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Nonlinear coupling of tearing modes in reversed field pinch plasmas with stepped pressure profiles
A theory of the three-wave coupling of triplets of tearing modes in toroidal pinches [i.e., either reversed field pinches (RFPs) or tokamaks] was proposed by R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)]. However, this theory only applies to toroidal pinches with negligible equilibrium plasma pressure gradients. Such a limitation is particularly inappropriate to RFPs. This paper generalizes the analysis of R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)] in order to take the equilibrium pressure gradient into account. However, for the sake of simplicity, a stepped pressure profile, rather than a continuous profile, is employed. In the limit in which the number of steps becomes very large, the results obtained from the generalized theory are presumably equivalent to those that would have been achieved using a continuous pressure profile. The generalized theory is used to investigate the formation of the characteristic toroidally localized pattern of phase-locked m = 1 and m = 0 tearing modes in RFP plasmas that is known as the “slinky” pattern. The incorporation of the equilibrium plasma pressure into the analysis is found to be of crucial importance when determining the properties of the pattern. This is the case because the plasma pressure controls the number of unstable m = 1 and m = 0 tearing modes, and also significantly affects the strength of three-wave coupling, as well as the phase relation between the phase-locked m = 1 and m = 0 modes.
Novel vertically aligned nanocomposite of Bi 2 WO 6 -Co 3 O 4 with room-temperature multiferroic and anisotropic optical response
A review of a new vertically aligned nanocomposite (VAN) structure based on two-dimensional (2D) layered oxides has been designed and self-assembled on both LaAlO 3 (001) and SrTiO 3 (001) substrates. The new VAN structure consists of epitaxially grown Co 3 O 4 nanopillars embedded in the Bi 2 WO 6 matrix with a unique 2D layered structure, as evidenced by the microstructural analysis. Physical property measurements show that the new Bi 2 WO 6 -Co 3 O 4 VAN structure exhibits strong ferromagnetic and piezoelectric response at room temperature as well as anisotropic permittivity response. This work demonstrates a new approach in processing multifunctional VANs structure based on the layered oxide systems towards future nonlinear optics, ferromagnets, and multiferroics.
Degradation of performance in ICF implosions due to Rayleigh–Taylor instabilities: A Hamiltonian perspective
The Rayleigh–Taylor instability (RTI) is an ubiquitous phenomenon that occurs in inertial-confinement-fusion (ICF) implosions and is recognized as an important limiting factor of ICF performance. To analytically understand the RTI dynamics and its impact on ICF capsule implosions, we develop a first-principle variational theory that describes an imploding spherical shell undergoing RTI. The model is based on a thin-shell approximation and includes the dynamical coupling between the imploding spherical shell and an adiabatically compressed fluid within its interior. Using a quasilinear analysis, we study the degradation trends of key ICF performance metrics (e.g., stagnation pressure, residual kinetic energy, and areal density) as functions of initial RTI parameters (e.g., the initial amplitude and Legendre mode), as well as the 1D implosion characteristics (e.g., the convergence ratio). We compare analytical results from the theory against nonlinear results obtained by numerically integrating the governing equations of this reduced model. Our findings emphasize the need to incorporate polar flows in the calculation of residual kinetic energy and demonstrate that higher convergence ratios in ICF implosions lead to significantly greater degradation of key performance metrics.
Data and scripts associated with the manuscript "Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling"
This package contains the data and scripts used in "Using Mutual Information for Global Sensitivity Analysis on Watershed Modeling" (Jiang et al., 2022). The ARW_SWAT.zip file contains the SWAT simulation and the sensitivity analysis result in the American River Watershed. The Portage_SWAT.zip file contains the SWAT simulation and the sensitivity analysis result in the Portage River Watershed. The src folder contains the source code of sensitivity analysis and plotting functions. The notebooks folder contains the Jupyter notebooks for performing sensitivity analysis and other post analyses.Global Sensitivity Analysis (GSA) often is applied to assess the sensitivity of model outputs to their inputs using ensemble simulations. However, increasing model complexity and the associated computational cost have limited the use of most GSA approaches for process-based watershed models. We propose to use Mutual Information (MI) as a computationally efficient GSA method for watershed modeling. Such MI computed from several hundred realizations usually can capture nonlinear relationships between inputs and outputs of interest. We perform MI-based watershed sensitivity analyses in studies of the Portage River Watershed in Ohio and the American River Watershed in Washington. In these studies, MI is used to evaluate the sensitivity of river discharges simulated by the Soil and Water Assessment Tool to no less than 20 parameters for each watershed. Our MI-based sensitivity analyses achieved convergence with about 300~500 realizations, a small fraction of the ensemble size (i.e., several thousand) required by the Sobol method. Nevertheless, MI yields similar sensitivity ranking compared to the Sobol method, especially for sensitive parameters. Our study thus sheds new light on the use of MI as an affordable GSA method for computationally intensive models such as the hyper-resolution, watershed hydrobiogeochemical models.
Data-driven optimization of mixed-integer bi-level multi-follower integrated planning and scheduling problems under demand uncertainty
The coordination of interconnected elements across the different layers of the supply chain is essential for all industrial processes and the key to optimal decision-making. Yet, the modeling and optimization of such interdependent systems are still burdensome. Here we address the simultaneous modeling and optimization of medium-term planning and short-term scheduling problems under demand uncertainty using mixed-integer bi-level multi-follower programming and data-driven optimization. Bi-level multi-follower programs model the natural hierarchy between different layers of supply chain management holistically, while scenario analysis and data-driven optimization allow us to retrieve the guaranteed feasible solutions of the integrated formulation under various demand considerations. We address the data-driven optimization of this challenging class of problems using the DOMINO framework, which was initially developed to solve single-leader single-follower bi-level optimization problems to guaranteed feasibility. This framework is extended to solve single-leader multi-follower stochastic formulations and its performance is characterized by well-known single and multi-product process scheduling case studies. Through our data-driven algorithmic approach, we present guaranteed feasible solutions to linear and nonlinear mixed-integer bi-level formulations of simultaneous planning and scheduling problems and further characterize the effects of the scheduling level complexity on the solution performance, which spans over several hundred continuous and binary variables, and thousands of constraints.
Ensemble cure kinetics network (ECK-Net): A method to derive cure kinetics of thermosetting resin
This paper introduces an Ensemble Cure Kinetics Network (ECK-Net), a neural network (NN)–based framework for modeling the cure kinetics of thermosetting resins within a phenomenological context. ECK-Net replaces traditional analytic models, which require extensive chemical insight and multiple isothermal/non-isothermal experiments, with a data-driven surrogate that maps nonlinear relationships between temperature, degree of cure, and reaction rate from differential scanning calorimetry data. The proposed approach predicts input-dependent kinetic coefficients of a generalized nth-order reaction equation rather than reaction rates directly, enabling a single unified model to represent various epoxy systems without relying on iso-conversional analysis or predefined functional forms. To ensure robustness, multiple independently trained networks under different random initializations are blended through an ensemble strategy, effectively mitigating the stochastic variability inherent to neural networks. The framework is validated using experimental datasets from multiple resin systems, including aerospace-grade materials (Toray 3900-2, Cycom 5320-1, and Hexcel 8552) and a windmill-grade resin (RIMR 035c). The model accurately reproduces the temporal evolution of the degree of cure under manufacturers’ recommended cure cycles across all tested resins systems, yielding Pearson’s correlation coefficients of 0.992, 0.994, 0.993, 0.997, respectively. To demonstrate process-level applicability, the trained network was implemented within the Abaqus environment to simulate out-of-autoclave (OOA) curing process of the CFRP panel composed of Toray T830H-6K/3900-2D prepreg. The simulation results showed excellent agreement with experimental temperature response (maximum peak temperature, simulation: 189.6 °C, experiment: 188.5 °C) and the final degree of cure (simulation: 0.948, experiment: 0.960 ± 0.013), confirming ECK-Net’s capability as a reliable alternative to conventional cure kinetics modeling methods.
Absolute stimulated Raman side scatter in direct-drive laser-produced plasmas
Production of suprathermal electrons by stimulated Raman scattering (SRS) is a principal concern for contemporary direct-drive inertial confinement fusion experiments at the National Ignition Facility and similar systems since such electrons penetrate and preheat the target core, preventing efficient implosion. The higher temperatures and longer scale lengths in these experiments favor SRS over two-plasmon decay, which predominated in earlier experiments. In particular, current experiments are expected to exceed the threshold for absolute Raman side scatter, which would then dominate the interaction since it grows temporally until saturated by nonlinear mechanisms such as hot-electron production. Until recently, analyses of SRS side scatter have treated the case of a single laser beam incident on a plasma, but the direct-drive approach to laser fusion employs a multitude of beams to drive the implosion. Here in this paper, we present an analysis that can be applied to an arbitrary number of beams with varied angles of incidence and polarizations. In the case of a single beam, it allows a physically motivated derivation and verification of an analytic threshold formula. In the general case of multiple beams and arbitrary orientation and polarizations, the threshold is found by numerical integration of a set of first-order linear partial differential equations.
Joint effects of climate, tree size, and year on annual tree growth derived from tree–ring records of ten globally distributed forests
Tree rings provide an invaluable long-term record for understanding how climate and other drivers shape tree growth and forest productivity. However, conventional tree-ring analysis methods were not designed to simultaneously test effects of climate, tree size, and other drivers on individual growth. This has limited the potential to test ecologically relevant hypotheses on tree growth sensitivity to environmental drivers and their interactions with tree size. Here, we develop and apply a new method to simultaneously model nonlinear effects of primary climate drivers, reconstructed tree diameter at breast height (DBH), and calendar year in generalized least squares models that account for the temporal autocorrelation inherent to each individual tree's growth. We analyze data from 3811 trees representing 40 species at 10 globally distributed sites, showing that precipitation, temperature, DBH, and calendar year have additively, and often interactively, influenced annual growth over the past 120 years. Growth responses were predominantly positive to precipitation (usually over ≥3-month seasonal windows) and negative to temperature (usually maximum temperature, over ≤3-month seasonal windows), with concave-down responses in 63% of relationships. Climate sensitivity commonly varied with DBH (45% of cases tested), with larger trees usually more sensitive. Trends in ring width at small DBH were linked to the light environment under which trees established, but basal area or biomass increments consistently reached maxima at intermediate DBH. Accounting for climate and DBH, growth rate declined over time for 92% of species in secondary or disturbed stands, whereas growth trends were mixed in older forests. These trends were largely attributable to stand dynamics as cohorts and stands age, which remain challenging to disentangle from global change drivers. By providing a parsimonious approach for characterizing multiple interacting drivers of tree growth, our method reveals a more complete picture of the factors influencing growth than has previously been possible.
BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale
Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and P- 13 C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.
Pathway-based analyses of gene expression profiles at low doses of ionizing radiation
Radiation exposure poses a significant threat to human health. Emerging research indicates that even low-dose radiation once believed to be safe, may have harmful effects. This perception has spurred a growing interest in investigating the potential risks associated with low-dose radiation exposure across various scenarios. To comprehensively explore the health consequences of low-dose radiation, our study employs a robust statistical framework that examines whether specific groups of genes, belonging to known pathways, exhibit coordinated expression patterns that align with the radiation levels. Notably, our findings reveal the existence of intricate yet consistent signatures that reflect the molecular response to radiation exposure, distinguishing between low-dose and high-dose radiation. Moreover, we leverage a pathway-constrained variational autoencoder to capture the nonlinear interactions within gene expression data. By comparing these two analytical approaches, our study aims to gain valuable insights into the impact of low-dose radiation on gene expression patterns, identify pathways that are differentially affected, and harness the potential of machine learning to uncover hidden activity within biological networks. This comparative analysis contributes to a deeper understanding of the molecular consequences of low-dose radiation exposure.
Onymous early‐life performance degradation analysis of recent photovoltaic module technologies
Abstract The cost of photovoltaic (PV) modules has declined by 85% since 2010. To achieve this reduction, manufacturers altered module designs and bill of materials; changes that could affect module durability and reliability. To determine if these changes have affected module durability, we measured the performance degradation of 834 fielded PV modules representing 13 module types from 7 manufacturers in 3 climates over 5 years. Degradation rates ( Rd ) are highly nonlinear over time, and seasonal variations are present in some module types. Mean and median degradation rate values of −0.62%/year and −0.58%/year, respectively, are consistent with rates measured for older modules. Of the 23 systems studied, 6 have degradation rates that will exceed the warranty limits in the future, whereas 13 systems demonstrate the potential of achieving lifetimes beyond 30 years, assuming Rd trends have stabilized.
Combining PCA and nonlinear fitting of peak models to re-evaluate C 1s XPS spectrum of cellulose
Cellulose is an example of a material that responds to XPS by the creation of new chemistry not present in the as-received sample. While improvements in instrumentation may be seen in general as beneficial to surface science, recent studies have shown that the consequences for some materials are detrimental. Here, in this work, these problems are illustrated through an analysis of cellulose spectra obtained during a degradation study. C 1s spectra are decomposed into two well-formed component curves that are open to chemical interpretation. In particular, a component-curve representative of pure cellulose is obtained as well as a second component curve that implies cellulose is degraded through the creation of carbon chemistry involving C—O, C$=$O and O—C$=$O. Since cellulose is a crystalline material, formed through the alignment of molecules under the influence of hydrogen bonds, the analysis and findings presented in this paper are relevant to any material analyzed by XPS whose properties are dependent on hydrogen bonds. The analysis techniques are based on an informed vectorial approach, which extracts directly from data spectral shapes that are used to monitor sample degradation via linear least squares optimization. Related mathematics of Principal Component Analysis and linear analysis are presented.
Integration of cryogenic energy storage with renewables and power plants: Optimal strategies and cost analysis
Energy storage is critical for overcoming challenges associated with the intermittency and the variable availability of renewable sources for decarbonizing the energy sector. Cryogenic energy storage (CES) is of interest due to its high technology readiness level, no geographical limitations, and moderate round-trip efficiency. The time-varying nature of demands and renewable availability needs to be considered at the design and integration stages of energy storage. We develop a mixed-integer nonlinear program (MINLP) model to obtain the energy storage costs on a daily basis for different scenarios that typically arise over an entire year. Using this optimization-based framework, we address key decision-making questions towards energy transition: What is the energy cost when CES is integrated with renewables and power plants? How does each scenario affect the overall energy cost? How much storage is needed for complete transition to renewables? What is the optimal integration towards 100% renewable energy? What are the optimal storage designs for both renewables and fossil-based power generation with current and future energy demands? Here, we discuss different scenarios and solutions to these questions.
Molecular Structure and Thermodynamics of CO 2 and Water Adsorption on Mica
The adsorption of CO 2 and water on clay surfaces plays a key role in applications, such as gas storage in saline aquifers and depleted hydrocarbon reservoirs, but is not yet fully understood. Here, we study the adsorption of CO 2 and water vapor using Grand Canonical Monte Carlo and molecular dynamics simulations. At a bulk pressure of 100 bar, pure CO 2 adsorbs strongly on mica and forms extensive layers next to it. CO 2 adsorption is lowered substantially if introducing water vapor above mica and is largely eliminated when the relative humidity (RH) approaches about 60%. When pure water vapor is introduced above a mica surface, a subnanometer thick liquid water film develops on it to form apparent liquid–solid and liquid–vapor interfaces simultaneously. Using the identification of truly interfacial molecules (ITIM) analysis, we delineate how individual water layers develop in this film as RH increases. We highlight that the water film is spatially heterogeneous and the true liquid–vapor interface emerges only at an RH of 60–80%. Introducing 100 bar of CO 2 into the water vapor above the mica surface modulates water adsorption nonlinearly: at RH = 0.01%, the water adsorption is reduced by ∼30%; as RH increases, the reduction is weakened, and eventually, enhancement of water adsorption by about 7% occurs at RH = 90%. These variations are attributed to the interplay of film thinning by high-pressure CO 2 , competition of mica surface sites by CO 2 molecules, and energetic and entropic stabilization of interfacial water by CO 2 molecules.
Consistent coupling algorithms for coupled core-edge simulations of plasma turbulence
Two schemes for coupling gyrokinetic simulations of microturbulence in tokamaks are proposed. The first scheme is based on an additive Schwarz domain decomposition. In this work, we show that, because the goal of turbulence is long-time averages of the dynamics rather than temporal accuracy, the iteration to self-consistency across domains, which is typically required by Schwarz schemes, can be avoided, thereby accelerating the computation. Second, we propose a coupling scheme that relies entirely on the addition of source terms, leaving the boundary conditions arbitrary. The practical motivations for such a scheme are discussed, and forms of the source terms that ensure consistency and stability are derived. The schemes are tested on a nonlinear, one-dimensional model problem, and the first scheme is further tested on the Hasegawa–Wakatani model.
Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry
Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.
Light induced ion migration studies in perovskite solar cell using nonlinear impedance spectroscopy
Complex interactions between mobile ions and charge carriers in perovskite solar cells (PSCs) make it challenging to fully understand their dynamic interplay. Exposure to light further complicates these interactions, altering the system’s dynamics and inducing nonlinear effects that lead to changes in the J−V curve. Understanding these effects is crucial for improving the operational stability of PSCs. Impedance spectroscopy (IS) is a powerful technique for evaluating relaxation processes in the frequency domain; however, it is limited in capturing nonlinear contributions. Here, in this work, nonlinear impedance spectroscopy (NLIS) is employed to analyze the higher harmonic response to AC perturbation, both in the dark and after short-term light exposure. A shift in the low-frequency (LF) higher harmonic peak is observed after open-circuit light exposure, attributed to an altered electric field suggesting ion re-distribution, whereas closed-circuit exposure shows no LF shift, indicating minimal ion movement. Additionally, light exposure reduces higher-order admittance, more notably in open-circuit conditions, suggesting decreased recombination. Temperature-dependent analysis was conducted to characterize the activation energy of migrating species, identifying iodide as the dominant migrating ion.