Simple Aggregation Model Research Articles

Connecting finite-time Lyapunov exponents with supersaturation and droplet dynamics in a turbulent bulk flow.

The impact of turbulent mixing on an ensemble of initially monodisperse water droplets is studied in a turbulent bulk that serves as a simplified setup for the interior of a turbulent ice-free cloud. A mixing model was implemented that summarizes the balance equationsof water vapor mixing ratio and temperature to an effective advection-diffusion equationfor the supersaturation field s(x,t). Our three-dimensional direct numerical simulations connect the velocity and scalar supersaturation fields in the Eulerian frame of reference to an ensemble of cloud droplets in the Lagrangian frame of reference. The droplets are modeled as point particles with and without effects due to inertia. The droplet radius is subject to growth by vapor diffusion. We report the dependence of the droplet size distribution on the box size, initial droplet radius, and the strength of the updraft, with and without gravitational settling. In addition, the three finite-time Lyapunov exponents λ_{1}≥λ_{2}≥λ_{3} are monitored which probe the local stretching properties along the particle tracks. In this way, we can relate regions of higher compressive strain to those of high local supersaturation amplitudes. For the present parameter range, the mixing process in terms of the droplet evaporation is always homogeneous, while it is inhomogeneous with respect to the relaxation of the supersaturation field. The probability density function of the third finite-time Lyapunov exponent, λ_{3}<0, is related to the one of the supersaturation s by a simple one-dimensional aggregation model. The probability density function (PDF) of λ_{3} and the droplet radius r are found to be Gaussian, while the PDF of the supersaturation field shows sub-Gaussian tails.

Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values.

Development of a Simple Kinetic Mathematical Model of Aggregation of Particles or Clustering of Receptors.

The process of clustering of plasma membrane receptors in response to their agonist is the first step in signal transduction. The rate of the clustering process and the size of the clusters determine further cell responses. Here we aim to demonstrate that a simple 2-differential equation mathematical model is capable of quantitative description of the kinetics of 2D or 3D cluster formation in various processes. Three mathematical models based on mass action kinetics were considered and compared with each other by their ability to describe experimental data on GPVI or CR3 receptor clustering (2D) and albumin or platelet aggregation (3D) in response to activation. The models were able to successfully describe experimental data without losing accuracy after switching between complex and simple models. However, additional restrictions on parameter values are required to match a single set of parameters for the given experimental data. The extended clustering model captured several properties of the kinetics of cluster formation, such as the existence of only three typical steady states for this system: unclustered receptors, receptor dimers, and clusters. Therefore, a simple kinetic mass-action-law-based model could be utilized to adequately describe clustering in response to activation both in 2D and in 3D.

Theory of ion aggregation and gelation in super-concentrated electrolytes.

In concentrated electrolytes with asymmetric or irregular ions, such as ionic liquids and solvent-in-salt electrolytes, ion association is more complicated than simple ion-pairing. Large branched aggregates can form at significant concentrations at even moderate salt concentrations. When the extent of ion association reaches a certain threshold, a percolating ionic gel network can form spontaneously. Gelation is a phenomenon that is well known in polymer physics, but it is practically unstudied in concentrated electrolytes. However, despite this fact, the ion-pairing description is often applied to these systems for the sake of simplicity. In this work, drawing strongly from established theories in polymer physics, we develop a simple thermodynamic model of reversible ionic aggregation and gelation in concentrated electrolytes accounting for the competition between ion solvation and ion association. Our model describes, with the use of several phenomenological parameters, the populations of ionic clusters of different sizes as a function of salt concentration; it captures the onset of ionic gelation and also the post-gel partitioning of ions into the gel. We discuss the applicability of our model, as well as the implications of its predictions on thermodynamic, transport, and rheological properties.

Synchronization and spatial patterns in forced swarmalators.

Swarmalators are particles that exhibit coordinated motion and, at the same time, synchronize their intrinsic behavior, represented by internal phases. Here, we study the effects produced by an external periodic stimulus over a system of swarmalators that move in two dimensions. The system represents, for example, a swarm of fireflies in the presence of an external light source that flashes at a fixed frequency. If the spatial movement is ignored, the dynamics of the internal variables are equivalent to those of Kuramoto oscillators. In this case, the phases tend to synchronize and lock to the external stimulus if its intensity is sufficiently large. Here, we show that in a system of swarmalators, the force also shifts the phases and angular velocities leading to synchronization with the external frequency. However, the correlation between phase and spatial location decreases with the intensity of the force, going to zero at a critical intensity that depends on the model parameters. In the regime of zero correlation, the particles form a static symmetric circular distribution, following a simple model of aggregation. Interestingly, for intermediate values of the force intensity, different patterns emerge, with the particles spiraling or splitting in two clusters centered at opposite sides of the stimulus' location. The spiral and two-cluster patterns are stable and active. The two clusters slowly rotate around the source while exchanging particles, or separate and collide repeatedly, depending on the parameters.

Model slicing for supporting complex analytics with elastic inference cost and resource constraints

Deep learning models have been used to support analytics beyond simple aggregation, where deeper and wider models have been shown to yield great results. These models consume a huge amount of memory and computational operations. However, most of the large-scale industrial applications are often computational budget constrained. In practice, the peak workload of inference service could be 10x higher than the average cases, with the presence of unpredictable extreme cases. Lots of computational resources could be wasted during off-peak hours and the system may crash when the workload exceeds system capacity. How to support deep learning services with dynamic workload cost-efficiently remains a challenging problem. In this paper, we address the challenge with a general and novel training scheme called model slicing , which enables deep learning models to provide predictions within the prescribed computational resource budget dynamically. Model slicing could be viewed as an elastic computation solution without requiring more computational resources. Succinctly, each layer in the model is divided into groups of contiguous block of basic components (i.e. neurons in dense layers and channels in convolutional layers), and then partially ordered relation is introduced to these groups by enforcing that groups participated in each forward pass always starts from the first group to the dynamically-determined rightmost group. Trained by dynamically indexing the rightmost group with a single parameter slice rate , the network is engendered to build up group-wise and residual representation. Then during inference, a sub-model with fewer groups can be readily deployed for efficiency whose computation is roughly quadratic to the width controlled by the slice rate. Extensive experiments show that models trained with model slicing can effectively support on-demand workload with elastic inference cost.

Aggregate Control Strategy for Thermostatically Controlled Loads with Demand Response

The improvement of intelligent appliances provides the basis for the demand response (DR) of residential loads. Thermostatically controlled loads (TCLs) are one of the most important DR resources and are characterized by a large load and a high degree of control. Due to its distribution characteristic, the aggregation of TCLs and their control are key issues in implementing the load control for the DR. In this study, we focus on air conditioning loads as an example of TCLs and propose a simple and transferable aggregate model by establishing a virtual house model, which accurately captures the aggregate flexibility. The deviation of the aggregate model is analyzed for the model evaluation. An air conditioning DR control scheme is proposed based on the aggregate model; it has the advantage of simple implementation and convenient control for the individual units. Simulations are performed in Gridlab-D to evaluate the accuracy and effectiveness of the proposed model and control method.

Thermodynamic properties of amyloid fibrils: A simple model of peptide aggregation

In this manuscript, we develop a two-dimensional coarse-grained model to study equilibrium properties of fibril-like structures made of amyloid proteins. The phase space of the model is sampled using Monte Carlo computer simulations. At low densities and high temperatures proteins are mostly present as monomers while at low temperatures and high densities particles self-assemble into fibril-like structures. The phase space of the model is explored and divided into different regions based on the structures present. We also estimate free-energies to dissociate proteins from fibrils based on the residual concentration of dissolved proteins. Consistent with experiments, the concentration of proteins in solution does not affects their equilibrium state. Also, we study the temperature dependence of the equilibrium state to estimate thermodynamic quantities, e.g., heat capacity and entropy, of amyloid fibrils.

Formation of the nitrogen aggregates in annealed diamond by neutron irradiation

Neutron heavy irradiation was performed on synthetic diamonds contain nitrogen atoms in isolated substitutional form (called “type Ib diamond”) and they were annealed under a pressure of 6 GPa. A large number of nitrogen B-aggregate which consists of four substitutional nitrogen atoms symmetrically surrounding a vacancy was formed within 30 m from single nitrogen atoms. Furthermore it is observed that, in these diamonds, single nitrogen atoms coexist with the B-aggregates, which is unexplainable by the simple nitrogen aggregation model.

An adaptive hawkes process formulation for estimating time-of-day zonal trip arrivals with location-based social networking check-in data

Location-Based Social Networking (LBSN) services, such as Foursquare, Facebook check-ins, and Geo-tagged Twitter tweets, have emerged as new secondary data sources for studying individual travel mobility patterns at a fine-grained level. However, the differences between human social behavioral and travel patterns can cause significant sampling bias for travel demand estimation. This paper presents a dynamic model to estimate time-of-day zonal trip arrival patterns. In the proposed model, the state propagation is formulated by the Hawkes process; the observation model implements LBSN sampling. The proposed model is applied to Foursquare check-in data collected from Austin, Texas in 2010 and calibrated with Origin-Destination (OD) data and time of day factor from Capital Area Metropolitan Planning Organization (CAMPO). The proposed model is compared with a simple aggregation model of trip purposes and time of day based on a prior daily OD estimation model using the LBSN data. The results illustrate the promising benefits of applying stochastic point process models and state-space modeling in time-of-day zonal arrival pattern estimation with the LBSN data. The proposed model can significantly reduce the number of parameters to calibrate in order to reduce the sampling bias of LBSN data for trip arrival estimation.

Kinetics of Formation and Asymmetrical Distribution of Hsp104-Bound Protein Aggregates in Yeast

Budding yeast cells have a finite replicative life span; that is, a mother cell produces only a limited number of daughter cells before it slows division and dies. Despite the gradual aging of the mother cell, all daughters are born rejuvenated and enjoy a full replicative lifespan. It has been proposed that entry of mother cells into senescence is driven by the progressive accumulation and retention of damaged material, including protein aggregates. This additionally allows the daughter cells to be born damage free. However, the mechanism underlying such asymmetrical segregation of protein aggregates by mother and daughter cells remains controversial, in part because of the difficulties inherent in tracking the dynamics and fate of protein aggregates in vivo. To overcome such limitations, we have developed single-cell real-time imaging methodology to track the formation of heat-induced protein aggregates in otherwise unperturbed dividing cells. By combining the imaging data with a simple computational model of protein aggregation, we show that the establishment of asymmetrical partitioning of protein aggregates upon division is driven by the large bud-specific dilution rate associated with polarized growth and the absence of significant mother/bud exchange of protein aggregates during the budded phase of the cell cycle. To our knowledge, this study sheds new light on the mechanism of establishment of a segregation bias, which can be accounted for by simple physical arguments.

Fractality à la carte: a general particle aggregation model.

In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters’ fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.

Using the experience curve model to project carbon dioxide emissions through 2040

Projections of long-term carbon dioxide (CO2) emissions in the literature vary over a wide range depending on both socio-economic development and mitigation policy. Therefore, any attempt to improve the accuracy of such projections is important. We present a simple aggregate model to project the future carbon intensity of economic output, which is then used to forecast energy-related CO2 emissions through 2040 for seven countries and three regions of the world. Our projection results are compared to those from the International Energy Outlook 2013 report. We find that our projections are significantly higher than those reported in the International Energy Outlook 2013 report.

Distinguishing the Discontinuity: A Network Perspective of Peer-Performance Ratings in Teams

Team members typically make unequal – and, from the outside, unquantifiable – contributions toward team goals. Acknowledging this challenge, managers frequently use peer-ratings to gain an insider perspective of individuals’ performance. To date, peer-rated performance has overwhelmingly been operationalized using simple aggregation models, whereby the mean of multiple ratings reflects a single composite score (ratings are considered interchangeable). This approach, however, overlooks teams’ idiosyncratic interactional patterns and, consequently, discounts the possibility of meaningful variance in the informational utility captured across raters. Addressing this limitation, we integrate information processing and social network theories to advance a novel framework for understanding within-team peer-ratings. Specifically, we posit that members’ network centrality represents their access to performance- related information, which is evidenced by systematic rating differences between central and peripheral team members. Next, using the empirically robust conscientiousness-performance relationship as a benchmark, we present results suggesting that central member ratings are also more valid performance indicators than peripheral ratings. Finally, we find that the information advantage associated with member centrality is contingent upon team-level network structures; high centralization broadens the informational gap between central and peripheral members, whereas increased network density decreases the gap.

Importance of heterogeneous aggregation for NP fate in natural and engineered systems

The growing interest in nanoparticles (NP) is inevitably translating into an increase of their emissions in the environment. On the other hand, the necessary knowledge about the fate and transport of these NPs in the environment remains limited. In particular it is critically important to understand how the interactions of NPs with the particles already present in environmental matrices affect their fate, transport, and eventually persistence in the environment.In this study we present a computer model that expands upon the existing simple homogeneous aggregation models to account for heterogeneous aggregation between NPs and the distribution of natural particles already present in environmental waters. The model follows the concentrations of purely nanoparticle aggregates, purely background particles aggregates, and mixed aggregates, as well as the composition of mixed aggregates. After analytical evaluation, we ran simulations to illustrate the complexity of heterogeneous aggregation and its impact on the fate of NPs.The model predicts that the impact of NP size on their persistence in the environment is accentuated for low affinity between NPs and background particles, and for low background particle concentration.

Historical and future learning about climate sensitivity

Equilibrium climate sensitivity measures the long-term response of surface temperature to changes in atmospheric CO2. The range of climate sensitivities in the Intergovernmental Panel on Climate Change Fifth Assessment Report is unchanged from that published almost 30 years earlier in the Charney Report. We conduct perfect model experiments using an energy balance model to study the rate at which uncertainties might be reduced by observation of global temperature and ocean heat uptake. We find that a climate sensitivity of 1.5 ◦ C can be statistically distinguished from 3 ◦ C by 2030, 3 ◦ C from 4.5 ◦ C by 2040, and 4.5 ◦ Cf rom 6 ◦ C by 2065. Learning rates are slowest in the scenarios of greatest concern (high sensitivities), due to a longer ocean response time, which may have bearing on wait-and-see versus precautionary mitigation policies. Learning rates are optimistic in presuming the availability of whole ocean heat data but pessimistic by using simple aggregated metrics and model physics.

Judgment aggregation in search for the truth

We analyze the problem of aggregating judgments over multiple issues from the perspective of whether aggregate judgments manage to efficiently use all voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives where voters' disagreements stem from conflicts of information rather than of interest. Combining the two bodies of literature, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. Assuming that voters share a preference for true collective judgments, we analyze the resulting strategic incentives and determine which voting rules efficiently use all private information. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of ‘yes’ votes exceeds a particular quota.

Development of a dynamic, mechanistic model of nutritional and reproductive processes in dairy cattle

Our knowledge of genetics, nutrient metabolism and reproductive physiology demands an integrated systems approach to both research and on-farm application. Existing mechanistic, dynamic and biochemical models exist which describe (1) nutrient metabolism and control of nutritional processes and (2) estrous cyclicity in lactating dairy cows. The metabolic model contains a simple aggregated model of lipogenesis, esterification and lipolysis; however, it is not sufficiently detailed to provide a research framework for future research. The estrous model describes the cyclicity of follicular development as well as several key reproductive hormones, but it does not contain any nutritional control as we understand it. Therefore, we developed a more detailed model of metabolism in adipose tissue, including uptake of glucose and fatty acids, fatty acid activation to the AcylCoA form, lipogenesis from acetate and butyrate, esterification of glycerol and fatty acids, and lipolysis and release of fatty acids and glycerol. The estrous model was expanded to include control of follicular growth by IGFI (~1 mm increase in diameter for a 20 ng/mL difference in IGFI; and degradation of estrogen and progesterone (~1.6 % increase in degradation per kg DM intake equivalent). Changes in follicular growth due to IGFI and increase in steroid degradation due to increased metabolic rate (as happens during lactation) demonstrate subtle and unpredictable changes in hormonal cyclicity, similar in fact to the complex effects of anabolic and catabolic signals in the cow. The model demonstrates behaviour and sensitivity to nutrient uptake and metabolic rate consistent with known biological processes. This model may be used to help interpret genomic and transcriptomic data, to pinpoint the most effective ways to select and manage for changes in productive and reproductive efficiency.

Adaptive Aggregation of Peptide Model Systems

Jet-cooled infrared spectra of acetylated glycine, alanine, and dialanine esters and their dimers are reported in the amide A and amide I-III regions. They serve as particularly simple peptide aggregation models and are found to prefer a single backbone conformation in the dimer that is different from the most stable monomer backbone conformation. In the case of alanine, evidence for topology-changing chirality discrimination upon dimer formation is found. The jet spectroscopic results are compared to gas phase spectra and quantum chemical calculations. They provide reliable benchmarks for the evaluation of the latter in the field of peptide interactions.

Impact of morphological parameters onto simulated light scattering patterns

We have investigated the impact of the variation of various parameters of fractal aggregates on simulated light scattering patterns. Static light scattering is commonly used to measure soot in a flame and such a study could help to improve experimental approaches. Aggregate models, used for our light scattering simulations, are based on real soot structures that can be found under laboratory conditions in a premixed ethane/air flame (McKenna-type burner, equivalence ratio ϕ=2.5). Our work was not focused on modeling and analysis of aggregates that are typically encountered in the atmosphere, therefore the results might be of limited interest to climate scientists. In our study, the variation of all parameters that enter into the standard fractal equation were investigated. Additionally effects when varying the overlap of primary particles, the incident wavelength and the complex refractive index are discussed. For numerical simulations two different codes were used, the T-Matrix (when particles are in point contact) and the DDScat program (which is capable of performing light scattering simulations by overlapping spheres). Comparisons between these two methods show very good agreement. The results demonstrate that the radius of gyration is responsible for the amount of light scattered towards the back direction while the total volume of an aggregate defines the shape of the light scattering patterns. Small changes of the fractal dimension can be neglected (provided that the fractal prefactor is accordingly modified in a suitable way). The overlap level, if the radius of gyration is kept constant, introduces barely visible changes to the light scattering diagrams which suggest that a simple aggregate model, composed of particles being in point contact, can be used instead of a structure in early sintering stage when overlap of primary particles is not so high.