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Machine learning and process-based modeling of spatiotemporal changes in active layer thickness across Alaska
Permafrost degradation poses a growing threat to infrastructure stability and ecosystem resilience in the rapidly warming Arctic. We investigated the spatiotemporal dynamics of active layer thickness (ALT) across Alaska by integrating field observations, environmental datasets, a physically based Stefan model, and machine learning (ML) techniques. Using weather projections from the Coupled Model Intercomparison Project Phase 6 under two Shared Socioeconomic Pathways (SSP 2-4.5 and SSP 5-8.5), we assessed ALT sensitivity to projected future weather conditions. The random forest (RF) model outperformed the Stefan approach in predicting ALT on the training dataset (R² = 0.84 vs. 0.53) but demonstrated lower generalizability on the test dataset (R² = 0.24 vs. 0.54). The root mean square error (RMSE) for the RF model for training and testing ranged from 14 to 22 cm, compared to 17 and 18 cm for the Stefan model. Variable importance analysis revealed that mean annual temperature and slope angle were the strongest predictors of ALT, accounting for 19% and 18% of the variance, respectively, followed by sediment transport index (14%) and stream power index (11%). Comparative analysis of baseline ALT predictions showed the Stefan model tended to project a thicker active layer (mean ± SD: 65 ± 16 cm), compared to the RF model (mean ± SD: 59 ± 8.8) cm). Both models indicated a latitudinal gradient in ALT, with shallower depths at higher latitudes. Projected ALT increases by 2100 were estimated at 3.3 ± 2.2 cm under SSP 2-4.5 and 5.9 ± 4.0 cm under SSP 5-8.5 for the ML model, whereas the Stefan model projected substantially larger increases of 13 ± 2.6 cm (SSP 2-4.5) and 28 ± 4.4 cm (SSP5-8.5). Spatial analysis showed the greatest ALT increases in northern Alaska, with relatively smaller changes in southern regions. These findings highlight the complex, multifactorial nature of ALT dynamics and the value of hybrid modeling approaches. As rising temperatures accelerate permafrost thaw, changes in ALT can disrupt ecosystems, damage infrastructures, and enhance the release of stored soil carbon, highlighting the urgent need for improved predictive capabilities to inform adaptation strategies in the Arctic.
Multilayer interface tracking model of pure tungsten oxidation
Here, we present a numerical model to predict oxide scale growth on tungsten surfaces under exposure to oxygen at high temperatures. The model captures the formation of four thermodynamically-compatible oxide sublayers, WO 2 , WO 2.72 , WO 2.9 , and WO 3 , on top of the metal substrate. Oxide layer growth is simulated by tracking the oxide/oxide and oxide/metal interfaces using a sharp-interface Stefan model coupled to diffusion kinetics. The model is parameterized using selected experimental measurements and electronic structure calculations of the diffusivities of all the oxide subphases involved. We simulate oxide growth at temperatures of 600°C and above, extracting the power law growth exponents in each case, which we find to deviate from classical parabolic growth in several cases. We conduct a comparison of the model predictions with an extensive experimental data set, with reasonable agreement at most temperatures. While many gaps in our understanding still exist, this work is a first attempt at embedding the thermodynamic and kinetic complexity of tungsten oxide growth into a comprehensive mesoscale kinetic model that attempts to capture the essential features of tungsten oxidation to fill existing knowledge gaps and guide and enhance future tungsten oxidation models.
Multi-scale model based design of membrane reactor/separator processes for intensified hydrogen production through the water gas shift reaction
This paper aims to first quantify the impact of various diffusion models (Maxwell-Stefan, Wilke, Dusty-Gas) on the predictions of a multi-scale membrane reactor/separator mathematical model, and to then demonstrate this model's use for the design and process intensification of membrane reactor/separator systems for hydrogen production. This multi-scale model captures velocity, temperature and species' concentration profiles along the catalyst pellet's radial direction, and along the reactor's axial direction, by solving the momentum, energy, and species transport equations, accounting for convection, conduction, reaction, and diffusion mechanisms. In the first part of work, the effect of pellet-scale design parameters (mean pore diameter, volumetric porosity, tortuosity factor, etc.) and various species' flux models on the model predictions is studied. In the second part, the study focuses on the comparison, in terms of their process intensification characteristics, of various hydrogen production processes. These include a conventional high-temperature shift reactor (HTSR)/low-temperature shift reactor (LTSR) sequence, a novel HTSR/membrane separator (MS)/LTSR/MS sequence, and a process that involves low-temperature shift membrane reactors-LTSMR in a series.
A general non-Fourier Stefan problem formulation that accounts for memory effects
The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. Further, on shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.
An implementation of the phase-field model based on coupled thermomechanical finite element solvers for large-strain twinning, explicit dynamic fracture and the classical Stefan problem
The implementation of a phase-field model in finite elements usually requires significant expertise and involves the development of a user element with additional degrees of freedom. An alternative implementation of the phase-field model within a thermo-mechanical finite element simulation package was presented in (Cho et al 2012 Int. J. Solids Struct. 49 1973–1992), where the phase-field variable is treated as the temperature degree of freedom. However, this approach has only been used for small strain phase-field modelling of martensitic transformations and quasistatic phase-field modelling of fracture. Here, we present a phase-field finite element implementation via the temperature degree of freedom for several additional cases from the literature: (i) the large-strain phase-field description of deformation twinning presented in (Clayton and Knap 2011 Physica D 240 841–858), (ii) phase-field description of brittle fracture with inertial effects based on the theory from (Molnár and Gravouil 2017, Finite Elem. Anal. Des. 130 27–38) and (Miehe et al 2010 Int. J. Numer. Methods Eng. 83 1273–1311) and (iii) the classical Stefan problem of solidification presented in (Mackenzie and Robertson 2002 J. Comput. Phys. 181 526–544). The last problem involves the temperature and phase-field variables as unknowns.
Electrochemical Measurement of Water Transport Numbers in Anion-Exchange Membranes
Anion-exchange membranes (AEMs) are a possible replacement for perfluorosulfonic-acid membranes in energy-conversion devices, primarily due to the hydroxide mobile ion allowing the devices to operate in alkaline conditions with less expensive electrocatalysts. However, the transport properties of AEMs remain understudied, especially electro-osmosis. In this work, an electrochemical technique, where the open-circuit voltage is measured between two ends of a membrane maintained at different relative humidities, is used to determine the water transport number of various ionomers, including Versogen and Sustainion AEMs and Nafion cation-exchange membrane (CEM), as a function of water content and temperature. In addition, the CEMs and AEMs are examined in differing single-ion forms, specifically proton and sodium (CEM) and hydroxide and carbonate (AEM). Carbonate-form AEMs have the highest transport number (∼11), followed by sodium-form CEMs (∼8), hydroxide-form AEMs (∼6), and proton-form CEMs (∼3). Finally, a multicomponent transport model based on the Stefan-Maxwell-Onsager framework of binary interactions is used to develop a link between water transport number and water-transport properties, extracting a range for the unmeasured membrane water permeability of Versogen as a function of water content.
Framework for predicting the fractionation of complex liquid feeds via polymer membranes
The separation of complex liquid hydrocarbon mixtures was recently demonstrated using the glassy polymer SBAD-1, showing that small molecule fractionation is possible by such organic membrane materials. Here, in this work, we develop a framework that will enable workable predictions of permeate flux and composition in complex hydrocarbon liquids through intrinsically porous glassy polymers. The predictions are made by incorporating experimentally-derived unary sorption and diffusion parameters in a Maxwell-Stefan framework coupled with multicomponent sorption models and various distinct diffusion phenomena. Across the range of sorption and diffusion phenomena considered, both the conventional Flory-Huggins model and the proposed Langmuir + Flory-Huggins sorption model combined with a simple average guest diffusivity or a more complex free-volume theory-based transport resulted in the lowest prediction error for three chosen multicomponent separations. The proposed Maxwell-Stefan framework simply requires pure component transport parameters to allow a fast approximation of the separation of multicomponent liquid hydrocarbon feeds that can potentially be extended to more complex feeds such as crude oil fractions.
Modeling polymer crystallisation induced by a moving heat sink
Recent experimental work has shown that polymer crystallisation can be used to “move” and organize nanoparticles (NP). As a first effort at modeling this situation, we consider the classical Stefan problem but with the modification that polymer crystallisation does not occur at a single temperature. Rather, the rate of crystallisation is proportional to its subcooling, and here we employ a form inspired by the classical Avrami model to describe this functional form. Our results for the movement of the polymer crystallisation front, as defined as the point where the crystallinity is 50%, closely track the results of the classical Stefan problem. Thus, at this level of approximation, the crystallisation kinetics of the polymer do not cause qualitative changes to the physics of this situation. Inspired by this fact we study the more interesting situation where the directional recrystallisation of a polymer melt is considered, e.g. , through the application of a moving heat sink over an initially molten polymer, reminiscent of a processing technique termed zone annealing. The polymer crystallisation shows that a steady state exists for a range of sink velocities. The solid–melt interface moves slightly ahead of the sink but at the same velocity. The steady-state distance between the sink and the interface decreases with increasing sink velocity – this is a consequence of the excess cooling provided by the sink over what is required to crystallise the melt. The most interesting new result is that the temperature of the crystal–melt interface decreases with increasing sink velocity. This is in line with the ansatz of Lovinger and Gryte who suggested that larger zone annealing velocities correspond to progressively larger effective undercoolings at which polymer crystallisation occurs.
Scalable statistical inference of photometric redshift via data subsampling
Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for bigger problems. But full probabilistic statistical models often outperform other models in quantifying uncertainties associated with model predictions. We develop a data-driven statistical modeling framework that combines the uncertainties from an ensemble of statistical models learned on smaller subsets of data carefully chosen to account for imbalances in the input space. We demonstrate this method on a photometric redshift estimation problem in cosmology, which seeks to infer a distribution of the redshift—the stretching effect in observing the light of far-away galaxies—given multivariate color information observed for an object in the sky. Our proposed method performs balanced partitioning, graph-based data subsampling across the partitions, and training of an ensemble of Gaussian process models.
Soft modes in $ \mathcal{N} $ = 2 SYK model
We study various properties of the soft modes in the $ \mathcal{N} $ = 2 supersymmetric SYK model.
Parametric Modeling and Economic Analysis of a 2MW th 3-Stream sCO 2 Heat Exchanger
Here, this paper presents the design and cost optimization of a novel 2MW th 3-stream sCO2 plate-fin heat exchanger. This heat exchanger design is unique in that it uses reduced metal oxide particle-to-sCO2 heat exchanger for cost-effective energy storage applications. The design uses low velocity, laminar air as the re-oxidizing reactant to transfer the heat of the re-oxidizing reaction to a sCO2 power loop. The design of the heat exchanger is based on a 2-D, 3-fluid plate/fin heat transfer model. The model parameterizes the size, shape, and number of passages of the heat exchanger to calculate the temperature profile, pressure drop, and fluid velocities of all three fluids. Global heat exchanger parameters such as the effectiveness and total heat transferred to the sCO2 are then calculated for overall performance. Due to the value and increased use of sCO2 heat exchangers in power cycles, a cost model of the system based on the unique high temperature/high pressure operating conditions was created using quotes from reference projects and market analysis. These quoted air-to-sCO2 heat exchangers are then processed using multiple weighting factors pertinent to heat exchanger design, including heat exchanger type, maximum temperature, differential pressures, fluids, duty, and more. These factors are then used in an exponential function in order to generate a parameterized cost curve. The design and cost of the heat exchanger are then optimized using the SMPSO genetic algorithm in Python. The optimization objectives for the system are to maximize the overall system effectiveness, including an air recuperator for preheating, and to minimize unit costs. Additional constraints are added to the system for the sCO2 and air pressure drops, air velocity to reduce particle entrainment, and the length and volume of the heat exchanger.
Use-Inspired, Process-Oriented GCM Selection: Prioritizing Models for Regional Dynamical Downscaling
Dynamical downscaling is a crucial process for providing regional climate information for broad uses, using coarser-resolution global models to drive higher-resolution regional climate simulations. The pool of global climate models (GCMs) providing the fields needed for dynamical downscaling has increased from the previous generations of the Coupled Model Intercomparison Project (CMIP). However, with limited computational resources, the need for prioritizing the GCMs for subsequent downscaling studies remains. GCM selection for dynamical downscaling should focus on evaluating processes relevant for providing boundary conditions to the regional models and be inspired by regional uses such as the response of extremes to changes in the boundary conditions. This leads to the need for metrics representing processes of relevance to diverse stakeholders and subregions of a domain. Procedures to account for metric redundancy and the statistical distinguishability of GCM rankings are required. Further, procedures for selecting realizations from ensembles of top-performing GCM simulations can be used to span the range of climate change signals in multiple ways. As a result, distinct weighting of metrics and prioritization of particular realizations may depend on user needs. We provide high-level guidelines for such region-specific evaluations and address how CMIP7 might enable dynamical downscaling of a representative sample of high-quality models across representative shared socioeconomic pathways (SSPs).
Boundary layer description of directional polymer crystallisation
Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger–Gryte ansatz.
Automated Model Selection for Gate Set Tomography
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Uncertainty quantification in breakup reactions
Breakup reactions are one of the favored probes to study loosely bound nuclei, particularly those in the limit of stability forming a halo. In order to interpret such breakup experiments, the continuum discretized coupled channel method is typically used. In this study, the first Bayesian analysis of a breakup reaction model is performed. Herein we use a combination of statistical methods together with a three-body reaction model (the continuum discretized coupled channel method) to quantify the uncertainties on the breakup observables due to the parameters in the effective potential describing the loosely bound projectile of interest. The combination of tools we develop opens the path for a Bayesian analysis of not only breakup processes, but also a wide array of complex processes that require computationally intensive reaction models.
Sequential Bayesian Experimental Design for Calibration of Expensive Simulation Models
Simulation models of critical systems often have parameters that need to be calibrated using observed data. For expensive simulation models, calibration is done using an emulator of the simulation model built on simulation output at different parameter settings. Using intelligent and adaptive selection of parameters to build the emulator can drastically improve the efficiency of the calibration process. The article proposes a sequential framework with a novel criterion for parameter selection that targets learning the posterior density of the parameters. The emergent behavior from this criterion is that exploration happens by selecting parameters in uncertain posterior regions while simultaneously exploitation happens by selecting parameters in regions of high posterior density. Furthermore, the advantages of the proposed method are illustrated using several simulation experiments and a nuclear physics reaction model.
Three-dimensional fracture continuum characterization aided by surface time-domain electromagnetics and hydrogeophysical joint inversion—proof-of-concept
Efficient and safe production of hydraulically fractured reservoirs benefits from the prediction of their geometrical attributes. Geophysical methods have the potential to provide data that are sensitive to fracture geometries, alleviating the typically sparse nature of in situ reservoir observations. Moreover, surface-based methods can be logistically and economically attractive since they avoid operational interference with the injection well infrastructure. Here, we investigate the potential of the surface-based time-domain electromagnetic (EM) method. EM methods can play an important role owing to their sensitivity to injection-induced fluid property changes. Two other advantageous factors are the EM signal-enhancing effect of vertical steel-cased wells and the fact that injected proppants can be enhanced to produce a stronger electrical conductivity contrast with the reservoir’s connate fluid. Nevertheless, an optimal fracture characterization will no doubt require the integration of EM and reservoir injection and production data. We hence carry out our investigations within a hydrogeophysical parameter estimation framework where EM data and injection flow rates are combined in a fully coupled way. Given the interdisciplinary nature of coupled hydrogeophysical inverse modeling, we dedicate one section to laying out key aspects in a didactic manner.