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At least 667 records · Page 37

Cryogenic single-port calibration for superconducting microwave resonator measurements

Superconducting circuit testing and materials loss characterization requires robust and reliable methods for the extraction of internal and coupling quality factors of microwave resonators. Additionally, a common method, imposed by limitations on the device design or experimental configuration, is the single-port reflection geometry, i.e. reflection-mode. However, impedance mismatches in cryogenic systems must be accounted for through calibration of the measurement chain while it is at low temperatures. In this paper, we demonstrate a data-based, single-port calibration using commercial microwave standards and a vector network analyzer with samples at millikelvin temperature in a dilution refrigerator, making this method useful for measurements of quantum phenomena. Finally, we cross reference our data-based, single-port calibration and reflection measurement with over-coupled 2D- and 3D-resonators against well established two-port techniques corroborating the validity of our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Evidence against naive truncations of the OPE from e + e − → hadrons below charm

The operator product expansion (OPE), truncated in dimension, is employed in many contexts. An example is the extraction of the strong coupling, $\alpha_s$, from hadronic $\tau$-decay data, using a variety of analysis methods based on finite-energy sum rules. Here, we reconsider a long-used method, which parametrizes non-perturbative contributions to the $I=1$ vector and axial vacuum polarizations with the OPE, setting several higher-dimension coefficients to zero in order to implement the method in practice. The assumption that doing this has a negligible effect on the value of $\alpha_s$ is tantamount to the assumption that the low-dimension part of the OPE converges rapidly with increasing dimension near the $\tau$ mass. Were this assumption valid, it would certainly have to be valid at energies above the $\tau$ mass as well. It follows that the method can be tested using data obtained from $e^+e^-\to\mbox{hadrons}$, as they are not limited by the kinematic constraints of $\tau$ decays. We carry out such an investigation using a recent high-precision compilation for the $R$ ratio, arguing that it provides insights into the validity of the strategy, even if it probes a different, though related channel. We find that $e^+e^-$-based tests call into question the implied assumption of rapid convergence of the low-dimension part of the OPE around the $\tau$ mass, and thus underscore the need to restrict finite-energy sum-rule analyses to observables which receive only contributions from lower-order terms in the OPE.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Towards a Verifiable Domain-Specific Language for Hardware-Accelerated Stencils

Defining a domain-specific language (DSL) that supports vector-calculus abstractions eases the porting of partial differential equation (PDE) solvers to specialized architectures. Sufficiently high-level abstractions empower users to express universal laws with sufficient generality that the laws must always hold true within their domain of validity. A broad class of PDE solvers employs stencil-based algorithms, the target domain of Berkeley Lab's stencil accelerator chip co-design project. First released as open-source in January 2026, the Formal software framework lays a foundation for defining an embedded DSL based on composable operators that implement mimetic numerical methods -- stencil algorithms that guarantee satisfaction of discrete versions of important vector calculus theorems. The Formal DSL will be the frontend to a new class of stencil-PDE accelerators developed jointly by LBNL, UHCL, and UC Berkeley through the DOE Competitive Portfolios for Computer Science Project. This offers the potential of an order of magnitude acceleration for this important category of computational methods to serve the DOE mission. Future work on the Formal DSL will facilitate software verification via type-safe templates that enable problem-specific correctness proofs relying upon generic function theory and carefully crafted unit tests.

Rouson, Damian↗

Data-driven Stellar Models

We developed a data-driven model to map stellar parameters ( T eff , log g , and [Fe/H]) accurately and precisely to broadband stellar photometry. This model must, and does, simultaneously constrain the passband-specific dust reddening vector in the Milky Way, R. The model uses a neural network to learn the (de-reddened) absolute magnitude in one band and colors across many bands, given stellar parameters from spectroscopic surveys and parallax constraints from Gaia. To demonstrate the effectiveness of this approach, we train our model on a data set with spectroscopic parameters from LAMOST, APOGEE, and GALAH, Gaia parallaxes, and optical and near-infrared photometry from Gaia, Pan-STARRS 1, Two Micron All Sky Survey and Wide-field Infrared Survey Explorer. Testing the model on these data sets leads to an excellent fit and a precise—and by construction—accurate prediction of the color–magnitude diagrams in many bands. This flexible approach rigorously links spectroscopic and photometric surveys, and also results in an improved, T eff -dependent R. As such, it provides a simple and accurate method for predicting photometry in stellar evolutionary models. Our model will form a basis to infer stellar properties, distances, and dust extinction from photometric data, which should be of great use in 3D mapping of the Milky Way. Our trained model can be obtained at doi:10.5281/zenodo.3902382.

79 ASTRONOMY AND ASTROPHYSICS↗

Versatility of the adenovirus-vectored foot-and-mouth disease vaccine platform across multiple foot-and-mouth disease virus serotypes and topotypes using a vaccine dose representative of the AdtA24 conditionally licensed vaccine

We investigated the serotype- and topotype versatility of a replication-deficient human adenovirus serotype 5 vectored foot-and-mouth disease (FMD) vaccine platform (AdtFMD). Sixteen AdtFMD recombinant subunit monovalent vaccines targeting twelve distinct FMD virus (FMDV) serotype/topotypes in FMD Regional Pools I-VII were constructed. The AdtA24 serotype conditionally licensed vaccine served as the basis for vaccine design and target dose for cattle clinical trials. Several vaccines contained an additional RGD motif genetic insertion in the adenovector fiber knob, and/or a full-length 2B gene insertion in the FMDV P1 gene cassette. In 13 of the 22 efficacy studies conducted, naïve control and AdtFMD vaccinated cattle were challenged intradermolingually at 2 weeks post-vaccination using a FMDV strain homologous to the AdtFMD vaccine strain. Each of the 16 AdtFMD vaccines were immunogenic based on the presence of homologous neutralizing antibodies in the serum of approximately 90% of total vaccinates (n = 375) on the day of challenge. Importantly, for 75% of vaccines tested, the effective dose that conferred 100% protection against clinical FMD was identical to or in some cases lower than, the minimum protective dose for the conditionally licensed AdtA24 vaccine formulated with ENABL® adjuvant. Results also confirmed the capability of the AdtFMD vaccine platform to differentiate infected from vaccinated animals (DIVA) across the five FMDV serotypes evaluated. Collectively, this comprehensive set of FMD cattle vaccine dose ranging studies highlights the serotype- and topotype versatility of the AdtFMD vaccine platform for further development, licensure, and application in FMD outbreak control and disease eradication efforts.

59 BASIC BIOLOGICAL SCIENCES↗

Anisotropic Flow in Fixed-Target 208 Pb + 20 Ne Collisions as a Probe of Quark-Gluon Plasma

The System for Measuring Overlap with Gas (SMOG2) at the LHCb detector enables the study of fixed-target ion-ion collisions at relativistic energies ($\sqrt{𝑠_{NN}}$ ∼ 100 GeV in the center of mass). Here, with input from ab initio calculations of the structure of 16 O and 20 Ne , we compute 3+1⁢D hydrodynamic predictions for the anisotropic flow of Pb+Ne and Pb+O collisions to be tested with upcoming LHCb data. This will allow the detailed study of quark-gluon plasma formation as well as experimental tests of the predicted nuclear shapes. Elliptic flow (𝑣 2 ) in Pb + Ne collisions is greatly enhanced compared to the Pb + O baseline due to the shape of 20 Ne , which is deformed in a bowling-pin geometry. Owing to the large 208 Pb radius, this effect is seen in a broad centrality range, a unique feature of this collision configuration. Larger elliptic flow further enhances the quadrangular flow (𝑣 4 ) of Pb + Ne collisions via nonlinear coupling, and impacts the sign of the kurtosis of the elliptic flow vector distribution (𝑐 2 ⁡{4}). Exploiting the shape of 20 Ne proves thus an ideal method to investigate the formation of quark-gluon plasma in fixed-target experiments at LHCb, and demonstrates the power of System for Measuring Overlap with Gas as a tool to image nuclear ground states.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

On the Investigation of Phase Fault Classification in Power Grid Signals: A Case Study for Support Vector Machines, Decision Tree and Random Forest

In monitoring the power grid, an ability to differentiate between fault types is essential to ensuring electrical safety. Accordingly, this study introduces a fault detection and classification method by considering different machine learning (ML) and feature extraction (FE) methods combinations. Specifically, the proposed method is established in two classification layers; the first layer determines the fault, and the second layer distinguishes the type of fault. Based on the proposed system model, this study seeks to determine the influential data attributes in a power grid signal using FE methods, including fast Fourier transform, power spectral density (PSD), auto-correlation, and wavelet transform (WT). A cross-comparison of the effectiveness of the Support Vector Machine (SVM), Decision Tree (DT), and Random Forest (RF) is also performed to accomplish the classification layers of the proposed method. The designed algorithm is analyzed under the various combinations of FE and ML methods, and outcomes are presented by considering the trade-off between computational complexity and prediction accuracy. The results reveal that the RF-based ML algorithm shows the most accurate classification performance with PSD, and the most time-saving of the models is the DT WT. Also, SVM emerges superior on a subsequent test of the simulated models on real-world signals.

Galbraith, Kelli↗

The Nab experiment: A precision measurement of unpolarized neutron beta decay

Neutron beta decay is one of the most fundamental processes in nuclear physics and provides sensitive means to uncover the details of the weak interaction. Neutron beta decay can evaluate the ratio of axial-vector to vector coupling constants in the standard model, λ = gA/gV, through multiple decay correlations. The Nab experiment will carry out measurements of the electron-neutrino correlation parameter a with a precision of δa/a = 10 -3 and the Fierz interference term b to δb = 3 × 10 -3 in unpolarized free neutron beta decay. These results, along with a more precise measurement of the neutron lifetime, aim to deliver an independent determination of the ratio λ with a precision of δλ/λ = 0.03% that will allow an evaluation of Vud and sensitively test CKM unitarity, independent of nuclear models. Nab utilizes a novel, long asymmetric spectrometer that guides the decay electron and proton to two large area silicon detectors in order to precisely determine the electron energy and an estimation of the proton momentum from the proton time of flight. The Nab spectrometer is being commissioned at the Fundamental Neutron Physics Beamline at the Spallation Neutron Source at Oak Ridge National Lab. We present an overview of the Nab experiment and recent updates on the spectrometer, analysis, and systematic effects.

Fry, Jason↗

A measurement of $H_0$ from DESI DR1 using energy densities

We present a new measurement of the Hubble constant, independent of standard rulers and robust to pre-recombination modifications such as Early Dark Energy (EDE), obtained by calibrating the total energy density of the Universe. We start using the present-day photon density as an anchor, and use the baryon-to-photon ratio from Big Bang Nucleosynthesis based measurements and the baryon-to-matter ratio from the baryons' imprint on galaxy clustering to translate to a physical matter density at present day. We then compare this to measurements of the ratio of the matter density to the critical density ($Ω_{\mathrm{m}}$), calculated using the relative positions of the baryon acoustic oscillations, to measure the critical density of the universe and hence $H_0$. The important measurements of the evolution of the energy density all happen at low redshift, so we consider this a low-redshift measurement. We validate our method both on a suite of $N$-body mocks and on noiseless theory vectors generated across a wide range of Hubble parameters in both $Λ$CDM and EDE cosmologies. Using DESI DR1 data combined with the angular CMB acoustic scale and the latest BBN constraints, we find $H_0 = 69.0 \pm 2.5$ km s$^{-1}$ Mpc$^{-1}$, consistent with existing early and late-time determinations of the Hubble constant. We consider the impact of non-standard dark energy evolution on our measurement. Future data, including that from further iterations of DESI and from Euclid, will add to these results providing a powerful test of the Hubble tension.

Krolewski, Alex [U. Waterloo (main); Waterloo U., ↗

Toward adaptive radiotherapy for head and neck patients: Uncertainties in dose warping due to the choice of deformable registration algorithm

Purpose: The aims of this work were to evaluate the performance of several deformable image registration (DIR) algorithms implemented in our in-house software (NiftyReg) and the uncertainties inherent to using different algorithms for dose warping. Methods: The authors describe a DIR based adaptive radiotherapy workflow, using CT and cone-beam CT (CBCT) imaging. The transformations that mapped the anatomy between the two time points were obtained using four different DIR approaches available in NiftyReg. These included a standard unidirectional algorithm and more sophisticated bidirectional ones that encourage or ensure inverse consistency. The forward (CT-to-CBCT) deformation vector fields (DVFs) were used to propagate the CT Hounsfield units and structures to the daily geometry for “dose of the day” calculations, while the backward (CBCT-to-CT) DVFs were used to remap the dose of the day onto the planning CT (pCT). Data from five head and neck patients were used to evaluate the performance of each implementation based on geometrical matching, physical properties of the DVFs, and similarity between warped dose distributions. Geometrical matching was verified in terms of dice similarity coefficient (DSC), distance transform, false positives, and false negatives. The physical properties of the DVFs were assessed calculating the harmonic energy, determinant of the Jacobian, and inverse consistency error of the transformations. Dose distributions were displayed on the pCT dose space and compared using dose difference (DD), distance to dose difference, and dose volume histograms. Results: All the DIR algorithms gave similar results in terms of geometrical matching, with an average DSC of 0.85 ± 0.08, but the underlying properties of the DVFs varied in terms of smoothness and inverse consistency. When comparing the doses warped by different algorithms, we found a root mean square DD of 1.9% ± 0.8% of the prescribed dose (pD) and that an average of 9% ± 4% of voxels within the treated volume failed a 2%pD DD-test (DD{sub 2%-pp}). Larger DD{sub 2%-pp} was found within the high dose gradient (21% ± 6%) and regions where the CBCT quality was poorer (28% ± 9%). The differences when estimating the mean and maximum dose delivered to organs-at-risk were up to 2.0%pD and 2.8%pD, respectively. Conclusions: The authors evaluated several DIR algorithms for CT-to-CBCT registrations. In spite of all methods resulting in comparable geometrical matching, the choice of DIR implementation leads to uncertainties in dose warped, particularly in regions of high gradient and/or poor imaging quality.

60 APPLIED LIFE SCIENCES↗

First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring

The Event Horizon Telescope (EHT) has mapped the central compact radio source of the elliptical galaxy M87 at 1.3 mm with unprecedented angular resolution. Here we consider the physical implications of the asymmetric ring seen in the 2017 EHT data. To this end, we construct a large library of models based on general relativistic magnetohydrodynamic (GRMHD) simulations and synthetic images produced by general relativistic ray tracing. We compare the observed visibilities with this library and confirm that the asymmetric ring is consistent with earlier predictions of strong gravitational lensing of synchrotron emission from a hot plasma orbiting near the black hole event horizon. The ring radius and ring asymmetry depend on black hole mass and spin, respectively, and both are therefore expected to be stable when observed in future EHT campaigns. Overall, the observed image is consistent with expectations for the shadow of a spinning Kerr black hole as predicted by general relativity. If the black hole spin and M87's large scale jet are aligned, then the black hole spin vector is pointed away from Earth. Models in our library of non-spinning black holes are inconsistent with the observations as they do not produce sufficiently powerful jets. At the same time, in those models that produce a sufficiently powerful jet, the latter is powered by extraction of black hole spin energy through mechanisms akin to the Blandford-Znajek process. We briefly consider alternatives to a black hole for the central compact object. Analysis of existing EHT polarization data and data taken simultaneously at other wavelengths will soon enable new tests of the GRMHD models, as will future EHT campaigns at 230 and 345 GHz.

79 ASTRONOMY AND ASTROPHYSICS↗

ModuleOT: A Hardware Security Module for Operational Technology: Preprint

With increasing penetration levels of distributed energy resources (DERs) on the distribution grid, as well as new technological advancements in the cyber space, new cyberattack vectors are being introduced, and the available attack surface is constantly increasing. Despite this increasing risk, the standard IEEE 1547-2018 does not yet recommend cybersecurity measures for DERs. To address this and to better protect data on the distribution grid - from the standpoints information security as well as operational security - ModuleOT has been developed. The module aims to significantly reduce cyberattack vectors by improving data privacy for user applications. This is accomplished by performing the core functions of encryption, authentication, authorization, certificate management, and user access control. The module integrates a custom security application with hardware cryptographic acceleration. The application secures all communications using Transmission Control Protocol over Internet Protocol (TCP/IP). These include the three most commonly used communications protocols for power systems information exchange: Modbus, Distributed Network Protocol 3 (DNP3), and Smart Energy Profile 2.0 (SEP2.0). These three protocols are also supported by IEEE 1547-2018 for all DER devices. This paper tests the data encryption/decryption feature on a physical networking test bed with emulated Modbus devices reporting grid data and presents the results.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Light Yield Measurements of Heavy Photon Search (HPS) Muon Scintillator Hodoscopes

The HPS is an experiment that will search for new heavy vector boson(s) in the mass range of 20 MeV/c2 to 1000 MeV/c2. One of the detectors used for this experiment is a muon hodoscope. We are interested in finding the light yield for the scintillator -- wavelength-shifting fiber coupling that will be used in this muon hodoscope. The muon hodoscope will have background signals distorting the data. In order to reduce the background, a threshold cut will be made on the signal coming from the photo-detector. Precision of this cut depends on the average number of photoelectrons, Npe. Previous tests have shown that Npe with Wavelength Shifting (WLS) fibers placed through the holes that go lengthwise down the scintillator is ?12/MeV. In this new muon hodoscope the scintillators will have WLS fibers glued inside the holes. The optical epoxy allows more light, changing Npe. To find Npe, two scintillators with fibers will be used, one of which will have glued WLS fibers. Light will be readout out using photo multiplier tubes (PMTs). The system of two scintillator-fiber-PMTs and one trigger PMT with a scintillator are placed in a dark box. First, position of a single photoelectron peaks is found using an LED light, then using the signal from cosmic muons from trigger PMT light yield is measured. Data are analyzed using ROOT macros. Result of this measurement suggests that light yield form glued fibers is higher than from WLS fibers without glue by a factor of ?1.7, which is sufficient for operation of the HPS muon hodoscope.

Skolnik, MariAnne↗

Glancing-incidence focussed ion beam milling: A coherent X-ray diffraction study of 3D nano-scale lattice strains and crystal defects

Here, this study presents a detailed examination of the lattice distortions introduced by glancing incidence Focussed Ion Beam (FIB) milling. Using non-destructive multi-reflection Bragg coherent X-ray diffraction we probe damage formation in an initially pristine gold micro-crystal following several stages of FIB milling. These experiments allow access to the full lattice strain tensor in the micro-crystal with ~25 nm 3D spatial resolution, enabling a nano-scale analysis of residual lattice strains and defects formed. Our results show that 30 keV glancing incidence milling produces fewer large defects than normal incidence milling at the same energy. However the resulting residual lattice strains have similar magnitude and extend up to ~50 nm into the sample. At the edges of the milled surface, where the ion-beam tails impact the sample at near-normal incidence, large dislocation loops with a range of Burgers vectors are formed. Further glancing incidence FIB polishing with 5 keV ion energy removes these dislocation loops and reduces the lattice strains caused by higher energy FIB milling. However, even at the lower ion energy, damage-induced lattice strains are present within a ~20 nm thick surface layer. These results highlight the need for careful consideration and management of FIB damage. They also show that low-energy FIB-milling is an effective tool for removing FIB-milling induced lattice strains. This is important for the preparation of micro-mechanical test specimens and strain microscopy samples.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems

This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.

97 MATHEMATICS AND COMPUTING↗

Clostridioides difficile Toxin A Remodels Membranes and Mediates DNA Entry Into Cells to Activate Toll-Like Receptor 9 Signaling

Background & Aims: Clostridioides difficile toxin A (TcdA) activates the innate immune response. TcdA co-purifies with DNA. Toll-like receptor 9 (TLR9) recognizes bacterial DNA to initiate inflammation. We investigated whether DNA bound to TcdA activates an inflammatory response in murine models of C difficile infection via activation of TLR9. Methods: We performed studies with human colonocytes and monocytes and macrophages from wild-type and TLR9 knockout mice incubated with TcdA or its antagonist (ODN TTAGGG) or transduced with vectors encoding TLR9 or small-interfering RNAs. Cytokine production was measured with enzyme-linked immunosorbent assay. We studied a transduction domain of TcdA (TcdA 57-80 ), which was predicted by machine learning to have cell-penetrating activity and confirmed by synchrotron small-angle X-ray scattering. Intestines of CD1 mice, C57BL6J mice, and mice that express a form of TLR9 that is not activated by CpG DNA were injected with TcdA, TLR9 antagonist, or both. Enterotoxicity was estimated based on loop weight to length ratios. A TLR9 antagonist was tested in mice infected with C difficile. We incubated human colon explants with an antagonist of TLR9 and measured TcdA-induced production of cytokines. Results: The TcdA 57-80 protein transduction domain had membrane remodeling activity that allowed TcdA to enter endosomes. TcdA-bound DNA entered human colonocytes. TLR9 was required for production of cytokines by cultured cells and in human colon explants incubated with TcdA. TLR9 was required in TcdA-induced mice intestinal secretions and in the survival of mice infected by C difficile. Even in a protease-rich environment, in which only fragments of TcdA exist, the TcdA 57-80 domain organized DNA into a geometrically ordered structure that activated TLR9. Conclusions: TcdA from C difficile can bind and organize bacterial DNA to activate TLR9. TcdA and TcdA fragments remodel membranes, which allows them to access endosomes and present bacterial DNA to and activate TLR9. Rather than inactivating the ability of DNA to bind TLR9, TcdA appears to chaperone and organize DNA into an inflammatory, spatially periodic structure.

59 BASIC BIOLOGICAL SCIENCES↗

Accurate Machine Learning for Predicting the Viscosities of Deep Eutectic Solvents

Deep eutectic solvents (DESs) are emerging as environmentally friendly designer solvents for mass transport and heat transfer processes in industrial applications; however, the lack of accurate tools to predict and thus control their viscosities under both a range of environmental factors and formulations hinders their general application. While DESs may serve as designer solvents, with nearly unlimited combinations, this unfortunately makes it experimentally infeasible to comprehensively measure the viscosities of all DESs of potential industrial interest. To assist in the design of DESs, we have developed several new machine learning (ML) models that accurately and rapidly predict the viscosities of a diverse group of DESs at different temperatures and molar ratios using, to date, one of the most comprehensive data sets containing the properties of over 670 DESs over a wide range of temperatures (278.15–385.25 K). Three ML models, including support vector regression (SVR), feed forward neural networks (FFNNs), and categorical boosting (CatBoost), were developed to predict DES viscosity as a function of temperature and molar ratio and contrasted with multilinear and two-factor polynomial regression baselines. Further, quantum chemistry-based, COSMO-RS-derived sigma profile (σ-profile) features were used as inputs for the ML models. The CatBoost model is excellent at externally predicting DES viscosity, as indicated by high R 2 (0.99) and low root-mean-square-error (RMSE) and average absolute relative deviations (AARD) (5.22%) values for the testing data sets, and 98% of the data points lie within the 15% of AARD deviations. Furthermore, SHapley additive explanation (SHAP) analysis was employed to interpret the ML results and rationalize the viscosity predictions. The result is an ML approach that accurately predicts viscosity and will aid in accelerating the design of appropriate DESs for industrial applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗