Search NASA⌕ Search

SEARCH · Search NASA

Results for “Value function”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 703 records · Page 39
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Centrality and pseudorapidity dependence of the charged-particle multiplicity density in Xe–Xe collisions at s NN = 5.44 TeV

In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, dN ch /dη and total charged-particle multiplicity, N$tot\atop{ch}$, in Xe–Xe collisions at a centre-of-mass energy per nucleon–nucleon pair of $ \sqrt{s_{NN}}$=5.44TeV. The measurements are performed as a function of collision centrality over a wide pseudorapidity range of -3.5<η<5. The values of dN ch /dη at mid-rapidity and N$tot\atop{ch}$ for central collisions, normalised to the number of nucleons participating in the collision (N part ) as a function of $ \sqrt{s_{NN}}$ follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of Npart, and up to the 5% most central collisions the trends are the same as the ones observed in Pb–Pb at a similar energy. For more central collisions, the Xe–Xe scaled multiplicities exceed those in Pb–Pb for a similar N part . The results are compared to phenomenological models and theoretical calculations based on different mechanisms for particle production in nuclear collisions. All considered models describe the data reasonably well within 15%.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Smart Meters Enabling Voltage Monitoring and Control Functionalities: The Last-Mile Voltage Stability Issue

It is a demanding yet challenging task to design the next generation of smart meters. This work investigates the new voltage monitoring and control function for the next-generation smart meters, and identifies its added values for power system voltage stability issues. In terms of voltage monitoring, the risk benefit analysis for adding voltage magnitudes to smart meter measurements is presented, and the risk mitigation strategies along with the co-simulation validation via GridLAB-D and NS-3 are proposed, all providing insight into the new function evaluation. In terms of voltage control, a new voltage stability control scheme is developed, which uses voltage measurements from smart meters and utilizes the observability and controllability of distributed energy resources and controllable loads. Different from traditional voltage control schemes focusing on voltage regulation and power quality monitoring from the utility perspective, the proposed control scheme can achieve the maximum real power transfer margin at the end user side, enabling the voltage stability issues being solved at the grid edge, i.e. the last-mile segment. It is the first work that considers voltage monitoring and control collectively for smart meter investment. It can help power engineering community supplement smart meter applications and shape the next-generation smart meters.

42 ENGINEERING↗
DOE OSTI2019

Competitive B2 and B33 Nucleation during Solidification of Ni 50 Zr 50 Alloy: Molecular Dynamics Simulation and Classical Nucleation Theory

We studied the homogenous nucleation of the stoichiometric B2 and B33 phases in the Ni 50 Zr 50 alloy using the persistent embryo method and the classical nucleation theory. The two phases become very close competitors at large supercoolings, which is consistent with the experimental observations. In the case of the B2 phase, the linear temperature dependence of the solid–liquid interface (SLI) free energy extrapolated to the melting temperature leads to the same value as the one obtained from the capillarity fluctuation method (CFM). In the case of the B33 phases, the SLI free energy is also a linear function of temperature at large supercoolings, but the extrapolation to the melting temperature leads to a value which is considerably different from the CFM value. This is persistent with the large anisotropy of the SLI properties of the B33 phase nearby the melting temperature observed in the simulation of the nominally flat interface migration.

36 MATERIALS SCIENCE↗
DOE OSTI2018

pnnl/ZebrafishBMD

ZebrafishBMD: A software tool to perform benchmark dose calculations using toxicity screening data of high-throughput zebrafish assays. High-content imaging of larval zebrafish behavior can be used as a screening approach to rapidly evaluate the relative potential for chemicals to cause toxicity. However, most statistical methods applied to these data transform movement values to incidence-based “hits” and calculate lowest effect levels (LELs), which loses individual fish resolution of behavior and defies hazard ranking due to reliance on applied dose levels. We developed a parallelizable workflow to calculate benchmark dose (BMD) values from dynamic, high-content zebrafish behavior data that scales for high throughput chemical screening. To capture the zebrafish movement response from light to dark stimulus, we summarized time-dependent data using both area under the curve and the immediate change at the transition point into two novel metrics that characterized abnormal behavior as a function of chemical concentration. The BMD workflow was applied to calculate BMD10 values of 1,060 ToxCast chemicals for 24 zebrafish endpoints, including behavior, mortality and morphology. ZebrafishBMD implements the BMD workflow and provides Matlab scripts to read the data (stored in a specific structure) from a .mat file, to calculate the behavioral endpoint values from movement versus time data, to construct concentrationresponse curves, to perform curve-fitting, and to calculate BMD10 values.

Thomas, Dennis↗
DOE OSTI2020

Underlying event properties in pp collisions at $ \sqrt{s} $ = 13 TeV

This article reports measurements characterizing the Underlying Event (UE) associated with hard scatterings at midrapidity (|η| < 0.8) in pp collisions at √s = 13 TeV. The hard scatterings are identified by the leading particle, the charged particle with the highest transverse momentum ( p T l e a d i n g ) in the event. Charged-particle number-densities and summed transverse-momentum densities are measured in different azimuthal regions defined with respect to the leading particle direction: Toward, Transverse, and Away. The Toward and Away regions contain the fragmentation products of the hard scatterings in addition to the UE contribution, whereas particles in the Transverse region are expected to originate predominantly from the UE. The study is performed as a function of p T l e a d i n g with three different p T thresholds for the associated particles, $p^{track}_T$ > 0.15, 0.5, and 1.0 GeV/c. The charged-particle density in the Transverse region rises steeply for low values of $p^{leading}_T$ and reaches a plateau. The results confirm the trend that the charged-particle density in the Transverse region shows a stronger increase with $\sqrt{s}$ an the inclusive charged-particle density at midrapidity. The UE activity is increased by approximately 20% when going from 7 TeV to 13 TeV pp collisions. The plateau in the Transverse region (5 < $p^{leading}_T$ < 40 GeV/c) is further characterized by the probability distribution of its charged-particle multiplicity normalized to its average value (relative transverse activity, R T ) and the mean transverse momentum as a function of R T Experimental results are compared to model calculations using PYTHIA 8 and EPOS LHC. The overall agreement between models and data is within 30%. These measurements provide new insights on the interplay between hard scatterings and the associated UE in pp collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Atomic Layer Deposition for Materials-Based H2 Storage: Opportunities and Limitations

The transportation demands in our growing hydrogen (H2) economy requires robust storage systems. The current commercially implemented technology in fuel cell cars relies on the well-established technology of hydrogen gas compressed to 350-700 bar, depending on the application. The compressed gas tanks in use today are bulky and cost intensive. To address this challenge, material-based storage is one of the long-term alternatives considered and constitutes the focus of this talk. Material-based storage is broadly defined as hydrogen bound to solid materials, with its binding strength varying from physisorption to porous materials, such as zeolites and metal organic frameworks, to chemisorption in (complex) metal hydrides. The ultimate targets set by the U.S. Department of Energy for this technology include a system gravimetric capacity of 6.5 wt% and volumetric capacity of 40 g/L at 100 bar, operating temperatures ranging between -40 C and +40 C and adsorption/desorption timescales of < 5 min. Storage in the form of physisorbed or chemisorbed hydrogen has guided the materials research, which metal- organic framework and (complex) metal hydrides being the most promising materials classes. A variety of these materials have met one or more of the targets, but it has remained elusive for a single material system to meet all these stringent requirements. Nano-encapsulation and low-concentration chemical additives have previously been employed separately to overcome such challenges. Functionalization via atomic layer deposition (ALD), however, offers unique characteristics that make it suitable for both, nano-encapsulation and "doping" with low-concentration additives. This deposition technique has sub-monolayer thickness control, is highly conformal in high-surface area materials and is self-limiting, i.e., once the gas-phase precursor reacts with the available surface sites, the surface reactions stop. In this presentation, we will showcase examples where ALD, more generally vapor-phase functionalization, on (complex) metal hydrides and organic frameworks has improved the material properties for H2 storage. In our first study, Al2O3 was deposited on magnesium borohydride, Mg(BH4)2, at room temperature using trimethylaluminum (TMA) and water. From our findings, encouraging initial results were obtained: the H2 desorption temperature was lowered by 60-120 degrees C, the desorbed gravimetric H2 capacity at temperatures < 250 degrees C was doubled, and the desorption kinetics increased by a factor of ~6 compared to uncoated Mg(BH4)2. However, hydrolysis reactions caused by residual surface -OH groups from the ALD water-pulse degraded the sample substantially. Through this study, the use of TMA was observed to be highly reactive with the Mg(BH4)2 surface species, leading to the strategy of exposing the sample only to TMA. The relative mole fraction of the vapor-phase additive can be precisely controlled with the number of TMA pulses and pulse duration. By tuning these parameters, we show in our second study that 10 pulses of TMA at ambient conditions were able to decrease the H2 desorption temperature by ~100 degrees C while retaining <95 % of its H2 capacity. We applied this approach with other additives such as BBr3, TiCl4 and tetrahydrofuran, and demonstrate that this unique approach opens the door to a new class of molecular additives and catalysts which cannot easily be introduced with conventional mechano-chemical or solvent-based techniques for (complex) metal-hydrides. In the case of metal organic frameworks, ALD is a promising technique to functionalize the pores with metal atoms or functional groups able to tune the gas selectivity and binding energy, for which ~15 kJ/mol has been established as the optimal value for H2 storage in sorbent materials. Vapor-phase techniques such as ALD have numerous benefits over other functionalization tools for H2 storage materials opening innumerable opportunities to the field. To exploit these opportunities, the current limitations on room temperature and water-less ALD processes needs to be overcome which will greatly expand the possibilities of encapsulation and incorporation of additives for organic frameworks and (complex) metal hydrides.

atomic layer deposition↗
DOE OSTI2021

Milestone 1.2.9: Radiolytic Gas Generation Measurements from Helium Backfilled Samples of AA1100 and AA6061 Coupons

Nearly 18 metric tons of aluminum-clad spent nuclear fuel (ASNF) is safely managed by the U.S. Department of Energy (DOE). These assemblies are currently in interim storage, with the intention of extended storage (>50 years) until final disposal. Strategies for the continued safe storage of this material are under evaluation, of which a key criterion is the extent of molecular hydrogen gas (H2) formation from the radiolysis of hydrated (oxy)hydroxide aluminum corrosion layers arising from in-reactor and wet storage conditions. Radiation-induced H2 formation has the potential to compromise cladding and storage canister integrity, in addition to promoting the formation of unfavorable gaseous environments. Consequently, understanding this radiation-induced phenomenon is essential for the development of predictive modeling capabilities to support technical considerations and the identification of radiation related challenges for the extended storage of ASNF. Here, we report radiolytic H2 yields (G-values, G(H2)) from the gamma irradiation of ‘pristine’ and pre-corroded aluminum coupons in helium (He) environments as a function of alloy composition (AA1100 and AA6061), relative humidity, and absorbed gamma dose. Measured yields were lower than corresponding values reported for argon environments, a positive result for proposed extended dry storage strategies that would employ helium as a backfill gas. Interestingly, the presented G(H2)He values are comparable to those previously measured in nitrogen environments, suggesting a He mediated H2 inhibition process, attributed here to Penning ionization.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2019

R-Functions Method in the Mathematical Modeling of Convective Heat Exchange in an Octahedral Fuel Assembly with 37 Fuel Elements

We consider conjugate boundary-value problems of heat exchange for the cases where a viscous incompressible liquid moves through channels with noncanonical cross section flowing around a bundle of rods. The influence of the type of packing on the velocity and temperature distributions is investigated. For the solution, we use the R-functions method in combination with the Ritz variational method. We consider the cases of cyclic, staggered, and rectangular packing of fuel elements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Physical implications of the extrapolation and statistical bootstrap of nucleon structure function ratios F 2 n F 2 p for mirror nuclei He 3 and H 3

A nuclear physics example of statistical bootstrap is used on the MARATHON nucleon structure function ratio data in the quark momentum fraction regions x B → 0 and x B → 1. The extrapolated F 2 ratio as quark momentum fraction x B → 1 is $\frac{F^n_2}{F^p_2}$ → 0.4 ± 0.05 and this value is compared to theoretical predictions. The extrapolated ratio when x B → 0 favors the simple model of isospin symmetry with the complete dominance of sea quarks at low momentum fraction. At high- x B , the proton quark distribution function ratio d/u is derived from the F 2 ratio and found to be d/u → 1/6. Our extrapolated values for both the $\frac{F^n_2}{F^p_2}$ ratio and the d/u parton distribution function ratio are within uncertainties of perturbative QCD values from quark counting, helicity conservation arguments, and a Dyson-Schwinger equation with a contact interaction model. In addition, it is possible to match the statistical bootstrap value to theoretical predictions by allowing two compatible models to act simultaneously in the nucleon wave function. Finally, one such example is nucleon wave functions composed of a linear combination of a quark-diquark state and a three-valence quark correlated state with coefficients that combine to give the extrapolated F 2 ratio at x B = 1.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

Guiding Principles for the Rational Design of Hybrid Materials: Use of DFT Methodology for Evaluating Non‐Covalent Interactions in a Uranyl Tetrahalide Model System

Abstract Together with the synthesis and experimental characterization of 14 hybrid materials containing [UO 2 X 4 ] 2− (X=Cl − and Br − ) and organic cations, we report on novel methods for determining correlation trends in their formation enthalpy (ΔH f ) and observed vibrational signatures. Δ H f values were analyzed through isothermal acid calorimetry and a Density Functional Theory+Thermodynamics (DFT+T) approach with results showing good agreement between theory and experiment. Three factors (packing efficiency, cation protonation enthalpy, and hydrogen bonding energy [ ]) were assessed as descriptors for trends in Δ H f . Results demonstrated a strong correlation between and Δ H f , highlighting the importance of hydrogen bonding networks in determining the relative stability of solid‐state hybrid materials. Lastly, we investigate how hydrogen bonding networks affect the vibrational characteristics of uranyl solid‐state materials using experimental Raman and IR spectroscopy and theoretical bond orders and find that hydrogen bonding can red‐shift U≡O stretching modes. Overall, the tightly integrated experimental and theoretical studies presented here bridge the trends in macroscopic thermodynamic energies and spectroscopic features with molecular‐level details of the geometry and electronic structure. This modeling framework forms a basis for exploring 3D hydrogen bonding as a tunable design feature in the pursuit of supramolecular materials by rational design.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Guiding Principles for the Rational Design of Hybrid Materials: Use of DFT Methodology for Evaluating Non‐Covalent Interactions in a Uranyl Tetrahalide Model System

Abstract Together with the synthesis and experimental characterization of 14 hybrid materials containing [UO 2 X 4 ] 2− (X=Cl − and Br − ) and organic cations, we report on novel methods for determining correlation trends in their formation enthalpy (ΔH f ) and observed vibrational signatures. Δ H f values were analyzed through isothermal acid calorimetry and a Density Functional Theory+Thermodynamics (DFT+T) approach with results showing good agreement between theory and experiment. Three factors (packing efficiency, cation protonation enthalpy, and hydrogen bonding energy [ ]) were assessed as descriptors for trends in Δ H f . Results demonstrated a strong correlation between and Δ H f , highlighting the importance of hydrogen bonding networks in determining the relative stability of solid‐state hybrid materials. Lastly, we investigate how hydrogen bonding networks affect the vibrational characteristics of uranyl solid‐state materials using experimental Raman and IR spectroscopy and theoretical bond orders and find that hydrogen bonding can red‐shift U≡O stretching modes. Overall, the tightly integrated experimental and theoretical studies presented here bridge the trends in macroscopic thermodynamic energies and spectroscopic features with molecular‐level details of the geometry and electronic structure. This modeling framework forms a basis for exploring 3D hydrogen bonding as a tunable design feature in the pursuit of supramolecular materials by rational design.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

On the interplay between magnetic field and anisotropy in holographic QCD

We investigate the combined effects of anisotropy and a magnetic field in strongly interacting gauge theories by the gauge/gravity correspondence. Our main motivation is the quark-gluon plasma produced in off-central heavy-ion collisions which exhibits large anisotropy in pressure gradients as well as large external magnetic fields. We explore two different configurations, with the anisotropy either parallel or perpendicular to the magnetic field, focusing on the competition and interplay between the two. A detailed study of the RG flow in the ground state reveals a rich structure where depending on which of the two, anisotropy or magnetic field, is stronger, intermediate geometries with approximate AdS 4 × $\mathbb{R}$ and AdS 3 × $\mathbb{R}$ 2 factors arise. This competition is also manifest in the phase structure at finite temperature, specifically in the dependence of the chiral transition temperature on anisotropy and magnetic field, from which we infer the presence of inverse magnetic and anisotropic catalyses of the chiral condensate. Finally, we consider other salient observables in the theory, including the quark-antiquark potential, shear viscosity, entanglement entropy and the butterfly velocity. We demonstrate that they serve as good probes of the theory, in particular, distinguishing between the effects of the magnetic field and anisotropy in the ground and plasma states. We also find that the butterfly velocity, which codifies how fast information propagates in the plasma, exhibits a rich structure as a function of temperature, anisotropy and magnetic field, exceeding the conformal value in certain regimes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

Chaos-based potentials in the one-dimensional tight-binding model probed by the inverse participation ratio

Chaos-based potentials are defined and implemented in the one-dimensional tight-binding model as a way of simulating disorder-controlled crystalline lattices. In this setting, disorder is handled with the aid of the chaoticity parameter. The inverse participation ratio (IPR) probes the response of the system to three different such potentials and shows consistent agreement with results given by the Lyapunov exponent Ly: the greater Ly(r) for the chaotic sequence as a function of the chaoticity parameter r, the greater the asymptotic value IPR(r) for the large-system ground state.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Upregulated circular RNA circ{sub 0}016760 indicates unfavorable prognosis in NSCLC and promotes cell progression through miR-1287/GAGE1 axis

Non-small cell lung cancer (NSCLC) is an aggressive malignancy with increasing worldwide incidence and is characterized by dismal prognosis due to its early recurrence and metastasis. Accumulating evidence documented that aberrantly expressed circular RNAs (circRNAs) are critically involved in tumorigenesis. In the current study, we focused on a novel circRNA, circ{sub 0}016760 in NSCLC. qRT-PCR was carried out to determine the expression level of circ{sub 0}016760 in tissue samples and cell lines. The clinical value of circ{sub 0}016760 was also investigated. The functions of circ{sub 0}016760 was explored by CCK-8, colony formation, flow cytometry, Transwell and animal experiments. Luciferase reporter assays were conducted to investigate the association between circ{sub 0}016760 and miR-1287 and miR-1287 and GAGE1. We found that circ{sub 0}016760 was enhanced in NSCLC tissues and cells and the upregulation of circ{sub 0}016760 is associated with advanced TNM stages, lymph node metastasis and adverse prognosis in NSCLC patients. Moreover, circ{sub 0}016760 could significantly promote cell growth and metastatic properties and inhibit cell apoptosis in NSCLC cells. In mechanism, circ{sub 0}016760 functioned as a sponge for miR-1287 and regulated the expression of GAGE1. Subsequently, functional assays illustrated that the oncogenic properties of circ{sub 0}016760 is partly attribute to the regulation of miR-1287/GAGE1 axis. In summary, circ{sub 0}016760/miR-1287/GAGE1 signaling might play vital roles in the tumorigenesis and progression of NSCLC.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Gradient flow based phase-field modeling using separable neural networks

Allen–Cahn equation is a reaction–diffusion equation and is widely used for modeling phase separation. Machine learning methods for solving the Allen–Cahn equation in its strong form suffer from inaccuracies in collocation techniques, errors in computing higher-order spatial derivatives, and the large system size required by the space–time approach. To overcome these challenges, we propose solving the gradient flow of the Ginzburg–Landau free energy functional, which is equivalent to the Allen–Cahn equation, thereby avoiding the second-order spatial derivatives associated with the Allen–Cahn equation. A minimizing movement scheme is employed to solve the gradient flow problem, eliminating the complexities of a space–time approach. We utilize a separable neural network that efficiently represents the phase field through low-rank tensor decomposition. As we use the minimizing movement scheme to numerically solve the gradient flow problem, we thus, refer to the proposed method as the Separable Deep Minimizing Movement (SDMM) method. The evaluation of the functional in the minimizing movement scheme using the Gauss quadrature technique bypasses the inaccuracies associated with collocation techniques traditionally used to solve partial differential equations. A hyperbolic tangent transformation is introduced on the phase field prior to the evaluation of the functional to ensure that it remains strictly bounded within the values of the two phases. For this transformation, theoretical guarantee for energy stability of the minimizing movement scheme is established. Our results suggest that this transformation helps to improve the accuracy and efficiency significantly. The proposed method resolves the challenges faced by state-of-the-art machine learning techniques, outperforming them in both accuracy and efficiency. It is also the first machine learning method to achieve an order of magnitude speed improvement over the finite element method. In addition to its formulation and computational implementation, several case studies illustrate the applicability of the proposed method.

42 ENGINEERING↗
DOE OSTI2018

A comparative study of shear band tracking strategies in three-dimensional finite elements with embedded weak discontinuities

We present a computational framework for the treatment of shear localization in metallic materials under dynamic loading, based on the integration of a shear band tracking strategy into an explicit 3D finite element formulation with embedded weak discontinuities. Within this computational framework, an embedded shear band’s mid-surface is represented by an iso-surface of a level set function, which is obtained by solving a heatconduction type boundary value problem (BVP). The solution of this BVP is carried out either globally over the entire problem domain, or locally at the level of individual elements in the mesh. In this paper, we present a detailed comparison of these global and local algorithmic implementations of the shear band tracking strategy. Numerical results obtained using these two implementations, and using a simplified formulation without shear band tracking, are presented and compared. Moreover, we compare the computational efficiency and parallel scaling performance of the local and global implementations. This comparative study shows that both implementations can simulate the initiation of two independent shear bands and their propagation past each other without merging, whereas only the global implementation can successfully simulate the merging of two branches of a single shear band. This study also confirms that the global implementation is more computationally intensive, since it requires a global system of linear equations associated with the level set BVP to be solved at each time step. Both implementations exhibit very good scalability in domain decomposition-based parallel simulations.

36 MATERIALS SCIENCE↗