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Field-gradient partitioning for fracture and frictional contact in the material point method: Field-gradient partitioning for fracture and frictional contact in the material point method [Fracture and frictional contact in material point method using damage-field gradients for velocity-field partitioning]
Contact and fracture in the material point method require grid-scale enrichment or partitioning of material into distinct velocity fields to allow for displacement or velocity discontinuities at a material interface. We present a new method which a kernel-based damage field is constructed from the particle data. The gradient of this field is used to dynamically repartition the material into contact pairs at each node. Our approach avoids the need to construct and evolve explicit cracks or contact surfaces and is therefore well suited to problems involving complex 3-D fracture with crack branching and coalescence. A straightforward extension of this approach permits frictional ‘self-contact’ between surfaces that are initially part of a single velocity field, enabling more accurate simulation of granular flow, porous compaction, fragmentation, and comminution of brittle materials. Finally, numerical simulations of self contact and dynamic crack propagation are presented to demonstrate the accuracy of the approach.
Metal-silicate Partitioning and Its Role in Core Formation and Composition on Super-Earths
We use a thermodynamic framework for silicate-metal partitioning to determine the possible compositions of metallic cores on super-Earths. We compare results using literature values of the partition coefficients of Si and Ni, as well as new partition coefficients calculated using results from laser shock-induced melting of powdered metal-dunite targets at pressures up to 276 GPa, which approaches those found within the deep mantles of super-Earths. We find that larger planets may have little to no light elements in their cores because the Si partition coefficient decreases at high pressures. The planet mass at which this occurs will depend on the metal-silicate equilibration depth. We also extrapolate the equations of state (EOS) of FeO and FeSi alloys to high pressures, and present mass–radius diagrams using self-consistent planet compositions assuming equilibrated mantles and cores. We confirm the results of previous studies that the distribution of elements between mantle and core will not be detectable from mass and radius measurements alone. While observations may be insensitive to interior structure, further modeling is sensitive to compositionally dependent properties, such as mantle viscosity and core freeze-out properties. We therefore emphasize the need for additional high pressure measurements of partitioning as well as EOSs, and highlight the utility of the Sandia Z-facilities for this type of work.
Understanding the Applicability of Gas/Particle Partitioning Theory to SOA using Novel Chemically-Speciated Partitioning Measurements (Final Report)
The main objective of this research grant project was to investigate the physical-chemical processes and properties of particles and partitioning gases that influence gas/particle (G/P) partitioning and timescales for equilibration, to directly determine the conditions under which equilibrium G/P partitioning theory can be applied to secondary organic aerosol (SOA). SOA constitutes a major component of submicron particles in the atmosphere, which have important implications for air quality, human and ecosystem health, radiation balance, and climate; however SOA formation, evolution and losses are not well understood. Use of novel on-line measurements of chemically-speciated partitioning measurements of both gas-phase and particle-phase components was a central component to advancing these scientific goals. The key approach was to conduct environmental chamber studies with systems of increasing complexity to determine G/P partitioning rates and equilibrium states for chemically-speciated SOA components. The project builds on our previous work on gas-wall partitioning that must be understood in order to study G/P partitioning in chambers, and to help extrapolate the results to be atmospherically relevant. The goal was to employ measurements and modeling to systematically determine when G/P partitioning theory accurately describes the distribution of oxidized organic compounds in the gas and aerosol phases, and when and why it does not (e.g., aerosol phase-state kinetic limitations, non-ideal mixing, phase separation, oligomer formation,), for chemical and physical conditions typically found throughout the continental boundary layer.
New Linear Partitioning Models Based on Experimental Water: Supercritical CO 2 Partitioning Data of Selected Organic Compounds
Partitioning coefficients of organic compounds between water and supercritical CO2 (sc-CO2) are necessary to assess the risk of migration of these chemicals from subsurface CO2 storage sites. Despite the large number of potential organic contaminants, the current data set of published water-sc-CO2 partitioning coefficients is very limited. Here, the partitioning coefficients of thiophene, pyrrole, and anisole were measured in situ over a range of temperatures and pressures using a novel pressurized batch reactor system with dual spectroscopic detectors: a near infrared spectrometer for measuring the organic analyte in the CO2 phase, and a UV detector for quantifying the analyte in the aqueous phase. Our measured partitioning coefficients followed expected trends based on volatility and aqueous solubility. The partitioning coefficients and literature data were then used to update a published poly-parameter linear free energy relationship and to develop five new linear free energy relationships for predicting water-sc-CO2 partitioning coefficients. Four of the models targeted a single class of organic compounds. Unlike models that utilize Abraham solvation parameters, the new relationships use vapor pressure and aqueous solubility of the organic compound at 25 °C and CO2 density to predict partitioning coefficients over a range of temperature and pressure conditions. The compound class models provide better estimates of partitioning behavior for compounds in that class than the model built for the entire dataset.
Quantitative investigation into the influence of temperature on carbide and austenite evolution during partitioning of a quenched and partitioned steel
Here, the influence of partitioning temperature on microstructural evolution during quenching and partitioning was investigated in a 0.38C-1.54Mn-1.48Si wt.% steel using Mössbauer spectroscopy and transmission electron microscopy. η-carbide formation occurs in the martensite during the quenching, holding, and partitioning steps. More effective carbon partitioning from martensite to austenite was observed at 450 than 400°C, resulting in lower martensite carbon contents, less carbide formation, and greater retained austenite amounts for short partitioning times. Conversely, greater austenite decomposition occurs at 450°C for longer partitioning times. Lastly, cementite forms during austenite decomposition and in the martensite for longer partitioning times at 450°C.
$\mathrm{RADICAL}$-Pilot and $\mathrm{PMIx}$/$\mathrm{PRRTE}$: Executing Heterogeneous Workloads at Large Scale on Partitioned $\mathrm{HPC}$ Resources
Execution of heterogeneous workflows on high-performance computing (HPC) platforms present unprecedented resource management and execution coordination challenges for runtime systems. Task heterogeneity increases the complexity of resource and execution management, limiting the scalability and efficiency of workflow execution. Re-source partitioning and distribution of tasks execution over portioned re-sources promises to address those problems but we lack an experimental evaluation of its performance at scale. Here this paper provides a performance evaluation of the Process Management Interface for Exascale (PMIx) and its reference implementation PRRTE on the leadership-class HPC plat-form Summit, when integrated into a pilot-based runtime system called RADICAL-Pilot. We partition resources across multiple PRRTE Distributed Virtual Machine (DVM) environments, responsible for launching tasks via the PMIx interface. We experimentally measure the work-load execution performance in terms of task scheduling/launching rate and distribution of DVM task placement times, DVM startup and termination overheads on the Summit leadership-class HPC platform. Integrated solution with PMIx/PRRTE enables using an abstracted, standardized set of interfaces for orchestrating the launch process, dynamic process management and monitoring capabilities. It extends scaling capabilities allowing to overcome a limitation of other launching mechanisms (e.g., JSM/LSF). Explored different DVM setup configurations provide insights on DVM performance and a layout to leverage it. Our experimental results show that heterogeneous workload of 65,500 tasks on 2048 nodes, and partitioned across 32 DVMs, runs steady with resource utilization not lower than 52%. While having less concurrently executed tasks resource utilization is able to reach up to 85%, based on results of heterogeneous workload of 8200 tasks on 256 nodes and 2 DVMs.
Off-shell Partition Functions in 3d Gravity
We explore three-dimensional gravity with negative cosmological constant via canonical quantization. We focus on chiral gravity which is related to a single copy of PSL(2,R) Chern-Simons theory and is simpler to treat in canonical quantization. Its phase space for an initial value surface Σ is given by the appropriate moduli space of Riemann surfaces. We use geometric quantization to compute partition functions of chiral gravity on three-manifolds of the form Σ×S 1 , where Σ can have asymptotic boundaries. Most of these topologies do not admit a classical solution and are thus not amenable to a direct semiclassical path integral computation. We use an index theorem that expresses the partition function as an integral of characteristic classes over phase space. In the presence of n asymptotic boundaries, we use techniques from equivariant cohomology to localize the integral to a finite-dimensional integral over $\overline{M}$ g,n , which we evaluate in low genus cases. Higher genus partition functions quickly become complicated since they depend in an oscillatory way on Newton's constant. There is a precise sense in which one can isolate the non-oscillatory part which we call the fake partition function. We establish that there is a topological recursion that computes the fake partition functions for arbitrary Riemann surfaces Σ. As a result, there is a scaling limit in which the model reduces to JT gravity and our methods give a novel way to compute JT partition functions via equivariant localization.
Evaluation of Carbon Partitioning in New Generation of Quench and Partitioning (Q&P) Steels
In this study, quenching and partitioning (Q&P) and a novel combined process of hot straining (HS) and Q&P (HSQ&P) treatments have been applied to a TRIP-assisted steel in a Gleeble®3S50 thermomechanical simulator. The heat treatments involved intercritical annealing at 800 °C and a two-step Q&P heat treatment with a partitioning time of 100 seconds at 400 °C. The “optimum” quench temperature of 318 °C was selected according to the constrained carbon equilibrium (CCE) criterion. The effects of high-temperature deformation (isothermal and non-isothermal) on the carbon enrichment of austenite, carbide formation, and the strain-induced transformation to ferrite (SIT) mechanism were investigated. Carbon partitioning from supersaturated martensite into austenite and carbide precipitation were confirmed by means of atom probe tomography (APT) and scanning transmission electron microscopy (STEM). Austenite carbon enrichment was clearly observed in all specimens, and in the HSQ&P samples, it was significantly greater than in Q&P, suggesting an additional carbon partitioning to austenite from ferrite formed by the deformation-induced austenite-to-ferrite transformation (DIFT) phenomenon. By APT, the carbon accumulation at austenite/martensite interfaces was observed, with higher values for HSQ&P deformed isothermally (≈ 11 at. pct), when compared with non-isothermal HSQ&P (≈ 9.45 at. pct) and Q&P (≈ 7.6 at. pct). Finally, a local Mn enrichment was observed in a ferrite/austenite interface, indicating ferrite growth under local equilibrium with negligible partitioning (LENP).
Stochastic modeling of phosphorus transport in the Three Gorges Reservoir by incorporating variability associated with the phosphorus partition coefficient
Phosphorus (P) fate and transport plays a crucial role in the ecology of rivers and reservoirs in which eutrophication is limited by P. A key uncertainty in models used to help manage P in such systems is the partitioning of P to suspended and bed sediments. By analyzing data from field and laboratory experiments, we stochastically characterize the variability of the partition coefficient (Kd) and derive spatio-temporal solutions for P transport in the Three Gorges Reservoir (TGR). We formulate a set of stochastic partial different equations (SPDEs) to simulate P transport by randomly sampling Kd from the measured distributions, to obtain statistical descriptions of the P concentration and retention in the TGR. The correspondence between predicted and observed P concentrations and P retention in the TGR combined with the ability to effectively characterize uncertainty suggests that a model that incorporates the observed variability can better describe P dynamics and more effectively serve as a tool for P management in the system. This study highlights the importance of considering parametric uncertainty in estimating uncertainty/variability associated with simulated P transport.
Charge partitioning and anomalous hole doping in Rh-doped Sr 2 IrO 4
The simultaneous presence of sizable spin-orbit interactions and electron correlations in iridium oxides has led to predictions of novel ground states including Dirac semimetals, Kitaev spin liquids, and superconductivity. Electron and hole doping studies of spin-orbit assisted Mott insulator Sr 2 IrO 4 are being intensively pursued due to extensive parallels with the La 2 CuO 4 parent compound of cuprate superconductors. In particular, the mechanism of charge doping associated with replacement of Ir with Rh ions remains controversial with profound consequences for the interpretation of electronic structure and transport data. Using x-ray absorption near edge structure measurements at the Rh L, K, and Ir L edges we observe anomalous evolution of charge partitioning between Rh and Ir with Rh doping. The partitioning of charge between Rh and Ir sites progresses in a way that holes are initially doped into the J eff = 1/2 band at low x only to be removed from it at higher x values. Furthermore, this anomalous hole doping naturally explains the reentrant insulating phase in the phase diagram of Sr 2 Ir 1–x Rh x O 4 and ought to be considered when searching for superconductivity and other emergent phenomena in iridates doped with 4d elements.
Microstructure and partitioning behavior characteristics in low carbon steels treated by hot-rolling direct quenching and dynamical partitioning processes
In this work, a new process and composition design are proposed for “quenching and partitioning” or Q&P treatment. Three low carbon steels were treated by hot-rolling direct quenching and dynamical partitioning processes (DQ&P). The effects of proeutectoid ferrite and carbon concentration on microstructure evolution and mechanical properties were investigated. The present work obtained DQ&P prototype steels with good mechanical properties and established a new notion on compositions for Q&P processing. Microstructures were characterized by means of electro probe microanalyzer (EPMA), scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), transmission electron microscopy (TEM) and X-ray diffraction (XRD), especially the morphology and size of retained austenite. Mechanical properties were measured by uniaxial tensile tests. The results indicated that introducing proeutectoid ferrite can increase the volume fraction of retained austenite and thus improve mechanical properties. TEM observation showed that retained austenite included the film-like inter-lath austenite and blocky austenite located in martensite/ferrite interfaces or surrounded by ferrites. It was interesting that when the carbon concentration is as low as ~ 0.078%, the film-like inter-lath untransformed austenite cannot be stabilized to room temperature and almost all of them transformed into twin martensite. The blocky retained austenite strengthened the interfaces and transformed into twin martensite during the tensile deformation process. The PSEs of specimens all exceeded 20 GPa.%. - Highlights: •This study focused on a new process: Q&P process applying dynamical partitioning. •Ferrite can increase the volume fraction of retained austenite. •The film-like austenite and the blocky austenite were observed. •The low carbon steels treated by new process reached PSEs higher than 20 GPa.%.
Reverse energy partitioning—An efficient algorithm for computing the density of states, partition functions, and free energy of solids
A robust and model free Monte Carlo simulation method is proposed to address the challenge in computing the classical density of states and partition function of solids. Starting from the minimum configurational energy, the algorithm partitions the entire energy range in the increasing energy direction (“upward”) into subdivisions whose integrated density of states is known. When combined with the density of states computed from the “downward” energy partitioning approach [H. Do, J. D. Hirst, and R. J. Wheatley, J. Chem. Phys. 135, 174105 (2011)], the equilibrium thermodynamic properties can be evaluated at any temperature and in any phase. The method is illustrated in the context of the Lennard-Jones system and can readily be extended to other molecular systems and clusters for which the structures are known.
A stable partitioned FSI algorithm for incompressible flow and deforming beams
An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame using two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature.
Composition and Pressure Effects on Partitioning of Ferrous Iron in Iron-Rich Lower Mantle Heterogeneities
Both seismic observations of dense low shear velocity regions and models of magma ocean crystallization and mantle dynamics support enrichment of iron in Earth’s lowermost mantle. Physical properties of iron-rich lower mantle heterogeneities in the modern Earth depend on distribution of iron between coexisting lower mantle phases (Mg,Fe)O magnesiowüstite, (Mg,Fe)SiO3 bridgmanite, and (Mg,Fe)SiO3 post-perovskite. The partitioning of iron between these phases was investigated in synthetic ferrous-iron-rich olivine compositions (Mg0.55Fe0.45)2SiO4 and (Mg0.28Fe0.72)2SiO4 at lower mantle conditions ranging from 33–128 GPa and 1900–3000 K in the laser-heated diamond anvil cell. The resulting phase assemblages were characterized by a combination of in situ X-ray diffraction and ex situ transmission electron microscopy. The exchange coefficient between bridgmanite and magnesiowüstite decreases with pressure and bulk Fe# and increases with temperature. Thermodynamic modeling determines that incorporation and partitioning of iron in bridgmanite are explained well by excess volume associated with Mg-Fe exchange. Partitioning results are used to model compositions and densities of mantle phase assemblages as a function of pressure, FeO-content and SiO2-content. Unlike average mantle compositions, iron-rich compositions in the mantle exhibit negative dependence of density on SiO2-content at all mantle depths, an important finding for interpretation of deep lower mantle structures.
Accurate Compression of Tabulated Chemistry Models with Partition of Unity Networks
Tabulated chemistry models are widely used to simulate large-scale turbulent fires in applications including energy generation and fire safety. Tabulation via piecewise Cartesian interpolation suffers from the curse-of-dimensionality, leading to a prohibitive exponential growth in parameters and memory usage as more dimensions are considered. Artificial neural networks (ANNs) have attracted attention for constructing surrogates for chemistry models due to their ability to perform high-dimensional approximation. However, due to well-known pathologies regarding the realization of suboptimal local minima during training, in practice they do not converge and provide unreliable accuracy. Partition of unity networks (POUnets) are a recently introduced family of ANNs which preserve notions of convergence while performing high-dimensional approximation, discovering a mesh-free partition of space which may be used to perform optimal polynomial approximation. In this work, we assess their performance with respect to accuracy and model complexity in reconstructing unstructured flamelet data representative of nonadiabatic pool fire models. Our results show that POUnets can provide the desirable accuracy of classical spline-based interpolants with the low memory footprint of traditional ANNs while converging faster to significantly lower errors than ANNs. For example, we observe POUnets obtaining target accuracies in two dimensions with 40 to 50 times less memory and roughly double the compression in three dimensions. We also address the practical matter of efficiently training accurate POUnets by studying convergence over key hyperparameters, the impact of partition/basis formulation, and the sensitivity to initialization.