuum electrical breakdown clustering and the induction of follow-up breakdowns

Understanding the underlying physics of vacuum electrical breakdown is of relevance for the development of technologies where breakdown is of significance, either as an intended part of device operation or as a cause of failure. One prominent contemporary case of the latter is high-gradient linear accelerators, where structures must be able to operate with both high surface electric fields and low breakdown rates. Temporal clustering of breakdowns has for long been observed in accelerating structures. In this work, the statistics of breakdown clustering were studied using data collected by a system applying DC voltage pulses over parallel disk electrodes in a vacuum chamber. It was found that the obtained distributions of cluster sizes can be explained by postulating that every breakdown induces a number of follow-up breakdowns that are Poisson-distributed with λ < 1. It was also found that the primary breakdown rate, i.e., the breakdown rate after discounting follow-up breakdowns, fluctuates over time but has no discernible correlation with cluster size. Considered together, these results provide empirical support for the interpretation that primary and follow-up breakdowns are categorically different kinds of events with different underlying causes and mechanisms. Furthermore, they support the interpretation that there is an actual causal relationship between the breakdowns in a cluster rather than them simply being concurrent events with a common underlying cause.

Active percolation in pusher-type microswimmers

The aggregation of microorganisms in colonies and biofilms underpins a myriad of biological processes, and has crucial implications in ecology and biomedical sciences. While much of our knowledge of microbial motion is based on single-cell mechanisms or cell-cell interactions, the origin of cooperativity in microbial communities is not yet fully understood. Here, we reveal the existence of a continuum percolation transition in two model suspensions of pusher-type microswimmers: an asymmetric dumbbell and a squirmer model. Clusters of swimmers held together by hydrodynamic forces dynamically aggregate and separate. Using simulations with explicit hydrodynamics and theory, we find that as the microswimmers' filling fraction increases, the cluster size distribution approaches a scale-free form and system-spanning clusters emerge.