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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 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Bismuth Subcarbonate Decorated Reduced Graphene Oxide Nanocomposite for the Sensitive Stripping Voltammetry Analysis of Pb(II) and Cd(II) in Water

In this paper, bismuth subcarbonate (BiO)2CO3-reduced graphene oxide nanocomposite incorporated in Nafion matrix ((BiO)2CO3-rGO-Nafion) was synthesized and further applied, for the first time, in the sensitive detection of Pb(II) and Cd(II) by square-wave anodic stripping voltammetry (SWASV). The as-synthesized nanocomposites were characterized by energy-dispersive spectroscopy (EDS), Raman spectroscopy, scanning electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), X-ray diffraction (XRD), cyclic voltammetry (CV), and electrochemical impedance spectroscopy (EIS). (BiO)2CO3 composite plays a key role in the improvement of the detection sensitivity, which can form multicomponent alloy with cadmium and lead. Additionally, the unique structure of rGO can enlarge the surface area and provide abundant active sites. Moreover, Nafion incorporation in the nanocomposite can effectively increase the adhesion and mechanical strength of the film, and further improve the preconcetration ability due to the cation-exchange capacity of its abundant sulfonate groups. As expected, the (BiO)2CO3-rGO/Nafion nanocomposite-modified glassy carbon electrode ((BiO)2CO3-rGO-Nafion/GCE) achieved low detection limits of 0.24 μg/L for Pb(II) and 0.16 μg/L for Cd(II), in the linear range of 1.0–60 μg/L, and showed some excellent performance, such as high stability, good selectivity, and sensitivity. Finally, synthetic water samples were prepared and further used to verify the practicability of the (BiO)2CO3-rGO-Nafion/GCE with satisfactory results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

A DYNAMIC DENSITY FUNCTIONAL THEORY APPROACH TO DIFFUSION IN WHITE DWARFS AND NEUTRON STAR ENVELOPES

We develop a multicomponent hydrodynamic model based on moments of the Born–Bogolyubov–Green–Kirkwood–Yvon hierarchy equations for physical conditions relevant to astrophysical plasmas. These equations incorporate strong correlations through a density functional theory closure, while transport enters through a relaxation approximation. This approach enables the introduction of Coulomb coupling correction terms into the standard Burgers equations. The diffusive currents for these strongly coupled plasmas is self-consistently derived. The settling of impurities and its impact on cooling can be greatly affected by strong Coulomb coupling, which we show can be quantified using the direct correlation function.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

PetroFit: A Python Package for Computing Petrosian Radii and Fitting Galaxy Light Profiles

PetroFit is an open-source Python package based on Astropy and Photutils that can calculate Petrosian profiles and fit galaxy images. It offers end-to-end tools for making accurate photometric measurements, estimating morphological properties, and fitting 2D models to galaxy images. Petrosian metric radii can be used for model parameter estimation and aperture photometry to provide accurate total fluxes. Correction tools are provided for improving Petrosian radii estimates affected by galaxy morphology. PetroFit also provides tools for sampling Astropy-based models (including custom profiles and multicomponent models) onto image grids and enables point-spread function convolution to account for the effects of seeing. These capabilities provide a robust means of modeling and fitting galaxy light profiles. We have made the PetroFit package publicly available on GitHub (PetroFit/petrofit) and PyPi (pip install petrofit).

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Extending the Calibration of C iv-based Single-epoch Black Hole Mass Estimators for Active Galactic Nuclei

We provide an updated calibration of C iv λ1549 broad emission line–based single-epoch (SE) black hole (BH) mass estimators for active galactic nuclei (AGNs) using new data for six reverberation-mapped AGNs at redshift z=0.005--0.028 with BH masses (bolometric luminosities) in the range 10{sup 6.5}--10{sup 7.5} M{sub ⊙} (10{sup 41.7}--10{sup 43.8} erg s{sup −1}). New rest-frame UV-to-optical spectra covering 1150–5700 Å for the six AGNs were obtained with the Hubble Space Telescope (HST). Multicomponent spectral decompositions of the HST spectra were used to measure SE emission-line widths for the C iv, Mg ii, and Hβ lines, as well as continuum luminosities in the spectral region around each line. We combine the new data with similar measurements for a previous archival sample of 25 AGNs to derive the most consistent and accurate calibrations of the C iv-based SE BH mass estimators against the Hβ reverberation-based masses, using three different measures of broad-line width: full width at half maximum (FWHM), line dispersion (σ{sub line}), and mean absolute deviation (MAD). The newly expanded sample at redshift z=0.005--0.234 covers a dynamic range in BH mass (bolometric luminosity) of logM{sub BH}/M{sub ⊙}=6.5--9.1 (logL{sub bol}/ erg s{sup −1} = 41.7--46.9), and we derive the new C iv-based mass estimators using a Bayesian linear regression analysis over this range. We generally recommend the use of σ{sub line} or MAD rather than FWHM to obtain a less biased velocity measurement of the C iv emission line, because its narrow-line component contribution is difficult to decompose from the broad-line profile.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Post-Newtonian Dynamical Modeling of Supermassive Black Holes in Galactic-scale Simulations

We present KETJU, a new extension of the widely used smoothed particle hydrodynamics simulation code GADGET-3. The key feature of the code is the inclusion of algorithmically regularized regions around every supermassive black hole (SMBH). This allows for simultaneously following global galactic-scale dynamical and astrophysical processes, while solving the dynamics of SMBHs, SMBH binaries, and surrounding stellar systems at subparsec scales. The KETJU code includes post-Newtonian terms in the equations of motions of the SMBHs, which enables a new SMBH merger criterion based on the gravitational wave coalescence timescale, pushing the merger separation of SMBHs down to ∼0.005 pc. We test the performance of our code by comparison to NBODY7 and rVINE. We set up dynamically stable multicomponent merger progenitor galaxies to study the SMBH binary evolution during galaxy mergers. In our simulation sample the SMBH binaries do not suffer from the final-parsec problem, which we attribute to the nonspherical shape of the merger remnants. For bulge-only models, the hardening rate decreases with increasing resolution, whereas for models that in addition include massive dark matter halos, the SMBH binary hardening rate becomes practically independent of the mass resolution of the stellar bulge. The SMBHs coalesce on average 200 Myr after the formation of the SMBH binary. However, small differences in the initial SMBH binary eccentricities can result in large differences in the SMBH coalescence times. Finally, we discuss the future prospects of KETJU, which allows for a straightforward inclusion of gas physics in the simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

Particle Acceleration in Mildly Relativistic Shearing Flows: The Interplay of Systematic and Stochastic Effects, and the Origin of the Extended High-energy Emission in AGN Jets

The origin of the extended X-ray emission in the large-scale jets of active galactic nuclei (AGNs) poses challenges to conventional models of acceleration and emission. Although electron synchrotron radiation is considered the most feasible radiation mechanism, the formation of the continuous large-scale X-ray structure remains an open issue. As astrophysical jets are expected to exhibit some turbulence and shearing motion, we here investigate the potential of shearing flows to facilitate an extended acceleration of particles and evaluate its impact on the resultant particle distribution. Our treatment incorporates systematic shear and stochastic second-order Fermi effects. We show that for typical parameters applicable to large-scale AGN jets, stochastic second-order Fermi acceleration, which always accompanies shear particle acceleration, can play an important role in facilitating the whole process of particle energization. We study the time-dependent evolution of the resultant particle distribution in the presence of second-order Fermi acceleration, shear acceleration, and synchrotron losses using a simple Fokker–Planck approach and provide illustrations for the possible emergence of a complex (multicomponent) particle energy distribution with different spectral branches. We present examples for typical parameters applicable to large-scale AGN jets, indicating the relevance of the underlying processes for understanding the extended X-ray emission and the origin of ultrahigh-energy cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2017

PS16dtm: A Tidal Disruption Event in a Narrow-line Seyfert 1 Galaxy

We present observations of PS16dtm (also known as SN 2016ezh), a luminous transient that occurred at the nucleus of a narrow-line Seyfert 1 galaxy hosting a 10{sup 6} M {sub ⊙} black hole. The light curve shows that PS16dtm exhibited a plateau phase for ∼100 days, during which it showed no color evolution, maintained a blackbody temperature of ∼1.7×10{sup 4} K, and radiated at approximately the Eddington luminosity of the supermassive black hole (SMBH). The spectra exhibit multicomponent hydrogen emission lines and strong Fe ii emission, show little time evolution, and closely resemble the spectra of NLS1s while being distinct from those of Type IIn supernovae (SNe IIn). Moreover, PS16dtm is undetected in the X-rays to a limit an order of magnitude below an archival X-ray detection of its host galaxy. These observations strongly link PS16dtm to activity associated with the SMBH and are difficult to reconcile with an SN origin or known forms of active galactic nucleus (AGN) variability. Therefore, we argue that PS16dtm is a tidal disruption event (TDE) in which the accretion of the stellar debris powers the rise in the continuum and excitation of the preexisting broad-line region, while obscuring the X-ray-emitting region of the preexisting AGN disk. We predict that PS16dtm will remain bright for years and that the X-ray emission will reappear on a similar timescale as the accretion rate declines. Placing PS16dtm in the context of other TDEs, we find that TDEs in AGN galaxies are more efficient and reach Eddington luminosities, likely due to interaction of the stellar debris with the preexisting accretion disk.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2019

BICEP2/Keck Array XI: Beam Characterization and Temperature-to-Polarization Leakage in the BK15 Data Set

Precision measurements of cosmic microwave background (CMB) polarization require extreme control of instrumental systematics. In a companion paper we have presented cosmological constraints from observations with the BICEP2 and Keck Array experiments up to and including the 2015 observing season (BK15), resulting in the deepest CMB polarization maps to date and a statistical sensitivity to the tensor-to-scalar ratio of σ ( r ) = 0.020. In this work we characterize the beams and constrain potential systematic contamination from main beam shape mismatch at the three BK15 frequencies (95, 150, and 220 GHz). Herein far-field maps of 7360 distinct beam patterns taken from 2010–2015 are used to measure differential beam parameters and predict the contribution of temperature-to-polarization leakage to the BK15 B -mode maps. In the multifrequency, multicomponent likelihood analysis that uses BK15, Planck , and Wilkinson Microwave Anisotropy Probe maps to separate sky components, we find that adding this predicted leakage to simulations induces a bias of Δ r = 0.0027 ± 0.0019. Future results using higher-quality beam maps and improved techniques to detect such leakage in CMB data will substantially reduce this uncertainty, enabling the levels of systematics control needed for BICEP Array and other experiments that plan to definitively probe large-field inflation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

The Paschen Jump as a Diagnostic of the Diffuse Nebular Continuum Emission in Active Galactic Nuclei*

Photoionization modeling of active galactic nuclei (AGN) predicts that diffuse continuum (DC) emission from the broad-line region makes a substantial contribution to the total continuum emission from ultraviolet through near-infrared wavelengths. Evidence for this DC component is present in the strong Balmer jump feature in AGN spectra, and possibly from reverberation measurements that find longer lags than expected from disk emission alone. However, the Balmer jump region contains numerous blended emission features, making it difficult to isolate the DC emission strength. In contrast, the Paschen jump region near 8200 Å is relatively uncontaminated by other strong emission features. Here, we examine whether the Paschen jump can aid in constraining the DC contribution, using Hubble Space Telescope Space Telescope Imaging Spectrograph spectra of six nearby Seyfert 1 nuclei. The spectra appear smooth across the Paschen edge, and we find no evidence of a Paschen spectral break or jump in total flux. We fit multicomponent spectral models over the range 6800–9700 Å and find that the spectra can still be compatible with a significant DC contribution if the DC Paschen jump is offset by an opposite spectral break resulting from blended high-order Paschen emission lines. The fits imply DC contributions ranging from ~10% to 50% at 8000 Å, but the fitting results are highly dependent on assumptions made about other model components. These degeneracies can potentially be alleviated by carrying out fits over a broader wavelength range, provided that models can accurately represent the disk continuum shape, Fe ii emission, high-order Balmer line emission, and other components.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2026

Revisiting the Supernova Engines in the 3C 397 and W49B Supernova Remnants

The nature of the supernova remnants (SNRs) 3C 397 and W49B has long been a subject of debate, with prior studies offering conflicting interpretations between thermonuclear and core-collapse scenarios. To help settle this debate, we present a systematic, spatially resolved, spectroscopic analysis of both remnants using XMM-Newton. By applying multicomponent thermal models, we derive key physical properties including elemental abundances, ejecta temperatures, ambient densities, and explosion energetics. We compare the inferred metal abundance ratios to a wide range of core-collapse and thermonuclear nucleosynthesis models, including new models whose explosion energies differ from the canonical value of 10 51 erg. We find that the observed Fe/Si and Ca/Si ratios in both SNRs are best matched by certain thermonuclear models. However, no model fully reproduces the complete set of observed abundance patterns. In 3C 397, high Fe enrichment and spatial abundance variations suggest interaction with a dense progenitor environment, and W49B’s composition is overall consistent with a thermonuclear origin; however, both require a low-energy (∼10 50 erg) supernova explosion. We additionally map the Fe Kα line centroid energies and find a spread, with W49B falling within the core-collapse region—highlighting both environmental complexity and the limitations of this diagnostic for supernova classification. Our results highlight the need for caution in relying on any single diagnostic or nucleosynthesis model for supernova typing, underscore the need for improved nucleosynthesis models, and motivate future high-resolution, high-throughput observations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Fantastic Fits with fantasy of Active Galactic Nuclei Spectra: Exploring the Fe II Emission near the Hα Line

In this study, a refined approach for multicomponent fitting of active galactic nuclei (AGNs) spectra is presented utilizing the newly developed Python code Fully Automated pythoN Tool for AGN Spectra analYsis (fantasy). AGN spectra are modeled by simultaneously considering the underlying broken power-law continuum, predefined emission line lists, and an Fe II model, which is here extended to cover the wavelength range 3700–11000 Å. The Fe II model, founded solely on atomic data, effectively describes the extensive emission of the complex iron ion in the vicinity of the Hγ and Hβ lines, as well as near the Hα line, which was previously rarely studied. The proposed spectral fitting approach is tested on a sample of high-quality AGN spectra from the Sloan Digital Sky Survey Data Release 17. The results indicate that when Fe II emission is present near Hβ, it is also detected redward from Hα, potentially contaminating the broad Hα line wings and thus affecting the measurements of its flux and width. The production of Fe II emission is found to be strongly correlated with Eddington luminosity and appears to be controlled by a similar mechanism as the hydrogen Balmer lines. The study highlights the benefits of fitting type 1 AGN spectra with the fantasy code, pointing that it may be used as a robust tool for analyzing a large number of AGN spectra in the coming spectral surveys.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A Quick Look at the 3 GHz Radio Sky. II. Hunting for DRAGNs in the VLA Sky Survey

Active galactic nuclei (AGNs) can often be identified in radio images as two lobes, sometimes connected to a core by a radio jet. This multicomponent morphology unfortunately creates difficulties for source finders, leading to components that are (a) separate parts of a wider whole, and (b) offset from the multiwavelength cross identification of the host galaxy. In this work we define an algorithm, DRAGN HUNTER , for identifying double radio sources associated with AGNs (DRAGNs) from component catalog data in the first epoch Quick Look images of the high-resolution (≈3" beam size) Very Large Array Sky Survey (VLASS). We use DRAGN HUNTER to construct a catalog of >17,000 DRAGNs in VLASS for which contamination from spurious sources is estimated at ≈11%. A “high-fidelity” sample consisting of 90% of our catalog is identified for which contamination is <3%. Host galaxies are found for ≈13,000 DRAGNs as well as for an additional 234,000 single-component radio sources. Using these data, we explore the properties of our DRAGNs, finding them to be typically consistent with Fanaroff–Riley class II sources and to allow us to report the discovery of 31 new giant radio galaxies identified using VLASS.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Simulating Atomic Dark Matter in Milky Way Analogs

Dark sector theories naturally lead to multicomponent scenarios for dark matter where a subcomponent can dissipate energy through self-interactions, allowing it to efficiently cool inside galaxies. We present the first cosmological hydrodynamical simulations of Milky Way analogs where the majority of dark matter is collisionless cold dark matter (CDM) but a subcomponent (6%) is strongly dissipative minimal atomic dark matter (ADM). The simulations, implemented in GIZMO and utilizing FIRE-2 galaxy formation physics to model the standard baryonic sector, demonstrate that the addition of even a small fraction of dissipative dark matter can significantly impact galactic evolution despite being consistent with current cosmological constraints. We show that ADM gas with roughly standard model–like masses and couplings can cool to form a rotating “dark disk” with angular momentum closely aligned with the visible stellar disk. The morphology of the disk depends sensitively on the parameters of the ADM model, which affect the cooling rates in the dark sector. The majority of the ADM gas gravitationally collapses into dark “clumps” (regions of black hole or mirror star formation), which form a prominent bulge and a rotating thick disk in the central galaxy. These clumps form early and quickly sink to the inner ∼kiloparsec of the galaxy, affecting the galaxy’s star formation history and present-day baryonic and CDM distributions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2019

Technical note: The role of evolving surface tension in the formation of cloud droplets

The role of surface tension ( σ ) in cloud droplet activation has long been ambiguous. Recent studies have reported observations attributed to the effects of an evolving surface tension in the activation process. However, the adoption of a surface-mediated activation mechanism has been slow and many studies continue to neglect the composition dependence of aerosol–droplet surface tension, using instead a value equal to the surface tension of pure water ( σ w ). In this technical note, we clearly describe the fundamental role of surface tension in the activation of multicomponent aerosol particles into cloud droplets. It is demonstrated that the effects of surface tension in the activation process depend primarily on the evolution of surface tension with droplet size, typically varying in the range 0.5 σ w ≲ σ ≤ σ w due to the partitioning of organic species with a high surface affinity. We go on to report some recent laboratory observations that exhibit behavior that may be associated with surface tension effects and propose a measurement coordinate that will allow surface tension effects to be better identified using standard atmospheric measurement techniques. Unfortunately, interpreting observations using theory based on surface film and liquid–liquid phase separation models remains a challenge. Our findings highlight the need for experimental measurements that better reveal the role of composition-dependent surface tensions, critical for advancing predictive theories and parameterizations of cloud droplet activation.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Prognostic simulations of mixed-phase clouds with model AC-1D v1.0: the impact of aerosol types and freezing parameterizations on ice crystal budgets

Mixed-phase clouds at high latitudes contribute to the uncertainty in predicting cloud feedbacks and climate sensitivity, mainly due to the complexity of microphysical processes that influence the partitioning between the supercooled liquid and ice phases, and hence, cloud radiative effects on regional scales. Particularly in Arctic mixed-phase clouds, the activation of ice-nucleating particles (INPs) from various aerosol populations remains a leading source of uncertainty. We developed an aerosol-cloud one-dimensional (AC-1D) model, which provides a novel framework to prognostically treat INP and ice crystal budgets while explicitly accounting for polydisperse and multicomponent aerosol that activate INPs following different freezing parameterizations. The AC-1D model is informed by large-eddy simulations to probe the impact of INP representation on predicted ice crystal number concentrations (N i ) and ice crystal budgets in mixed-phase Arctic stratus. We apply three immersion freezing (IMF) parameterizations, two time-independent (singular) and one time-dependent (classical nucleation theory), to predict the evolution of the INP reservoir and resulting ice crystal budget from polydisperse mineral dust, organic (humic-like substances), and sea spray aerosol particle size distributions. Our analysis focuses on how variations in aerosol number concentration and cloud system parameters such as cloud cooling rate, cloud-top entrainment rate, and ice crystal fall speed influence the INP reservoir and ice crystal budgets. Furthermore, this study investigates the competitive ice nucleation dynamics in mixed aerosol environments and provides a process-level quantification of the INP budget terms, which directly controls ice crystal budgets. For all studied case scenarios, the aerosol types and associated particle size distributions significantly impact INP and N i , and the choice between a time-dependent and a singular freezing description yields orders-of-magnitude differences in the predicted INP and N i over the 10 h simulation time, reflecting typical cloud lifetimes. Our results show that the influence of cloud cooling, INP entrainment, and sedimentation varies significantly depending on the chosen freezing parameterization. These findings underscore the critical need for robust IMF parameterizations and precise cloud system observations to enhance the accuracy of models in predicting mixed-phase cloud structure and evolution.

Arctic clouds↗
DOE OSTI2019

The effects of changing climate on estuarine water levels: a United States Pacific Northwest case study

Climate change impacts on extreme water levels (WLs) at two United States Pacific Northwest estuaries are investigated using a multicomponent process-based modeling framework. The integrated impact of climate change on estuarine forcing is considered using a series of sub-models that track changes to oceanic, atmospheric, and hydrologic controls on hydrodynamics. This modeling framework is run at decadal scales for historic (1979–1999) and future (2041–2070) periods with changes to extreme WLs quantified across the two study sites. It is found that there is spatial variability in extreme WLs at both study sites with all recurrence interval events increasing with further distance into the estuary. This spatial variability is found to increase for the 100-year event moving into the future. It is found that the full effect of sea level rise is mitigated by a decrease in forcing. Short-recurrence-interval events are less buffered and therefore more impacted by sea level rise than higher-returninterval events. Finally, results show that annual extremes at the study sites are defined by compound events with a variety of forcing contributing to high WLs.

Parker, Kai↗
DOE OSTI2024

Data for "Integrated ab initio modelling of atomic order and magnetic anisotropy for rare-earth-free magnet design: effects of alloying additions in L1 0 FeNi."

We describe an integrated modelling approach to accelerate the search for novel, single-phase, multicomponent materials with high magnetocrystalline anisotropy (MCA). For a given system we predict the nature of atomic ordering, its dependence on the magnetic state, and then proceed to describe the consequent MCA, magnetisation, and magnetic critical temperature (Curie temperature). Crucially, within our modelling framework, the same ab initio description of a material’s electronic structure determines all aspects. We demonstrate this holistic method by studying the effects of alloying additions in FeNi, examining systems with the general stoichiometries Fe 4 Ni 3 X and Fe 3 Ni 4 X, for additives including X = Pt, Pd, Al, and Co. The atomic ordering behaviour predicted on adding these elements, fundamental for determining a material’s MCA, is rich and varied. Equiatomic FeNi has been reported to require ferromagnetic order to establish the tetragonal L1 0 order suited for significant MCA. Our results show that when alloying additions are included in this material, annealing in an applied magnetic field and/or below a material’s Curie temperature may also promote tetragonal order, along with an appreciable effect on the predicted hard magnetic properties.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Optimal Membrane Cascade Design for Critical Mineral Recovery Through Logic-based Superstructure Optimization

Critical minerals and rare earth elements play an important role in our climate change initiatives, particularly in applications related with energy storage. Here, we use discrete optimization approaches to design a process for the recovery of Lithium and Cobalt from battery recycling, through membrane separation. Our contribution involves proposing a Generalized Disjunctive Programming (GDP) model for the optimal design of a multistage diafiltration cascade for Li-Co separation. By solving the resulting nonconvex mixed-integer nonlinear program model to global optimality, we investigated scalability and solution quality variations with changes in the number of stages and elements per stage. Results demonstrate the computational tractability of the nonlinear GDP formulation for design of membrane separation processes while opening the door for decom-position strategies for multicomponent separation cascades. Future work aims to extend the GDP formulation to account for stage installation and explore various decomposition techniques to enhance solution efficiency.

Ovalle, Daniel↗