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At least 1,531 records · Page 85
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A new biogeochemical modelling framework (FLaMe-v1.0) for lake methane emissions on the regional scale: development and application to the European domain

This study presents a new physical-biogeochemical modelling framework for simulating lake methane (CH 4 ) emissions at regional scales. The new model, FLaMe-v1.0 (Fluxes of Lake Methane), rests on an innovative, computationally efficient lake clustering approach that enables the simulation of CH 4 emissions across a large number of lakes. Building on the Canadian Small Lake Model (CSLM) that simulates the lake physics, we develop a suite of biogeochemical modules to simulate transient dynamics of organic Carbon (C), Oxygen (O 2 ), and CH 4 . We first test the performance of FLaMe-v1.0 by analyzing physical and biogeochemical processes in two theoretical lakes with characteristics that can be considered representative for many lakes (an oligotrophic, deep lake driven by cold climate versus a eutrophic, shallow lake driven by warm climate). Next, we evaluate the model by comparing simulated and observed timeseries of CH 4 emissions in four well-surveyed lakes. We then apply FLaMe-v1.0 at the European scale to evaluate simulated diffusive and ebullitive lake CH 4 fluxes against in-situ measurements in both boreal and central European regions. Finally, we provide a first assessment of the spatio-temporal variability in CH 4 emissions from European lakes with a surface area comprised between 0.1–1000 km 2 (n= 108 407, total area = 1.33 × 105 km 2 ), indicating a total emission of 0.97 ± 0.23 Tg CH 4 yr −1 , with the uncertainty constrained by combining FLaMe-v1.0 and machine learning techniques. Moreover, 30 % and 70 % of these CH 4 emissions are through diffusive and ebullitive pathways, respectively. Annually averaged CH 4 emission rates per unit lake area during 2010–2016 have a South-to-North decreasing gradient, resulting in a mean over the European domain as 7.39 g CH 4 m −2 yr −1 . Our simulations reveal a strong seasonality (with ice-blocking effects accounted for) in European lake CH 4 emissions, with nearly ten times higher emissions during late summer than during winter. This pronounced seasonal variation highlights the importance of accounting for the sub-annual variability in CH 4 emissions to accurately constrain regional CH 4 budgets. In the future, FLaMe-v1.0 could be embedded into Earth System Models to investigate the feedback between climate warming and global lake CH 4 emissions.

Maisonnier, Manon [Free Univ. of Brussels (Belgium↗
DOE OSTI2018

Numerical Simulation and Model Analyses of In-situ Biogeochemical Remediation of Chromium at the LANL - 18306

Environmental management problems associated with contamination of groundwater resources with heavy metals (such as chromium) typically require complex biogeochemical model simulations and analysis of in situ remediation. Frequently, the in situ remediation is the only viable treatment option. In these cases, a three-dimensional reactive transport model of relevant biogeochemical processes is invaluable. Recently, we have developed a novel unique biogeochemical simulator called CHROTRAN (http://chrotran.lanl.gov; Hansen et al. 2017, Vesselinov et al. 2018a) capable to represent the full three-dimensional dynamics of processes associated with in situ biogeochemical remediation of heavy metals in heterogeneous aquifers. CHROTRAN accounts for spatial and temporal transients of (1) the heavy metal to be remediated, (2) introduced amendments (e.g., through well injection), and (3) biomass growth and decay. The introduced amendments can include (1) an electron donor (e.g., molasses), (2) a nontoxic-conservative bio-inhibitor (e.g., ethanol), and (3) a biocide (e.g., dithionite). In addition, direct abiotic reduction by donor-metal interaction as well as donor-driven biomass growth and bio-reduction are modeled in CHROTRAN. Other critical processes, such as donor sorption, bio-fouling and biomass death are also modeled. CHROTRAN can simulate the groundwater flow dynamics introduced due a series of injection and extraction wells and account for reduction of aquifer permeability near the wells due bio clogging. CHROTRAN is based on the existing PFLOTRAN (http://pflotran.org; Lichtner et al, 2017a) code framework, taking advantage of the reaction interface allowing for implementation of complex model features and leverage other facets of PFLOTRAN, such as multi-component geochemistry and high-performance computing. Here, we present numerical simulations and model analyses related to the Los Alamos National Laboratory (LANL) chromium site. The analyses are performed by coupling of CHROTRAN with MADS (Model Analysis and Decision Support; http://mads.lanl.gov; Vesselinov et al., 2018b). We present analyses related to uncertainty quantification of model predictions, sensitivity of model parameters and remedial decision support. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Time Correlations from Steady-State Expectation Values

Recovering properties of correlation functions is typically challenging. On the one hand, experimentally, it requires measurements with a temporal resolution finer than the system’s dynamics. On the other hand, analytical or numerical analysis requires solving the system evolution. Here, we use recent results of quantum metrology with continuous measurements to derive general lower bounds on the relaxation and second-order correlation times that are both easy to calculate and measure. These bounds are based solely on steady-state expectation values and their derivatives with respect to a system parameter, and can be readily extended to the autocorrelation of arbitrary observables. We validate our method on two examples of critical quantum systems: a critical driven-dissipative resonator, where the bound matches analytical results for the dynamics, and the infinite-range Ising model, where only the steady state is solvable, and thus the bound provides information beyond the reach of existing analytical approaches. Our results can be applied to the experimental characterization of ultrafast systems and to the theoretical analysis of many-body models whose dynamics are hard to compute.

Górecki, Wojciech [INFN, Pavia] (ORCID:00000001991↗
DOE OSTI2014

TU-F-17A-03: An Analytical Respiratory Perturbation Model for Lung Motion Prediction

Purpose: Breathing irregularity is common, causing unreliable prediction in tumor motion for correlation-based surrogates. Both tidal volume (TV) and breathing pattern (BP=ΔVthorax/TV, where TV=ΔVthorax+ΔVabdomen) affect lung motion in anterior-posterior and superior-inferior directions. We developed a novel respiratory motion perturbation (RMP) model in analytical form to account for changes in TV and BP in motion prediction from simulation to treatment. Methods: The RMP model is an analytical function of patient-specific anatomic and physiologic parameters. It contains a base-motion trajectory d(x,y,z) derived from a 4-dimensional computed tomography (4DCT) at simulation and a perturbation term Δd(ΔTV,ΔBP) accounting for deviation at treatment from simulation. The perturbation is dependent on tumor-specific location and patient-specific anatomy. Eleven patients with simulation and treatment 4DCT images were used to assess the RMP method in motion prediction from 4DCT1 to 4DCT2, and vice versa. For each patient, ten motion trajectories of corresponding points in the lower lobes were measured in both 4DCTs: one served as the base-motion trajectory and the other as the ground truth for comparison. In total, 220 motion trajectory predictions were assessed. The motion discrepancy between two 4DCTs for each patient served as a control. An established 5D motion model was used for comparison. Results: The average absolute error of RMP model prediction in superior-inferior direction is 1.6±1.8 mm, similar to 1.7±1.6 mm from the 5D model (p=0.98). Some uncertainty is associated with limited spatial resolution (2.5mm slice thickness) and temporal resolution (10-phases). Non-corrected motion discrepancy between two 4DCTs is 2.6±2.7mm, with the maximum of ±20mm, and correction is necessary (p=0.01). Conclusion: The analytical motion model predicts lung motion with accuracy similar to the 5D model. The analytical model is based on physical relationships, requires no training, and therefore is potentially more resilient to breathing irregularities. On-going investigation introduces airflow into the RMP model for improvement. This research is in part supported by NIH (U54CA137788/132378). AY would like to thank MSKCC summer medical student research program supported by National Cancer Institute and hosted by Department of Medical Physics at MSKCC.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Improved Coupling of Hydrodynamics and Nuclear Reactions via Spectral Deferred Corrections

© 2019. The American Astronomical Society. All rights reserved. Simulations in stellar astrophysics involve the coupling of hydrodynamics and nuclear reactions under a wide variety of conditions, from simmering convective flows to explosive nucleosynthesis. Numerical techniques such as operator splitting (most notably Strang splitting) are usually employed to couple the physical processes, but this can affect the accuracy of the simulation, particularly when the burning is vigorous. Furthermore, Strang splitting does not have a straightforward extension to higher-order integration in time. We present a new temporal integration strategy based on spectral deferred corrections, and describe the second- and fourth-order implementations in the open source, finite-volume, compressible hydrodynamics code Castro. One notable advantage to these schemes is that they combine standard low-order discretizations for individual physical processes in a way that achieves an arbitrarily high order of accuracy. We demonstrate the improved accuracy of the new methods on several test problems of increasing complexity.

Nucleosynthesis↗
DOE OSTI2020

Mathematical Modeling of Liquid-Phase Alkylation of Benzene with Ethylene Considering the Process Unsteadiness

Ethylbenzene is a key intermediate in the manufacture of styrene that is an important industrial monomer. Ethylbenzene is produced by benzene alkylation using either gas-phase or liquid-phase methods. The liquid-phase alkylation that uses liquid acidic catalysts needs to be improved. We develop a mathematical model for the liquid-phase benzene alkylation. The reaction scheme, designed with a due analysis of desired and side reactions, and with the analysis of the formation of deactivating agents, reflects, in particular, the influence of the concentration of heavy hydrocarbons on the catalyst activity. The account of the catalyst deactivation by heavy alkylaromatics allows predictions of the temporal changes in the outputs of the alkylation process. In particular, the decrease of the ethylbenzene concentration by 2–3 wt % and increase of the polyalkylate outlet concentration by 1.5–2 wt % are the results of the catalyst deactivation. These effects, however, can be compensated by 1.3-time increase of polyalkylate supply and by the temperature increase up to 398 K. Finally, the calculations also show that it is possible to decrease the supply of fresh catalyst from 0.498 to 0.472 t/hour without loss in the yield of ethylbenzene.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

RED-BL: Evaluating dynamic workload relocation for data center networks

In this study, we present RED-BL (Relocate Energy Demand to Better Locations), a framework to minimize the electricity cost for operating data center networks over consecutive intervals of fixed duration. Within each interval, RED-BL provides a mapping of workload to a set of geographically distributed data centers. To this end, RED-BL uses the geographical and temporal variations in electricity prices as exhibited by electrical energy markets. In addition, we incorporate the transition costs associated with a change in workload mapping from one interval to the next, over a planning window comprising multiple such intervals. This results in a sequence of workload mappings that is optimal over the entire planning window, even though the workload mapping in a given interval may not be locally optimal. Our evaluation of RED-BL uses electricity prices from the US markets and workload traces from live Internet applications with millions of users. We find that RED-BL can reduce the electric bill by as much as 45% compared to the case when the workload is uniformly distributed. When compared to existing workload relocation solutions, for a wide range of data center deployment sizes, RED-BL achieves electricity cost savings that are 8.28% higher, on average. This seemingly modest reduction can save millions of dollars for the operators. The cost of this saving is an inexpensive computation at the start of each planning window.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

From clutter to clarity: Emergent neural operators via questionnaire metrics

Real-world datasets in chemical engineering and bioengineering processes—such as those from catalytic reactors, multiphase flows, polymerization reactors, bioreactors, and clinical trials—can often be unlabeled or disorganized, rendering the training of existing supervised learning models ineffective at learning the underlying dynamics. To salvage these datasets for decision-making, we first seek to obtain clarity from the cluttered data. Here, we present a framework for developing “structural” generative models, discovering emergent equations, and constructing efficient emulators from scrambled datasets by integrating unsupervised organizational learning techniques (Questionnaires) with advanced deep learning architectures (Deep Hidden Physics Models and Deep Operator Networks). Our approach is demonstrated on two illustrative model systems: (a) a 1D advection–diffusion partial differential equation representing a winding underground pipe and (b) an ensemble of Stuart–Landau oscillators, an agent-based system of coupled ordinary differential equations. In both cases, we successfully reconstruct meaningful spatial, temporal, and parameter embeddings from scrambled data, enabling good predictions of system dynamics. As a result, we highlight the framework’s potential for broader applications, enabling data-driven system identification in fields with inherently disorganized or hidden parameter spaces.

42 ENGINEERING↗
DOE OSTI2024

High- and Mid-Fidelity Modeling Comparison for a Floating Marine Turbine System: Preprint

There is a lack of suitable numerical tools, particularly open-source tools, that can be used for designing and optimizing marine turbine systems. The National Renewable Energy Laboratory (NREL) has added features to their widely used mid-fidelity wind turbine modeling code, OpenFAST, to enable modeling of axial flow marine turbines. This necessitated the addition of several physical effects relevant to marine turbines that can be neglected for wind turbines. These include buoyant loads, added mass and inertia loads, wave-current superposition, and changes to the coordinate systems. This updated version of OpenFAST allows for the modeling of both fixed and floating marine turbine systems at a speed comparable to real time. While efficient for long simulations, large sets of load cases, and design studies, mid-fidelity codes cannot capture all of the potentially important physical phenomenon impacting marine turbine systems. High-fidelity computational fluid dynamics (CFD) simulations can capture more flow effects with fewer assumptions and provide detailed body pressure mapping and flow-field information. It is important to compare predictions between mid-fidelity and high-fidelity codes, both to verify the models and to understand the limitations. A floating marine turbine system designed by NREL was modeled both with OpenFAST and with the commercial CFD code, STARCCM+. The CFD model used a 3-D unsteady Reynolds-averaged Navier-Stokes solver for a volume-of-fluid numerical wave and current tank. The blade-resolved simulations used the sliding-interface technique for the spinning rotor and an overset grid to accommodate the rigid-body motion of the floating system. The mooring system was modelled with a custom coupling of the CFD solver with the open-source code, MoorDyn. This improves upon the existing quasi-static catenary solver in STARCCM+, which lacks seabed contact or line-to-line connections. Spatial and temporal convergence studies were conducted. The simulation results for a combined current and wave condition are compared between OpenFAST and CFD, highlighting the capabilities of the mid-fidelity code and identifying the areas where a high-fidelity approach is needed.

CFD↗
DOE OSTI2020

Automated detection of part quality during two-photon lithography via deep learning

Two-photon lithography (TPL) is an additive manufacturing technique for fabricating three-dimensional objects with nanoscale features. A main challenge of TPL is the routine and labor-intensive task of finding suitable light dosage parameters, i.e. writing speed and laser intensity that induce photo-polymerization within a wide variety of candidate photo-curing polymers. Another challenge is the monitoring required during fabrication. In this work, we apply machine learning (ML) models to accelerate the process of identifying optimal light dosage parameters and automate the detection of part quality. We curate TPL videos of different parts fabricated under a range of light dosage parameters using different resins and train spatial-temporal ML models on this data. Our results show that ML models can detect TPL part quality with a 95.1% accuracy in milliseconds. We also evaluate classification failures and identify two operating modes: parameter optimization and part quality detection. Last but not least, we publicly release this labelled dataset so that it may serve as a useful benchmark to the community. Our approach to process optimization and part quality detection addresses important aspects of TPL industrialization, is applicable beyond TPL and should benefit other additive manufacturing techniques with similar barriers to operating at industrial scale.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Modern deep neural networks for Direct Normal Irradiance forecasting: A classification approach

The escalating energy demand and the adverse environmental impacts of fossil-fuel use necessitate a shift towards cleaner and renewable alternatives. Concentrated Solar Power (CSP) technology emerges as a promising solution, offering a carbon-free alternative for power generation. The efficiency and profitability of CSP depend on the Direct Normal Irradiance (DNI) component of solar radiation; hence, accurate DNI forecasting can help optimize CSP plants’ operations and performance. The unpredictable nature of weather phenomena, particularly cloud cover, introduces uncertainty into DNI projections. Existing DNI forecasting models use meteorological factors, which are both challenging to estimate numerically over short prediction windows and expensive to model through data at a sufficiently high spatial and temporal resolution. This research addresses the challenge by presenting a novel approach that formulates DNI prediction as a multi-class classification problem, departing from conventional regression-based methods. The primary objective of this classification framework is to identify optimal periods aligning with specific operational thresholds for CSP plants, contributing to enhanced dispatch optimization strategies. We model the DNI classification problem using four advanced deep neural networks – rectified linear unit (ReLU) networks, 1D residual networks (ResNets), bidirectional long short-term memory (BiLSTM) networks, and transformers – achieving accuracies up to 93.5% without requiring meteorological parameters.

14 SOLAR ENERGY↗
DOE OSTI2024

Wall modes and the transition to bulk convection in rotating Rayleigh-Bénard convection

We investigate states of rapidly rotating Rayleigh-Bénard convection in a cylindrical cell over a range of Rayleigh numbers 3 × 10 5 ≤ Ra ≤ 5 × 10 9 and Ekman numbers 10 − 6 ≤ Ek ≤ 10 − 4 for Prandtl number Pr = 0.8 and aspect ratios 1 / 5 ≤ Γ ≤ 5 using direct numerical simulations. We characterize, for perfectly insulating sidewall boundary conditions, the first transition to convection via wall mode instability and the nonlinear growth and instability of the resulting wall mode states, including a secondary transition to time dependence. We show how the radial structure of the vertical velocity u z and the temperature T is captured well by the linear eigenfunctions of the wall mode instability where the radial width of u z is δ u z ∼ Ek 1 / 3 r / H whereas δ T ∼ e − k r ( k is the wave number of a laterally infinite wall mode state). The disparity in spatial scales for Ek = 10 − 6 means that the heat transport is dominated by the radial structure of u z since T varies slowly over the radial scale δ u z . We further describe how the transition to a state of bulk convection is influenced by the presence of the wall mode states. We use temporal and spatial scales as measures of the local state of convection and the Nusselt number Nu as representative of global transport. Our results elucidate the evolution of the wall state of rotating convection and confirm that wall modes are strongly linked with the boundary zonal flow being the robust remnant of nonlinear wall mode states. We also show how the heat transport ( Nu ) contributions of wall modes and bulk modes are related and discuss approaches to disentangling their relative contributions. Published by the American Physical Society 2024

58 GEOSCIENCES↗
DOE OSTI2020

Hanford Site-wide Natural Recharge Boundary Condition for Groundwater Models

The purpose of this environmental calculation file (ECF) is to document the development of a tool that generates temporally and spatially variable representations of natural recharge for the Hanford Site. A key feature of the recharge evolution tool (RET) is that it applies sanctioned natural recharge rates varying as a function of the condition/cover of the ground surface and soil type at different points in time. No hydrologic calculations are performed by the RET, this script works as a lookup database between spatial and temporal datasets to assign research-based recharge rates to corresponding regions throughout the Hanford Site. This work will support vadose zone and groundwater models for the Hanford Site. Although efforts will focus on generating recharge estimates for the entirety of the Hanford Site, the focus scope of this work will be the Central Plateau Area to support the Composite Analysis Vadose Zone facet. In other words, the reliability of this calculation will be greatest within the Central Plateau Area and decrease with departures from that geographic region.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2017

Space dependent, full orbit effects on runaway electron dynamics in tokamak plasmas

The dynamics of RE (runaway electrons) in fusion plasmas span a wide range of temporal scales, from the fast gyro-motion, ∼10−11 s, to the observational time scales, ∼10−2→1 s. To cope with this scale separation, RE are usually studied within the bounce-average or the guiding center approximations. Although these approximations have yielded valuable insights, a study with predictive capabilities of RE in fusion plasmas calls for the incorporation of full orbit effects in configuration space in the presence of three-dimensional magnetic fields. We present numerical results on this problem using the Kinetic Orbit Runaway electrons Code that follows relativistic electrons in general electric and magnetic fields under the full Lorentz force, collisions, and radiation losses. At relativistic energies, the main energy loss is due to radiation damping, which we incorporate using the Landau-Lifshitz formulation of the Abraham-Lorentz-Dirac force. The main focus is on full orbit effects on synchrotron radiation. It is shown that even in the absence of magnetic field stochasticty, neglecting orbit dynamics can introduce significant errors in the computation of the total radiated power and the synchrotron spectra. The statistics of collisionless (i.e., full orbit induced) pitch angle dispersion, and its key role played on synchrotron radiation, are studied in detail. Numerical results are also presented on the pitch angle dependence of the spatial confinement of RE and on full orbit effects on the competition of electric field acceleration and radiation damping. Finally, full orbit calculations are used to explore the limitations of gyro-averaging in the relativistic regime. To explore the practical impact of the results, DIII-D and ITER-like parameters are used in the simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Hydrodynamic Analysis and Optimization of Aquantis Marine Turbine: Cooperative Research and Development (Final Report)

The primary aim of this proposal is to improve the accurate prediction of hydrodynamic performance and dynamic load responses of the AQ10 floating axial-flow tidal turbine with a tri-cat mooring configuration. The validation of reduced-order modeling approaches with high-fidelity model will be implemented. Additionally, the frequency response domain, Response Amplitude Floating Wind (RAFT) toolbox plus an optimizer expanded for marine hydrokinetic turbines under the Submarine Hydrokinetic And Riverine Kilo-megawatt. Systems (SHARKS) program will be used for designing and exploring different key design parameters (platform dimension, mooring layout and its parameters) of next marine hydrokinetic (MHK) turbine generation.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Time-warping invariant quantum recurrent neural networks via quantum-classical adaptive gating

Adaptive gating plays a key role in temporal data processing via classical recurrent neural networks (RNNs), as it facilitates retention of past information necessary to predict the future, providing a mechanism that preserves invariance to time warping transformations. This paper builds on quantum RNNs (QRNNs), a dynamic model with quantum memory, to introduce a novel class of temporal data processing quantum models that preserve invariance to time-warping transformations of the (classical) input-output sequences. The model, referred to as time warping-invariant QRNN (TWI-QRNN), augments a QRNN with a quantum–classical adaptive gating mechanism that chooses whether to apply a parameterized unitary transformation at each time step as a function of the past samples of the input sequence via a classical recurrent model. The TWI-QRNN model class is derived from first principles, and its capacity to successfully implement time-warping transformations is experimentally demonstrated on examples with classical or quantum dynamics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Performance Analysis of Speculative Parallel Adaptive Local Timestepping for Conservation Laws

Stable simulation of conservation laws, such as those used to model fluid dynamics and plasma physics applications, requires the satisfaction of the so-called Courant-Friedrichs-Lewy condition. By allowing regions of the mesh to advance with different timesteps that locally satisfy this stability constraint, significant work reduction can be attained when compared to a time integration scheme using a single timestep size. However, parallelizing this algorithm presents considerable difficulty. Since the stability condition depends on the state of the system, dependencies become dynamic and potentially non-local. In this article, we present an adaptive local timestepping algorithm using an optimistic (Timewarp-based) parallel discrete event simulation. We introduce waiting heuristics to limit misspeculation and a semi-static load balancing scheme to eliminate load imbalance as parts of the mesh require finer or coarser timesteps. Last, we outline an interface for separating the physics of the specific conservation law from the temporal integration allowing for productive adoption of our proposed algorithm. We present a misspeculation study for three conservation laws, demonstrating both the productivity of the local timestepping API, for which 74% of the lines of code are reused across different conservation laws, and the robustness of the waiting heuristics—at most 1.5% of element updates are rolled back. Our performance studies demonstrate up to a 2.8× speedup versus a baseline unoptimized local timestepping approach, a 4x improvement in per-node throughput compared to an MPI parallelization of synchronous timestepping, and scalability up to 3,072 cores on NERSC’s Cori Haswell partition.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Recurrent dynamics in an epidemic model due to stimulated bifurcation crossovers

Epidemics are known to persist in the form of recurrence cycles. Despite intervention efforts through vaccination and targeted social distancing, peaks of activity for infectious diseases like influenza reappear over time. Analysis of a stochastic model is here undertaken to explore a proposed cycle-generating mechanism – the bifurcation crossover. Time series from simulations of the model exhibit oscillations similar to the temporal signature of influenza activity. Power-spectral density indicates a resonant frequency, which corresponds to the annual seasonality of influenza in temperate zones. The study finds that intervention actions influence the extinguishability of epidemic activity. Asymptotic solution to a backward Kolmogorov equation corresponds to a mean extinction time that is a function of both intervention efficacy and population size. Intervention efficacy must be greater than a certain threshold to increase the chances of extinguishing the epidemic. Agreement of the model with several phenomenological features of epidemic cycles lends to it a tractability that may serve as early warning of imminent outbreaks.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗