Best-fit Coefficients Research Articles

Experiment and kinetics study on OH∗ chemiluminescence up to 3150 K in hydrogen combustion behind reflected shock waves

Chemiluminescence of OH∗ is commonly employed as an optical indicator for the combustion process. It is widely recognized that the generation of OH∗ in hydrogen flames is primarily governed by the reaction H + O + M=>OH∗+M. In this study, the time histories of OH∗ chemiluminescence from the A→X band around 308 nm were recorded behind reflected shock waves for stoichiometric and lean H2/O2 mixtures highly diluted in argon over the temperature range of 1130–3150 K and at the pressure of approximately 0.9 atm. Based on the time histories of OH∗ chemiluminescence, the best-fit reaction rate coefficient for the reaction H + O + M=>OH∗+M was determined as k = 3.17 × 1027exp(-121968 cal mol−1/RT) + 2.25 × 1017exp(-4246 cal mol−1/RT) cm6 mol−2 s−1 over the temperature range studied. Furthermore, by using the current rate coefficient in mechanism predictions, the predicted time histories and relative peak intensities of OH∗ chemiluminescence are in good agreement with experimental results reported in literature.

The hyperplane of early-type galaxies: using stellar population properties to increase the precision and accuracy of the fundamental plane as a distance indicator

ABSTRACT We use deep spectroscopy from the SAMI (Sydney-AAO Multi-object Integral) Galaxy Survey to explore the precision of the fundamental plane (FP) of early-type galaxies as a distance indicator for future single-fibre spectroscopy surveys. We study the optimal trade-off between sample size and signal-to-noise ratio (SNR), and investigate which additional observables can be used to construct hyperplanes with smaller intrinsic scatter than the FP. We add increasing levels of random noise (parametrized as effective exposure time) to the SAMI spectra to study the effect of increasing measurement uncertainties on the FP- and hyperplane-inferred distances. We find that, using direct-fit methods, the values of the FP and hyperplane best-fitting coefficients depend on the spectral SNR, and reach asymptotic values for a mean $\langle \mathrm{ SNR} \rangle =40\, \mathrm{\mathring{\rm A}}^{-1}$. As additional variables for the FP we consider three stellar-population observables: light-weighted age, stellar mass-to-light ratio, and a novel combination of Lick indices ($I_\mathrm{age}$). For an $\langle \mathrm{ SNR} \rangle =45~\mathrm{\mathring{\rm A}}^{-1}$ (equivalent to 1-h exposure on a 4-m telescope), all three hyperplanes outperform the FP as distance indicators. Being an empirical spectral index, $I_\mathrm{age}$ avoids the model-dependent uncertainties and bias underlying age and mass-to-light ratio measurements, yet yields a 10 per cent reduction of the median distance uncertainty compared to the FP. We also find that, as a by-product, the $I_\mathrm{age}$ hyperplane removes most of the reported environment bias of the FP. After accounting for the different SNR, these conclusions also apply to a 50 times larger sample from SDSS-III (Sloan Digital Sky Survey). However, in this case, only $\mathrm{ age}$ removes the environment bias.

Comparing the Evolution of Land Surface Temperature and Driving Factors between Three Different Urban Agglomerations in China

Increases in land surface temperature (LST) and the urban heat island effect have become major challenges in the process of urban development. However, few studies have examined variations in LST between different urban agglomerations (UAs). Based on MODIS LST data, we quantitatively analyzed the spatial and temporal evolution patterns of LST in three different UAs in China from 2000 to 2020—Beijing–Tianjin–Hebei (BTH) at the national level, the Shandong Peninsula (SP) at the regional level, and Central Shanxi (CS) at the city level—by employing urban agglomeration built-up area intensity (UABI), linear regression analyses, and geodetic detector models. The results showed the following: (1) The spatial and temporal evolution pattern of the LST in BTH was the most regularized; the spatial pattern of the LST in SP gradually evolved from “two points” to “a single branch”; and the LST of CS was easily influenced by the neighboring big cities. (2) The best-fitting coefficients for BTH, SP, and CS were R2BTH = 0.58, R2SP = 0.66, and R2CS = 0.58, respectively; every 10% increase in UABI warmed the LSTs in BTH, SP, and CS by 1.47 °C, 1.27 °C, and 1.83 °C, respectively. (3) The ranking of single-factor influence was DEM (digital elevation model) > UABI > NDVI > T2m (air temperature at 2 m) > POP (population). The UABI interacting with DEM had the strongest warming effect on LST, with the maximum value q(UABI ∩ DEM) BTH = 0.951. All factor interactions showed an enhancement of the LST in CS, but factors interacting with POP showed a weaker effect in BTH and SP, for which q(NDVI ∩ POP) BTH = 0.265 and q(T2m ∩ POP) SP = 0.261. As the development of UAs gradually matures, the interaction with POP might have a cooling effect on the environment to a certain degree.

Creep Behavior of Fiber Reinforced Mortars and Its Effect to Reduce the Differential Shrinkage Stress

This research aims to develop durable repair materials that can resist shrinkage cracking by exploring the role of creep in reducing shrinkage stress. In this regard, the creep effect can only be quantified if an accurate creep prediction model and theoretical analysis of the shrinkage stress in the patch repair system exist. For this purpose, the research was carried out in the following sequences: first, the research investigated the short-term creep of the patch repair materials containing accelerator and micro-synthetic fibers in the 0.00–0.12% volume fraction range. This short-term creep was measured on five-cylinder specimens (having a diameter of 75 mm and a height of 275 mm). Three specimens were used to determine the deformation of the repair material under unloading conditions, while those remaining were used to determine the total deformation under loading conditions. The amount of creep deformation was determined by taking away the unloaded (shrinkage) and instantaneous (elastic) deformations from the total deformation of the loaded specimens. Secondly, a modified prediction model of ACI 209R-08 is introduced to accurately capture the rate and magnitude of the observed creep of the repair materials. Finally, a formulated theoretical analysis of shrinkage stress in the patch repair system was proposed to examine how creep potentially reduces the repair material's cracking tendency. The results show that the asymptotic value of the creep curve is attained at an earlier age and that its magnitude is greater than that of most concrete. The modified ACI 209R-08 prediction model can closely estimate the repair materials' creep behavior. The best-fit line, residual values, and coefficient of error analyses confirm the modified model's prediction accuracy. The analysis of tensile stress development in the repair layer suggests that creep can reduce stress by up to 50%. With such a reduction, the repair material is expected to be durable in resisting shrinkage and cracking tendency. Doi: 10.28991/CEJ-2023-09-08-014 Full Text: PDF

From field observations to temporally dynamic soil surface roughness retrievals in the U.S. Corn Belt

Soil surface roughness in the U.S. Corn Belt varies outside of the growing season due to rainfall and soil management activities such as tillage. This is not consistent with the assumption that roughness is a static parameter in the Soil Moisture Active Passive (SMAP) soil moisture retrieval algorithm. SMAPVEX16-IA, an extensive field campaign focused on calibration of SMAP retrievals in croplands, occurred during a period when roughness is theoretically at a minima. Satellite-scale measurements of rms height and correlation length collected via pinboard, gridboard, and lidar methodologies resulted in a ensemble of model roughness coefficients that, at h = [0.13, 0.97], is significantly rougher than the original SMAP assumption in croplands of h = 0.108. Comparing simulated brightness temperatures using the ensemble h to SMAP observations resulted in a best-fit angular sensitivity coefficient of N=−2 for both horizontal and vertical polarizations. Satellite-scale h is then retrieved for a four-year study period (excluding growing seasons) via the single channel algorithm from SMAP brightness temperatures and in situ observations of soil moisture and temperature. Roughness retrievals are highly variable in the spring as rainfall events decrease h followed by an increase during soil dry-down; h steadily increases in the fall post-harvest as fields are tilled across the network. Retrievals of h are effectively independent of polarization and demonstrate the potential to simultaneously retrieve soil moisture and roughness in the absence of crops. These soil roughness retrievals could provide new information on tillage and other soil management activities.

The l = 2 spherical harmonic expansion coefficients of the sky brightness distribution between 0.5 and 7 MHz

Context. The opacity of the ionosphere prevents comprehensive Earth-based surveys of low frequency ν ≲ 10 MHz astrophysical radio emissions. The limited available data in this frequency regime show a downturn in the mean sky brightness at ν ≲ 3 MHz in a divergence from the synchrotron emission power-law that is observed at higher frequencies. The turning over of the spectrum coincides with a shift in the region of maximum brightness from the Galactic plane to the poles. This implicates free-free absorption by interstellar ionized gas, whose concentration in the plane causes radiation that propagates in this region to suffer stronger absorption than radiation from the poles. Aims. Using observations from Parker Solar Probe (PSP), we evaluate the l = 0 and l = 2 spherical harmonic expansion coefficients of the radio brightness distribution at 56 frequencies between 0.5 and 7 MHz. These data quantify free-free absorption’s global effects on the brightness distribution, which provides new constraints on the distribution of free electrons in the Galaxy. Methods. The auto and cross spectra of the voltages induced on crossed short dipole antennas by radiation from a nonpolarized extended brightness distribution are linear combinations of the distribution’s l = 0 and l = 2 expansion coefficients. We extracted the least squares solution to these coefficients from PSP’s measurements of the radio background. Also, we generated hypothetical low frequency brightness maps that incorporated free-free absorption and tested their compatibility with the data. The maps primarily depended on models of the Galactic emissivity and distribution of free electrons. A comparison of the maps’ expansion coefficients with the empirical coefficients provided an indication of these input models’ accuracies. Results. An average reduced x2 ≈ 1.04 of the spherical harmonic analysis between 0.5 and 7 MHz indicates that PSP’s antennas act approximately as ideal short dipoles in this frequency band. The best-fit expansion coefficients show that, with decreasing frequency, the mean sky brightness decreases at ν < 3 MHz and the Galactic plane darkens relative to the poles. At ν > 0.6 MHz, these observations can be reproduced in synthetic brightness maps in which the Galactic emissivity maintains a power-law form and free-free absorption is modeled using free electron distributions derived from pulsar measurements. At lower frequencies, the empirical mean brightness falls below the mean in this model, possibly signifying a cutoff in the synchrotron power-law.

Dynamics of di-2-ethylhexyl phthalate (DEHP) in the indoor air of an office

Largely limited by measurement technique, dynamics of semivolatile organic compounds (SVOCs) in the indoor air is not well understood. This study reports time-resolved measurements of airborne concentration of di-2-ethylhexyl phthalate (DEHP) in an office, using semivolatile thermal desorption aerosol gas chromatography (SV-TAG). The measurements were conducted in two separate periods during the summer-to-fall transition in 2020, each for more than 10 days. The indoor gas-plus-particle DEHP concentration varied by more than one order of magnitude in each observation period, and the temporal pattern exhibited possible influences of the indoor temperature, particle mass concentration, and outdoor DEHP concentrations. Further analysis focusing on window-closed conditions (i.e., with less outdoor contribution) reveals that the DEHP dynamics was primarily driven by variations in the indoor temperature ( R 2 = 0.85) during the first, warmer period (24–29 °C), and by variations in the particle mass concentration ( R 2 = 0.83) during the subsequent cooler period (20–23 °C). The unexpected transition of the key driving factor with change of the temperature was qualitatively justified by a simplified mechanistic model. Moreover, the particle fraction of DEHP was measured during the latter, cooler period, and it exhibited strong dependence on particle concentration, which can be fitted assuming gas-particle equilibrium partitioning, with a best-fit apparent partitioning coefficient of 0.053 ± 0.006 m 3 /μg at 20 ± 1 °C. Overall, these results improve our understanding of real-world SVOC dynamics. • In a warmer period variation in temperature drove DEHP dynamics in an office. • In a cooler period variation in particle concentration drove DEHP dynamics in the office. • Transition of the key driving factor with change in temperature was justified by mechanistic model. • Observed gas/particle partitioning of DEHP can be fitted assuming equilibrium state.

Parameterization on formation free energy of dislocation loops up to 1100 K in bcc iron

This work provides a simple analytical formula with a set of best-fit coefficients for evaluating formation free energies of prismatic dislocation loops as a function of temperature in body-centered-cubic iron. The parameterization is made based on the anisotropic elastic self-energies and corresponding non-linear core-energies of edge dislocations. The variation of these two energy terms with temperature is estimated by including temperature-dependent elastic stiffness tensors in the anisotropic elasticity calculation, and based on the stability of C15 clusters and dislocation loops, respectively. The new analytical formula explicitly contains temperature and is valid for temperatures up to 1100 K.

The Diffusion Coefficient of the Splashback Mass Function as a Probe of Cosmology

Abstract We present an analytic model for the splashback mass function of dark matter halos, which is parameterized by a single coefficient and constructed in the framework of the generalized excursion set theory and the self-similar spherical infall model. The value of the single coefficient that quantifies the diffusive nature of the splashback boundary is determined at various redshifts by comparing the model with the numerical results from the Erebos N-body simulations for the Planck and the WMAP7 cosmologies. Showing that the analytic model with the best-fit coefficient provides excellent matches to the numerical results in the mass range of 5 ≤ M/(1012 h −1 M ⊙) < 103, we employ the Bayesian and Akaike Information Criterion tests to confirm that our model is most preferred by the numerical results compared to previous models at redshifts of 0.3 ≤ z ≤ 3 for both of the cosmologies. We also found that the diffusion coefficient decreases almost linearly with redshift, converging to zero at a certain threshold redshift, z c , whose value significantly differs between the Planck and WMAP7 cosmologies. Our result implies that the splashback mass function of dark matter halos at z ≥ z c is well described by a parameter-free analytic formula and that z c may have the potential to independently constrain the initial conditions of the universe.

Detecting High-Resolution Intramural Vascular Wall Strain Signals Using DICOM Data.

Maintaining dialysis vascular access is a source of considerable morbidity in patients with end-stage renal disease (ESRD). High-resolution radiofrequency (RF) ultrasound vascular strain imaging has been applied experimentally in the vascular access setting to assist in diagnosis and management. Unfortunately, high-resolution RF data are not routinely accessible to clinicians. In contrast, the standard DICOM formatted B-mode ultrasound data are widely accessible. However, B-mode, representing the envelope of the RF signal, is of much lower resolution. If strain imaging could use open-source B-mode data, these imaging techniques could be more broadly investigated. We conducted experiments to detect wall strain signals with submillimeter tracking resolutions ranging from 0.2 mm (3 pixels) to 0.65 mm (10 pixels) using DICOM B-mode data. We compared this submillimeter tracking to the overall vascular distensibility as the reference measurements to see if high-strain resolution strain could be detected using open-source B-Mode data. We measured the best-fit coefficient of determination between signals, expressed as the percentage of strain waveforms that exhibited a correlation with a p value of 0.05 or less. The lowest percentage was 86.7%, and most were 90% and higher. This indicates high-resolution strain signals can be detected within the vessel wall using B-mode DICOM data.

Breaking the Dark Degeneracy with the Drifting Coefficient of the Field Cluster Mass Function

Abstract We present a numerical analysis supporting the evidence that the redshift evolution of the drifting coefficient of the field cluster mass function is capable of breaking several cosmic degeneracies. This evidence is based on the data from the CoDECS and DUSTGRAIN-pathfinder simulations performed separately for various nonstandard cosmologies including coupled dark energy, f(R) gravity, and combinations of f(R) gravity with massive neutrinos as well as for the standard Λ cold dark matter (ΛCDM) cosmology. We first numerically determine the field cluster mass functions at various redshifts in the range of 0 ≤ z ≤ 1 for each cosmology. Then, we compare the analytic formula developed in previous works with the numerically obtained field cluster mass functions by adjusting its drifting coefficient, β, at each redshift. It is found that the analytic formula with the best-fit coefficient provides a good match to the numerical results at all redshifts for all of the cosmologies. The empirically determined redshift evolution of the drifting coefficient, β(z), turns out to significantly differ among different cosmologies. It is also shown that even without using any prior information on the background cosmology the drifting coefficient, β(z), can discriminate with high statistical significance the degenerate nonstandard cosmologies not only from the ΛCDM but also from one another. It is concluded that the evolution of the departure from the Einstein–de Sitter state and spherically symmetric collapse processes quantified by β(z) is a powerful probe of gravity and dark sector physics.

Evaluation of an Attachment–Detachment Kinetic Model for Flotation

This paper compares model predictions from a novel kinetic model with data from five fundamental single-mineral literature flotation datasets. The empirical correlations proposed by Safari and Deglon (2018) are modified to improve their robustness, requiring only a single best-fit regression coefficient per mineral type. Experimental and model-predicted rate constants were compared on a parity chart where a reasonable linear correlation was observed, with a gradient of 0.95 and an overall R2 value of 0.97. Thereafter experimental and model-predicted trends from the flotation datasets were compared for particle size, contact angle, agitation, and gas flow rate. Model-predicted trends were reasonably accurate for most of the flotation datasets, but under-predicted the rate constant for larger particles for the data of Pyke (2004). In general model predictions were reasonably accurate, which is considered quite good, as these were obtained by fitting a single parameter per mineral type to several large flotation datasets, totaling 330 rate constants.

A Priori Validation of Subgrid-scale Models for Astrophysical Turbulence

Abstract We perform a priori validation tests of subgrid-scale (SGS) models for the turbulent transport of momentum, energy, and passive scalars. To this end, we conduct two sets of high-resolution hydrodynamical simulations with a Lagrangian code: an isothermal turbulent box with rms Mach numbers of 0.3, 2, and 8, and the classical wind tunnel where a cold cloud traveling through a hot medium gradually dissolves due to fluid instabilities. Two SGS models are examined: the eddy diffusivity (ED) model widely adopted in astrophysical simulations and the “gradient model” due to Clark et al. We find that both models predict the magnitude of the SGS terms equally well (correlation coefficient >0.8). However, the gradient model provides excellent predictions for the orientation and shape of the SGS terms while the ED model predicts both poorly, indicating that isotropic diffusion is a poor approximation to the instantaneous turbulent transport. The best-fit coefficient of the gradient model is in the range of [0.16, 0.21] for the momentum transport, and the turbulent Schmidt number and Prandtl number are both close to unity, in the range of [0.92, 1.15].

Sound-Absorption Properties of Materials Made of Esparto Grass Fibers

Research on sound-absorbing materials made of natural fibers is an emerging area in sustainable materials. In this communication, the use of raw esparto grass as an environmentally friendly sound-absorbing material is explored. Measurements of the normal-incidence sound-absorption coefficient and airflow resistivity of three different types of esparto from different countries are presented. In addition, the best-fit coefficients for reasonable prediction of the sound-absorption performance by means of simple empirical formulae are reported. These formulae require only knowledge of the airflow resistivity of the fibrous material. The results presented in this paper are an addition to the characterization of available natural fibers to be used as alternatives to synthetic ones in the manufacturing of sound-absorbing materials.

Paβ, Hα, and Attenuation in NGC 5194 and NGC 6946

Abstract We combine Hubble Space Telescope Paschen β (Paβ) imaging with ground-based, previously published Hα maps to estimate the attenuation affecting Hα, A(Hα), across the nearby, face-on galaxies NGC 5194 and NGC 6946. We estimate A(Hα) in ∼2000 independent 2″ ∼ 75 pc diameter apertures in each galaxy, spanning out to a galactocentric radius of almost 10 kpc. In both galaxies, A(Hα) drops with radius, with a bright, high-attenuation inner region, though in detail the profiles differ between the two galaxies. Regions with the highest attenuation-corrected Hα luminosity show the highest attenuation, but the observed Hα luminosity of a region is not a good predictor of attenuation in our data. Consistent with much previous work, the IR-to-Hα color does a good job of predicting A(Hα). We calculate the best-fit empirical coefficients for use combining Hα with 8, 12, 24, 70, or 100 μm to correct for attenuation. These agree well with previous work, but we also measure significant scatter around each of these linear relations. The local atomic plus molecular gas column density, N(H), also predicts A(Hα) well. We show that a screen with magnitude ∼0.2 times that expected for a Milky Way gas-to-dust value does a reasonable job of explaining A(Hα) as a function of N(H). This could be expected if only ∼40% of gas and dust directly overlap regions of Hα emission.

Biochemical and structural analyses reveal that the tumor suppressor neurofibromin (NF1) forms a high-affinity dimer

Biochemical and structural analyses reveal that the tumor suppressor neurofibromin (NF1) forms a high-affinity dimer

Empirical modelling of wetting patterns in a controlled drip irrigation system for sandy loam soils

The soil wetting pattern is an important factor to fulfil the adequacy of water requirements in a controlled drip irrigation system. The soil wetting pattern is a parameter that is considered in the installation of irrigation systems and control instruments in the field. This study aimed to developed estimate vertical and horizontal soil wetting in the application of control systems using soil moisture sensor in drip irrigation systems. This research conducted in laboratory experiments with surface drip irrigation involved soil sample from pepper plantation, three discharge rates, and 26 soil moisture sensors. The empirical model provides estimated the soil wetted as a parameter of application time, emitter discharge, soil bulk density, initial soil moisture content, and saturated hydraulic conductivity. The development of empirical formulas for predicting wetted radius at different soil depths is carried out by non-linear regression analysis to obtain empirical best-fit coefficients. The empirical model of this study can estimate the full wetting pattern with acceptable accuracy and performs that represent a good performance of a controlled drip irrigation system. The result of performance appraisal validation for the wetted radius and wetted depth on sandy loam soils was assessed based on the lowest mean error was -2.86 and -0.284 cm as well as the highest efficiency model was 0.959 and 0.857 respectively.

One-Dimensional Annular Diffuser Model for Preliminary Turbomachinery Design

Annular diffusers are frequently used in turbomachinery applications to recover the discharge kinetic energy and increase the total-to-static isentropic efficiency. Despite its strong influence on turbomachinery performance, the diffuser is often neglected during the preliminary design. In this context, a one-dimensional flow model for annular diffusers that accounts for the impact of this component on turbomachinery performance was developed. The model allows use of arbitrary equations of state and to account for the effects of area change, heat transfer, and friction. The mathematical problem is formulated as an implicit system of ordinary differential equations that can be solved when the Mach number in the meridional direction is different than one. The model was verified against a reference case to assess that: (1) the stagnation enthalpy is conserved and (2) the entropy computation is consistent and it was found that the error of the numerical solution was always smaller than the prescribed integration tolerance. In addition, the model was validated against experimental data from the literature, finding that deviation between the predicted and measured pressure recovery coefficients was less than 2% when the best-fit skin friction coefficient is used. Finally, a sensitivity analysis was performed to investigate the influence of several input parameters on diffuser performance, concluding that: (1) the area ratio is not a suitable optimization variable because the pressure recovery coefficient increases asymptotically when this variable tends to infinity, (2) the diffuser should be designed with a positive mean wall cant angle to recover the tangential fraction of kinetic energy, (3) the mean wall cant angle is a critical design variable when the maximum axial length of the diffuser is constrained, and (4) the performance of the diffuser declines when the outlet hub-to-tip ratio of axial turbomachines is increased because the channel height is reduced.

Modeling of partial dome collapse of La Soufri\xe8re of Guadeloupe volcano: implications for hazard assessment and monitoring

Over the past 9,150 years, at least 9 flank collapses have been identified in the history of La Soufrière of Guadeloupe volcano. On account of the volcano’s current unrest, the possibility of such a flank collapse should not be dismissed in assessing hazards for future eruptive magmatic as well as non-magmatic scenarios. We combine morphological and geophysical data to identify seven unstable structures (volumes ranging from 1 × 106 m3 to 100 × 106 m3), including one that has a volume compatible with the last recorded flank collapse in 1530 CE. We model their dynamics and emplacement with the SHALTOP numerical model and a simple Coulomb friction law. The best-fit friction coefficient to reproduce the 1530 CE event is tan(7°) = 0.13, suggesting the transformation of the debris avalanche into a debris flow, which is confirmed by the texture of mapped deposits. Various friction angles are tested to investigate less water-rich and less mobile avalanches. The most densely populated areas of Saint-Claude and Basse-Terre, and an area of Gourbeyre south of the Palmiste ridge, are primarily exposed in the case of the more voluminous and mobile flank collapse scenarios considered. However, topography has a prominent role in controlling flow dynamics, with barrier effects and multiple channels. Classical mobility indicators, such as the Heim’s ratio, are thus not adequate for a comprehensive hazard analysis.

Optimized Phase Field Model for Diblock Copolymer Melts

Self-consistent field theory (SCFT) is a versatile framework for investigating self-assembly and thermodynamic properties in broad classes of polymer systems. Nonetheless, it is expensive to implement in higher space dimensions d as propagator fields of d + 1 dimensions must be resolved in a numerical SCFT simulation. In principle, SCFT can be exactly reduced to a phase field (or density functional) theory involving only d-dimensional species density fields, but the density functional of the reduced theory is not known analytically. Although asymptotic approximations to the functional are available in the literature, e.g., the Ohta–Kawasaki (OK) model for diblock copolymers, these functionals tend to produce inaccurate and unreliable predictions. Here, we present a phase field mapping technique adapted from force-matching concepts in the particle coarse-graining literature to best-fit coefficients in a trial density functional using data obtained from low-dimensional SCFT simulations. Such a mapping schem...