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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.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Quantum chemically calculated Abraham parameters for quantifying and predicting polymer hydrophobicity

The leakage and accumulation of plastic in the environment is a significant and growing problem with numerous detrimental impacts and has led to a push toward the design and development of more environmentally benign materials. To this end, we have developed a quantum chemistry-based model for predicting the mobility of polymer materials from molecular structure. Hydrophobicity is used as a surrogate for mobility given that hydrophobic interactions drive much of the partitioning of contaminants in and out of various environmentally relevant compartments. To model polymer hydrophobicity, we adjusted a previously developed Quantum Chemically Calculated Abraham Parameter model to calculate Abraham parameters of small molecules from molecular structure information. The resulting model predicted the octanol-water partition coefficient (K OW ) of polymer repeating units with a root mean square error (RMSE) of 0.48 (log scale). Additionally, the hydrophobicity of high molecular weight polymer materials was captured through solubility parameters and Nile red staining experiments from the literature and predicted with RMSEs of 1.21 (J/cc) 0.5 and 3.42 nm, respectively. Finally, to test the environmental applicability of the model, the relative adsorption capacity of three polymers was predicted and used to unify sorption isotherms across multiple sorbates and polymer sorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

High-performance reversible adhesive from PET waste for underwater, structural, and pressure-sensitive applications

Developing versatile, tough, and sustainable adhesives that function effectively in both wet and dry environments is a major challenge. Here, we report a bioinspired design for versatile, tough, and reversible adhesives upcycled from consumer poly(ethylene terephthalate) (PET) waste. Our approach uses solvent-free, room-temperature dynamic cross-linking of deconstructed PET macromonomers with a diacetoacetate cross-linker, generating a dynamic, vinylogous urethane–bonded, amphiphilic adhesive. Tunable cross-linker concentration and amphiphilicity yield versatile adhesives suitable for underwater, structural, and pressure-sensitive applications on diverse substrates. Our adhesive exhibits high lap-shear strength and work of debonding under both wet and dry conditions, outperforming common commercial adhesives. The dynamic bonds enable thermal repair, on-demand multicycle debonding/rebonding, facile removal, and chemical recycling. Our strategy of transforming plastic waste into versatile, tough, and reversible adhesives offers a sustainable solution for both plastic waste management and next-generation adhesive design while also providing a commercially viable pathway for valorizing plastic waste.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Hydrogen embrittlement of Zircaloy-4 fabricated by ultrasonic additive manufacturing

Ultrasonic additive manufacturing (UAM) was successfully applied to the zirconium material system to create a planar geometry. Following fabrication, SS-J3 type tensile specimens of the UAM and wrought Zircaloy-4 with a nominal gage section of 5×1.2×0.75 mm were machined for hydriding studies and mechanical testing. The SS-J3 type tensile specimens were gas-charged with hydrogen using a custom system that precisely controls hydrogen gas flow rate, hydrogen partial pressure, and temperature. To avoid altering the UAM material, the maximum process temperature was limited to 550°C. Using different initial hydrogen gas pressures and flow rates, various hydrogen contents (70–1755 wppm) were achieved for Zircaloy-4 specimens. Tensile testing shows that, regardless of hydrogen content, all UAM specimens measured yield strengths in the range of 557±16 MPa and ultimate tensile strengths of 660±4MPa. However, total elongation clearly decreased as a function of increasing hydrogen content. Further, at the lowest hydrogen content, the total plastic elongation measured 21.5%, and this value decreased to less than 2% when the hydrogen content was increased to 1000 wppm. Cross-sectional optical microscopy images revealed that the hydride distributions are randomly oriented. For the low hydrogen content specimen, these randomly distributed hydrides are isolated from each other. A sandwiched structure, consisting of high-density and low-density layers, was also observed for the specimens with hydrogen content between 200 and 400 wppm. As the hydrogen content increases, the hydrides diffuse into the low-density hydride layers to form a network across the whole specimen. Although the tensile properties of UAM and wrought Zircaloy-4 exhibit the same behavior with increasing hydrogen content, the distinctions in grain orientations led to differences in the hydride orientations at low and intermediate hydrogen concentrations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Statistical evaluation of microscale stress conditions leading to void nucleation in the weak shock regime

Here, we investigate the heterogeneity of the stress state driven by anisotropic deformation response at the single crystal level through five statistical volume element (SVE) calculations of polycrystalline BCC tantalum. This work focuses on grain boundaries as a prominent material defect type prone to void nucleation based upon experimental observations of predominantly intergranular void nucleation in this material. The SVEs are constructed to be statistically representative of larger volumes of material and are meshed such that mean and standard deviation of grain size and orientation information is reconstructed. The computational meshes feature hexahedral (brick) elements and smooth conformal grain boundaries where significant stress concentration is known to occur, a tail effect of interest in the extreme events process of dynamic ductile damage. An existing micromechanical crystallographic plasticity model shown to capture the single crystal behavior of BCC tantalum well is used to perform the polycrystal calculations. The model includes representation of the non-Schmid effect of non-planar screw dislocation kinetics in tantalum. A three-dimensional stress state time profile predicted by damage modeling of a flyer plate impact experiment is applied as boundary conditions to each SVE. Resulting grain boundary stress state statistics are strongly non-Gaussian. Significant structural evolution is observed within the compressive hold before unloading into tension in the stress profile. Strong angular dependence of grain boundary traction magnitude with shock direction is observed. Non-Schmid effects continue to suggest their influence on propensity of microstructural defect types to nucleate voids. A general void nucleation criterion is proposed using probability theory. The general framework is specified to polycrystalline BCC tantalum in the weak shock regime to include the SVE calculations and literature molecular dynamics calculations of grain boundary void nucleation strength. Probability density functions (PDFs) are used to describe the interaction between the local stress state heterogeneity and the distributed grain boundary void nucleation strength state. A causation entropy maximization procedure removes the requirement for ad hoc selection of a PDF functional form and provides a rigorous procedure for data-based PDF determination. The resulting physically informed PDF describes the spatial appearance frequency of nucleated voids as a function of applied macroscale pressure. Lower length scale physics are thus packaged in a precise and computationally efficient way to provide computational plasticity insight to macroscale dynamic ductile damage models.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Perturbation of nanoplastics on biomembranes: molecular insights from neutron scattering

Plastic waste is now pervasive in the environment, breaking down into microplastics and nanoplastics under many environmental conditions. These particles have been found in various ecosystems and even in human tissues, raising significant environmental and health concerns. In this study, we investigated the interaction of polystyrene nanoplastics, with and without surface modifications, on biomembrane structures using contrast-matching small-angle neutron scattering and neutron spin echo spectroscopy. The neutron contrast matching enabled the selective study of biomembranes in the presence of nanoplastics. Two model membranes were employed: a simple zwitterionic bilayer (i.e., dimyristoylphosphatidylcholine [DMPC]) and an Escherichia coli lipid extract as a bacterial membrane model. The results show profound membrane disruptions, including possible thinning, vesicle fragmentation, lipid monolayer formation, and inter-vesicle aggregation, with the more severe effects observed in DMPC membranes. Notably, E. coli membranes exhibited greater resilience, suggesting that natural membranes with diverse lipid compositions may reduce susceptibility to perturbation by extracellular nanoplastics. Here, these findings highlight potential risks posed by environmental nanoplastic particles to biological membranes, with insights into molecular-level interactions and the environmental toxicity of nanoplastics. This work provides a foundation for future studies into nanoplastic–biomembrane interactions and their broader implications for health and environment using neutrons.

Qian, Shuo [Oak Ridge National Laboratory (ORNL), ↗
DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

A Multiphysics Thermoelastoviscoplastic Damage Internal State Variable Constitutive Model including Magnetism

We present a macroscale constitutive model that couples magnetism with thermal, elastic, plastic, and damage effects in an Internal State Variable (ISV) theory. Previous constitutive models did not include an interdependence between the internal magnetic (magnetostriction and magnetic flux) and mechanical fields. Although constitutive models explaining the mechanisms behind mechanical deformations caused by magnetization changes have been presented in the literature, they mainly focus on nanoscale structure–property relations. A fully coupled multiphysics macroscale ISV model presented herein admits lower length scale information from the nanoscale and microscale descriptions of the multiphysics behavior, thus capturing the effects of magnetic field forces with isotropic and anisotropic magnetization terms and moments under thermomechanical deformations. For the first time, this ISV modeling framework internally coheres to the kinematic, thermodynamic, and kinetic relationships of deformation using the evolving ISV histories. For the kinematics, a multiplicative decomposition of deformation gradient is employed including a magnetization term; hence, the Jacobian represents the conservation of mass and conservation of momentum including magnetism. The first and second laws of thermodynamics are used to constrain the appropriate constitutive relations through the Clausius–Duhem inequality. The kinetic framework employs a stress–strain relationship with a flow rule that couples the thermal, mechanical, and magnetic terms. Experimental data from the literature for three different materials (iron, nickel, and cobalt) are used to compare with the model’s results showing good correlations.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Photovoltaic Cable Connectors: A Comparative Assessment of the Present State of the Industry

The consequences of failure for balance-of-systems components (such as photovoltaic (PV) cable connectors) include offline module string(s); low system voltage; arc, ground, insulation, and overtemperature faults; triggered fuse(s); system shutdown; and fire. The degradation modes for connectors are studied here through an industry survey and its subsequent examination, which are compared with field-degraded specimens. A total of 117 specimens were obtained from a variety of locations and climates or accelerated tests. A failure analysis for connectors from PV installations was developed (and applied to 54 specimens), including nondestructive examinations (photography, a custom resistance-current scan, and X-ray computed tomography) and destructive examinations (featuring milling of the external plastic, extraction of the internal convolute spring, and potting and polishing in cross section). Surface and through-thickness composition of the metal pins and springs was quantified using scanning electron microscopy with energy-dispersive X-ray spectroscopy. Fourier transform infrared spectroscopy was used to verify the base polymer materials and compare the chemical structure of the connector body, bushing, end nut, and o-ring. Thermogravimetric analysis and differential scanning calorimetry were used to further verify the degradation of the same polymeric components.

cable connectors↗
DOE OSTI2025

Hypersonic Jets of Detonation Products in the Hydrodynamic Collapse of Macroscopic Voids

Localizing the energetic output from detonation waves has been a long-standing challenge in applied detonation physics. Here, energy localization is achieved via machined millimeter scale voids in pressed samples of PBX 9501, an HMX (1,3,5,7-Tetranitro-1,3,5,7-tetrazocane)-based plastic bonded explosive. A main mechanism of energy localization in these systems, the formation of hydrodynamic jets of dense product gases, is characterized experimentally using a semicylindrical geometry in witness plate impact experiments and streak imaging of the jet propagating into the air. The distance at which the jet is optimally developed is identified and the supersonic flow structure in the vicinity of this feature is explored using hydrocode simulations. This analysis found that most of the kinetic energy of the hydrodynamic jet arises from pressure gradients induced by geometrically mediated squeeze flow lateral to the direction of detonation propagation. This work presents a new development in the control of energetic output from detonation waves and applications to detonation wave shaping are discussed.

42 ENGINEERING↗
DOE OSTI2024

Photovoltaic Cable Connectors: A Comparative Assessment of the Present State of the Industry [Slides]

The consequences of failure for balance of systems (BoS) components (such as PV cable connectors) include offline module string(s); low system voltage; arc, ground, insulation, and over-temperature faults; triggered fuse(s); system shutdown; and fire. The degradation modes for connectors are studied here through an industry survey and its subsequent examination, which are compared to field-degraded specimens. 117 specimens were obtained from a variety of locations and climates or accelerated tests. A failure analysis for connectors from PV installations was developed (and applied to 54 specimens) including nondestructive examinations (photography, a custom resistance-current scan, and X-ray computed tomography) and destructive examinations (featuring milling of the external plastic, extraction of the internal convolute spring, and potting and polishing in cross-section). Surface and through-thickness composition of the metal pins and springs was quantified using scanning electron microscopy with energy-dispersive X-ray spectroscopy. Fourier-transform infrared spectroscopy was used to verify the base polymer materials and compare the chemical structure of the connector body, bushing, end nut, and o-ring. Thermogravimetric analysis and differential scanning calorimetry were used to further verify the degradation of the same polymeric components. Updated from 2023 NIST/UL Workshop on Photovoltaic Materials Durability (website: https://events.ul.com/WPMogn?rt=aAuoWsl4E0KaORLCMeOgfA) and 2024 PVRW workshop (https://pvrw.nrel.gov/past-proceedings).

14 SOLAR ENERGY↗
DOE OSTI2025

Sustainable, degradable and malleable low-dielectric-constant thermosets derived from biomass for recyclable green electronics

In view of their excellent thermal and chemical resistance, favorable adhesion properties, high tensile strength, and other advantages, epoxy thermosets have numerous industrial applications such as coating, adhesive, and composite material production. However, bisphenol A (BPA)-based resins, which account for a significant fraction of the above thermosets, adversely affect human health by interfering with the normal functioning of the endocrine system and cannot be easily decomposed and recycled. Herein, degradable and sustainable bio-based epoxy thermosets with crosslinked network structures are prepared by the epoxidation of isosorbide with epichlorohydrin and the curing of the produced isosorbide diglycidyl ether (ISDGE) with cyclic lactones through a cationic ring-opening reaction. The ISDGE thermosets fully decompose into soluble and recyclable products under mildly basic conditions within three days, which is ascribed to the presence of ester moieties within the polymer network structure. Compared to a representative BPA-based epoxy, ISDGE-based thermosets exhibit lower dielectric constants and are more flexible. Moreover, the glass fibers in ISDGE-based prepregs can be fully recovered after on-demand degradation. Furthermore, our work provides promising eco-friendly alternatives to conventional epoxy thermosets and paves the way for the reduction of plastic waste generation and the development of recyclable green electronics.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Release dynamics of nanodiamonds created by laser-driven shock-compression of polyethylene terephthalate

Laser-driven dynamic compression experiments of plastic materials have found surprisingly fast formation of nanodiamonds (ND) via X-ray probing. This mechanism is relevant for planetary models, but could also open efficient synthesis routes for tailored NDs. We investigate the release mechanics of compressed NDs by molecular dynamics simulation of the isotropic expansion of finite size diamond from different P-T states. Analysing the structural integrity along different release paths via molecular dynamic simulations, we found substantial disintegration rates upon shock release, increasing with the on-Hugnoiot shock temperature. We also find that recrystallization can occur after the expansion and hence during the release, depending on subsequent cooling mechanisms. Our study suggests higher ND recovery rates from off-Hugoniot states, e.g., via double-shocks, due to faster cooling. Laser-driven shock compression experiments of polyethylene terephthalate (PET) samples with in situ X-ray probing at the simulated conditions found diamond signal that persists up to 11 ns after breakout. In the diffraction pattern, we observed peak shifts, which we attribute to thermal expansion of the NDs and thus a total release of pressure, which indicates the stability of the released NDs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Upcycling Polyethylene Waste into Hybrid Graphitic Porous Carbon Materials Used in High‐Performance Zinc‐Ion Hybrid Capacitors

Polyethylene (PE) waste is a challenge to upcycle into useful materials because this plastic tends to decompose into volatile compounds when heated at relatively low temperatures. In this work, mixtures of PE wastes into a hybrid graphitic porous carbon (HGPC) by a thermal oxidation pretreatment step, with assistance of an inert solid additive (KCl), to functionalize, crosslink, and stabilize the PE waste followed by carbonization and catalytic graphitization steps with a potassium carbonate catalyst, are upcycled. The PE waste‐derived HGPC (PW‐HGPC) has a hybrid structure composed of graphene‐like carbon nanosheets grown on the surface of carbon particles, high porosity with specific surface area, up to 1,763 m 2 g −1 , and good graphitic degree with average Raman I 2D / I G ratios of 0.53. When used as cathode material for zinc‐ion hybrid capacitors, this PW‐HGPC exhibits an excellent specific capacity, up to 126.7 mAh g −1 , at high mass loading of 10 mg cm −2 . Moreover, PW‐HGPC exhibits remarkable cycling stability with capacity retention of >94% after 10 000 cycles. Additionally, the KCl is recycled and reused over five times. This method provides a new solution for upcycling PE wastes into high value‐added carbon materials, not only for zinc‐ion hybrid capacitors but also for other electrochemical energy storage device applications.

hybrid graphitic porous carbon↗
DOE OSTI2025

Elasto-viscoplastic fast Fourier transform modeling framework for assessing microstructural effects on stress intensity factors characterizing fracture toughness

A large-strain elasto-viscoplastic fast Fourier transform (LS-EVPFFT) model with non-periodic (NP) velocity-based boundary conditions is adapted to simulate the sensitivity of stress intensity factors on microstructure for 304L stainless steel. The material was characterized via electron backscattered diffraction (EBSD) serial-sectioning to obtain a measured 3-D microstructural cell to perform simulations. The NP-LS-EVPFFT model, including the simulation setup and boundary conditions, was verified using a crystal plasticity finite element (CPFE) model. To this end, the generation of meshes of notched specimens was developed, which involved creating Python scripts for mesh “cutting” in Abaqus, and Sculpt scripts in Cubit for meshing of the measured microstructural cell processed with DREAM.3D. The complexity of the mesh preparation highlighted the advantages of the FFT-based model, which circumvents the mesh generation process. Given the efficiency of the FFT-based model, statistical distribution of stress intensity factors in function of crystal orientation at the crack tip, grain structure, and crystallographic texture surrounding the crack tip were predicted. Further, the distributions reveal about 10% variation of stress intensity factors with microstructure with the most significant sensitivity found to be the crystal orientation at the crack tip. The methodology developed in this work is discussed as a practical simulation tool for predicting the sensitivity of stress intensity factors on microstructural variability in metallic materials.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Mechanisms of Polyethylene Terephthalate Pellet Fragmentation into Nanoplastics and Assimilable Carbons by Wastewater Comamonas

Comamonadaceae bacteria are enriched on poly(ethylene terephthalate) (PET) microplastics in wastewaters and urban rivers, but the PET-degrading mechanisms remain unclear. Here, we investigated these mechanisms with Comamonas testosteroniKF-1, a wastewater isolate, by combining microscopy, spectroscopy, proteomics, protein modeling, and genetic engineering. Compared to minor dents on PET films, scanning electron microscopy revealed significant fragmentation of PET pellets, resulting in a 3.5-fold increase in the abundance of small nanoparticles (<100 nm) during 30-day cultivation. Infrared spectroscopy captured primarily hydrolytic cleavage in the fragmented pellet particles. Solution analysis further demonstrated double hydrolysis of a PET oligomer, bis(2-hydroxyethyl) terephthalate, to the bioavailable monomer terephthalate. Supplementation with acetate, a common wastewater co-substrate, promoted cell growth and PET fragmentation. Of the multiple hydrolases encoded in the genome, intracellular proteomics detected only one, which was found in both acetate-only and PET-only conditions. Homology modeling of this hydrolase structure illustrated substrate binding analogous to reported PET hydrolases, despite dissimilar sequences. Mutants lacking this hydrolase gene were incapable of PET oligomer hydrolysis and had a 21% decrease in PET fragmentation; re-insertion of the gene restored both functions. Thus, we have identified constitutive production of a key PET-degrading hydrolase in wastewater Comamonas, which could be exploited for plastic bioconversion.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Structural insights into strigolactone catabolism by carboxylesterases reveal a conserved conformational regulation

Phytohormone levels are regulated through specialized enzymes, participating not only in their biosynthesis but also in post-signaling processes for signal inactivation and cue depletion. Arabidopsis thaliana (At) carboxylesterase 15 (CXE15) and carboxylesterase 20 (CXE20) have been shown to deplete strigolactones (SLs) that coordinate various growth and developmental processes and function as signaling molecules in the rhizosphere. Here, we elucidate the X-ray crystal structures of AtCXE15 (both apo and SL intermediate bound) and AtCXE20, revealing insights into the mechanisms of SL binding and catabolism. The N-terminal regions of CXE15 and CXE20 exhibit distinct secondary structures, with CXE15 characterized by an alpha helix and CXE20 by an alpha/beta fold. These structural differences play pivotal roles in regulating variable SL hydrolysis rates. Our findings, both in vitro and in planta, indicate that a transition of the N-terminal helix domain of CXE15 between open and closed forms facilitates robust SL hydrolysis. The results not only illuminate the distinctive process of phytohormone breakdown but also uncover a molecular architecture and mode of plasticity within a specific class of carboxylesterases.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Polyolefin blends with co-continuous architectures enabled by dynamic covalent crosslinking

Blending polymers produces brittle materials due to macrophase separation and poor interfacial adhesion, which is exemplified by mixtures of polyolefins. This presents a formidable challenge for the mechanical recycling of mixed plastic waste. Here, we demonstrate that dynamic covalent crosslinking of immiscible polyolefin blends creates macrophase separated co-continuous architectures, yet they display excellent mechanical properties, which challenges the conventional wisdom regarding morphology-property relationships in polymer blend compatibilization. We find that the position and orientation of dynamic crosslinks and their influence on crystallinity are key to understanding the structure-morphology-property relationships. In particular, high-resolution microscopy imaging reveals alignment of crystallite planes with strong orientational preference, particularly at polymer-polymer interfaces, which contribute to material performance. We further demonstrate that changes in crosslinker density and valency allow the properties of binary and ternary polyolefin blends to be tuned in a modular fashion.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The latent variable proximal point algorithm for variational problems with inequality constraints

The latent variable proximal point (LVPP) algorithm is a framework for solving infinite-dimensional variational problems with pointwise inequality constraints. The algorithm is a saddle point reformulation of the Bregman proximal point algorithm. At the continuous level, the two formulations are equivalent, but the saddle point formulation is more amenable to discretization because it introduces a structure-preserving transformation between a latent function space and the feasible set. Working in this latent space is much more convenient for enforcing inequality constraints than the feasible set, as discretizations can employ general linear combinations of suitable basis functions, and nonlinear solvers can involve general additive updates. LVPP yields numerical methods with observed mesh-independence for obstacle problems, contact, fracture, plasticity, and others besides; in many cases, for the first time. The framework also extends to more complex constraints, providing means to enforce convexity in the Monge–Ampère equation and handling quasi-variational inequalities, where the underlying constraint depends implicitly on the unknown solution. Here, in this paper, we describe the LVPP algorithm in a general form and apply it to ten problems from across mathematics.

Inequality constraints↗