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At least 433 records · Page 24

Quantum phase transition dynamics in the two-dimensional transverse-field Ising model

The quantum Kibble-Zurek mechanism (QKZM) predicts universal dynamical behavior near the quantum phase transitions (QPTs). It is now well understood for the one-dimensional quantum matter. Higher-dimensional systems, however, remain a challenge, complicated by the fundamentally different character of the associated QPTs and their underlying conformal field theories. In this work, we take the first steps toward theoretical exploration of the QKZM in two dimensions for interacting quantum matter. We study the dynamical crossing of the QPT in the paradigmatic Ising model by a joint effort of modern state-of-the-art numerical methods, including artificial neural networks and tensor networks. As a central result, we quantify universal QKZM behavior close to the QPT. We also note that, upon traversing further into the ferromagnetic regime, deviations from the QKZM prediction appear. We explain the observed behavior by proposing an extended QKZM taking into account spectral information as well as phase ordering. Our work provides a testing platform for higher-dimensional quantum simulators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Domain patterns and super-elasticity of freestanding BiFeO 3 membranes via phase-field simulations

Super-elasticity of functional ferroelectric oxides offers promises for integrating ferroelectric films into flexible electronics. However, super-elastic deformation is a complex phenomenon related to possibly multiple concurrent mechanisms. Fundamentally understanding how multiple mechanisms contribute to the super-elasticity of ferroelectric oxides is crucial to realizing their potential flexible electronic applications. In this study, we employ phase-field simulations to model the dynamics of ferroelectric domain patterns of freestanding BiFeO 3 membranes to understand the origin of their super-elasticity under substantial bending deformation (5% strain). It is demonstrated that both a reversible Rhombohedral-Tetragonal (R-T) phase transition and a nearly reversible domain evolution of BiFeO 3 membranes contribute to accommodating the large deformation and thus their super-elasticity. The dynamics of domain evolution also reveal the formation of an exotic ferroelectric vortex and polarization rotation before the phase transition. We constructed a diagram of phases and domain patterns as a function of the membrane thickness and bending angle, which allows one to readily predict the emergence of T phase and ferroelectric vortex in bent BFO membranes. These results not only provide fundamental understanding of mesoscale super-elastic mechanisms but also reveal exotic domain states of ferroelectric membranes.

36 MATERIALS SCIENCE↗

Dendrite-resolved, full-melt-pool phase-field simulations to reveal non-steady-state effects and to test an approximate model

In this report we study the epitaxial, columnar growth of (multiply oriented) dendrites/cells for a spot melt in a polycrystalline Al–Cu substrate using two-dimensional, phase-field, direct numerical simulations (DNS) at the full-melt-pool scale. Our main objective is to compare the expensive DNS model to a much cheaper but approximate “line” model in which a single-crystal phase-field simulation is confined to a narrow rectangular geometry. To perform this comparison, we develop algorithms that automatically extract quantities of interest (QoIs) from both DNS and line models. These QoIs allow us to quantitatively assess the assumptions in the line model and help us analyze its discrepancy with the DNS model. We consider four sets of heat source parameters, mimicking welding and additive manufacturing conditions, that create a combination shallow and deep melt pools. Our largest DNS simulation used 16K x 14K grid points in space. Our main findings can be summarized as follows. Under AM conditions, the QoIs of line models are in excellent agreement with the full DNS results for both shallow and deep melt pools. Under welding conditions, the primary spacing of the DNS model is smaller than the prediction of line model. We identify a geometric crowding effect that accounts for the discrepancies between the DNS and line models. We propose two potential mechanisms that determine the response of the microstructure to geometric crowding.

36 MATERIALS SCIENCE↗

Roadmap on multiscale materials modeling

Modeling and simulation is transforming modern materials science, becoming an important tool for the discovery of new materials and material phenomena, for gaining insight into the processes that govern materials behavior, and, increasingly, for quantitative predictions that can be used as part of a design tool in full partnership with experimental synthesis and characterization. Modeling and simulation is the essential bridge from good science to good engineering, spanning from fundamental understanding of materials behavior to deliberate design of new materials technologies leveraging new properties and processes. This Roadmap presents a broad overview of the extensive impact computational modeling has had in materials science in the past few decades, and offers focused perspectives on where the path forward lies as this rapidly expanding field evolves to meet the challenges of the next few decades. The Roadmap offers perspectives on advances within disciplines as diverse as phase field methods to model mesoscale behavior and molecular dynamics methods to deduce the fundamental atomic-scale dynamical processes governing materials response, to the challenges involved in the interdisciplinary research that tackles complex materials problems where the governing phenomena span different scales of materials behavior requiring multiscale approaches. The shift from understanding fundamental materials behavior to development of quantitative approaches to explain and predict experimental observations requires advances in the methods and practice in simulations for reproducibility and reliability, and interacting with a computational ecosystem that integrates new theory development, innovative applications, and an increasingly integrated software and computational infrastructure that takes advantage of the increasingly powerful computational methods and computing hardware.

36 MATERIALS SCIENCE↗

Impact of the plastic deformation microstructure in metals on the kinetics of recrystallization: A phase-field study

The sensitivity of recrystallization kinetics in metals to the heterogeneity of microstructure and deformation history is a widely accepted experimental fact. However, most of the available recrystallization models employ either a mean field approach or use grain-averaged parameters, and thus neglecting the mesoscopic heterogeneity induced by prior deformation. Here in the present study, we investigate the impact of deformation-induced dislocation (subgrain) structure on the kinetics of recrystallization in metals using the phase-field approach. The primary focus here is upon the role of dislocation cell boundaries. The free energy formulation of the phase-field model accounts for the heterogeneity of the microstructure by assigning localized energy to the resulting dislocation microstructure realizations generated from experimental data. These microstructure realizations are created using the universal scaling laws for the spacing and the misorientation angles of both the geometrically necessary and incidental dislocation boundaries. The resulting free energy is used into an Allen-Cahn based model of recrystallization kinetics, which are solved using the finite element method. The solutions thus obtained shed light on the critical role of the spatial heterogeneity of deformation in the non-smooth growth of recrystallization nuclei and on the final grain structure. The results showed that, in agreement with experiment, the morphology of recrystallization front exhibits protrusions and retrusions. By resolving the subgrain structure, the presented algorithm paves the way for developing predictive kinetic models that fully account for the deformed state of recrystallizing metals.

36 MATERIALS SCIENCE↗

Study of Void Formation at the Lithium|Solid Electrolyte Interface

There is growing recognition of the critical role of void formation in lithium metal anodes in solid-state batteries and its impact on electrochemical performance. While experimental studies have demonstrated the challenges ensuing from void formation at the lithium metal interface with the solid electrolyte, there is a need to understand and quantify the role of intrinsic transport properties in lithium metal and the impact of external stimuli, such as temperature, pressure, and current density. Here, we develop this understanding by constructing a phase field-based model that captures the evolution of void domains at the lithium-solid electrolyte interface. Growth of the pores is driven by the fast removal of lithium from the interface during stripping at high current densities. Relative magnitudes of the bulk and surface lithium diffusivities, along with the applied current density, dictate the final pore morphology. Increasing the temperature results in faster diffusion, while external applied pressure causes creep flow of lithium, both of which help to mitigate the evolution of voids by quickly transporting metal from the bulk to the interface. Finally, a phase map as a function of temperature and pressure is developed as a guide to determine the regions that can lead to the stable cycling of lithium metal.

25 ENERGY STORAGE↗

Investigation of fracture in porous materials: a phase-field fracture study informed by ReaxFF

Microscopic features (e.g, pore shapes, sizes, and distribution) in porous material substantially affect the overall mechanical properties such as stiffness and strength. In turn, these material properties determine the macroscopic behaviors of fracture in the porous material. In certain cases, macroscopic properties can be derived from the porous skeleton and void ratio (i.e., porosity), but in many other cases, such derivation is a challenging task. This paper presents a numerical investigation of microporosity and micropore shapes effect on the macrofracture behavior in porous amorphous silica. For this study, we extend the recently-proposed combined molecular dynamic (MD) and phase-field (PF) fracture modeling approach by including different pore shapes in the atomistic domain. In the MD simulations, we adopt ReaxFF to evaluate the material properties, where four different micropore cases are considered. Based on the material properties derived from MD simulations, the macrofracture propagation of porous media is studied using hybrid PF simulation. In the characterization of the pore structure, the concept of pore ligament is proposed to relate the pore shape and the critical energy release rate. Two classical fracture problems were used to evaluate the effect of pore shape on the macrofracture behavior. The results of the case study show that although the micropore shapes change the macrofracture behaviors, these effects vary with the geometry and loading conditions of macroscopic boundary value problems. Furthermore, the case study also shows that the influence of micropore structure can be captured at the macroscopic level through the material properties derived from the MD simulations.

42 ENGINEERING↗

Study of Nonclassical Fields in Phase-Sensitive Reservoirs

We show that the reservoir influence can be modeled by an infinite array of beam splitters. The superposition of the input fields in the beam splitter is discussed with the convolution laws for their quasiprobabilities. We derive the Fokker-Planck equation for the cavity field coupled with a phase-sensitive reservoir using the convolution law. We also analyze the amplification in the phase-sensitive reservoir with use of the modified beam splitter model. We show the similarities and differences between the dissipation and amplification models. We show that a super-Poissonian input field cannot become sub-Poissonian by the phase-sensitive amplification.

Kim, Myung Shik↗

The effect of local chemical ordering on Frank-Read source activation in a refractory multi-principal element alloy

In this work, we investigate the operation of Frank-Read (FR) sources in a refractory multi-principal element alloy (MPEA). Simulations of discrete dislocation motion in MPEAs is enabled by the development of a phase field dislocation dynamics model that treats the atomic-scale fluctuations in lattice energies across the glide plane, present due to local ordering in the chemical composition within the nominally random MPEA atomic structure. We consider, through simulation, a range of length scales over which ordering occurs, varying from short-range lengths, a few times dislocation core width, to long-range lengths, an order of magnitude longer than the core. Characteristic of this body-centered cubic MPEA, the simulations also include screw/edge character dependence in glide resistance, as informed by atomic scale simulation. The critical stresses to activate the source for the same source size are found to be statistically distributed, as a direct consequence of the underlying variation in lattice energy. Furthermore, analysis of critical state for activating edge and screw FR sources in the MPEA reveals that FR source operation occurs via a two-step mechanism, involving athermal kink-pair formation, unlike the conventional FR source operation in a material with no composition fluctuations. This mechanism lowers the average critical stress required to activate the FR source and causes the statistical dispersion in critical stress to depend on the range of composition ordering. More importantly, it leads to a more severe dependence of source strength on FR source length than predicted by line tension alone.

36 MATERIALS SCIENCE↗

A phase-field fracture formulation for generalized standard materials: The interplay between thermomechanics and damage

Accurately modeling fracture of ductile materials poses open challenges in the field of computational mechanics due to the multiphysics nature of their failure processes. Integrating the interplay between thermodynamics and damage into ductile fracture models is vital for predicting critical failure modes. Here, in this paper, we develop a versatile phase-field (PF) framework for modeling ductile fracture, taking into account finite-strain elasto-plasticity. The framework stems from a variational formulation of constitutive relations for generalized standard materials (GSMs), whose response is described by a Helmholtz free energy and a dissipation pseudo-potential. Its variational structure is based on a minimum principle for a functional that expresses the sum of power densities for reversible and irreversible processes. By minimizing this functional with a constraint on a von Mises yield function, we derive the evolution equation for the equivalent plastic strain and an associative flow rule. This constrained optimization problem is analytically solved for a wide class of thermo-viscoplasticity models. The key innovations of the current work include (i) a cubic plastic degradation function that accounts for a non-vanishing damage-dependent yield stress, (ii) closed-form expressions of the Helmholtz free energy and dissipation pseudo-potential for three thermo-viscoplasticity models, (iii) an extended Johnson–Cook plasticity model with a nonlinear hardening law, and (iv) a plastic work heat source that depends on the plastic degradation function and a variable Taylor–Quinney (TQ) coefficient. The capabilities of the proposed framework are tested with the aid of four ductile fracture problems, including the Sandia Fracture Challenge. In each of these problems, we examine the evolution of relevant field variables such as the PF order parameter, the equivalent plastic strain, the temperature, and the internal power dissipation density, in addition to the overall structural response quantified by the force–displacement curve. These numerical studies demonstrate that the proposed framework effectively represents ductile fracture, yielding computational results that exhibit good agreement with experimental data.

36 MATERIALS SCIENCE↗

A Boundary Element Model for Assessing Large‐Scale Pressurization in Faulted Geological Storage Systems

Assessing large-scale pressurization at the regional scale—a possible outcome of large subsurface storage applications such as wastewater injection and geological carbon sequestration—presents significant computational challenges. These challenges are particularly pronounced when accounting for complex geologic structures with multiple reservoir and caprock layers, fault zones, and wells. This study introduces a computationally efficient model that integrates single-phase semi-analytical solutions with a boundary element (BE) approach. The model simulates pressure propagation in multilayered 3D systems, including vertical faults, caprock, basement, and confining units. We apply this new model to a representative scenario involving CO 2 injection near a partially sealing fault with verification against an independent two-phase flow model. Results demonstrate that our model accurately captures far-field pressure responses and that, outside the CO 2 plume zone, pressure predictions from single-phase and two-phase models are nearly identical. This supports the use of single-phase models like ours for efficient estimation of far-field pressure changes. Additionally, we demonstrate its effectiveness at a large scale, incorporating multiple wells and faults. With its ability to represent multiple wells, fault zones, and geological heterogeneity, our model is well suited for assessments of basin-scale pressurization. Its computational efficiency also makes it a promising tool for integration with optimization frameworks aimed at designing and managing injection strategies in faulted storage systems.

Cihan, A. [Lawrence Berkeley National Laboratory (↗

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↗

Variable Sampling Mapping

The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.

Smith, Jeffrey, S.↗

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↗

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↗