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At least 199 records · Page 11

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Metrics for Intercomparison of Remapping Algorithms (MIRA) protocol applied to Earth system models

Abstract. Strongly coupled nonlinear phenomena such as those described by Earth system models (ESMs) are composed of multiple component models with independent mesh topologies and scalable numerical solvers. A common operation in ESMs is to remap or interpolate component solution fields defined on their computational mesh to another mesh with a different combinatorial structure and decomposition, e.g., from the atmosphere to the ocean, during the temporal integration of the coupled system. Several remapping schemes are currently in use or available for ESMs. However, a unified approach to compare the properties of these different schemes has not been attempted previously. We present a rigorous methodology for the evaluation and intercomparison of remapping methods through an independently implemented suite of metrics that measure the ability of a method to adhere to constraints such as grid independence, monotonicity, global conservation, and local extrema or feature preservation. A comprehensive set of numerical evaluations is conducted based on a progression of scalar fields from idealized and smooth to more general climate data with strong discontinuities and strict bounds. We examine four remapping algorithms with distinct design approaches, namely ESMF Regrid (Hill et al., 2004), TempestRemap (Ullrich and Taylor, 2015), generalized moving least squares (GMLS) (Trask and Kuberry, 2020) with post-processing filters, and WLS-ENOR (Li et al., 2020). By repeated iterative application of the high-order remapping methods to the test fields, we verify the accuracy of each scheme in terms of their observed convergence order for smooth data and determine the bounded error propagation using challenging, realistic field data on both uniform and regionally refined mesh cases. In addition to retaining high-order accuracy under idealized conditions, the methods also demonstrate robust remapping performance when dealing with non-smooth data. There is a failure to maintain monotonicity in the traditional L2-minimization approaches used in ESMF and TempestRemap, in contrast to stable recovery through nonlinear filters used in both meshless GMLS and hybrid mesh-based WLS-ENOR schemes. Local feature preservation analysis indicates that high-order methods perform better than low-order dissipative schemes for all test cases. The behavior of these remappers remains consistent when applied on regionally refined meshes, indicating mesh-invariant implementations. The MIRA intercomparison protocol proposed in this paper and the detailed comparison of the four algorithms demonstrate that the new schemes, namely GMLS and WLS-ENOR, are competitive compared to standard conservative minimization methods requiring computation of mesh intersections. The work presented in this paper provides a foundation that can be extended to include complex field definitions, realistic mesh topologies, and spectral element discretizations, thereby allowing for a more complete analysis of production-ready remapping packages.

58 GEOSCIENCES↗

Optimal, centralized dynamic curbside parking space zoning

In this paper we formulate a dynamic mixed integer program for optimally zoning curbside parking spaces subject to transportation policy-inspired constraints and regularization terms. First, we illustrate how given some objective of curb zoning valuation as a function of zone type (paid parking, bus stop, etc.), dynamically rezoning involves unrolling this optimization program over a fixed time horizon. Second, we implement two different solution methods given an example curb zoning valuation. In the first method, we solve long horizon dynamic zoning problems via approximate dynamic programming. In the second method, we employ Dantzig-Wolfe decomposition to break-up the mixed-integer program into a master problem and several sub-problems that can be solved in parallel. This speeds up the computational solve-time of the MIP considerably. We present simulation results and comparisons of the different employed techniques on vehicle arrival-rate data obtained for a neighborhood in downtown Seattle, Washington, USA.

Nazir, Mohammad Nawaf↗

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Kandil, Osama A.↗

Weakly solvating electrolytes: a solvation-centric paradigm for rechargeable metal batteries

Electrolyte design has long followed a solvation-first paradigm that prioritizes solvents capable of maximizing salt dissociation and ionic conductivity, while treating interfacial degradation and rheological limitations as secondary constraints. Although this approach has enabled significant progress in lithium-ion and sodium-ion batteries, it inherently favors solvent-dominated solvation structures that destabilize reactive metal interfaces. Weakly solvating electrolytes (WSEs) offer a fundamentally different strategy. By using solvents with intrinsically low donor strength and minimal electrostatic affinity for cations, WSEs suppress cation–solvent coordination and promote anion-rich solvation shells without relying on salt superconcentration. This shift lowers desolvation barriers, redirects interfacial decomposition pathways, and supports the formation of inorganic-rich, stable interphases. In this review, we discuss the molecular and solvation criteria that distinguish WSEs from conventional and concentrated or locally concentrated electrolyte systems, examine their implementation across different chemistries, and identify unresolved design challenges. WSEs are presented not as a niche formulation, but as a solvation-centric framework for rethinking electrolyte function in metal battery technologies.

Karbak, Mehdi [Pacific Northwest National Laborato↗

A Decomposition-Based Learn-To-Optimize Approach with Feasibility Layer Assistance for Sub-Hourly Unit Commitment

Sub-hourly unit commitment (UC) with 15-min intervals is gaining significant attention as a way to respond rapidly to the fluctuations in electricity supply and demand introduced by renewable resources. However, the increased temporal resolution and complex inter-temporal dependencies pose substantial computational challenges for traditional optimization methods. To this end, this paper explores a decomposition-based learn-to-optimize approach. Building on recent advances in machine learning, our method revisits the long- overlooked Lagrangian relaxation framework, which is a classical decomposition technique that enables tractable subproblem solving. These smaller subproblems are inherently well-suited for machine learning, as their reduced dimensionality and structural regularity allow predictive models to efficiently learn and generalize solution patterns. We thus propose a generic predictive model, which embeds Gated Recurrent Units (GRUs) and Attention in the encoder-decoder structure, and integrate a rule-based feasibility layer to capture temporal dependencies, reduce training effort, and improve feasibility w.r.t. unit-level constraints. Our method has been validated on the IEEE 118-bus system, demonstrating promising performance in solving sub-hourly UC problems efficiently and feasibly.

97 MATHEMATICS AND COMPUTING↗

Measuring the thermal and ionization state of the low- z IGM using likelihood free inference

ABSTRACT We present a new approach to measure the power-law temperature density relationship $T=T_0 (\rho/ \bar{\rho })^{\gamma -1}$ and the UV background photoionization rate $\Gamma _{{{{\rm H\, {\small I}}}}{}}$ of the intergalactic medium (IGM) based on the Voigt profile decomposition of the Ly α forest into a set of discrete absorption lines with Doppler parameter b and the neutral hydrogen column density $N_{\rm H\, {\small I}}$. Previous work demonstrated that the shape of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution is sensitive to the IGM thermal parameters T0 and γ, whereas our new inference algorithm also takes into account the normalization of the distribution, i.e. the line-density dN/dz, and we demonstrate that precise constraints can also be obtained on $\Gamma _{{{{\rm H\, {\small I}}}}{}}$. We use density-estimation likelihood-free inference (DELFI) to emulate the dependence of the $b-N_{{{{\rm H\, {\small I}}}}{}}$ distribution on IGM parameters trained on an ensemble of 624 nyx hydrodynamical simulations at z = 0.1, which we combine with a Gaussian process emulator of the normalization. To demonstrate the efficacy of this approach, we generate hundreds of realizations of realistic mock HST/COS data sets, each comprising 34 quasar sightlines, and forward model the noise and resolution to match the real data. We use this large ensemble of mocks to extensively test our inference and empirically demonstrate that our posterior distributions are robust. Our analysis shows that by applying our new approach to existing Ly α forest spectra at z ≃ 0.1, one can measure the thermal and ionization state of the IGM with very high precision ($\sigma _{\log T_0} \sim 0.08$ dex, σγ ∼ 0.06, and $\sigma _{\log \Gamma _{{{{\rm H\, {\small I}}}}{}}} \sim 0.07$ dex).

79 ASTRONOMY AND ASTROPHYSICS↗

Constraints on triple oxygen isotope kinetics

The general assumption that systems are in equilibrium is convenient, but imperfect. Instead, the partial or full expression of kinetic reaction steps may need to be determined. Using an isotope fractionation Monte-Carlo model under the harmonic approximation (Figure 1 envelopes), we find the range of kinetic isotope effects (i.e., resulting from unidirectional chemical reactions) contains and exceeds the range of accessible equilibrium isotope effects. For the 16O-17O-18O system, accessible kinetic isotope effects can yield Δ′17O variations as large 0.8‰ from a single kinetic fractionation step. Reactions that yield the largest deviations from equilibrium are those with the largest molecular mass difference between decomposition fragments, typically the two products, such as a gas and solid generated from the thermal decomposition of an initial solid. For example, previously published experiments on the thermal decomposition of calcite (CaCO3) and dehydroxylation of brucite (Mg(OH)2) are matched by density functional theory models of each kinetic isotope effect, thus revealing their origin in mass-dependent reaction. Beyond oxygen, our approach applies to any system with more than two isotopes.

Oxygen isotopes↗

Global models: Robot sensing, control, and sensory-motor skills

Robotics research has begun to address the modeling and implementation of a wide variety of unstructured tasks. Examples include automated navigation, platform servicing, custom fabrication and repair, deployment and recovery, and science exploration. Such tasks are poorly described at onset; the workspace layout is partially unfamiliar, and the task control sequence is only qualitatively characterized. The robot must model the workspace, plan detailed physical actions from qualitative goals, and adapt its instantaneous control regimes to unpredicted events. Developing robust representations and computational approaches for these sensing, planning, and control functions is a major challenge. The underlying domain constraints are very general, and seem to offer little guidance for well-bounded approximation of object shape and motion, manipulation postures and trajectories, and the like. This generalized modeling problem is discussed, with an emphasis on the role of sensing. It is also discussed that unstructured tasks often have, in fact, a high degree of underlying physical symmetry, and such implicit knowledge should be drawn on to model task performance strategies in a methodological fashion. A group-theoretic decomposition of the workspace organization, task goals, and their admissible interactions are proposed. This group-mechanical approach to task representation helps to clarify the functional interplay of perception and control, in essence, describing what perception is specifically for, versus how it is generically modeled. One also gains insight how perception might logically evolve in response to needs of more complex motor skills. It is discussed why, of the many solutions that are often mathematically admissible to a given sensory motor-coordination problem, one may be preferred over others.

Schenker, Paul S.↗

Quarkyonic matter equation of state in beta-equilibrium

Quark matter may appear due to a hadronic-quark transition in the core of a hybrid star. Quarkyonic matter is an approach in which both quarks and nucleons appear as quasiparticles in a crossover transition, and provides an explicit realization of early ideas concerning quark matter (e.g., the MIT bag model). This description has recently been employed by McLerran and Reddy to model chargeless (pure neutron) matter with an approach that has the virtue that the speed of sound rises quickly at a neutron-quark transition so as to satisfy observational constraints on the neutron star maximum mass (≳ 2 $M_⊙$) and the radius of a 1.4 $M_⊙$ star ($R_{1.4}$ ≲ 13.5 km). Traditional models involving first-order transitions result in softer pressure-energy density relations that have difficulty satisfying these constraints except with very narrow choices of parameters. Here, we propose a variation of quarkyonic matter involving protons and leptons whose energy can be explicitly minimized to achieve both chemical and beta equilibrium, which cannot be done in the chargeless formulation. Quarkyonic stellar models are able to satisfy observed mass and radius constraints with a wide range of model parameters, avoiding the obligatory fine-tuning of conventional hybrid star models, including requiring the transition density to be very close to the nuclear saturation density. Our formulation fits experimental and theoretical properties of the nuclear symmetry energy and pure neutron matter, and contains as few as three free parameters. This makes it an ideal tool for the study of high-density matter that is an efficient alternative to piecewise polytrope or spectral decomposition methods.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

How deep should we go to understand roots at the top of the world?

Harsh environmental conditions and the short summers of northern, high-latitude biomes impose unique constraints on the plants that live in the arctic tundra and the boreal forest. To escape the harsh aboveground environment, plants in these habitats often allocate a large portion of their biomass belowground to facilitate nutrient acquisition. In turn, the proximity of living plant roots to vast stores of sequestered soil carbon in these biomes means that shifts in rooting depth distribution and the size of the root–soil interface could significantly contribute to ongoing climate change. Indeed, plant ‘priming’ of rhizosphere decomposition via root exudation, particularly from shallowly distributed roots, can lead to losses of carbon from tundra soils. While we have a hard-won understanding of the distribution of plant communities across the arctic tundra and the boreal forest from direct field observations scaled to the landscape level using climate-informed mapping techniques (i.e. the Circumpolar Arctic Vegetation Map (CAVM); Walker et al. , 2005), these vegetation maps are only the tip of the iceberg (Iversen et al. , 2015). Root form and function remain hidden beneath the land surface. In an article recently published in New Phytologist , Blume-Werry et al. (2023, 10.1111/nph.18998) asked whether rooting depth distribution, and ensuing carbon emissions, could be inferred from commonly used vegetation mapping classifications across the pan-Arctic. An important question to guide our understanding, mapping, and prediction of belowground characteristics and ecosystem feedbacks at the top of the world. Unfortunately, they found that the answer was ‘not quite’. While rooting depth distribution varied demonstrably, in turn causing substantial changes in modeled carbon emissions via rhizosphere ‘priming’, variation across rooting depth profiles did not correspond with vegetation mapping classes. If we are unable to predict belowground rooting depth distributions across large spatial scales by leveraging aboveground vegetation community distributions, how then should belowground researchers proceed?

59 BASIC BIOLOGICAL SCIENCES↗

Effect of contrast on the perception of direction of a moving pattern

A series of experiments examining the effect of contrast on the perception of moving plaids was performed to test the hypothesis that the human visual system determines the direction of a moving plaid in a two-staged process: decomposition into component motion followed by application of the intersection-of-contraints rule. Although there is recent evidence that the first tenet of the hypothesis is correct, i.e., that plaid motion is initially decomposed into the motion of the individual grating components, the nature of the second-stage combination rule has not yet been established. It was found that when the gratings within the plaid are of different contrast the preceived direction is not predicted by the intersection-of-constraints rule. There is a strong (up to 20 deg) bias in the direction of the higher-constrast grating. A revised model, which incorporates a contrast-dependent weighting of perceived grating speed as observed for one-dimensional patterns, can quantitatively predict most of the results. The results are then discussed in the context of various models of human visual motion processing and of physiological responses of neurons in the primate visual system.

Stone, L. S.↗

Linkages between terrestrial ecosystems and the atmosphere

The primary research issue in understanding the role of terrestrial ecosystems in global change is analyzing the coupling between processes with vastly differing rates of change, from photosynthesis to community change. Representing this coupling in models is the central challenge to modeling the terrestrial biosphere as part of the earth system. Terrestrial ecosystems participate in climate and in the biogeochemical cycles on several temporal scales. Some of the carbon fixed by photosynthesis is incorporated into plant tissue and is delayed from returning to the atmosphere until it is oxidized by decomposition or fire. This slower (i.e., days to months) carbon loop through the terrestrial component of the carbon cycle, which is matched by cycles of nutrients required by plants and decomposers, affects the increasing trend in atmospheric CO2 concentration and imposes a seasonal cycle on that trend. Moreover, this cycle includes key controls over biogenic trace gas production. The structure of terrestrial ecosystems, which responds on even longer time scales (annual to century), is the integrated response to the biogeochemical and environmental constraints that develop over the intermediate time scale. The loop is closed back to the climate system since it is the structure of ecosystems, including species composition, that sets the terrestrial boundary condition in the climate system through modification of surface roughness, albedo, and, to a great extent, latent heat exchange. These separate temporal scales contain explicit feedback loops which may modify ecosystem dynamics and linkages between ecosystems and the atmosphere. The long-term change in climate, resulting from increased atmospheric concentrations of greenhouse gases (e.g., CO2, CH4, and nitrous oxide (N2O)) will further modify the global environment and potentially induce further ecosystem change. Modeling these interactions requires coupling successional models to biogeochemical models to physiological models that describe the exchange of water, energy, and biogenic trace gases between the vegetation and the atmosphere at fine time scales. There does not appear to be any obvious way to allow direct reciprocal coupling of atmospheric general circulation models (GCM's), which inherently run with fine time steps, to ecosystem or successional models, which have coarse temporal resolution, without the interposition of physiological canopy models. This is equally true for biogeochemical models of the exchange of carbon dioxide and trace gases. This coupling across time scales is nontrivial and sets the focus for the modeling strategy.

Bretherton, Francis↗

Implementation of non-hierarchic decomposition for multidisciplinary system optimization

Modular prototype software has been designed to implement the method of non-hierarchic decomposition for optimization of coupled, multidisciplinary systems. The modules are intended to be run concurrently on separate processors and to automate all aspects of the method except for the objective function and subspace analysis subroutines, which are inherently problem-dependent. Minimal analysis of problem structure is required, since the software is designed to handle arbitrary system coupling with full generality. The basic feasibility of the approach has been confirmed using six example problems, with varying degrees of lateral coupling among the subspace constraints and dependent variables. Results are given for two of the test problems.

Eason, Ernest D.↗

Dynamic Analysis of Reynolds Number Effects on Trailing Edge Transonic Vortex Shedding and Its Impact on Turbine Blade Aerodynamic Performance

Time-resolved, high-speed self-aligned focusing schlieren images were acquired in the NASA Glenn Research Center Transonic Turbine Blade Cascade facility to help understand the aerodynamic behavior of high-pressure, thick trailing edge turbine blades. The trailing edge thickness of 9% of axial chord tested represents simulated ceramic matrix composite fabrication constraints, which was verified previously to possess a high-loss flow regime at high inlet turbulence conditions over a narrow range of Reynolds numbers and at a fixed design exit Mach number of 0.74. Our high-speed images, which were acquired at 10 distinct Reynolds numbers, show a significant increase in energy from flow oscillations due to transonic vortex shedding at Reynolds numbers corresponding to the high loss conditions. For those conditions, strong acoustic waves turn into shock waves. Spectral Proper Orthogonal Decomposition of the high-speed images shows acoustic waves from trailing edge vortex shedding at all conditions, with increased spectral energy at the high-loss conditions and slightly increasing frequency (about 6%) as a function of Reynolds number. Analysis of potential feedback timing is performed using velocity fields from a previous LES simulation, considering different feedback mechanisms. Most noteworthy is the acoustic/shock-boundary layer interaction mechanism on the suction surface at the blade geometric throat, which likely plays an important role in realistic curved blade passages.

Trailing Edge↗

Factorization of Binary Matrices: Rank Relations, Uniqueness and Model Selection of Boolean Decomposition

The application of binary matrices are numerous. Representing a matrix as a mixture of a small collection of latent vectors via low-rank decomposition is often seen as an advantageous method to interpret and analyze data. In this work, we examine the factorizations of binary matrices using standard arithmetic (real and nonnegative) and logical operations (Boolean and $\mathbb{Z}$ 2 ). We examine the relationships between the different ranks, and discuss when factorization is unique. In particular, we characterize when a Boolean factorization X = W$\land$H has a unique W, a unique H (for a fixed W), and when both W and H are unique, given a rank constraint. We introduce a method for robust Boolean model selection, called BMFk, and show on numerical examples that BMFk not only accurately determines the correct number of Boolean latent features but reconstruct the pre-determined factors accurately.

97 MATHEMATICS AND COMPUTING↗

Constraints on triple oxygen isotope kinetics

Triple oxygen isotope measurements have been used as tracers for classifying meteorites, as indicators of atmospheric chemistry and as a proxy for primary productivity among other uses. These utilities rely on the mass dependency of most chemical reactions: δ17O is proportional to δ18O by roughly a factor of 0.5. However,in detail it is known that mass-dependency factorsvary. Constraints on mass dependency are well established for equilibrium isotope effects, but similar constraints for kinetic isotope effects are lacking.Here, we provide constraints for isotope effects generated by unidirectional chemical reactions (i.e. kinetic isotope effects, KIEs). A simplified Monte Carlo model is used to estimatethe range of kinetic isotope effects. It is found that the range of KIEs exceeds the range of equilibrium isotope effects such that some mass dependent kinetic isotope effects could be mistaken for being mass-independent. For the16O-17O-18O system,Δ′17Ovariations as large 0.8‰ can be generated from a single reaction step. Two case studies from published literature, on the thermal decomposition of calcite (CaCO3) and brucite (Mg(OH)2), are used to test the extreme limits of the modeled results. Isotope fractionationsgenerated fromdensity functional theory models of the surface reaction steps are shownto match the published data. The fractionation models are strictly mass dependent thus this result suggests thermal decomposition of calcite is also mass dependent. Although oxygen is the focus here, our approach applies to any system with more than two isotopes.

J. A. Hayles↗

Cognition and procedure representational requirements for predictive human performance models

Models and modeling environments for human performance are becoming significant contributors to early system design and analysis procedures. Issues of levels of automation, physical environment, informational environment, and manning requirements are being addressed by such man/machine analysis systems. The research reported here investigates the close interaction between models of human cognition and models that described procedural performance. We describe a methodology for the decomposition of aircrew procedures that supports interaction with models of cognition on the basis of procedures observed; that serves to identify cockpit/avionics information sources and crew information requirements; and that provides the structure to support methods for function allocation among crew and aiding systems. Our approach is to develop an object-oriented, modular, executable software representation of the aircrew, the aircraft, and the procedures necessary to satisfy flight-phase goals. We then encode in a time-based language, taxonomies of the conceptual, relational, and procedural constraints among the cockpit avionics and control system and the aircrew. We have designed and implemented a goals/procedures hierarchic representation sufficient to describe procedural flow in the cockpit. We then execute the procedural representation in simulation software and calculate the values of the flight instruments, aircraft state variables and crew resources using the constraints available from the relationship taxonomies. The system provides a flexible, extensible, manipulative and executable representation of aircrew and procedures that is generally applicable to crew/procedure task-analysis. The representation supports developed methods of intent inference, and is extensible to include issues of information requirements and functional allocation. We are attempting to link the procedural representation to models of cognitive functions to establish several intent inference methods including procedural backtracking with concurrent search, temporal reasoning, and constraint checking for partial ordering of procedures. Finally, the representation is being linked to models of human decision making processes that include heuristic, propositional and prescriptive judgement models that are sensitive to the procedural content in which the valuative functions are being performed.

Corker, K.↗