Accelerating phase-field based predictions: A case study with surrogate models trained using machine learning methods.
Abstract not provided.
Dingreville, Remi Philippe Michel↗
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Improving GCM Predictability of Mixed-Phase Clouds and Aerosol Interactions at High Latitudes with ARM Observations
The overachieving goal of this project is to improve the predictability of mixed-phase clouds and aerosol interactions in the Community Atmosphere Model version 6 (CAM6) through comparison with the ARM observations. There are three main objectives of the proposed study: (1) Improve the representation of ice microphysical processes in mixed-phase clouds; (2) Test the performance of ice microphysics in CESM-CAM6 with the ARM observations in northern and southern high latitudes; and (3) Examine mixed-phase cloud microphysics-aerosol-turbulence-radiation interactions in CESM-CAM6. In this project, we have (1) Improved the representation of ice microphysical processes in mixed-phase clouds in CESM-CAM6 by implementing the marine organic aerosol (MOA) and treating the ice nucleating particles (INPs) from MOA and its impacts on mixed-phase clouds. We improved the treatment of ice depositional growth through the Wegener–Bergeron–Findeisen (WBF) process by considering the subgrid heterogeneous distributions between liquid droplets and ice crystals in mixed-phase clouds; (2) Tested the performance of ice microphysics in CESM-CAM6 with the ARM observations at high latitudes. We compared the simulated INP concentrations with the ARM observations, e.g., from M-PACE, ISDAC, INPOP, and other data (Mace Head, Zeppelin, CAPRICORN). We examined the impact of improved WBF treatment on model simulated Arctic mixed-phase clouds observed in the M-PACE field campaign. Seasonal variations of modeled mixed-phase cloud properties (LWO, IWP) are compared with the ground-based remote sensing retrievals at the ARM’s NSA $Utqia\dot{g}vik$ site; and (3) Examined mixed-phase cloud microphysics-aerosol-dynamics-radiation interactions in CESM-CAM6 that include the impacts of MOA INPs, and impacts of different model parameterizations (CLUBB versus UW turbulence & shallow convection schemes, MG2 versus MG1) on high-latitude mixed-phase cloud properties. Aerosol indirect effects of MOA through the liquid phase (droplet activation) and ice phase processes (e.g., the glaciation indirect effect) were investigated.
54 ENVIRONMENTAL SCIENCES↗
On the convexity of phase-field fracture formulations: Analytical study and comparison of various degradation functions
Efficient and accurate fracture modeling is of great importance in applications where catastrophic outcomes under extreme scenarios are possible. The phase-field (PF) approach to fracture received significant attention over the past decade, due to its capability to capture complicated fracture patterns (e.g., crack merging and branching). Specifically, crack initiation and propagation are modeled via minimization of the total energy functional, which is regularized with the aid of a phase field. Despite the promising results and modeling capabilities of the PF method in many applications, the solution of fracture problems remains computationally challenging mainly due to the non-convexity of the total energy functional with respect to the combined unknown (phase field and displacement) fields. Understanding the effects of their coupling on convexity is crucial in order to address frequently encountered hurdles in fracture modeling (e.g., inefficient solvers and non-physical crack nucleation). In this paper, we develop convexity criteria for a wide class of PF fracture formulations. For this class of formulations, the second variation of the total energy functional is expressed in terms of Hessian matrices (evaluated at individual material points). Depending on the choice of geometric crack functions and degradation functions, we classify the formulations into three categories and analytically study each one separately. To study the sign of the second variation, we derive inequalities which are satisfied at material points when the Hessian matrix is locally positive semi-definite. These inequalities provide objective criteria for comparing degradation functions. Finally, the applicability of the proposed convexity criteria is demonstrated in the context of a one-dimensional problem, solved using a conventional monolithic solver.
97 MATHEMATICS AND COMPUTING↗
Sprain energy consequences for damage localization and fracture mechanics
The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the “sprain,” as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ( C 0 ) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.
Science & Technology - Other Topics↗
On the nature of the extreme-ultraviolet late phase of solar flares
The extreme-ultraviolet (EUV) late phase of solar flares is a second peak of warm coronal emissions (e.g., Fe XVI) for many minutes to a few hours after the GOES soft X-ray peak. It was first observed by the EUV Variability Experiment on board the Solar Dynamics Observatory (SDO). The late-phase emission originates from a second set of longer loops (late-phase loops) that are higher than the main flaring loops. It is suggested to be caused by either additional heating or long-lasting cooling. In this paper, we study the role of long-lasting cooling and additional heating in producing the EUV late phase using the enthalpy based thermal evolution of loops model. We find that a long cooling process in late-phase loops can well explain the presence of the EUV late-phase emission, but we cannot exclude the possibility of additional heating in the decay phase. Moreover, we provide two preliminary methods based on the UV and EUV emissions from the Atmospheric Imaging Assembly on board SDO to determine whether or not additional heating plays a role in the late-phase emission. Using nonlinear force-free field modeling, we study the magnetic configuration of the EUV late phase. It is found that the late phase can be generated either in hot spine field lines associated with a magnetic null point or in large-scale magnetic loops of multipolar magnetic fields. In this paper, we also discuss why the EUV late phase is usually observed in warm coronal emissions and why the majority of flares do not exhibit an EUV late phase.
79 ASTRONOMY AND ASTROPHYSICS↗
Electroweak phase transition in the U(1){sup '} MSSM
In this work, we have investigated the nature of the electroweak phase transition in the U(1) extended minimal supersymmetric standard model without introducing any exotic fields. The effective potential has been estimated exactly at finite temperature taking into account the whole particle spectrum. For reasonable values of the lightest Higgs and neutralino, we found that the electroweak phase transition could be strongly first order due to: (1) the interactions of the singlet with the doublets in the effective potential, and (2) the evolution of the wrong vacuum that delays the transition.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Energy Saving Quantification on Ductless Heat Pump (DHP) in Existing Homes
In residential retrofit applications, ductless mini-split heat pumps (DHP) are often reported to have high-energy savings potential, depending on the system they are supplementing or replacing. However, recently, there have been a number of utility studies and analyses indicating these energy savings are not being achieved when the existing system is left in place for backup heating or air conditioning. The Pacific Northwest National Laboratory conducted a three-phase project to help determine which control strategies would have the most energy savings impact in various climate zones around the United States. The first phase developed the standalone simulation model for the PNNL Lab Homes and investigated the energy-saving potential from different control strategies and HVAC system configurations. The second phase focused on conducting experiments in the PNNL Lab Homes, which tested the most promising solutions that were modeled in the first phase. The third phase used the field data to calibrate the simulation model and then extrapolated the results to different climate locations and different building sizes. This report focuses on the third phase of the study, including five major parts: model calibration, parametric model setup, results, a sensitivity analysis of air leakage rate, and conclusions.
32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
General Diffuse-Interface Theories and an Approach to Predictive Tumor Growth Modeling
While a large and growing literature exists on mathematical and computational models of tumor growth, to date tumor growth models are largely qualitative in nature, and fall far short of being able to provide predictive results important in life-and-death decisions. This is largely due to the enormous complexity of evolving biological and chemical processes in living tissue and the complex interactions of many cellular and vascular constituents in living organisms. Several new technologies have emerged, however, which could lead to significant progress in this important area: (i) the development of so-called phase-field, or diffuse-interface models, which can be developed using continuum mixture theory, and which provide a general framework for modeling the action of multiple interacting constituents. These are based on generalizations of the Cahn–Hilliard models for spinodal decomposition, and have been used recently in certain tumor growth theories; (ii) the emergence of predictive computational methods based on the use of statistical methods for calibration, model validation, and uncertainty quantification; (iii) advances in imaging, experimental cell biology, and other medical observational methodologies; and (iv) the advent of petascale computing that makes possible the resolution of features at scales and at speeds that were unattainable only a short time in the past. Here we develop a general phenomenological thermomechanical theory of mixtures that employs phase-field or diffuse interface models of surface energies and reactions and which provides a framework for generalizing existing theories of the types that are in use in tumor growth modeling. In principle, the framework provides for the effects of M solid constituents, which may undergo large deformations, and for the effect of N - M fluid constituents, which could include highly nonlinear, non-Newtonian fluids. We then describe several special cases which have the potential of providing acceptable models of tumor growth. We then describe the beginning steps of the development of Bayesian methods for statistical calibration, model validation, and uncertainty quantification, which, with further work, could produce a truly predictive tool for studying tumor growth. In particular, we outline the processes of statistical calibration and validation that can be employed to determine if tumor growth models, drawn from the broad class of models developed here, are valid for prediction of key quantities of interest critical to making decisions on various medical protocols. We also describe how uncertainties in such key quantities of interest can be quantified in ways that can be used to establish confidence in predicted outcomes.
59 BASIC BIOLOGICAL SCIENCES↗
Evolution of the large-scale tail of primordial magnetic fields
Cosmic magnetic fields may be generated during early cosmic phase transition, such as the QCD or electroweak transitions. The magnitude of the remainder of such fields at the present epoch crucially depends on the exponent n of their (initially super-Hubble) large-scale tail, i.e., B{sub {lambda}{approx}{lambda}}{sup -n}. It has been claimed that causality requires n=5/2, contrary to much earlier claims of n=3/2. Here we analyze this question in detail. First, we note that contrary to current belief, the large-scale magnetic field tail is not established at the phase transition itself, but rather continuously evolves up to the present epoch. Neglecting turbulent flows we find n=7/2, i.e., very strongly suppressed large-scale fields. However, in the inevitable presence of turbulent flows we find that the large-scale magnetic field tail has sufficient time to evolve to that of the fluid turbulence. For white noise fluid turbulence this yields n=3/2 up to a certain scale and n=5/2 beyond for the magnetic field spectrum. This picture is also not changed when primordial viscosity and fluid flow dissipation is taken into account. Appreciable primordial magnetic fields originating from cosmic phase transitions thus seem possible.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
A Stochastic Reduced-Order Model for Statistical Microstructure Descriptors Evolution
Integrated computational materials engineering (ICME) models have been a crucial building block for modern materials development, relieving heavy reliance on experiments and significantly accelerating the materials design process. However, ICME models are also computationally expensive, particularly with respect to time integration for dynamics, which hinders the ability to study statistical ensembles and thermodynamic properties of large systems for long time scales. To alleviate the computational bottleneck, we propose to model the evolution of statistical microstructure descriptors as a continuous-time stochastic process using a non-linear Langevin equation, where the probability density function (PDF) of the statistical microstructure descriptors, which are also the quantities of interests (QoIs), is modeled by the Fokker–Planck equation. In this work, we discuss how to calibrate the drift and diffusion terms of the Fokker–Planck equation from the theoretical and computational perspectives. The calibrated Fokker–Planck equation can be used as a stochastic reduced-order model to simulate the microstructure evolution of statistical microstructure descriptors PDF. Considering statistical microstructure descriptors in the microstructure evolution as QoIs, we demonstrate our proposed methodology in three integrated computational materials engineering (ICME) models: kinetic Monte Carlo, phase field, and molecular dynamics simulations.
97 MATHEMATICS AND COMPUTING↗
Perspective—Mass Conservation in Models for Electrodeposition/Stripping in Lithium Metal Batteries
Electrochemical models at different scales and varying levels of complexity have been used in the literature to study the evolution of the anode surface in lithium metal batteries. This includes continuum, mesoscale (phase-field approaches), and multiscale models. In this paper, using a motivating example of a moving boundary model in one dimension, we show how battery models need proper formulation for mass conservation, especially when simulated over multiple charge and discharge cycles. The article concludes with some thoughts on mass conservation and proper formulation for multiscale models.
25 ENERGY STORAGE↗
Quantum phase transitions in long-range interacting hyperuniform spin chains in a transverse field
Hyperuniform states of matter are characterized by anomalous suppression of long-wavelength density fluctuations. While most of the interesting cases of disordered hyperuniformity are provided by complex many-body systems such as liquids or amorphous solids, classical spin chains with certain long-range interactions have been shown to demonstrate the same phenomenon. Such spin-chain systems are ideal models for exploring the effects of quantum mechanics on hyperuniformity. It is well-known that the transverse field Ising model shows a quantum phase transition (QPT) at zero temperature. Under the quantum effects of a transverse magnetic field, classical hyperuniform spin chains are expected to lose their hyperuniformity. High-precision simulations of these cases are complicated because of the presence of highly nontrivial long-range interactions. We perform an extensive analysis of these systems using density matrix renormalization group simulations to study the possibilities of phase transitions and the mechanism by which they lose hyperuniformity. Even for a spin chain of length 30, we see discontinuous changes in properties like the “τ order metric” of the ground state, the measure of hyperuniformity, and the second cumulant of the total magnetization along the x-direction, all suggestive of first-order QPTs. An interesting feature of the phase transitions in these disordered hyperuniform spin chains is that, depending on the parameter values, the presence of a transverse magnetic field may lead remarkably to an increase in the order of the ground state as measured by the “τ order metric,” even if hyperuniformity is lost. Therefore, it would be possible to design materials to target specific novel quantum behaviors in the presence of a transverse magnetic field. Our numerical investigations suggest that these spin chains can show no more than two QPTs. We further analyze the long-range interacting spin chains via the Jordan-Wigner mapping onto a system of spinless fermions, showing that under the pairwise-interaction approximation and a mean-field treatment, there can be at most two quantum phase transitions. Here, based on these numerical and theoretical explorations, we conjecture that for spin chains with long-range pair interactions that have convergent cosine transforms, there can be a maximum of two quantum phase transitions at zero temperature.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Quark-mass dependence of the three-flavor QCD phase diagram at zero and imaginary chemical potential: Model prediction
We draw the three-flavor phase diagram as a function of light- and strange-quark masses for both zero and imaginary quark-number chemical potential, using the Polyakov-loop extended Nambu-Jona-Lasinio model with an effective four-quark vertex depending on the Polyakov loop. The model prediction is qualitatively consistent with 2+1 flavor lattice QCD prediction at zero chemical potential and with degenerate three-flavor lattice QCD prediction at imaginary chemical potential.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Coupling of Spark Plasma Sintering with Advanced Modeling to Enable Process Scale-Up: Presentation to DOE-NE [Slides]
The research goal of this project is to develop at Idaho National Laboratory (INL) a first-of-its-kind Multiphysics Object-Oriented Simulation Environment (MOOSE)-based, multiscale, multiphysics spark plasma sintering (SPS) modeling and simulation code application, termed “Freya.” Freya will simulate the thermo-mechanical-electrical aspects of the SPS fabrication process and will be paired with lower length scale sub-models, such as phase-field, to predict the resulting microstructure. SPS is an advanced manufacturing process that can be used to solve a variety of material manufacturing challenges; however, this process is an extremely challenging problem for modeling and simulation. The SPS process is inherently multiphysics and multi-scale, with the macroscale electro-thermo-mechanical behavior linked intricately to the microstructure evolution of the part being sintered. Accurate modeling and simulation tools, specifically geared towards the SPS process, are needed to predict the influence of the multiple variables involved in the manufacturing process. Modeling and simulation accuracy is achieved and demonstrated through comparison to multiple validation experiments. The validation efforts for Freya include both separate effects and complete multiphysics SPS process experiments. One of the key benefits this Laboratory Directed Research & Development (LDRD) project offers stems from the emphasis placed on experimental validation of the Freya models, both on the individual length scales and of the final coupled multiscale multiphysics simulations. Experimental validation of Freya’s multiscale coupling capability provides the technical credibility necessary for potential future industry and research partners to accept the simulation predictions.
36 MATERIALS SCIENCE↗
Parallel simulation via SPPARKS of on-lattice kinetic and Metropolis Monte Carlo models for materials processing
Abstract SPPARKS is an open-source parallel simulation code for developing and running various kinds of on-lattice Monte Carlo models at the atomic or meso scales. It can be used to study the properties of solid-state materials as well as model their dynamic evolution during processing. The modular nature of the code allows new models and diagnostic computations to be added without modification to its core functionality, including its parallel algorithms. A variety of models for microstructural evolution (grain growth), solid-state diffusion, thin film deposition, and additive manufacturing (AM) processes are included in the code. SPPARKS can also be used to implement grid-based algorithms such as phase field or cellular automata models, to run either in tandem with a Monte Carlo method or independently. For very large systems such as AM applications, the Stitch I/O library is included, which enables only a small portion of a huge system to be resident in memory. In this paper we describe SPPARKS and its parallel algorithms and performance, explain how new Monte Carlo models can be added, and highlight a variety of applications which have been developed within the code.
36 MATERIALS SCIENCE↗
Modeling Multiple Time Scales during Glass Formation with Phase-Field Crystals
The dynamics of glass formation in monatomic and binary liquids are studied numerically using a microscopic field theory for the evolution of the time-averaged atomic number density. A stochastic framework combining phase-field crystal free energies and dynamic density functional theory is shown to successfully describe several aspects of glass formation over multiple time scales. Agreement with mode coupling theory is demonstrated for underdamped liquids at moderate supercoolings, and a rapidly growing dynamic correlation length is found to be associated with fragile behavior.
36 MATERIALS SCIENCE↗
Phase separation versus supersolid behavior in frustrated antiferromagnets
We investigate the competition between spin supersolidity and phase separation in a frustrated spin-half model of weakly coupled dimers. We start by considering systems of hard-core bosons on the square lattice, onto which the low-energy physics of the herein investigated spin model can be mapped, and devise a criterion for gauging the interplay between supersolid order and domain-wall formation based on strong-coupling arguments. Effective bosonic models for the spin model are derived via the contractor renormalization (CORE) algorithm and we propose to combine a self-consistent cluster mean-field solution with our criterion for the occurrence of phase separation to derive the phase diagram as a function of frustration and magnetic field. In the limit of strong frustration, the model is shown to be unstable toward phase separation, in contradiction with recently published results. However, a region of stable supersolidity is identified for intermediate frustration, in a parameter range of possible experimental relevance.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗