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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Insight into Strong QCD and the Emergence of Mass from N* Experiments

Studies of nucleon resonance (N*) electroexcitation amplitudes (?vpN* electrocouplings) within a broad range of virtual photon four-momentum squared Q2 offer unique information on many facets of the strong interaction in the regime of large QCD running coupling (sQCD regime) seen in the generation of different resonances. The results on the ?vpN* electrocouplings from exclusive meson electroproduction data measured with the CLAS detector at JLab and their impact on understanding of sQCD dynamics will be presented in this talk. These CLAS data have provided the first and only available results on the evolution of the ?vpN* electrocouplings with Q2 to 5 GeV2 for most N* states in the mass range up to 1.8 GeV. A successful description of the CLAS results on the Q2-evolution of the ?(1232)3/2+, N(1440)1/2+, and ?(1600)3/2+ electrocouplings has been achieved within the continuum Schwinger method (CSM) by employing the same momentum dependence of the dressed quark mass inferred from the QCD Lagrangian, which also reproduces the experimental results on the pion elastic electromagnetic form factor and parton distribution function, and the nucleon elastic form factor. This success has demonstrated the capability for gaining insight into the emergence of hadron mass (EHM) from the exploration of the Q2-evolution of the ?vpN* electrocouplings. These studies also allow us to establish either universality or environmental sensitivity of the dressed quark mass function and to explore qq-correlation amplitudes of different spin-parities and the mixing between configurations of different orbital angular momentum. Exploration of the resonance electroexcitation with the CLAS12 detector and in the future with a possible 22 GeV machine at JLab offer the only foreseen opportunity to extend information on the ?vpN* electrocouplings for Q2 from 5-30 GeV2. Analyses of these results will cover the full range of distances where the dominant part of hadron mass and N* structure emerge from QCD.

Mokeev, Victor↗
DOE OSTI2021

In-Home Mobility Frequency and Stability in Older Adults Living Alone With or Without MCI: Introduction of New Metrics

Background: Older adults spend a considerable amount of time inside their residences; however, most research investigates out-of-home mobility and its health correlates. We measured indoor mobility using room-to-room transitions, tested their psychometric properties, and correlated indoor mobility with cognitive and functional status. Materials and Methods: Community-dwelling older adults living alone ( n = 139; age = 78.1 ± 8.6 years) from the Oregon Center for Aging & Technology (ORCATECH) and Minority Aging Research Study (MARS) were included in the study. Two indoor mobility features were developed using non-parametric parameters (frequency; stability): Indoor mobility frequency (room-to-room transitions/day) was detected using passive infrared (PIR) motion sensors fixed on the walls in four geographic locations (bathroom; bedroom; kitchen; living room) and using door contact sensors attached to the egress door in the entrance. Indoor mobility stability was estimated by variances of number of room-to-room transitions over a week. Test-retest reliability (Intra-class coefficient, ICC) and the minimal clinically important difference (MCID) defined as the standard error of measurement (SEM) were generated. Generalized estimating equations models related mobility features with mild cognitive impairment (MCI) and functional status (gait speed). Results: An average of 206 days (±127) of sensor data were analyzed per individual. Indoor mobility frequency and stability showed good to excellent test-retest reliability (ICCs = 0.91[0.88–0.94]; 0.59[0.48–0.70]). The MCIDs of mobility frequency and mobility stability were 18 and 0.09, respectively. On average, a higher indoor mobility frequency was associated with faster gait speed (β = 0.53, p = 0.04), suggesting an increase of 5.3 room-to-room transitions per day was associated with an increase of 10 cm/s gait speed. A decrease in mobility stability was associated with MCI (β = −0.04, p = 0.03). Discussion: Mobility frequency and stability in the home are clinically meaningful and reliable features. Pervasive-sensing systems deployed in homes can objectively reveal cognitive and functional status in older adults who live alone.

Wu, Chao-Yi↗
DOE OSTI2024

Predictive Modeling of NOx Emissions from Lean Direct Injection of Hydrogen and Hydrogen/Natural Gas Blends Using Flame Imaging and Machine Learning

This research paper explores the use of machine learning to relate images of flame structure and luminosity to measured NOx emissions. Images of reactions produced by 16 aero-engine derived injectors for a ground-based turbine operated on a range of fuel compositions, air pressure drops, preheat temperatures and adiabatic flame temperatures were captured and postprocessed. The experimental investigations were conducted under atmospheric conditions, capturing CO, NO and NOx emissions data and OH* chemiluminescence images from 27 test conditions. The injector geometry and test conditions were based on a statistically designed test plan. These results were first analyzed using the traditional analysis approach of analysis of variance (ANOVA). The statistically based test plan yielded 432 data points, leading to a correlation for NOx emissions as a function of injector geometry, test conditions and imaging responses, with 70.2% accuracy. As an alternative approach to predicting emissions using imaging diagnostics as well as injector geometry and test conditions, a random forest machine learning algorithm was also applied to the data and was able to achieve an accuracy of 82.6%. This study offers insights into the factors influencing emissions in ground-based turbines while emphasizing the potential of machine learning algorithms in constructing predictive models for complex systems.

08 HYDROGEN↗
DOE OSTI2023

Global polarization of hyperons and spin alignment of vector mesons in quark matters

Relativistic heavy ion collider (RHIC) as a dedicated nuclear facility has made a few major discoveries in physics. This year marks the 30th year STAR Collaboration formation and the 23th year of STAR detector operation and data collection at RHIC. In the last two decades, STAR has collected many datasets, exhibiting scientific versatility and flexibility of the RHIC facility. The total dataset in the first year is less than 1 million good events, and currently there are about 1 billion events per dataset. The Global Hyperon Polarization was proposed in 2004. This immediately prompted the STAR Collaboration to search for this phenomenon from the early datasets. The null results were presented at Quark Matter Conference in Shanghai in 2006 and subsequently published. Although there were peripheral and continuous efforts in the following decade, no positive result has been observed experimentally. This situation changed in the following decade with the upgrade of high data rate and time-of-flight (TOF) detector and the progress of the Beam Energy Scan Phase I (BES-I). The experimental discoveries of the global polarization of hyperons in 2017 and the spin alignment of vector mesons in 2023 at RHIC-STAR confirm the theory which was established nearly twenty years ago. The theory and these measurements open the way to studying the properties of the hot and dense nuclear matter created in high-energy heavy ion collisions from a new degree of freedom, spin. We briefly review these discoveries from the proposals of theory to the experimental measurements, and summarize the related measurements at the existing facilities and the theoretical explanations to the original proposal. The basic understanding and the original proposal are still valid and fundamental, that is, the angular momentum of system can transform into a spin effect observable in experiment. However, it appears that in each case a new model is needed to explain the new experimental observation. We need a more basic theory to help us unify all these spin related phenomena. Over the past five years, STAR has successfully installed 3 new detectors and we have begun to see the physical analysis results from datasets with those new functions. What makes the STAR detector viable after 20 years of operation is its continuous evolution through successful upgrades, with new scientific programs added year by year. The next big thing is to forward upgrade a tracking system (3 layers of silicon strips and 4 layers of sTGC chambers) and a calorimetry system (electromagnetic and hadronic calorimeters). In addition to studying the spin structure of protons by using the polarized proton beams at RHIC, the upgrades also provide a unique ability to investigate the origin of Λ Global Polarization as a function of rapidity and rapidity (de-)correlations in Au+Au collisions.

Physics↗
DOE OSTI2023

From Inside Out: How the Buried Interface, Shell Defects, and Surface Chemistry Conspire to Determine Optical Performance in Nonblinking Giant Quantum Dots

“Giant” or core/thick‐shell quantum dots (gQDs) are an important class of solid‐state quantum emitter characterized by strongly suppressed blinking and photobleaching under ambient conditions, and reduced nonradiative Auger processes. Together, these qualities provide distinguishing and useful functionality as single‐ and ensemble‐photon sources. For many applications, operation at elevated temperatures and under intense photon flux is desired, but performance is strongly dependent on the synthetic method employed for thick‐shell growth. Here, a comprehensive analysis of gQD structural properties “from the inside out” as a function of shell‐growth method is reported: successive ionic layer adsorption and reaction (SILAR) and high‐temperature continuous injection (HT‐CI), or sequential combinations of the two. Key correlations across synthesis methods, structural features (interfacial alloying, stacking‐fault density and surface‐ligand identity), and performance metrics (quantum yield, single‐gQD photoluminescence under thermal/photo stress, charging behavior and quantum‐optical properties) are identified. Surprisingly, it is found that interfacial alloying is the strongest indicator of gQD stability under stress, but this parameter is not the determining factor for Auger suppression. Furthermore, quantum yield is strongly influenced by surface chemistry and can approach unity even in the case of high shell‐defect density, while introduction of zinc‐blende stacking faults increases the likelihood that a gQD exhibits charged‐state emission.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2020

A Computational Theory for the Emergence of Grammatical Categories in Cortical Dynamics

A general agreement in psycholinguistics claims that syntax and meaning are unified precisely and very quickly during online sentence processing. Although several theories have advanced arguments regarding the neurocomputational bases of this phenomenon, we argue that these theories could potentially benefit by including neurophysiological data concerning cortical dynamics constraints in brain tissue. In addition, some theories promote the integration of complex optimization methods in neural tissue. In this paper we attempt to fill these gaps introducing a computational model inspired in the dynamics of cortical tissue. In our modeling approach, proximal afferent dendrites produce stochastic cellular activations, while distal dendritic branches–on the other hand–contribute independently to somatic depolarization by means of dendritic spikes, and finally, prediction failures produce massive firing events preventing formation of sparse distributed representations. The model presented in this paper combines semantic and coarse-grained syntactic constraints for each word in a sentence context until grammatically related word function discrimination emerges spontaneously by the sole correlation of lexical information from different sources without applying complex optimization methods. By means of support vector machine techniques, we show that the sparse activation features returned by our approach are well suited—bootstrapping from the features returned by Word Embedding mechanisms—to accomplish grammatical function classification of individual words in a sentence. In this way we develop a biologically guided computational explanation for linguistically relevant unification processes in cortex which connects psycholinguistics to neurobiological accounts of language. We also claim that the computational hypotheses established in this research could foster future work on biologically-inspired learning algorithms for natural language processing applications.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Acceptance dependence of factorial cumulants, long-range correlations, and the antiproton puzzle

We analyze joint factorial cumulants of protons and antiprotons in relativistic heavy-ion collisions and point out that they obey the scaling Ĉnmp,p¯∝〈Np〉n〈Np¯〉m as a function of acceptance when only long-range correlations are present in the system, such as global baryon conservation and volume fluctuations. This hypothesis can be directly tested experimentally without the need for corrections for volume fluctuations. We show that if correlations among protons and antiprotons are driven by global baryon conservation and volume fluctuations only, the equality Ĉ2p/〈Np〉2=Ĉ2p¯/〈Np¯〉2 holds for large systems created in central collisions. We point out that the experimental data of the STAR Collaboration from phase I of the Relativistic Heavy Ion Collider (RHIC) beam energy scan (BES) are approximately consistent with the scaling Ĉnmp,p¯∝〈Np〉n〈Np¯〉m, but the normalized antiproton correlations are stronger than those of protons, −Ĉ2p¯/〈Np¯〉2>−Ĉ2p/〈Np〉2. Existing theoretical baselines, based on global baryon conservation and volume fluctuations, cannot explain the data, which we refer to as the antiproton puzzle. We also discuss high-order factorial cumulants which can be measured with sufficient precision within phase II of RHIC-BES.

Bzdak, Adam↗
DOE OSTI2020

Direct Correlation of Charge Carrier Transport to Local Crystal Quality in Lead Halide Perovskites

Although solution processing methods provide an attractive route toward development of low-cost functional materials, these accessible fabrication approaches can engender high concentrations of microscopic structural defects that are detrimental to performance. In lead halide perovskites, structural disorder derived from solution processing has been implicated as an important determiner of photophysical properties. However, a direct correlation between the functional properties of these materials and the local crystal structure in which non-equilibrium states evolve has remained elusive, in part because structural heterogeneities occur on length scales that defy conventional characterization techniques. To address this knowledge gap, in this work we have combined ultrafast pump–probe microscopy and electron backscattering diffraction to directly correlate charge carrier transport with the local diffraction pattern contrast, an indicator of crystal quality. Spatial correlation of these measurements strongly suggests that even on individual single crystal CsPbBr3 domains, microscopic variability in the crystal quality profoundly impacts the efficiency of charge carrier transport.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Polarizabilities of neutral atoms and atomic ions with a noble gas electron configuration

Atomic polarizabilities play an important role in the development of force fields for molecular simulations, as well as for the development of qualitative concepts of atomic and molecular behavior. Coupled cluster theory at the coupled cluster singles doubles triples level with very large correlation-consistent basis sets with extended diffuse functions has been used to predict the polarizabilities of the atomic neutrals, mono-cations and mono-anions with a noble gas configuration. Additional corrections for scalar relativistic and spin–orbit effects were also included for the electron configurations of Kr, Xe, and Rn. The results are in excellent agreement with experiment or with other high level calculations where available. The current results for most of these species represent the best available values for the polarizabilities. The results show that the polarizability of H - is very difficult to calculate without extremely diffuse functions. The polarizability of H - is the largest value, 34.05 Å 3 , calculated for all species in the current study. The polarizabilities of the remaining halogen anions are also the best available values. The polarizabilities of the halogen anions (excluding F - ) and H - have a linear correlation with the electron affinity of the neutral atom. Spin– orbit effects, even for closed shell species, cannot be ignored for quantitative accuracy, and the inclusion of spin–orbit effects for Fr + , Rn, and At - increases the polarizability by 4%, 6%, and 15%, respectively.

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

Nonunitary Variational Quantum Eigensolver with the Localized Active Space Method and Cost Mitigation

Accurately describing strongly correlated systems with affordable quantum resources remains a central challenge for quantum chemistry applications on near and intermediate term quantum computers. The localized active space self-consistent field (LASSCF) approximates the complete active space self-consistent field (CASSCF) by generating active space-based wave functions within specific fragments while treating interfragment correlation with mean-field approach, hence is computationally less expensive. Hardware-efficient ansatzes (HEA) offer affordable and shallower circuits, yet they often fail to capture the necessary correlation. Previously, Jastrow-factor-inspired nonunitary qubit operators were proposed to use with HEA for variational quantum eigensolver (VQE) calculations (so-called nuVQE), as they do not increase circuit depths and recover correlation beyond the mean-field level for Hartree–Fock initial states. Here, in this study, we explore running nuVQE with LASSCF as the initial state. The method, named LAS-nuVQE, is shown to recover interfragment correlations, reach chemical accuracy with a small number of gates (<70) in both H 4 and square cyclobutadiene (C 4 H 4 ), and produces more accurate energetics than its HEA counterparts at all circuit depths. To further address the inherent symmetry-breaking in HEA, we implemented spin-constrained LAS-nuVQE to extend the capabilities of HEA further and show spin-pure results for square cyclobutadiene. We also mitigate the increased measurement overhead of nuVQE via Pauli grouping and shot-frugal sampling, reducing measurement costs by up to 2 orders of magnitude compared to ungrouped operator, and show that one can achieve better accuracy with a small number of shots (10 3–4 ) per one expectation value calculation compared to noiseless simulations with one or two orders of magnitude more shots. Finally, wall clock time estimates show that, with our measurement mitigation protocols, nuVQE becomes a cheaper and more accurate alternative than vanilla VQE with HEA. Taken together, these developments illustrate a practical pathway toward performing multireference chemical simulations with accuracy and affordable resources on today’s quantum hardware, achieving both accuracy and affordability in challenging correlated systems.

Wang, Qiaohong [Univ. of Chicago, IL (United State↗
DOE OSTI2023

Anisotropic magneto-resistivity and magnetocaloric effect in DyAl 2

Here, in this study, we experimentally and theoretically investigate the correlation between the anisotropic magnetic resistivity and magnetocaloric effect in DyAl 2 single crystals. DyAl 2 crystallizes in the C15 Laves phase structure with cubic symmetry. While some earlier studies revealed that the isothermal entropy change in dialuminides follows a similar trend as the electrical resistivity change as a function of temperature and magnetic field, the correlation between anisotropic behavior of these two physical parameters is yet to be explored to the best of our knowledge. To address this gap, we measured electrical resistivity of DyAl 2 single crystals along two different directions in zero and applied magnetic fields and compared the experimental results with our theoretical model. For the theoretical analysis, we employed a model Hamiltonian in the mean-field approximation, considering the exchange interaction, Zeeman effect, and crystalline electric field associated with the cubic symmetry. Our findings reveal a significant dependence of DyAl 2 resistivity on the direction of the applied magnetic field, in agreement with our theoretical results. These outcomes emphasize the interplay between magnetocaloric effect and magneto-resistivity, underscoring the potential of the magnetocaloric effect as a valuable tool for gaining deeper insights into basic physical properties including electron transport behavior.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Effect of Passive Administration of Monoclonal Antibodies Recognizing Simian Immunodeficiency Virus (SIV) V2 in CH59-Like Coil/Helical or β -Sheet Conformations on Time of SIV mac251 Acquisition

The monoclonal antibodies (MAbs) NCI05 and NCI09, isolated from a vacci nated macaque that was protected from multiple simian immunodeficiency virus (SIV) chal lenges, both target an overlapping, conformationally dynamic epitope in SIV envelope vari able region 2 (V2). Here, we show that NCI05 recognizes a CH59-like coil/helical epitope, whereas NCI09 recognizes a b-hairpin linear epitope. In vitro, NCI05 and, to a lesser extent, NCI09 mediate the killing of SIV-infected cells in a CD4-dependent manner. Compared to NCI05, NCI09 mediates higher titers of antibody-dependent cellular cytotoxicity (ADCC) to gp120-coated cells, as well as higher levels of trogocytosis, a monocyte function that contributes to immune evasion. We also found that passive administration of NCI05 or NCI09 to macaques did not affect the risk of SIV mac251 acquisition compared to controls, demonstrating that these anti-V2 antibodies alone are not protective. However, NCI05 but not NCI09 mucosal levels strongly correlated with delayed SIV mac251 acquisition, and functional and structural data suggest that NCI05 targets a transient state of the viral spike apex that is partially opened, compared to its prefusion-closed conformation.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Systematic Improvement of Quantum Monte Carlo Calculations in Transition Metal Oxides: sCI-Driven Wavefunction Optimization for Reliable Band Gap Prediction

Accurate determination of the electronic properties of correlated oxides remains a significant challenge for computational theory. Traditional Hubbard-corrected density functional theory (DFT+U) frequently encounters limitations in precisely capturing electron correlation, particularly in predicting band gaps. We introduce a systematic methodology to enhance the accuracy of diffusion Monte Carlo (DMC) simulations for both ground and excited states, focusing on LiCoO 2 as a case study. By employing a selected configuration interaction (sCI) approach, we demonstrate the capability to optimize wavefunctions beyond the constraints of single-reference DFT+U trial wavefunctions. Here, we show that the sCI framework enables accurate prediction of band gaps in LiCoO 2 , closely aligning with experimental values and substantially improving traditional computational methods. The study uncovers a nuanced mixed state of t 2g and e g orbitals at the band edges that is not captured by conventional single-reference methods, further elucidating the limitations of PBE+U in describing d-d excitations. Our findings advocate for the adoption of beyond-DFT methodologies, such as sCI, to capture the essential physics of excited-state wavefunctions in strongly correlated materials. The improved accuracy in band gap predictions and the ability to generate more reliable trial wavefunctions for DMC calculations underscore the potential of this approach for broader applications in the study of correlated oxides. This work not only provides a pathway for more accurate simulations of electronic structures in complex materials but also suggests a framework for future investigations of the excited states of other challenging systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Analytic gradients for compressed multistate pair-density functional theory

Photochemical reactions often involve states that are closely coupled due to near degeneracies, for example by proximity to conical intersections. Therefore, a multistate method is used to accurately describe these states; for example, ordinary perturbation theory is replaced by quasidegenerate perturbation theory. Multiconfiguration pair-density functional theory (MC-PDFT) provides an efficient way to approximate the full dynamical correlation energy of strongly correlated systems, and we recently proposed compressed multistate pair-density functional theory (CMS-PDFT) to treat closely coupled states. In the present paper, we report the implementation of analytic gradients for CMS-PDFT in both OpenMolcas and PySCF, and here we illustrate the use of these gradients by applying the method to the excited states of formaldehyde and phenol.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Cosmological angular trispectra and non-Gaussian covariance

Angular cosmological correlators are infamously difficult to compute due to the highly oscillatory nature of the projection integrals. Motivated by recent development on analytic approaches to cosmological perturbation theory, in this paper we present an efficient method for computing cosmological four-point correlations in angular space, generalizing previous works on lower-point functions. This builds on the FFTLog algorithm that approximates the matter power spectrum as a sum over power-law functions, which makes certain momentum integrals analytically solvable. The computational complexity is drastically reduced for correlators in a "separable" form—we define a suitable notion of separability for cosmological trispectra, and derive formulas for angular correlators of different separability classes. As an application of our formalism, we compute the angular galaxy trispectrum at tree level, with and without primordial non-Gaussianity. This includes effects of redshift space distortion and bias parameters up to cubic order. We also compute the non-Gaussian covariance of the angular matter power spectrum due to the connected four-point function, beyond the Limber approximation. Finally, we demonstrate that, in contrast to the standard lore, the Limber approximation can fail for the non-Gaussian covariance computation even for large multipoles.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Achieving performance portability in Gaussian basis set density functional theory on accelerator based architectures in NWChemEx

The numerical integration of the exchange–correlation (XC) potential is one of the primary computational bottlenecks in Gaussian basis set Kohn–Sham density functional theory (KS-DFT). To achieve optimal performance and accuracy, care must be taken in this numerical integration to preserve local sparsity as to allow for near linear weak scaling with system size. This leads to an integration scheme with several performance critical kernels which must be hand optimized for each architecture of interest. As the set of available accelerator hardware goes more diverse, a key challenge for developers of KS-DFT software is to maintain performance portability across a wide range of computational architectures. In this article, we examine a modular software design pattern which decouples the implementation details of performance critical kernels from the expression of high-level algorithmic workflows in a device-agnostic language such as C++; thus allowing for developers to target existing and emerging accelerator hardware within a single code base. We consider the efficacy of such a design pattern in the numerical integration of the XC potential by demonstrating its ability to achieve performance portability across a set of accelerator architectures which are representative of those on current and future U.S. Department of Energy Leadership Computing Facilities.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Predicting the Mechanical Response of Polyhydroxyalkanoate Biopolymers Using Molecular Dynamics Simulations

Polyhydroxyalkanoates (PHAs) have emerged as a promising class of biosynthesizable, biocompatible, and biodegradable polymers to replace petroleum-based plastics for addressing the global plastic pollution problem. Although PHAs offer a wide range of chemical diversity, the structure–property relationships in this class of polymers remain poorly established. In particular, the available experimental data on the mechanical properties is scarce. In this contribution, we have used molecular dynamics simulations employing a recently developed forcefield to predict chemical trends in mechanical properties of PHAs. Specifically, we make predictions for Young’s modulus, and yield stress for a wide range of PHAs that exhibit varying lengths of backbone and side chains as well as different side chain functional groups. Deformation simulations were performed at six different strain rates and six different temperatures to elucidate their influence on the mechanical properties. Our results indicate that Young’s modulus and yield stress decrease systematically with increase in the number of carbon atoms in the side chain as well as in the polymer backbone. In addition, we find that the mechanical properties were strongly correlated with the chemical nature of the functional group. The functional groups that enhance the interchain interactions lead to an enhancement in both the Young’s modulus and yield stress. Finally, we applied the developed methodology to study composition-dependence of the mechanical properties for a selected set of binary and ternary copolymers. Overall, our work not only provides insights into rational design rules for tailoring mechanical properties in PHAs, but also opens up avenues for future high throughput atomistic simulation studies geared towards identifying functional PHA polymer candidates for targeted applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗