Spreading Model Research Articles

A gradual Proterozoic transition from an unstable stagnant lid to the modern plate tectonic system

When did plate tectonics begin on Earth, and what preceded it? Published thermo-mechanical mantle evolution models imply that the early history of planets with a composition and size similar to Earth and Venus should be characterized by periodic mantle overturns of 30–100 Myr duration, separated by stable lid phases of 100–300 Myr. This is best described as an unstable stagnant lid because this term captures the Jekyll and Hyde duality of such worlds, which alternate between a stagnant lid sensu stricto phase between mantle overturns, and a mobile lid phase during overturns. Mantle overturn upwelling zones would rework and resurface large tracts of pre-existing Hadean crust and basalt-dominated Archean-style oceanic lithosphere (ASOL). Basal anatexis of ASOL c. 40–50 km thick (or melting within down-drips) could generate tonalite–trondhjemite–granodiorite (TTG) melts and create proto-continental nuclei, while garnet pyroxenite restites delaminate into the mantle. With further reworking, low-K tonalitic rocks would remelt to produce granodiorite and granite, completing the transfer of radioactive elements out of the lower crust. Mantle overturns would generate large-scale lateral currents in the upper mantle that would push against Archean-aged sub-continental lithospheric mantle keels, causing continental drift and orogenesis despite the absence of plate boundary forces such as slab-pull. This is corroborated by the observed displacement of Lakshmi Planum (>1000 km) on Venus, a planet with no arcs nor ridges. Recent models suggest that the Abitibi Greenstone Belt formed as an oceanic tract behind a detached ribbon continent during the partial break-up of the Southern Superior Craton and may be a sample of Archean oceanic lithosphere. The Abitibi Greenstone Belt has c. 50 km of apparent stratigraphy composed of 2–10 Myr mafic–felsic bimodal volcanic cycles that follow assimilation–fractionation trends indicating the contamination of mantle-derived basalts with TTG-like anatectites derived from older basalts. ASOL of this type would be difficult to subduct due to its weakness and buoyancy, but would be fertile and could generate large amounts of second-stage melts. There are no sheeted dykes, precluding a seafloor spreading model, while the absence of basal cumulates or attached mantle means that this type of ASOL should not be called an ophiolite. Archean–Proterozoic unconformities are followed by the deposition of iron formations, clastic and volcanic rocks, which are only rarely affected by sagduction. The increase in siliciclastic input and decreasing sagduction reflect near-global Late Archean emergence of stiffening granitic continents from the oceans due to secular cooling and intra-continental differentiation. Albeit associated with continent-derived siliciclastic debris, many Paleoproterozoic volcanic (and plutonic) rocks resemble Archean rocks geochemically. The similarity of magmatic rocks and hot orogenic styles in the Archean and Paleoproterozoic could imply that the overall geodynamic regime was similar in both. The Siderian–Rhyacian quiet period could therefore represent a stagnant lid phase that followed the 2.5 Ga Archean overturn. When the next mantle overturn ruptured the lid at c. 2.2–2.0 Ga (and again at c. 1.9–1.8 Ga), continents would have been set into motion, forming arcs and ridges. Once initiated, arc and ridge segments needed to multiply and propagate to create a world-girdling system. Mesoproterozoic rocks preserve clear evidence of plate mobility, subduction and orogenesis, but, ophiolites, the geological record of seafloor spreading, are extremely rare prior to 1 Ga. The Earth at 2.0 Ga was probably still largely covered by ASOL, possibly similar to the Abitibi Greenstone Belt, but how and where it was all destroyed and replaced by modern oceanic lithosphere are mysteries. Given the volume of ASOL involved, recognizable by-products of this global-scale reworking process should exist. Voluminous anorthosite–mangerite–charnockite–granite/gabbro suite rocks are mostly of Proterozoic age, requiring either an ephemeral source or a unique process. Trace element inversion models applied to massif anorthosites imply they crystallized from high-La/Yb melts that do not resemble tholeiitic basalts, invalidating the notion that they are flotation cumulates from basaltic underplates. Model anorthosite-forming melts can, however, be explained by high-pressure melting of an ASOL-like basalt source with garnet-bearing residues. I posit that massif anorthosites record the destruction of an ephemeral source (ASOL) at Proterozoic convergent margins. When the last ASOL was crushed between converging continents or consumed by an overprinting arc ( c. 0.8–1 Ga), anorthosite–mangerite–charnockite–granite/gabbro suite rocks ceased to form and the Earth became a modern plate tectonic planet.

Evaluation of an In‐Canopy Wind and Wind Adjustment Factor Model for Wildfire Spread Applications Across Scales

AbstractThe representation of vegetative sub‐canopy wind is critical in numerical weather prediction (NWP) models for the determination of the air‐surface exchange processes of heat, momentum, and trace gases. Because of the relationship between wind speed and fire behaviors, the influence of the canopy on near‐surface wind speed is critical for prognostic fire spread models used in regional NWP models. In practice, the wind speed at the midflame point of fires (midflame wind speed) is used to determine the rate of fire spread. However, the wind speeds from most in situ measurements and NWP models are taken at some reference height above the canopy and fire flames. Hence, this study develops a modular and computationally‐efficient one‐dimensional model set composed of a canopy wind model and a wind adjustment factor (WAF) model for NWP applications across scales. The model set uses prescribed foliage shape functions to represent the vertical vegetation profile and its impacts on the three‐dimensional structure of horizontal wind speeds. Results from the canopy wind model well agree with ground‐based observations with average mean absolute bias, root mean square error and determination coefficients around 0.18 m s−1, 0.40 m s−1and 0.90, respectively. The WAF model provides midflame wind speeds by estimating the WAF based on canopy, fire and flame characteristics. Various user‐definable options provide flexibility to adapt to variations in canopy characteristics and additional complexities associated with wildfires. The model set is expected to improve NWP models by providing an improved representation of the sub‐grid wind flows at any spatial scale.

Generative Algorithms for Fusion of Physics-Based Wildfire Spread Models with Satellite Data for Initializing Wildfire Forecasts

Abstract Increases in wildfire activity and the resulting impacts have prompted the development of high-resolution wildfire behavior models for forecasting fire spread. Recent progress in using satellites to detect fire locations further provides the opportunity to use measurements toward improving fire spread forecasts from numerical models through data assimilation. This work develops a physics-informed approach for inferring the history of a wildfire from satellite measurements, providing the necessary information to initialize coupled atmosphere–wildfire models from a measured wildfire state. The fire arrival time, which is the time the fire reaches a given spatial location, acts as a succinct representation of the history of a wildfire. In this work, a conditional Wasserstein generative adversarial network (cWGAN), trained with WRF–SFIRE simulations, is used to infer the fire arrival time from satellite active fire data. The cWGAN is used to produce samples of likely fire arrival times from the conditional distribution of arrival times given satellite active fire detections. Samples produced by the cWGAN are further used to assess the uncertainty of predictions. The cWGAN is tested on four California wildfires occurring between 2020 and 2022, and predictions for fire extent are compared against high-resolution airborne infrared measurements. Further, the predicted ignition times are compared with reported ignition times. An average Sørensen’s coefficient of 0.81 for the fire perimeters and an average ignition time difference of 32 min suggest that the method is highly accurate. Significance Statement To initialize coupled atmosphere–wildfire simulations in a physically consistent way based on satellite measurements of active fire locations, it is critical to ensure the state of the fire and atmosphere aligns at the start of the forecast. If known, the history of a wildfire may be used to develop an atmospheric state matching the wildfire state determined from satellite data in a process known as spinup. In this paper, we present a novel method for inferring the early stage history of a wildfire based on satellite active fire measurements. Here, inference of the fire history is performed in a probabilistic sense and physics is further incorporated through the use of training data derived from a coupled atmosphere–wildfire model.

Mathematical Modeling of Schistosomiasis Transmission Using Reaction-Diffusion Equations

Schistosomiasis, a neglected tropical disease caused by parasitic trematodes of the genus \textit{Schistosoma}, affects millions of people in tropical and subtropical regions lacking access to clean water and proper hygiene. With its impact on health and well-being, the World Health Organization aspires to eliminate schistosomiasis by 2030. This work addresses the challenge of effective control in endemic areas by integrating diffusion in each sub-population using reaction-diffusion equations. The proposed model includes treated individuals who have undergone massive drug administration and a time-dependent function that models the change in human behavior. We present a Partial Differential Equation (PDE) model of schistosomiasis spread that incorporates population movement and human behavior change. Mathematical analysis explores the system's dynamics according to the infection threshold $R_0$, shedding light on the disease's behavior. Sensitivity analysis is used to identify the key parameters affecting disease spread. Numerical simulations under different scenarios elucidate the impact of human behavior on disease dynamics. This research contributes to a deeper understanding of schistosomiasis transmission and provides insights into control strategies.

Leveraging Simulation Data to Understand Bias in Predictive Models of Infectious Disease Spread

The spread of infectious diseases is a highly complex spatiotemporal process, difficult to understand, predict, and effectively respond to. Machine learning and artificial intelligence (AI) have achieved impressive results in other learning and prediction tasks; however, while many AI solutions are developed for disease prediction, only a few of them are adopted by decision-makers to support policy interventions. Among several issues preventing their uptake, AI methods are known to amplify the bias in the data they are trained on. This is especially problematic for infectious disease models that typically leverage large, open, and inherently biased spatiotemporal data. These biases may propagate through the modeling pipeline to decision-making, resulting in inequitable policy interventions. Therefore, there is a need to gain an understanding of how the AI disease modeling pipeline can mitigate biased input data, in-processing models, and biased outputs. Specifically, our vision is to develop a large-scale micro-simulation of individuals from which human mobility, population, and disease ground-truth data can be obtained. From this complete dataset—which may not reflect the real world—we can sample and inject different types of bias. By using the sampled data in which bias is known (as it is given as the simulation parameter), we can explore how existing solutions for fairness in AI can mitigate and correct these biases and investigate novel AI fairness solutions. Achieving this vision would result in improved trust in such models for informing fair and equitable policy interventions.

Analysis of SEIQV Epidemic Model on the Spread of Covid-19 in Jember Regency

Covid-19 is a disease that attacks the respiratory system caused by infection with SARSCoV-2. Efforts to prevent the spread of Covid-19 by vaccination. The spread of disease can be modeled into a mathematical equation. The model used in this study is the SEIQV Model. The disease spread model is analyzed by finding the equilibrium point and the stability of the equilibrium point as well as the basic reproduction number. In the Covid-19 distribution model, a bifurcation analysis is carried out which is needed to determine changes in stability and changes in the number of equilibrium points. Then perform a numerical solution using the fourth-order Runge-Kutta method which is simulated using MATLAB.

Analysis of a delayed MISCR rumor spread model with refutation mechanism

Analysis of a delayed MISCR rumor spread model with refutation mechanism

Differences between Chronically Hepatitis B Virus-Infected Pregnant Women with and without Intrafamilial Infection: From Viral Gene Sequences to Clinical Manifestations.

This study aimed to investigate the differences between pregnant women with chronic hepatitis B virus (HBV) infection and intrafamilial infection and those without intrafamilial infection. HBV-DNA was extracted from the sera of 16 pregnant women with chronic hepatitis B (CHB) and their family members for gene sequencing and phylogenetic analyses. A total of 74 pregnant women with CHB were followed up from the second trimester to 3 months postpartum. Viral markers and other laboratory indicators were compared between pregnant women with CHB with and without intrafamilial infection. The phylogenetic tree showed that HBV lines in the mother-spread pedigree shared a node, whereas there was an unrelated genetic background for HBV lines in individuals without intrafamilial infection. From delivery to 3 months postpartum, compared with those without intrafamilial infection, pregnant women with intrafamilial infection were related negatively to HBV-DNA (β = -0.43, 95% confidence interval [CI]: -0.76 to -0.12, p = 0.009), HBeAg (β = -195.15, 95% CI: -366.35 to -23.96, p = 0.027), and hemoglobin changes (β = -8.09, 95% CI: -15.54 to -0.64, p = 0.035) and positively to changes in the levels of alanine aminotransferase (β = 73.9, 95% CI: 38.92-108.95, p < 0.001) and albumin (β = 2.73, 95% CI: 0.23-5.23, p = 0.033). The mother-spread pedigree spread model differs from that of non-intrafamilial infections. Pregnant women with intrafamilial HBV infection have less hepatitis flares and liver damage, but their HBV-DNA and HBeAg levels rebound faster after delivery, than those without intrafamilial infection by the virus.

Stochastic bulk density in the fire spread model

AbstractIn this study, we investigate the impact of inherent randomness on fire spread rates, with a particular focus on the stochastic parameter ε, representing the ratio of effective to actual fuel bulk density. By employing various probability distributions, such as the beta random distribution model ε, we explore the complex interplay between wind and slope factors in determining fire behavior. Our 3D visualizations and density plots illuminate the multidimensional nature of fire spread, emphasizing the significant role of stochastic variability in enhancing the accuracy of fire behavior models. This approach not only deepens our theoretical understanding but also provides valuable insights for improving fire management strategies.

Optimization of embedded cooling for hotspots based on compound plate thermal spreading model

Heat fluxes of GaN-based high electron mobility transistors (HEMTs) can reach dozens of kilowatts per square centimeter, and the heat is generated only within a small area with feature size of micrometer to millimeter length scales, which poses a huge challenge for thermal management. In this study, an embedded microfluidic cooling solution is proposed to dissipate heat from the hotspots, and thermal test vehicles are fabricated using the Micro-Electro-Mechanical System (MEMS) process. Cooling performances of hotspots with sizes ranging from 40 × 40 μm2 to 500 × 500 μm2 and varying locations are demonstrated. Thermal resistances of the test samples are analysed and the heat transfer coefficient can achieve 1.5 × 105 W/(m2∙K) using embedded microchannel cooling. We propose a compound plate spreading thermal resistance model to demonstrate the effect of the dielectric layer and the size of the heat source on heat dissipating capability of the microfluidic cooling system. Based on the thermal spreading model, when the heat source is small, integrating high thermal conductivity materials near the heat source can reduce its total thermal resistance by two orders of magnitude. By balancing the heat spreading resistance with the convective resistance of microchannel cooling, we find that ∼1 mm can be considered as the critical length for distinguishing the primary thermal management approach for different sized hotspots. This paper provides useful design guidelines for embedded microchannel cooling of devices with localized heat generation patterns, such as HEMT devices.

The impact of social interventions on COVID-19 spreading based on multilayer commuter networks

From March to June 2022, Shanghai was struck by a new coronavirus variant, Omicron, resulting in the infected cases of at least 600,000 people. Despite implementing a strict containment policy of city-wide silence (i.e., residents were not allowed to go out unless necessary), the outbreak cannot be effectively prevented within a short period of time. A significant academic and practical question is: how could we prevent and control outbreak of COVID-19 in large, densely populated cities like Shanghai? It is necessary to develop a rational epidemic spreading model for large cities, in order to accurately predict the trend of disease and quantitatively assess the impact of non-pharmaceutical interventions. In this paper, a multilayer commuter metapopulation network model is constructed to capture commuting flows and the size of epidemic outbreak during commuting between districts. The model accurately predicts epidemic spreading in each district of Shanghai. Assuming strict city-wide lockdowns, with each district locked down and limited inter-district commuting as social zones, simulations demonstrate significant suppression of outbreaks due to social-level interventions. For example, a 1-fold increase in PCR (Polymerase Chain Reaction) testing efficiency reduces the size of epidemic outbreak by approximately 70%. Larger districts require stricter controls to prevent exponential growth. Lockdowns effectively prevent epidemic outbreak at low disease rates but less so at high rates. Liberalized policies lead to varied outbreak trends, with economically developed regions peaking earlier due to higher population densities. This study provides a comprehensive framework for quantitatively evaluating the impact of social and regional controls on urban epidemics.

Data-Driven Wildfire Spread Modeling of European Wildfires Using a Spatiotemporal Graph Neural Network

Wildfire spread models are an essential tool for mitigating catastrophic effects associated with wildfires. However, current operational models suffer from significant limitations regarding accuracy and transferability. Recent advances in the availability and capability of Earth observation data and artificial intelligence offer new perspectives for data-driven modeling approaches with the potential to overcome the existing limitations. Therefore, this study developed a data-driven Deep Learning wildfire spread modeling approach based on a comprehensive dataset of European wildfires and a Spatiotemporal Graph Neural Network, which was applied to this modeling problem for the first time. A country-scale model was developed on an individual wildfire time series in Portugal while a second continental-scale model was developed with wildfires from the entire Mediterranean region. While neither model was able to predict the daily spread of European wildfires with sufficient accuracy (weighted macro-mean IoU: Portugal model 0.37; Mediterranean model 0.36), the continental model was able to learn the generalized patterns of wildfire spread, achieving similar performances in various fire-prone Mediterranean countries, indicating an increased capacity in terms of transferability. Furthermore, we found that the spatial and temporal dimensions of wildfires significantly influence model performance. Inadequate reference data quality most likely contributed to the low overall performances, highlighting the current limitations of data-driven wildfire spread models.

A taxonomy of concurrent upward flame spread models and sources of uncertainty

The use of flame spread models as a tool in fire safety engineering practice is subject to uncertainties arising from the assumptions inherent in the models and the input parameters required to implement them. Research on flame spread continues to add complexity to existing models, which places a greater onus on suitable input parameters to provide the knowledge needed to implement them. This approach is appropriate when experimental datasets are available for the validation of models for research purposes. However, it can be detrimental for design applications when there is limited knowledge about the underlying parameters for model verification in a broad range of design applications. Therefore, increasing complexity in flame spread models has the potential to reduce the strength of any such decisions made. In this article we provide a comprehensive review of the complexity of different flame spread models. This review classifies model approaches based on their inherent assumptions and sub-models to describe the complexity of the problem. It shows that, while complex modelling approaches may be necessary to adequately represent complex phenomena such as flame spread, the impact of uncertainties associated with the additional inputs is not always quantified or justified.

Impact of message fatigue in information-disease coupled dynamics on temporal simplicial networks

During information diffusion, individuals typically experience fatigue and mental exhaustion due to repeated exposure to similar information, which is a state called message fatigue. To address message fatigue in information diffusion and group interactions, we developed a novel coupled information-disease spreading model within the framework of multiplex temporal networks. Here, the information network simulates the process of disease-related information diffusion using a temporal simplicial network. Furthermore, we utilize a threshold model to characterize the effects of message fatigue. We describe the dynamic evolutionary equations of the model by the microscopic Markov chain (MMC) approach to determine the epidemic threshold. We also validated the proposed model using a number of Monte Carlo (MC) simulations. The experimental results of the MC simulations and MMC theoretical results are in good agreement. Our research has shown that message fatigue can lead to a two-stage change in the information-disease coupled spreading. Raising the threshold for message fatigue and preventing a large number of individuals from experiencing it can help inhibit the disease spreading. In short, excessive publicizing of related-disease information can backfire. The results can facilitate us to accurately capture the spreading characteristics of real-world diseases.

Mathematical modeling and flow thermodynamics study of borosilicate glass melt after external addition of Cr2O3

This article uses a high-temperature sintering imaging instrument to test the flowability of borosilicate glass melt doped with Cr2O3, and establishes a mathematical model for high-temperature glass melt spreading. Discuss the glass melt from a thermodynamic perspective by combining model interpretation with experimental characterization. The results indicate that the thermodynamic judgment formula for high-temperature flow spreading of borosilicate glass is: Q≥ρ[A0exp(−T/k0)+S0]−M·δ[A0exp(−T/k0)+S0]1/2. To improve the high-temperature flow ability of borosilicate glass, it is necessary to increase the spreading activation energy Q. On the other hand, it is necessary to reduce the spreading coefficients A0、 k0 and S0. As a refractory metal oxide and active oxide, Cr2O3 plays a role in reducing the spreading coefficient of glass systems.

Mathematical Modelling of Gonorrhoea Spread in Northern Ireland between 2012 and 2022

Mathematical Modelling of Gonorrhoea Spread in Northern Ireland between 2012 and 2022

Predicting nodal metastasis progression of oral tongue cancer using a hidden Markov model in MRI.

The presence of occult nodal metastases in patients with oral tongue squamous cell carcinomas (OTSCCs) has implications for treatment. More than 30% of patients will have occult nodal metastases, yet a considerable number of patients undergo unnecessary invasive neck dissection to confirm nodal status. In this work, we propose a probabilistic model for lymphatic metastatic spread that can quantify the risk of microscopic involvement at the lymph node level (LNL) given the location of macroscopic metastases and the tumor stage using the MRI method. A total of 108 patients of OTSCCs were included in the study. A hidden Markov model (HMM) was used to compute the probabilities of transitions between states over time based on MRI. Learning of the transition probabilities was performed via Markov chain Monte Carlo sampling and was based on a dataset of OTSCC patients for whom involvement of individual LNLs was reported. Our model found that the most common involvement was that of level I and level II, corresponding to a high probability of 𝑝b1 = 0.39 ± 0.05, 𝑝b2 = 0.53 ± 0.09; lymph node level I had metastasis, and the probability of metastasis in lymph node II was high (93.79%); lymph node level II had metastasis, and the probability of metastasis in lymph node III was small (7.88%). Lymph nodes progress faster in the early stage and slower in the late stage. An HMM can produce an algorithm that is able to predict nodal metastasis evolution in patients with OTSCCs by analyzing the macroscopic metastases observed in the upstream levels, and tumor category.

Network Spreading from Network Dimension.

Continuous-state network spreading models provide critical numerical and analytic insights into transmission processes in epidemiology, rumor propagation, knowledge dissemination, and many other areas. Most of these models reflect only local features such as adjacency, degree, and transitivity, so can exhibit substantial error in the presence of global correlations typical of empirical networks. Here, we propose mitigating this limitation via a network property ideally suited to capturing spreading. This is the network correlation dimension, which characterizes how the number of nodes within range of a source typically scales with distance. Applying the approach to susceptible-infected-recovered processes leads to a spreading model which, for a wide range of networks and epidemic parameters, can provide more accurate predictions of the early stages of a spreading process than important established models of substantially higher complexity. In addition, the proposed model leads to a basic reproduction number that provides information about the final state not available from popular established models.

An Analytical Friction Model for Handling and Spreading of Carbon Fiber Tows for Composite Prepregging Applications

Abstract A novel co-extrusion system for continuous fiber-reinforced thermoplastic composites in filament and narrow-tape format was designed, fabricated, and tested. The new modified pultrusion process, called In Situ Impregnation, impregnates continuous dry fiber reinforcement tows in situ with thermoplastic matrix for applications ranging from 3D printing using robotic manipulation to automated fiber placement. The technical goal of the system is to directly co-extrude and impregnate a reinforcement fiber tow (carbon) with thermoplastic matrix injected by an extruder fed with thermoplastic pellets. This approach uses inexpensive materials instead of “prepreg” tow in order to streamline the additive manufacturing process, cut costs for advanced composites manufacturing, and deliver fully customizable fiber orientation. The purpose of this paper is to discuss analytical modeling of friction and fiber tensioning in the system which allows for the full impregnation of the fibers. Experiments were conducted on a working pultrusion system where load was adjusted through the tensioning system to better understand the amount of friction throughout the system, the magnitude of tension in the fiber tow, and to validate the models. The resulting friction model can be used by machine designers to estimate the tension in tows, ropes, fibers, etc. in similar tensioning devices, and estimate automated system specifications such as motor requirements. A brief description of the new manufacturing process is also provided. Future work includes commercialization of the technology, automation of the manufacturing system, and further modeling work to predict fiber spreading behavior based on geometric factors.

FORECASTING TECHNOLOGY ADOPTION BEHAVIOUR AND AGRICULTURAL PRODUCTION GROWTH

In this paper, we proposed a simple mathematical model for farmers in the Ranchi district to adopt and implement agricultural technologies. We used the Fisher-Pry model, which is a very effective model in the study of technological adoption. The model's output is a Sigmoid curve, or S-shaped curve, that develops exponentially at first, then approximately linearly, and lastly asymptotically. We have studied the models of technology spread using a basic case study and brought in a real-world situation. Mathematically, it is possible to predict that adoption will rise to the number m/2 when 50% of the farmers have adopted the technology, after which it will slow down. In a real-life situation, the point of inflection might occur before or after m/2.We also collected data on some of the food crops, and net irrigated area of Ranchi district from 2011 to 2020, and evaluated it graphically/mathematically. We examined the advantages of technology in agriculture using utility functions, by employing basic scenarios and selecting between different technologies for adoption