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At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

Field Demonstration of The Krauklis Seismic Wave In A Novel Mva Method For Geologic CO 2 Storage

The Energy & Environmental Research Center (EERC) conducted a feasibility study of a new, low-impact geophysics monitoring method designed to incrementally track the saturation front of CO 2 injected into a reservoir. The method leverages a new way of transmitting energy from the surface to the reservoir and employs a new subsurface signal called the Krauklis wave (K-wave) and other guided waves for seismic monitoring. The EERC partnered with Seismos, Inc., the company that holds the exclusive technology license for this method, to advance development of K-wave technology, and Denbury Onshore, LLC, to field-test the system. The system was field-tested at Denbury’s Bell Creek oil field, currently undergoing CO 2 -based enhanced oil recovery (EOR) in southeastern Montana. The K-wave system uses a wellhead-mounted source to propagate energy down the wellbore in the form of a tube wave and through the well perforations into the reservoir. Part of the energy transmitted through the perforations into the reservoir converts to slow moving K-waves and/or other guided waves that are expected to propagate through the formation to neighboring wells. The propagated signal would induce tube waves in the neighboring wells that return to the surface to be recorded with a wellhead-mounted receiver. The propagation time of the signal is directly affected by the presence of CO 2 between the wells, so the difference in transit time of the returning signal between pre- and postinjection data sets could be used to help define the lateral extent of a CO 2 saturation front. Objectives of the study were to demonstrate, validate, and evaluate the K-wave method’s ability to monitor the morphology of injected CO 2 and estimate saturation distribution. Results from the demonstration were to be compared to conventional 4-D surface seismic methods, dynamic reservoir simulations, and CO 2 breakthrough data to validate the technology and provide useful information that may result in improvements. Prior to mobilizing for the full-scale K-wave baseline survey, a field test was conducted to better understand wellhead hardware configurations and test the response from the Bell Creek reservoir using three wells. Useful operational information resulted but signal from the first-generation gas release/gas injection source was not recorded in neighboring wells. After the initial field test, numerical modeling of the K-wave method was initiated using parameters specific to the Bell Creek Field. Modeling results indicated that the fundamental concepts behind the K-wave method exhibited problems and revealed a significantly greater attenuation of the signal at the wellbore perforations than expected, totaling on the order of 10-8 from source well to receiver well over a 400-m well spacing. Modeling also showed that greater source frequency bandwidth was needed to produce guided waves within a 30-foot-thick reservoir layer such as that at Bell Creek and that reservoir layer seismic velocity would need to be slower than the velocities of the bounding layers in order to act as a wave guide opposite to what exists at Bell Creek. Modeling results prompted a second field test with a stronger, second-generation displacement source developed in the interim. Concurrent with the second field test, a 3-D seismic survey was acquired to serve as a baseline for project validation and to serve as a monitor data set for the portion of the project area where CO 2 injection had already commenced. The new source was tested using a four-well geometry and failed to produce a detectable signal, which appeared to confirm modeling results and indicated that the Bell Creek Field is not an ideal site for the K-wave test. It was concluded that a source with sufficient strength and bandwidth could not be built to overcome the factors discovered by the modeling within a reasonable amount of time. Several other sites undergoing CO 2 -based EOR were also evaluated; however, none of these sites was amenable because of geology, limitations of source and receiver hardware, or the advanced state of the CO 2 flood. In addition, two other configurations of the source and receiver layout were considered; however, these design modifications either changed the scope of the project or did not meet the goals of the Carbon Storage Program. In consultation with the U.S. Department of Energy (DOE) Project Manager and Technology Manager, a no-go decision was invoked to forego additional expenditures as the technology would not meet current project objectives. Project activities to date have moved the technology forward by developing modeling equations that can be applied elsewhere, advanced the state of wellhead sensors and sources, and spurred improvements to field operations. The 3-D seismic survey in the project area and the dynamic reservoir simulations done as part of this study have provided value for ongoing and future synergistic activities at Bell Creek related to DOE carbon storage goals.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

Evaluating the Community Land Model in a pine stand with shading manipulations and 13 CO 2 labeling

Carbon partitioning and flow through ecosystems regulates land surface atmosphere CO 2 exchange and thus is a key, albeit uncertain component of mechanistic models. The Partitioning in Trees and Soil (PiTS) experiment-model project tracked C partitioning through a young Pinus taeda stand following pulse-labeling with 13 CO 2 and two levels of shading. The field component of this project provided process-oriented data that was used to evaluate and improve terrestrial biosphere model simulations of rapid shifts in carbon partitioning and hydrological dynamics under varying environmental conditions. Here we tested the performance of the Community Land Model version 4 (CLM4) in capturing short-term carbon and water dynamics in relation to manipulative shading treatments, and the timing and magnitude of carbon fluxes through various compartments of the ecosystem. To constrain CLM4 to closely simulate pretreatment conditions, we calibrated select model parameters with the pretreatment observational data. Compared to CLM4 simulations with default parameters, CLM4 with calibrated model parameters was better able to simulate pretreatment vegetation carbon pools, light response curves, and other initial states and fluxes of carbon and water. Over a 3-week treatment period, the calibrated CLM4 generally reproduced the impacts of shading on average soil moisture at 15-95 cm depth, transpiration, relative change in stem carbon, and soil CO 2 efflux rate, although some discrepancies in the estimation of magnitudes and temporal evolutions existed. CLM4, however, was not able to track the progression of the 13 CO 2 label from the atmosphere through foliage, phloem, roots or surface soil CO 2 efflux, even when optimized model parameters were used. This model bias arises, in part, from the lack of a short-term non-structural carbohydrate storage pool and progressive timing of within-plant transport, thus indicating a need for future work to improve the allocation routines in CLM4. Overall, these types of detailed evaluations of CLM4, paired with intensive field manipulations, can help to identify model strengths and weaknesses, model uncertainties, and additional observations necessary for future model development.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2018

Clutter identification based on kernel density estimation and sparse recovery

A cognitive radar framework is being developed to dynamically detect changes in the clutter characteristics, and to adapt to these changes by identifying the new clutter distribution. In our previous work, we have presented a sparse-recovery based clutter identification technique. In this technique, each column of the dictionary represents a specific distribution. More specifically, calibration radar clutter data corresponding to a specific distribution is transformed into a distribution through kernel density estimation. When the new batch of radar data arrives, the new data is transformed to a distribution through the same kernel density estimation method and its distribution characteristics is identified through sparse-recovery. In this paper, we extend our previous work to consider different kernels and kernel parameters for sparse-recovery-based clutter identification and the numerical results are presented as well. The impact of different kernels and kernel parameters are analyzed by comparing the identification accuracy of each scenario.

Wang, Haokun↗
DOE OSTI2016

Accurate and efficient prediction of fine-resolution hydrologic and carbon dynamic simulations from coarse-resolution models

The topography, and the biotic and abiotic parameters are typically upscaled to make watershed-scale hydrologic-biogeochemical models computationally tractable. However, upscaling procedure can produce biases when nonlinear interactions between different processes are not fully captured at coarse resolutions. Here, we applied the Proper Orthogonal Decomposition Mapping Method (PODMM) to downscale the field solutions from a coarse (7 km) resolution grid to a fine (220 m) resolution grid. PODMM trains a reduced-order model (ROM) with coarse-resolution and fine-resolution solutions, here obtained using PAWS+CLM, a quasi-3-D watershed processes model that has been validated for many temperate watersheds. Subsequent fine-resolution solutions were approximated based only on coarse-resolution solutions and the ROM. The approximation errors were efficiently quantified using an error estimator. By jointly estimating correlated variables and temporally varying the ROM parameters, we further reduced the approximation errors by up to 20%. We also improved the method's robustness by constructing multiple ROMs using different set of variables, and selecting the best approximation based on the error estimator. The ROMs produced accurate downscaling of soil moisture, latent heat flux, and net primary production with O(1000) reduction in computational cost. The subgrid distributions were also nearly indistinguishable from the ones obtained using the fine-resolution model. Compared to coarse-resolution solutions, biases in upscaled ROM solutions were reduced by up to 80%. This method has the potential to help address the long-standing spatial scaling problem in hydrology and enable long-time integration, parameter estimation, and stochastic uncertainty analysis while accurately representing the heterogeneities.

58 GEOSCIENCES↗
DOE OSTI2023

Structural characterization of tin in toothpaste by dynamic nuclear polarization enhanced 119 Sn solid-state NMR spectroscopy

Stannous fluoride (SnF 2 ) is an effective fluoride source and antimicrobial agent that is widely used in commercial toothpaste formulations. The antimicrobial activity of SnF 2 is partly attributed to the presence of Sn(II) ions. However, it is challenging to directly determine the Sn speciation and oxidation state within commercially available toothpaste products due to the low weight loading of SnF 2 (0.454 wt% SnF 2 , 0.34 wt% Sn) and the amorphous, semi-solid nature of the toothpaste. Here, we show that dynamic nuclear polarization (DNP) enables 119 Sn solid-state NMR experiments that can probe the Sn speciation within commercially available toothpaste. Solid-state NMR experiments on SnF 2 and SnF 4 show that 19 F isotropic chemical shift and 119 Sn chemical shift anisotropy (CSA) are highly sensitive to the Sn oxidation state. DNP-enhanced 119 Sn magic-angle turning (MAT) 2D NMR spectra of toothpastes resolve Sn(II) and Sn(IV) by their 119 Sn chemical shift tensor parameters. Fits of DNP-enhanced 1D 1 H → 119 Sn solid-state NMR spectra allow the populations of Sn(II) and Sn(IV) within the toothpastes to be estimated. This analysis reveals that three of the four commercially available toothpastes contained at least 80% Sn(II), whereas one of the toothpaste contained a significantly higher amount of Sn(IV).

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

Optimizing process-based models to predict current and future soil organic carbon stocks at high-resolution

From hillslope to small catchment scales (< 50 km 2 ), soil carbon management and mitigation policies rely on estimates and projections of soil organic carbon (SOC) stocks. Here we apply a process-based modeling approach that parameterizes the MIcrobial-MIneral Carbon Stabilization (MIMICS) model with SOC measurements and remotely sensed environmental data from the Reynolds Creek Experimental Watershed in SW Idaho, USA. Calibrating model parameters reduced error between simulated and observed SOC stocks by 25%, relative to the initial parameter estimates and better captured local gradients in climate and productivity. The calibrated parameter ensemble was used to produce spatially continuous, high-resolution (10 m 2 ) estimates of stocks and associated uncertainties of litter, microbial biomass, particulate, and protected SOC pools across the complex landscape. Here, subsequent projections of SOC response to idealized environmental disturbances illustrate the spatial complexity of potential SOC vulnerabilities across the watershed. Parametric uncertainty generated physicochemically protected soil C stocks that varied by a mean factor of 4.4 × across individual locations in the watershed and a – 14.9 to + 20.4% range in potential SOC stock response to idealized disturbances, illustrating the need for additional measurements of soil carbon fractions and their turnover time to improve confidence in the MIMICS simulations of SOC dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Cross-machine comparison of runaway electron generation during tokamak start-up for extrapolation to ITER

A cross-machine comparison of global parameters that determine the runaway electron (RE) generation and loss process during tokamak start-up was carried out with the aim to extrapolate these to ITER. The study found that all considered discharges, also those that do not show signs of RE, are non-thermal at the start, i.e. have a streaming parameter larger than 0.1. During the current ramp-up the electric field, E, remains above the critical value, E c , that allows RE in the plasma. The distinction to be made is not if RE can form but, if sufficient RE can form fast enough such that they are detected or start to dominate the dynamics of the tokamak discharge. The dynamics of the value of E, density and temperature during tokamak are key to the formation of RE. It was found that larger devices operate with E closer to E c , due to their higher temperatures, hence the RE generation is relatively slower. The slower time scales for the formation of RE, estimated to be of the order of 100s of ms in ITER simplifies the development of avoidance schemes. The RE confinement time is also an important determinant of the entire process and is found to increase with the device size. The study also revealed that drift orbit losses, a mechanism often attributed as the main RE loss mechanism during the early tokamak discharge, are actually more difficult to achieve. RE losses might be more likely attributed to RE diffusion due to magnetic turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2017

Predicting Total Dissolved Gas Travel Time in Hydropower Reservoirs

Large spills at hydropower facilities can produce environmentally unfavorable supersaturated total dissolved gas (TDG) conditions. Enhanced coordination between adjacent hydropower facilities is required when a large, brief spill creates a pulse of TDG that is transported into a downstream reservoir. A premium is placed on quick and simple methods and relationships that can support short-term decision making under dynamic conditions. This paper presents an empirically-based methodology to quantify and assess the relationship between mean hourly river flow and TDG travel time between an upstream hydropower spillway and a downstream dam. The analysis is conducted for reservoirs in the mid-Columbia River system and is limited to summer months when spill events that create high TDG are most common. A two-step filter and cross-correlation procedure is used to isolate high strength TDG events and characterize the time delay between when the TDG event is initiated upstream and when it is detected downstream. Spill flow, powerhouse flow, and TDG measurements are used to develop a bulk parameter estimation of mean TDG time delay as a function of mean river flow. The approach reveals an inverse power law relationship between mean river flow and mean TDG travel time. The relationship provides hydropower operators with a new, simplified decision support tool. In conclusion, the generalized methodology could be applied to other reservoir systems where TDG minimization is a critical management objective.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Partial muon capture rates in A = 3 and A = 6 nuclei with chiral effective field theory

Searches for neutrinoless-double beta decay rates are crucial in addressing questions within fundamental symmetries and neutrino physics. The rates of these decays depend not only on unknown parameters associated with neutrinos, but also on nuclear properties. In order to reliably extract information about the neutrino, one needs an accurate treatment of the complex many-body dynamics of the nucleus. Neutrinoless-double beta decays take place at momentum transfers on the order of 100 MeV/$c$ and require both nuclear electroweak vector and axial current matrix elements. Muon capture, a process in the same momentum transfer regime, has readily available experimental data to validate these currents. In this work, we present results of {\it ab initio} calculations of partial muon capture rates for $^3$He and $^6$Li nuclei using variational and Green's Function Monte Carlo computational methods. We estimate the impact of the three-nucleon interactions, the cutoffs used to regularize two-nucleon ($2N$) interactions, and the energy range of $2N$ scattering data used to fit these interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2019

Electron-phonon coupling induced defect recovery and strain relaxation in Ni and equiatomic NiFe alloy

In this work, we study the effects of local heating due to electron-phonon coupling in cumulative 10 MeV Ni ion irradiation on pre-damaged pure Ni and equiatomic NiFe alloy. In particular, we estimate the defect recovery in NiFe compared to pure Ni due to the chemical disorder. Furthermore, the simulations are done using the two-temperature molecular dynamics approach that includes the electronic stopping and electron-phonon interactions. A total of 50% of the damage that consists of isolated point defects and small defect clusters is recovered in NiFe, whereas no noticeable recovery is observed in elemental Ni. We have also demonstrated strain relaxation associated with defect recombination based on the results from both simulation and X-ray diffraction measurements in NiFe. The damage recovery primarily depends on pre-existing damage level, defect configuration, ion energy (stopping powers) and electron-phonon coupling parameter of the materials of interest.

36 MATERIALS SCIENCE↗
DOE OSTI2015

On non-autonomous dynamical systems

In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2017

Galaxy Cluster Mass Reconstruction Project – III. The impact of dynamical substructure on cluster mass estimates

With the advent of wide-field cosmological surveys, we are approaching samples of hundreds of thousands of galaxy clusters. While such large numbers will help reduce statistical uncertainties, the control of systematics in cluster masses is crucial. Here we examine the effects of an important source of systematic uncertainty in galaxy-based cluster mass estimation techniques: the presence of significant dynamical substructure. Dynamical substructure manifests as dynamically distinct subgroups in phase-space, indicating an ‘unrelaxed’ state. This issue affects around a quarter of clusters in a generally selected sample. We employ a set of mock clusters whose masses have been measured homogeneously with commonly used galaxy-based mass estimation techniques (kinematic, richness, caustic, radial methods). We use these to study how the relation between observationally estimated and true cluster mass depends on the presence of substructure, as identified by various popular diagnostics. We find that the scatter for an ensemble of clusters does not increase dramatically for clusters with dynamical substructure. However, we find a systematic bias for all methods, such that clusters with significant substructure have higher measured masses than their relaxed counterparts. This bias depends on cluster mass: the most massive clusters are largely unaffected by the presence of significant substructure, but masses are significantly overestimated for lower mass clusters, by ~ 10 percent at 10 14 and ≳ 20 percent for ≲ 10 13.5 . Finally, the use of cluster samples with different levels of substructure can therefore bias certain cosmological parameters up to a level comparable to the typical uncertainties in current cosmological studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

THE B/C AND SUB-IRON/IRON COSMIC RAY RATIOS—FURTHER EVIDENCE IN FAVOR OF THE SPIRAL-ARM DIFFUSION MODEL

The boron to carbon (B/C) and sub-Fe/Fe ratios provide an important clue on cosmic ray (CR) propagation within the Galaxy. These ratios estimate the grammage that the CRs traverse as they propagate from their sources to Earth. Attempts to explain these ratios within the standard CR propagation models require ad hoc modifications and even with those these models necessitate inconsistent grammages to explain both ratios. As an alternative, physically motivated model, we have proposed that CRs originate preferably within the galactic spiral arms. CR propagation from dynamic spiral arms has important imprints on various secondary to primary ratios, such as the B/C ratio and the positron fraction. We use our spiral-arm diffusion model with the spallation network extended up to nickel to calculate the sub-Fe/Fe ratio. We show that without any additional parameters the spiral-arm model consistently explains both ratios with the same grammage, providing further evidence in favor of this model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A disk-based dynamical mass estimate for the young binary AK SCO

We present spatially and spectrally resolved Atacama Large Millimeter/submillimeter Array (ALMA) observations of gas and dust in the disk orbiting the pre-main sequence (pre-MS) binary AK Sco. By forward-modeling the disk velocity field traced by CO J = 2–1 line emission, we infer the mass of the central binary, M{sub ∗}=2.49±0.10 M{sub ⊙}, a new dynamical measurement that is independent of stellar evolutionary models. Assuming the disk and binary are co-planar within ∼2°, this disk-based binary mass measurement is in excellent agreement with constraints from radial velocity monitoring of the combined stellar spectra. These ALMA results are also compared with the standard approach of estimating masses from the location of the binary in the Hertzsprung–Russell diagram, using several common pre-MS model grids. These models predict stellar masses that are marginally consistent with our dynamical measurement (at ∼2σ), but are systematically high (by ∼10%). These same models consistently predict an age of 18 ± 1 Myr for AK Sco, in line with its membership in the Upper Centaurus–Lupus association but surprisingly old for it to still host a gas-rich disk. As ALMA accumulates comparable data for large samples of pre-MS stars, the methodology employed here to extract a dynamical mass from the disk rotation curve should prove extraordinarily useful for efforts to characterize the fundamental parameters of early stellar evolution.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A Behavioral Robotics Approach to Radiation Mapping Using Adaptive Sampling

Radiation mapping is a desirable task to automate because of the inherent risks involved and its tedious nature. A novel system was designed to address this by combining various existing technologies, utilizing behavior-based robotics and Bayesian optimization. The system uses a quadruped robot equipped with a manipulator and gamma detector to take measurements at locations that are selected based on the uncertainty of a surrogate model used to estimate the true radiation field. The robot uses input from the world with depth cameras to avoid collisions with the robot’s body, and unreachable points for the end effector are addressed by both allowing for a soft collision with the environment to occur, prompting the system to abandon that point, and varying the exploration tendency of the optimization based on consecutive collisions. This approach provides unique traversability and adaptability over other strategies in the literature. Experiments were performed by placing a Cesium-137 source on the ground and varying geometric setups and an optimization parameter demonstrating the adaptability to diverse environments and the increased robustness resulting from the designed behavior. The results additionally demonstrate that dynamically adjusting the optimization algorithm’s exploration tendency based on the arm’s collision history improves the system’s ability to navigate cluttered environments and construct accurate radiation maps without getting stuck in unreachable areas.

Adams, Joel↗
DOE OSTI2013

Experimental evidence of a collinear antiferromagnetic ordering in the frustrated CoAl2O4 spinel

Nuclear magnetic resonance (NMR), neutron diffraction (ND), x-ray diffraction, magnetic susceptibility χ, and specific-heat measurements on the frustrated A-site spinel CoAl2O4 compound reveal a collinear antiferromagnetic ordering below TN = 9.8(2) K. A high-quality powder sample characterized by x-ray diffraction that indicates a relatively low Co-Al inversion parameter x=0.057(20) in (Co1-xAlx)[Al2-xCox]O4, shows a broad maximum around 15 K in χ(T) and a sharp peak at TN in heat capacity Cp. The average-ordered magnetic moment of Co2+ (S=32) ions at the A site is estimated to be 2.4(1) μB from NMR and 1.9(5) μB from ND which are smaller than the expected value of 3 μB for S=32 and g = 2. Antiferromagnetic spin fluctuations and correlations in the paramagnetic state are revealed from the χ, NMR, and ND measurements, which are due to spin frustration and site inversion effects in the system. The ND data also show short-range dynamic magnetic ordering that persists to a temperature that is almost twice TN.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Variational quantum algorithm for estimating the quantum Fisher information

The quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state and can be regarded as a reliability measure of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed state is in general a computationally demanding task. In this paper we present a variational quantum algorithm called variational quantum Fisher information estimation (VQFIE) to address this task. By estimating lower and upper bounds on the QFI, based on bounding the fidelity, VQFIE outputs a range in which the actual QFI lies. This result can then be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. In contrast to previous approaches, VQFIE does not require knowledge of the explicit form of the sensor dynamics. We simulate the algorithm for a magnetometry setup and demonstrate the tightening of our bounds as the state purity increases. For this example, we compare our bounds with literature bounds and show that our bounds are tighter.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Accuracy of maximum likelihood estimates of a two-state model in single-molecule FRET

Photon sequences from single-molecule Förster resonance energy transfer (FRET) experiments can be analyzed using a maximum likelihood method. Parameters of the underlying kinetic model (FRET efficiencies of the states and transition rates between conformational states) are obtained by maximizing the appropriate likelihood function. In addition, the errors (uncertainties) of the extracted parameters can be obtained from the curvature of the likelihood function at the maximum. We study the standard deviations of the parameters of a two-state model obtained from photon sequences with recorded colors and arrival times. The standard deviations can be obtained analytically in a special case when the FRET efficiencies of the states are 0 and 1 and in the limiting cases of fast and slow conformational dynamics. These results are compared with the results of numerical simulations. The accuracy and, therefore, the ability to predict model parameters depend on how fast the transition rates are compared to the photon count rate. In the limit of slow transitions, the key parameters that determine the accuracy are the number of transitions between the states and the number of independent photon sequences. In the fast transition limit, the accuracy is determined by the small fraction of photons that are correlated with their neighbors. The relative standard deviation of the relaxation rate has a “chevron” shape as a function of the transition rate in the log-log scale. The location of the minimum of this function dramatically depends on how well the FRET efficiencies of the states are separated.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗