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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 307 records · Page 17
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

The Generality of the GUGA MRCI Approach in COLUMBUS for Treating Complex Quantum Chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

The JOREK non-linear extended MHD code and applications to large-scale instabilities and their control in magnetically confined fusion plasmas

JOREK is a massively parallel fully implicit non-linear extended magneto-hydrodynamic (MHD) code for realistic tokamak X-point plasmas. It has become a widely used versatile simulation code for studying large-scale plasma instabilities and their control and is continuously developed in an international community with strong involvements in the European fusion research programme and ITER organization. This article gives a comprehensive overview of the physics models implemented, numerical methods applied for solving the equations and physics studies performed with the code. A dedicated section highlights some of the verification work done for the code. A hierarchy of different physics models is available including a free boundary and resistive wall extension and hybrid kinetic-fluid models. The code allows for flux-surface aligned iso-parametric finite element grids in single and double X-point plasmas which can be extended to the true physical walls and uses a robust fully implicit time stepping. Particular focus is laid on plasma edge and scrape-off layer (SOL) physics as well as disruption related phenomena. Among the key results obtained with JOREK regarding plasma edge and SOL, are deep insights into the dynamics of edge localized modes (ELMs), ELM cycles, and ELM control by resonant magnetic perturbations, pellet injection, as well as by vertical magnetic kicks. Also ELM free regimes, detachment physics, the generation and transport of impurities during an ELM, and electrostatic turbulence in the pedestal region are investigated. Regarding disruptions, the focus is on the dynamics of the thermal quench (TQ) and current quench triggered by massive gas injection and shattered pellet injection, runaway electron (RE) dynamics as well as the RE interaction with MHD modes, and vertical displacement events. Also the seeding and suppression of tearing modes (TMs), the dynamics of naturally occurring TQs triggered by locked modes, and radiative collapses are being studied.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Evaluating opportunities to improve material and energy impacts in commodity supply chains

When evaluated at the scale of individual processes, next-generation technologies may be more energy and emissions intensive than current technology. Furthermore, many advanced technologies have the potential to reduce material and energy consumption in upstream or downstream processing stages. In order to fully understand the benefits and consequences of technology deployment, next-generation technologies should be evaluated in context, as part of a supply chain. This work presents the Materials Flow through Industry (MFI) supply chain modeling tool. The MFI tool is a cradle-to-gate linear network model of the US industrial sector that can model a wide range of manufacturing scenarios, including changes in production technology and increases in industrial energy efficiency. The MFI tool was developed to perform supply chain scale analyses in order to quantify the impacts and benefits of next-generation technologies and materials at that scale. For the analysis presented in this paper, the MFI tool is utilized to explore a case study comparing three lightweight vehicle supply chains to the supply chain of a conventional, standard weight vehicle. Several of the lightweight vehicle supply chains are evaluated under manufacturing scenarios that include next-generation production technologies and next-generation materials. Results indicate that producing lightweight vehicles is more energy and emission intensive than producing the non-lightweight vehicle, but the fuel saved during vehicle use offsets this increase. In this case study, greater reductions in supply chain energy and emissions were achieved through the application of the next-generation technologies than from application of energy efficiency increases.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2017

On the Preconditioning of a Newton-Krylov Solver for a High-Order reconstructed Discontinuous Galerkin Discretization of All-Speed Compressible Flow with Phase Change for Application in Laser-Based Additive Manufacturing

This dissertation focuses on the development of a fully-implicit, high-order compressible ow solver with phase change. The work is motivated by laser-induced phase change applications, particularly by the need to develop large-scale multi-physics simulations of the selective laser melting (SLM) process in metal additive manufacturing (3D printing). Simulations of the SLM process require precise tracking of multi-material solid-liquid-gas interfaces, due to laser-induced melting/ solidi cation and evaporation/condensation of metal powder in an ambient gas. These rapid density variations and phase change processes tightly couple the governing equations, requiring a fully compressible framework to robustly capture the rapid density variations of the ambient gas and the melting/evaporation of the metal powder. For non-isothermal phase change, the velocity is gradually suppressed through the mushy region by a variable viscosity and Darcy source term model. The governing equations are discretized up to 4th-order accuracy with our reconstructed Discontinuous Galerkin spatial discretization scheme and up to 5th-order accuracy with L-stable fully implicit time discretization schemes (BDF2 and ESDIRK3-5). The resulting set of non-linear equations is solved using a robust Newton-Krylov method, with the Jacobian-free version of the GMRES solver for linear iterations. Due to the sti nes associated with the acoustic waves and thermal and viscous/material strength e ects, preconditioning the GMRES solver is essential. A robust and scalable approximate block factorization preconditioner was developed, which utilizes the velocity-pressure (vP) and velocity-temperature (vT) Schur complement systems. This multigrid block reduction preconditioning technique converges for high CFL/Fourier numbers and exhibits excellent parallel and algorithmic scalability on classic benchmark problems in uid dynamics (lid-driven cavity ow and natural convection heat transfer) as well as for laser-induced phase change problems in 2D and 3D.

42 ENGINEERING↗
DOE OSTI2025

Frequency-domain modeling of floating wind arrays with shared mooring lines

A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems. The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analog to the modeling capabilities of the floating support structure in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.

17 WIND ENERGY↗
DOE OSTI2020

Interpreting and Stabilizing Machine-Learning Parametrizations of Convection

Neural networks are a promising technique for parameterizing subgrid-scale physics (e.g., moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption. For instance, it is not fully understood why neural network parameterizations often cause dramatic instability when coupled to atmospheric fluid dynamics. This paper introduces tools for interpreting their behavior that are customized to the parameterization task. First, we assess the nonlinear sensitivity of a neural network to lower-tropospheric stability and the midtropospheric moisture, two widely studied controls of moist convection. Second, we couple the linearized response functions of these neural networks to simplified gravity wave dynamics, and analytically diagnose the corresponding phase speeds, growth rates, wavelengths, and spatial structures. To demonstrate their versatility, these techniques are tested on two sets of neural networks, one trained with a super-parameterized version of the Community Atmosphere Model (SPCAM) and the second with a near-global cloud-resolving model (GCRM). Additionally, even though the SPCAM simulation has a warmer climate than the cloud-resolving model, both neural networks predict stronger heating/drying in moist and unstable environments, which is consistent with observations. Moreover, the spectral analysis can predict that instability occurs when GCMs are coupled to networks that support gravity waves that are unstable and have phase speeds larger than 5 m s -1 . In contrast, standing unstable modes do not cause catastrophic instability. Using these tools, differences between the SPCAM-trained versus GCRM-trained neural networks are analyzed, and strategies to incrementally improve both of their coupled online performance unveiled.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2019

Developing a radiation-aging model for polymeric foam cushions

Motivation: A major component of the A&L constitutive modeling effort over the last couple of years has involved developing a thermal aging model for foam cushions. Through extensive studies of uniaxial compression data, we have established that the Ogden N = 2 Hyperfoam in conjunction with the Tobolsky two-network model [Ref. 4] provides an accurate theoretical framework to describe the results, both for the traditional (stochastic) as well as the AM (3D-printed) foam pads. The results display numerical accuracy over a wide range of compression levels, from low to moderate up to slightly over 90% of lock-up. Over the last few weeks we have been exploring radiation aging data on a specific 3D printed foam, i.e., SE1700 AM FCT foam, to see if the Ogden + Tobolsky model can explain such data as well, and if so, how the various model parameters change as a function of dosage. As this report shows, the answer is indeed yes. We find that the modulus of the second (i.e., induced network) increases nearly proportionally with the radiation dosage, with a smaller sub-linear decrease in the primary shear modulus of the original network. This is consistent with the interpretation that exposure to energetic gamma-radiation is dominated by the formation of new cross-links. Significance: An important goal of A&L modeling efforts is to develop a fully age-aware materials model that can describe the joint effects of commonly present aging drivers like temperature, radiation, humidity, etc. Such a model is necessary to assess the lifetime of essential components like polymeric foams and rubber pads.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Understanding the Physics Representation of Deep Learning Models in Environmental Applications

Deep learning (DL) models have been popular in earth and environmental modeling and analysis, which exhibit huge potential in capturing and reconstructing the non-linearity of relevant environmental processes. They are extensively used as analytical tools or emulators for multiple domains (atmosphere, land surface, ocean, and biogeochemistry). Despite their success, their internal working mechanism remains largely unknown. Such a lack of knowledge hinders the identification of physically consistent models that are fully adaptive to non-stationary climate, as well as the development of physics-informed machine learning such as physics-informed neural network (PINN). To establish preliminary knowledge and framework of such physics representation evaluation, this project focuses on an improved understanding of DL models in the environmental applications. DL models are increasingly applied to environmental modeling and prediction. However, they have been evaluated mostly from a performance perspective, and there is a gap in understanding how they represent the known physics internally. Such knowledge is especially critical when applying DL models under climate change conditions, where new inputs are likely outside the ranges of the training datasets. In this project, we reveal how the known physical processes are represented within DL models from both statistical and mechanistic perspectives. Leveraging the traditional model evaluations that focus more on the accuracies of predictions, we establish a framework that examines both the accuracy and physics representation of DL models. This analysis framework can identify DL models that make the correct predictions based on correct physics, thus enhancing the existing explainable artificial intelligence (explainable-AI) portfolio. It lays a foundation for developing novel metrics to evaluate the emerging DL models in environmental applications. This knowledge also informs the development of physics-informed DL models by revealing the direct connections between the known physical processes and specific model components or structures.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

AI-Enabled Operations at Fermi Complex: Multivariate Time Series Prediction for Outage Prediction and Diagnosis

The Main Control Room of the Fermilab accelerator complex continuously gathers extensive time-series data from thousands of sensors monitoring the beam. However, unplanned events such as trips or voltage fluctuations often result in beam outages, causing operational downtime. This downtime not only consumes operator effort in diagnosing and addressing the issue but also leads to unnecessary energy consumption by idle machines awaiting beam restoration. The current threshold-based alarm system is reactive and faces challenges including frequent false alarms and inconsistent outage-cause labeling. To address these limitations, we propose an AI-enabled framework that leverages predictive analytics and automated labeling. Using data from $2,703$ Linac devices and $80$ operator-labeled outages, we evaluate state-of-the-art deep learning architectures, including recurrent, attention-based, and linear models, for beam outage prediction. Additionally, we assess a Random Forest-based labeling system for providing consistent, confidence-scored outage annotations. Our findings highlight the strengths and weaknesses of these architectures for beam outage prediction and identify critical gaps that must be addressed to fully harness AI for transitioning downtime handling from reactive to predictive, ultimately reducing downtime and improving decision-making in accelerator management.

Jain, Milan [PNL, Richland] (ORCID:000000021676111↗
DOE OSTI2016

Three species one-dimensional kinetic model for weakly ionized plasmas

A three species one-dimensional kinetic model is presented for a spatially homogeneous weakly ionized plasma subjected to the action of a time varying electric field. Planar geometry is assumed, which means that the plasma evolves in the privileged direction of the field. The energy transmitted to the electric charges is channelized to the neutrals thanks to collisions, a mechanism that influences the plasma dynamics. Charge-charge interactions have been designed as a one-dimensional collision term equivalent to the Landau operator used for fully ionized plasmas. Charge-neutral collisions are modelled by a conservative drift-diffusion operator in the Dougherty's form. The resulting set of coupled integro-differential equations is solved with the stable and robust propagator integral method. This semi–analytical method feasibility accounts for non–linear effects without appealing to linearisation or simplifications, providing conservative physically meaningful solutions even for initial or emerging sharp velocity distribution function profiles. It is found that charge-neutral collisions exert a significant effect since a quite different plasma evolution arises if compared to the collisionless limit. In addition, substantial differences in the system motion are found for constant and temperature dependent collision frequencies cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Power spectrum precision for redshift space distortions

Redshift space distortions in galaxy clustering offer a promising technique for probing the growth rate of structure and testing dark energy properties and gravity. We consider the issue of to what accuracy they need to be modeled in order not to unduly bias cosmological conclusions. Fitting for nonlinear and redshift space corrections to the linear theory real space density power spectrum in bins in wavemode, we analyze both the effect of marginalizing over these corrections and of the bias due to not correcting them fully. While naively subpercent accuracy is required to avoid bias in the unmarginalized case, in the fitting approach the Kwan-Lewis-Linder reconstruction function for redshift space distortions is found to be accurately selfcalibrated with little degradation in dark energy and gravity parameter estimation for a next generation galaxy redshift survey such as BigBOSS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Lagrangian or Eulerian; real or Fourier? Not all approaches to large-scale structure are created equal

We present a pedagogical systematic investigation of the accuracy of Eulerian and Lagrangian perturbation theories of large-scale structure. We show that significant differences exist between them especially when trying to model the Baryon Acoustic Oscillations (BAO). We find that the best available model of the BAO in real space is the Zel'dovich Approximation (ZA), giving an accuracy of ∼<3% at redshift of z = 0 in modelling the matter 2-pt function around the acoustic peak. All corrections to the ZA around the BAO scale are perfectly perturbative in real space. Any attempt to achieve better precision requires calibrating the theory to simulations because of the need to renormalize those corrections. In contrast, theories which do not fully preserve the ZA as their solution, receive O(1) corrections around the acoustic peak in real space at z = 0, and are thus of suspicious convergence at low redshift around the BAO. As an example, we find that a similar accuracy of 3% for the acoustic peak is achieved by Eulerian Standard Perturbation Theory (SPT) at linear order only at z ≈ 4. Thus even when SPT is perturbative, one needs to include loop corrections for z∼<4 in real space. In Fourier space, all models perform similarly, and are controlled by the overdensity amplitude, thus recovering standard results. However, that comes at a price. Real space cleanly separates the BAO signal from non-linear dynamics. In contrast, Fourier space mixes signal from short mildly non-linear scales with the linear signal from the BAO to the level that non-linear contributions from short scales dominate. Therefore, one has little hope in constructing a systematic theory for the BAO in Fourier space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Beyond real: alternative unitary cluster Jastrow models for molecular electronic structure calculations on near-term quantum computers

Near-term quantum devices require wavefunction ansätze that are expressive while also of shallow circuit depth in order to both accurately and efficiently simulate molecular electronic structure. While the unitary coupled cluster ansatz (e.g., UCCSD) has become a standard, the high gate count associated with the implementation of this limits its feasibility on noisy intermediate-scale quantum (NISQ) hardware. k -Fold unitary cluster Jastrow (uCJ) ansätze mitigate this challenge by providing O( kN 2 ) circuit scaling and favorable linear depth circuit implementation. Previous work has focused on the real orbitalrotation (Re-uCJ) variant of uCJ, which allows an exact (Trotter-free) implementation. Here we extend and generalize the k -fold uCJ framework by introducing two new variants, Im-uCJ and g-uCJ, which incorporate imaginary and fully complex orbital rotation operators, respectively. Similar to Re-uCJ, both of the new variants achieve quadratic gate-count scaling. Our results focus on the simplest k = 1 model, and show that the uCJ models frequently maintain energy errors within chemical accuracy (∼1 kcal mol −1 ). Both g-uCJ and Im-uCJ are more expressive in terms of capturing electron correlation and are also more accurate than the earlier Re-uCJ ansatz. We further show that Im-uCJ and g-uCJ circuits can also be implemented exactly, without any Trotter decomposition. Numerical tests using k = 1 on H 2 , H 3 + , Be 2 , C 2 H 4 , C 2 H 6 and C 6 H 6 in various basis sets confirm the practical feasibility of these shallow Jastrow-based ansätze for applications on near-term quantum hardware.

Tkachenko, Nikolay V. [University of California, B↗
DOE OSTI2014

Tropical Pacific response to continental ice sheet topography

The last glacial maximum was marked by maximum land ice extent and lowest greenhouse gases concentration during the last ice age. We investigate the effect of glacial continental ice sheet topography on the large-scale tropical ocean–atmosphere climate, in particular the tropical Pacific, in an intermediate complexity coupled model. Increasing the thickness of continental ice sheets causes a southward displaced Pacific Intertropical Convergence Zone (ITCZ) and a strengthening (weakening) of northern (southern) hemisphere winter Hadley cell. The equatorial zonal sea surface temperature gradient weakened with an increased continental ice sheets thickness, the reduction being caused by cooling in the western equatorial Pacific and warming in the eastern equatorial Pacific. The evolution of the tropical climate with changing ice thickness has distinct quasi-linear and nonlinear parts. While the linear part is a direct response to the ice topographic changes, the nonlinear part was a finding of the tropical thermocline adjustment. Our analysis of a fully-coupled transient deglacial simulation strongly indicates the dominant role of ice sheet topography in determining the deglacial evolution of the simulated Pacific climate. The thickness of continental ice sheet, separate from ice albedo effect, has significant impact on the tropical ocean–atmosphere climate in particular with the meridional displacement in the Pacific ITCZ. The altered circulation states seen in the model may aid understanding of the relationship between tropical and high-latitude climate records in glacial-interglacial cycles.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

A perturbative formalism for electronic transitions through conical intersections in a fully quadratic vibronic model

We consider a fully quadratic vibronic model Hamiltonian for studying photoinduced electronic transitions through conical intersections. Using a second order perturbative approximation for diabatic couplings, we derive an analytical expression for the time evolution of electronic populations at a given temperature. This formalism extends upon a previously developed perturbative technique for a linear vibronic coupling Hamiltonian. The advantage of the quadratic model Hamiltonian is that it allows one to use separate quadratic representations for potential energy surfaces of different electronic states and a more flexible representation of interstate couplings. We explore features introduced by the quadratic Hamiltonian in a series of 2D models, and then apply our formalism to the 2,6-bis(methylene) adamantyl cation and its dimethyl derivative. The Hamiltonian parameters for the molecular systems have been obtained from electronic structure calculations followed by a diabatization procedure. The evolution of electronic populations in the molecular systems using the perturbative formalism shows a good agreement with that from variational quantum dynamics.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

SU-E-T-70: A Radiobiological Model of Reoxygenation and Fractionation Effects

Purpose: To develop a simple reoxygenation model that fulfills the following goals:1-Quantify the reoxygenation effect in biologically effective dose (BED) and compare it to the repopulation effect.2-Model the hypoxic fraction in tumors as a function of the number of fractions.3-Develop a simple analytical expression for a reoxygenation term in BED calculations. Methods: The model considers tumor cells in two compartments: one normoxic population of cells and one hypoxic compartment including cells under a range of reduced oxygen concentrations. The surviving fraction is predicted using the linear-quadratic (LQ) model. A hypoxia reduction factor (HRF) is used to quantify reductions in radiosensitivity parameters α-A and β-A as cellular oxygen concentration decreases. The HRF is defined as the ratio of the dose at a specific level of hypoxia to the dose under fully aerobic conditions to achieve equal cell killing. The model assumes that a fraction of the hypoxic cells ( ) moves from the hypoxic to the aerobic compartment after each daily fraction. As an example, we consider standard fractionation for NSCLC (d=2Gy,n=33) versus a SBRT (n=5, d=10Gy) fractionation and compare the loss in reoxygenation biological effect with the gain in repopulation biological effect. Results: An analytic expression for the surviving fraction after n daily treatments is derived and the reoxygenation term in the biological effect is calculated. Reoxygenation and repopulation effects are the same order of magnitude for potential doubling time Td values of 2 to 5 days. The hypoxic fraction increases or decreases with n depending on the reoxygenation rate Δ. For certain combinations of parameters, the biological effect of reoxygenation goes as -(n-1)*ln(1-Δ) providing a simple expression that can be introduced in BED calculations. Conclusion: A novel radiobiological model was developed that can be used to evaluate the effect of reoxygenation in fractionated radiotherapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Dynamics in entangled polyethylene melts [Multi time scale dynamics in entangled polyethylene melts]

Polymer dynamics creates distinctive viscoelastic behavior as a result of a coupled interplay of motion at the atomic length scale and motion of the entire macromolecule. Capturing the broad time and length scales of polymeric motion however, remains a challenge. Using linear polyethylene as a model system, we probe the effects of the degree of coarse graining on polymer dynamics. Coarse-grained (CG) potentials are derived using iterative Boltzmann inversion with λ methylene groups per CG bead (denoted CGλ) with λ = 2,3,4 and 6 from a fully-atomistic polyethylene melt simulation. By rescaling time in the CG models by a factor α, the chain mobility for the atomistic and CG models match. We show that independent of the degree of coarse graining, all measured static and dynamic properties are essentially the same once the dynamic scaling factor α and a non-crossing constraint for the CG6 model are included. The speedup of the CG4 model is about 3 times that of the CG3 model and is comparable to that of the CG6 model. Furthermore, using these CG models we were able to reach times of over 500 μs, allowing us to measure a number of quantities, including the stress relaxation function, plateau modulus and shear viscosity, and compare directly to experiment.

36 MATERIALS SCIENCE↗
NASA NTRS1988

The effect of an electric field on the morphological stability of the crystal-melt interface of a binary alloy

A fully time-dependent linear stability analysis of the morphological stability of a planar interface during directional solidification of a binary alloy at constant velocity in the presence of an electric field, is performed. The electromigration of solute and the differing electrical conductivities of solid and liquid for a model in which the temperature gradient is constant are taken into account. The present results are compared with the constitutional supercooling criterion, and it is shown there may be substantial differences. A modified constitutional supercooling criterion which is valid over a large range of conditions is derived. It is also found under certain conditions that the onset of instability may be time dependent.

Wheeler, A. A.↗