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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 955 records · Page 53
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Methyl α‐D‐galactopyranosyl‐(1→3)‐β‐D‐galactopyranoside and methyl β‐D‐galactopyranosyl‐(1→3)‐β‐D‐galactopyranoside: Glycosidic linkage conformation determined from MA'AT analysis

Abstract MA'ATanalysis has been applied to two biologically‐importantO‐glycosidic linkages in two disaccharides, α‐D‐Galp‐(1→3)‐β‐D‐GalpOMe (3) and β‐D‐Galp‐(1→3)‐β‐D‐GalpOMe (4). Using density functional theory (DFT) to obtain parameterized equations relating a group of trans‐O‐glycosidic NMR spin‐couplings to eitherphi(ϕ') orpsi(ψ'), and experimental 3 J COCH , 2 J COC , and 3 J COCC spin‐couplings measured in aqueous solution in 13 C‐labeled isotopomers, probability distributions ofϕ'andψ'in each linkage were determined and compared to those determined by aqueous 1‐μs molecular dynamics (MD) simulation. Good agreement was found between theMA'ATand single‐state MD conformational models of these linkages for the most part, with modest (approximately <15°) differences in the mean values ofϕ'andψ', although the envelope of allowed angles (encoded in circular standard deviations or CSDs) is consistently larger forϕ'determined fromMA'ATanalysis than from MD for both linkages. TheMA'ATmodel of the α‐Galp‐(1→3)‐β‐Galplinkage agrees well with those determined previously using conventional NMR methods ( 3 J COCH values and/or 1 H‐ 1 H NOEs), but some discrepancy was observed for the β‐Galp‐(1→3)‐β‐Galplinkage, which may arise from errors in the conventions used to describe the linkage torsion angles. Statistical analyses of X‐ray crystal structures show ranges ofϕ'andψ'for both linkages that include the mean angles determined fromMA'ATanalyses, although both angles adopt a wide range of values in the crystalline state, withϕ'in β‐Galp‐(1→3)‐β‐Galplinkages showing greater‐than‐expected conformational variability.

Chemistry↗
DOE OSTI2022

Atomic structure and Mott nature of the insulating charge density wave phase of 1T-TaS 2

Here, using x-ray pair distribution function (PDF) analysis and computer modeling, we explore structure models for the complex charge density wave (CDW) phases of layered 1T-TaS 2 that both well capture their atomic-level features and are amenable to electronic structure calculations. The models give the most probable position of constituent atoms in terms of 3D repetitive unit cells comprising a minimum number of Ta–S layers. Structure modeling results confirm the emergence of star-of-David (SD) like clusters of Ta atoms in the high-temperature incommensurate (IC) CDW phase and show that, contrary to the suggestions of recent studies, the low-temperature commensurate (C) CDW phase expands upon cooling thus reducing lattice strain. The C-CDW phase is also found to preserve the stacking sequence of Ta–S layers found in the room temperature, nearly commensurate (NC) CDW phase to a large extent. DFT based on the PDF refined model shows that bulk C-CDW 1T-TaS 2 also preserves the insulating state of individual layers of SD clusters, favoring the Mott physics description of the metal-to-insulator (NC-CDW to C-CDW) phase transition in 1T-TaS 2 . Our work highlights the importance of using precise crystal structure models in determining the nature of electronic phases in complex materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Inference of Unresolved Point Sources at High Galactic Latitudes Using Probabilistic Catalogs

The detection of point sources in images is a fundamental operation in astrophysics, and is crucial for constraining population models of the underlying point sources or characterizing the background emission. Standard techniques fall short in the crowded-field limit, losing sensitivity to faint sources and failing to track their covariance with close neighbors. We construct a Bayesian framework to perform inference of faint or overlapping point sources. The method involves probabilistic cataloging, where samples are taken from the posterior probability distribution of catalogs consistent with an observed photon count map. In order to validate our method, we sample random catalogs of the gamma-ray sky in the direction of the North Galactic Pole (NGP) by binning the data in energy and point-spread function classes. Using three energy bins spanning 0.3–1, 1–3, and 3–10 GeV, we identify 270{sub −10}{sup +30} point sources inside a 40{sup ∘}×40{sup ∘} region around the NGP above our point-source inclusion limit of 3×10{sup −11} cm{sup −2} s{sup −1} sr{sup −1} GeV{sup −1} at the 1–3 GeV energy bin. Modeling the flux distribution as a power law, we infer the slope to be −1.92{sub −0.05}{sup +0.07} and estimate the contribution of point sources to the total emission as 18{sub −2}{sup +2}%. These uncertainties in the flux distribution are fully marginalized over the number as well as the spatial and spectral properties of the unresolved point sources. This marginalization allows a robust test of whether the apparently isotropic emission in an image is due to unresolved point sources or of truly diffuse origin.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2018

A Langevin approach to multi-scale modeling

In plasmas, distribution functions often demonstrate long anisotropic tails or otherwise significant deviations from local Maxwellians. The tails, especially if they are pulled out from the bulk, pose a serious challenge for numerical simulations as resolving both the bulk and the tail on the same mesh is often challenging. A multi-scale approach, providing evolution equations for the bulk and the tail individually, could offer a resolution in the sense that both populations could be treated on separate meshes or different reduction techniques applied to the bulk and the tail population. In this paper, we propose a multi-scale method which allows us to split a distribution function into a bulk and a tail so that both populations remain genuine, non-negative distribution functions and may carry density, momentum, and energy. The proposed method is based on the observation that the motion of an individual test particle in a plasma obeys a stochastic differential equation, also referred to as a Langevin equation. Finally, this allows us to define transition probabilities between the bulk and the tail and to provide evolution equations for both populations separately.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2019

Quantitative Uncertainty Analysis for Diffraction

Current software uses a least squares statistical method. For each model parameter, current software yields a point estimate and estimated standard error for each point estimate. In contrast, we have employed a Bayesian approach with sampling algorithm to provide a full posterior probability density function on each model parameter. This yields a different type of solution (probabilistic) with better fidelity. The Quantitative Uncertainty Analysis for Diffraction (QUAD) package returns a matrix of affect model parameters as a function of iteration through the MCMC analysis. QUAD is a Python code that allows for analysis of X-ray and neutron diffraction data to infer the structure of materials with quantifiable certainty. The code uses Bayesian statistics and Markov chain sampling algorithms to create posterior probability distributions on all material structure parameters that are modeled by a researcher. The statistical packages use the open source GSASII project as a library to calculate model diffraction patterns.

Fancher, ChristopherM↗
DOE OSTI2017

A transformed path integral approach for solution of the Fokker–Planck equation

A novel path integral (PI) based method for solution of the Fokker–Planck equation is presented. The proposed method, termed the transformed path integral (TPI) method, utilizes a new formulation for the underlying short-time propagator to perform the evolution of the probability density function (PDF) in a transformed computational domain where a more accurate representation of the PDF can be ensured. The new formulation, based on a dynamic transformation of the original state space with the statistics of the PDF as parameters, preserves the non-negativity of the PDF and incorporates short-time properties of the underlying stochastic process. New update equations for the state PDF in a transformed space and the parameters of the transformation (including mean and covariance) that better accommodate nonlinearities in drift and non-Gaussian behavior in distributions are proposed (based on properties of the SDE). Owing to the choice of transformation considered, the proposed method maps a fixed grid in transformed space to a dynamically adaptive grid in the original state space. The TPI method, in contrast to conventional methods such as Monte Carlo simulations and fixed grid approaches, is able to better represent the distributions (especially the tail information) and better address challenges in processes with large diffusion, large drift and large concentration of PDF. Additionally, in the proposed TPI method, error bounds on the probability in the computational domain can be obtained using the Chebyshev's inequality. The benefits of the TPI method over conventional methods are illustrated through simulations of linear and nonlinear drift processes in one-dimensional and multidimensional state spaces. The effects of spatial and temporal grid resolutions as well as that of the diffusion coefficient on the error in the PDF are also characterized.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A Risk-Informed Approach to Trustworthiness Assessment in Digital Twins-Based Autonomous Control

In autonomous control systems, digital twins (DTs) are used to perform diagnostic and prognostic functions. The trustworthiness of these DTs is dependent on quality and coverage of the training data, model accuracy and integrity of sensor data. This work introduces a methodology to determine the trustworthiness of a DT system given faulty sensor data using a risk informed approach. Bayesian Belief Networks (BBNs) are used to propagate uncertainties and determine the probability of trustable recommendations. The decision to trust the control action provided by the DT is based on the DT output, expert opinion, and severity of problems. The performance of DTs is reliant on the data they are trained on. When they encounter out of distribution data, the trustworthiness of the recommendations decreases. To address this issue, we include an expert component that provides input on sensor degradation. For this, we utilize a generative artificial intelligence (AI) model, such as Generative Pretrained Transformer (GPT). The GPT functions as an expert with broad knowledge. The GPT is fine-tuned to understand and discriminate sensor degradation scenarios using manufactured data. This methodology is demonstrated through a case study on a Nearly Autonomous Management and Control System (NAMAC) during a steady state scenario. Various sensor degradation types with different severity levels are considered. Degraded sensor data is processed by the DT system and the fine-tuned GPT. Finally, using the BBN, we combine the GPT information and the DT output with its sources of uncertainty. This provides an output regarding the trustworthiness of the DT recommendation.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2013

Bayesian calibration of thermodynamic models for the uptake of CO{sub 2} in supported amine sorbents using ab initio priors

A statistical methodology was applied to the simultaneous calibration and validation of thermodynamic models for the uptake of CO{sub 2} in mesoporous silica-supported amines. The methodology is Bayesian, and follows the procedure introduced by Kennedy and O'Hagan. One key aspect of the application presented is the use of quantum chemical calculations to define prior probability distributions for physical model parameters. Inclusion of this prior information proved to be crucial to the identifiability of model parameters against experimental thermogravimetric data. Through the statistical analysis, a quantitative assessment of the accuracy of various quantum chemical methods is produced. Another important aspect of the current approach is the conditioning of the model form discrepancy – a critical component of the Kennedy and O'Hagan methodology – to the experimental data in such a manner that it becomes an implicit function of the model parameters and thereby connected with the posterior distribution. It is shown that the inclusion of prior information in the analysis leads to a shifting of uncertainty from the posterior distribution for model parameters to this conditioned model form discrepancy. Prospects for more accurate model predictions and propagation of uncertainty in upscaling and extrapolation through a “model-plus-discrepancy” approach are discussed. The synthesis methods and thermogravimetric characterization of hybrid grafted/impregnated mesoporous silica-supported amine sorbents are presented, along with the details of the quantum chemical study, which shows that a carbamic acid–base acceptor complex is the most stable form of adsorbed CO{sub 2} in both alkanol- and ethyleneamines.

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

A priori filtered chemical source term modeling for LES of high Karlovitz number premixed flames

Assumptions behind closure models for the filtered source term are studied a priori using results from DNS of turbulent n-heptane/air premixed flames at varying Karlovitz numbers. Simulations with both detailed chemistry and tabulated chemistry, as well as unity and non-unity Lewis numbers, are used to determine if finite-rate chemistry and differential diffusion effects affect the filtered chemical source terms. While the unfiltered source term shows large fluctuations, the filtered source terms from detailed chemistry and tabulated chemistry are in good agreement at sufficiently large filter widths (Δ ≳ l F ). Using the concept of optimal estimators, it is shown that a tabulation approach using the filtered progress variable and its variance can predict accurately the filtered chemical source terms. Finally, the filtered source terms from the DNS are compared to predictions from two commonly assumed sub-filter probability density function models. Both models show deviations from the filtered DNS source terms but predict accurately the mean turbulent flame speed. In conclusion, the results illustrate the potential of using simple tabulated chemistry approaches based on presumed PDFs for LES of premixed flames in the thin and distributed reaction zones regimes.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Application of Gaussian Bayes classifier to differentiate chlorine-based chemical agents

The Portable Isotopic Neutron Spectroscopy (PINS) is a commercialized system developed by Idaho National Laboratory (INL) to examine chemical warfare agents (CWA) non-destructively, utilizing Prompt Gamma Neutron Activation Analysis (PGNAA) techniques. The PINS system takes advantage of a high-resolution gamma-ray spectrum from a mechanically-cooled high-purity germanium (HPGe) detector. One of the difficult technical challenges is to discriminate the chlorine-based chemical agents. Especially, CN, CNB, CNS and CG have similar chemical compositions to make it hard to discriminate them with a higher confidence. Current identification algorithms for PINS systems with 252-Cf sources have been improved and updated continuously as more field data became available, and new algorithms was studied to complement the current algorithms by adopting the Gaussian Bayes classifier. These new algorithms were intended to be applied to a subset of chlorine-based chemical agents, and their main goal is discriminate CN, CNB, CNS and CG with their ratios of the chlorine neutron inelastic 1763keV peak to the chlorine thermal neutron capture 1959keV peak, which is referred to as the “Cl i/c” or “clic” ratio in this study. The Cl i/c ratios were assumed to follow Gaussian distributions with the means and the standard deviations unique to their corresponding chemical agents. The prior probabilities of these four chemical agents were optimized with a collection of field data to achieve the best performance in terms of precision or positive predictive value (PPV). Finally, their posterior probabilities as functions of the Cl i/c ratio were implemented in the current version of PINS analysis software in order to be tested with more field data.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2021

OSSOS. XXI. Collision Probabilities in the Edgeworth–Kuiper Belt

Here, we present results on the intrinsic collision probabilities, P {sub I}, and range of collision speeds, V {sub I}, as a function of the heliocentric distance, r, in the trans-Neptunian region. The collision speed is one of the parameters that serves as a proxy for a collisional outcome (e.g., disruption and scattering of fragments, or formation of a crater, as both processes are related to the impact energy). We utilize an improved and debiased model of the trans-Neptunian object (TNO) region from the “Outer Solar System Origins Survey” (OSSOS). It provides a well-defined model of TNO orbital distribution, based on multiple opposition observations of more than 1000 bodies. We compute collisional probabilities for the OSSOS models of the main classical, resonant, detached+outer, and scattering TNO populations. The intrinsic collision probabilities and collision speeds are computed using Öpik’s approach, as revised and modified by Wetherill for noncircular and inclined orbits. The calculations are carried out for each of the dynamical TNO groups, allowing for inter-population collisions as well as collisions within each TNO population, resulting in 28 combinations in total. Our results indicate that collisions in the trans-Neptunian region are possible over a wide range in (r, V {sub I}) phase space. Although collisions are calculated to happen within r ∼ 20–200 au and V {sub I} ∼ 0.1 km s{sup −1} to as high as V {sub I} ∼ 9 km s{sup −1}, most of the collisions are likely to happen at low relative velocities V {sub I} < 1 km s{sup −1} and are dominated by the main classical belt.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

A risk map methodology to assess the spatial and temporal distribution of leakage into groundwater from Geologic Carbon Storage

The risks to potable aquifers due to brine leakage through plugged and abandoned (P&A) wells is highly uncertain and a potentially significant contributor to the risk profile in Geologic Carbon Storage (GCS). This uncertainty stems from the unknown location of wells and the large variance of P&A wellbore permeability, making the spatial assessment of P&A brine leakage risk challenging. A new methodology is presented to generate “risk maps”, or spatial distributions of brine leakage risk to groundwater resources as defined with no-impact or Maximum Contaminant Level (MCL) thresholds. The methodology utilizes probability theory, thereby avoiding the use of computationally expensive Monte Carlo simulations while maintaining flexibility in modeling techniques. These maps provide quantitative probabilities of risk as a function of time to inform site selection and monitoring during and post-injection, conducive to the US EPA's permitting of class-VI wells and the so-called “area of review”, AoR. As a demonstration of the methodology, a numerical model of a hypothetical fully-coupled system spanning from the injection reservoir to the USDW is used to assess the evolution of brine leakage through P&A wells. Risk maps of CO 2 leakage can also be generated with this methodology for a comprehensive assessment of GCS leakage risk.

58 GEOSCIENCES↗
DOE OSTI2013

Symmetric generalized binomial distributions

In two recent articles, we have examined a generalization of the binomial distribution associated with a sequence of positive numbers, involving asymmetric expressions of probabilities that break the symmetry win-loss. We present in this article another generalization (always associated with a sequence of positive numbers) that preserves the symmetry win-loss. This approach is also based on generating functions and presents constraints of non-negativeness, similar to those encountered in our previous articles.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2015

EUD-based biological optimization for carbon ion therapy

Purpose: Treatment planning for carbon ion therapy requires an accurate modeling of the biological response of each tissue to estimate the clinical outcome of a treatment. The relative biological effectiveness (RBE) accounts for this biological response on a cellular level but does not refer to the actual impact on the organ as a whole. For photon therapy, the concept of equivalent uniform dose (EUD) represents a simple model to take the organ response into account, yet so far no formulation of EUD has been reported that is suitable to carbon ion therapy. The authors introduce the concept of an equivalent uniform effect (EUE) that is directly applicable to both ion and photon therapies and exemplarily implemented it as a basis for biological treatment plan optimization for carbon ion therapy. Methods: In addition to a classical EUD concept, which calculates a generalized mean over the RBE-weighted dose distribution, the authors propose the EUE to simplify the optimization process of carbon ion therapy plans. The EUE is defined as the biologically equivalent uniform effect that yields the same probability of injury as the inhomogeneous effect distribution in an organ. Its mathematical formulation is based on the generalized mean effect using an effect-volume parameter to account for different organ architectures and is thus independent of a reference radiation. For both EUD concepts, quadratic and logistic objective functions are implemented into a research treatment planning system. A flexible implementation allows choosing for each structure between biological effect constraints per voxel and EUD constraints per structure. Exemplary treatment plans are calculated for a head-and-neck patient for multiple combinations of objective functions and optimization parameters. Results: Treatment plans optimized using an EUE-based objective function were comparable to those optimized with an RBE-weighted EUD-based approach. In agreement with previous results from photon therapy, the optimization by biological objective functions resulted in slightly superior treatment plans in terms of final EUD for the organs at risk (OARs) compared to voxel-based optimization approaches. This observation was made independent of the underlying objective function metric. An absolute gain in OAR sparing was observed for quadratic objective functions, whereas intersecting DVHs were found for logistic approaches. Even for considerable under- or overestimations of the used effect- or dose–volume parameters during the optimization, treatment plans were obtained that were of similar quality as the results of a voxel-based optimization. Conclusions: EUD-based optimization with either of the presented concepts can successfully be applied to treatment plan optimization. This makes EUE-based optimization for carbon ion therapy a useful tool to optimize more specifically in the sense of biological outcome while voxel-to-voxel variations of the biological effectiveness are still properly accounted for. This may be advantageous in terms of computational cost during treatment plan optimization but also enables a straight forward comparison of different fractionation schemes or treatment modalities.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2019

Future climate emulations using quantile regressions on large ensembles

The study of climate change and its impacts depends on generating projections of future temperature and other climate variables. For detailed studies, these projections usually require some combination of numerical simulation and observations, given that simulations of even the current climate do not perfectly reproduce local conditions. We present a methodology for generating future climate projections that takes advantage of the emergence of climate model ensembles, whose large amounts of data allow for detailed modeling of the probability distribution of temperature or other climate variables. The procedure gives us estimated changes in model distributions that are then applied to observations to yield projections that preserve the spatiotemporal dependence in the observations. We use quantile regression to estimate a discrete set of quantiles of daily temperature as a function of seasonality and long-term change, with smooth spline functions of season, long-term trends, and their interactions used as basis functions for the quantile regression. A particular innovation is that more extreme quantiles are modeled as exceedances above less extreme quantiles in a nested fashion, so that the complexity of the model for exceedances decreases the further out into the tail of the distribution one goes. We apply this method to two large ensembles of model runs using the same forcing scenario, both based on versions of the Community Earth System Model (CESM), run at different resolutions. The approach generates observation-based future simulations with no processing or modeling of the observed climate needed other than a simple linear rescaling. The resulting quantile maps illuminate substantial differences between the climate model ensembles, including differences in warming in the Pacific Northwest that are particularly large in the lower quantiles during winter. We show how the availability of two ensembles allows the efficacy of the method to be tested with a “perfect model” approach, in which we estimate transformations using the lower-resolution ensemble and then apply the estimated transformations to single runs from the high-resolution ensemble. Finally, we describe and implement a simple method for adjusting a transformation estimated from a large ensemble of one climate model using only a single run of a second, but hopefully more realistic, climate model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

Estimation of iodine nutrition and thyroid function status in late-gestation pregnant women in the United States: Development and application of a population-based pregnancy model

Previously, a deterministic biologically-based dose-response (BBDR) pregnancy model was developed to evaluate moderate thyroid axis disturbances with and without thyroid-active chemical exposure in a near-term pregnant woman and fetus. In the current study, the existing BBDR model was adapted to include a wider functional range of iodine nutrition, including more severe iodine deficiency conditions, and to incorporate empirically the effects of homeostatic mechanisms. The extended model was further developed into a population-based model and was constructed using a Monte Carlo-based probabilistic framework. In order to characterize total (T4) and free (fT4) thyroxine levels for a given iodine status at the population-level, the distribution of iodine intake for late-gestation pregnant women in the U.S was reconstructed using various reverse dosimetry methods and available biomonitoring data. The range of median (mean) iodine intake values resulting from three different methods of reverse dosimetry tested was 196.5–219.9 μg of iodine/day (228.2–392.9 μg of iodine/day). There was minimal variation in model-predicted maternal serum T4 and ft4 thyroxine levels from use of the three reconstructed distributions of iodine intake; the range of geometric mean for T4 and fT4, was 138–151.7 nmol/L and 7.9–8.7 pmol/L, respectively. The average value of the ratio of the 97.5th percentile to the 2.5th percentile equaled 3.1 and agreed well with similar estimates from recent observations in third-trimester pregnant women in the U.S. In addition, the reconstructed distributions of iodine intake allowed us to estimate nutrient inadequacy for late-gestation pregnant women in the U.S. via the probability approach. The prevalence of iodine inadequacy for third-trimester pregnant women in the U.S. was estimated to be between 21% and 44%. Taken together, the current work provides an improved tool for evaluating iodine nutritional status and the corresponding thyroid function status in pregnant women in the U.S. This model enables future assessments of the relevant risk of thyroid hormone level perturbations due to exposure to thyroid-active chemicals at the population-level. - Highlights: • A population-based thyroid function model for pregnant women was developed. • The model was used specifically study the late-gestation pregnant women in the U.S. • The prevalence of iodine inadequacy was estimated in the sub-population studied. • Developed model well predicts trimester-specific thyroid hormone reference ranges. • The model can be further used to study thyroid perturbations at a population level.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

Wang-Landau density of states based study of the folding-unfolding transition in the mini-protein Trp-cage (TC5b)

We present the results of a high-statistics equilibrium study of the folding/unfolding transition for the 20-residue mini-protein Trp-cage (TC5b) in water. The ECEPP/3 force field is used and the interaction with water is treated by a solvent-accessible surface area method. A Wang-Landau type simulation is used to calculate the density of states and the conditional probabilities for the various values of the radius of gyration and the number of native contacts at fixed values of energy—along with a systematic check on their convergence. All thermodynamic quantities of interest are calculated from this information. The folding-unfolding transition corresponds to a peak in the temperature dependence of the computed specific heat. This is corroborated further by the structural signatures of folding in the distributions for radius of gyration and the number of native contacts as a function of temperature. The potentials of mean force are also calculated for these variables, both separately and jointly. A local free energy minimum, in addition to the global minimum, is found in a temperature range substantially below the folding temperature. The free energy at this second minimum is approximately 5 k{sub B}T higher than the value at the global minimum.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗