Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical errors”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 973 records · Page 54
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

On the minimum number of radiation field parameters to specify gas cooling and heating functions

Fast and accurate approximations of gas cooling and heating functions are needed for hydrodynamic galaxy simulations. We use machine learning to analyze atomic gas cooling and heating functions in the presence of a generalized incident local radiation field computed by Cloudy. We characterize the radiation field through binned radiation field intensities instead of the photoionization rates used in our previous work. We find a set of 6 energy bins whose intensities exhibit relatively low correlation. We use these bins as features to train machine learning models to predict Cloudy cooling and heating functions at fixed metallicity. We compare the relative SHapley Additive exPlanation (SHAP) value importance of the features. From the SHAP analysis, we identify a feature subset of 3 energy bins (0.5-1, 1-4, and 13-16Ry) with the largest importance and train additional models on this subset. We compare the mean squared errors and distribution of errors on both the entire training data table and a randomly selected 20% test set withheld from model training. The machine learning models trained with 3 and 6 bins, as well as 3 and 4 photoionization rates, have comparable accuracy everywhere, with errors ≳10 times smaller than for the interpolation table of Gnedin and Hollon (2012). We conclude that 3 energy bins (or 3 analogous photoionization rates: molecular hydrogen photodissociation, neutral hydrogen HI, and fully ionized carbon CVI) are sufficient to characterize the dependence of the gas cooling and heating functions on our assumed incident radiation field model.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Improving initialization and evolution accuracy of cosmological neutrino simulations

Neutrino mass constraints are a primary focus of current and future large-scale structure (LSS) surveys. Non-linear LSS models rely heavily on cosmological simulations — the impact of massive neutrinos should therefore be included in these simulations in a realistic, computationally tractable, and controlled manner. Here, a recent proposal to reduce the related computational cost employs a symmetric neutrino momentum sampling strategy in the initial conditions. We implement a modified version of this strategy into the Hardware/Hybrid Accelerated Cosmology Code (HACC) and perform convergence tests on its internal parameters. We illustrate that this method can impart Script $\mathcal{O}$(1%) numerical artifacts on the total matter field on small scales, similar to previous findings, and present a method to remove these artifacts using Fourier-space filtering of the neutrino density field. Moreover, we show that the converged neutrino power spectrum does not follow linear theory predictions on relatively large scales at early times at the 15% level, prompting a more careful study of systematics in particle-based neutrino simulations. We also present an improved method for backscaling linear transfer functions for initial conditions in massive neutrino cosmologies that is based on achieving the same relative neutrino growth as computed with Boltzmann solvers. Our self-consistent backscaling method yields sub-percent accuracy in the total matter growth function. Comparisons for the non-linear power spectrum with the Mira-Titan emulator at a neutrino mass of m ν = 0.15 eV are in very good agreement with the expected level of errors in the emulator and in the direct N-body simulation.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Clustering High-dimensional Toxicogenomics Data with Rare Signals

Toxicogenomics studies the gene and protein activities to drug treatments or toxic exposures. As the drugs and genes are numerous, toxicogenomics data are naturally high dimensional, with dimension sizes up to millions. In addition, the distribution of toxicogenomics data is oftentimes skewed, and they contain rare but important signals representing a cell or organism’s response to toxicity. The combination of high dimension and extremely skewed distribution of toxicogenomics data makes clustering analysis extremely challenging.We present our study of clustering toxicogenomics data using classical approaches such as principal component analysis as well as deep learning approaches such as auto-encoders. Our experiments show that these approaches fail to preserve rare signals and produce high-quality clusters. We then explore augmenting matrix factorization with deep learning techniques such as attention mechanism to produce latent representations for clustering. Our technique is able to better preserve rare signals after dimensionality reduction than prior approaches. Furthermore, we combine our augmented matrix factorization with a mechanism similar to autoencoder to balance separable clusters and low regeneration errors. Our experiments demonstrate better clustering with our proposed approach.

Cong, Guojing↗
DOE OSTI2020

H2OI95: A Stand-Alone Fortran Code for Evaluating the IAPWS-95 Equation-of-State Model for Water (Rev. 1)

H2OI95 is a stand-alone Fortran code for evaluating the IAPWS-95 equation-of-state model for the thermodynamic properties of water. It also evaluates the corresponding thermochemical properties of water consistent with the CODATA recommendations. The IAPWS-95 model is based on a model equation for the dimensionless Helmholtz energy for which the primary variables are the inverse reduced temperature (τ = T cr /T ) and reduced density (δ = ρ/ρ cr ). Here T is the absolute temperature (K), ρ is density (kg/m³), and the subscript “ cr ” refers to the critical point of water (647.096 K and 22.064 MPa pressure in this model, for which ρ cr is 322 kg/m³). The code solves four basic types of problems, distinguished by the specified inputs: 1. Temperature (K) and density (ρ kg/m³) or reduced density (δ) 2. Temperature (K) and pressure (MPa). 3. Temperature (K) on the saturation (liquid-vapor equilibrium) curve 4. Pressure (MPa) on the saturation curve. Each type of problem is run using a corresponding input (text) file. All but the first type of problem require iteration. For example, to solve for desired temperature and pressure, the reduced density must be adjusted to give the desired pressure. Iteration is accomplished using the Newton-Raphson method, though the secant method is also used in solving the fourth type of problem. For the last three types of problems, H2OI95 has been used to conduct numerical studies of convergence and the problem of multiple numerical solutions, some of which are not physically valid. Obtaining valid results depends mainly on appropriate choice of starting values for the density. The default values used in H2OI95 appear to consistently lead to generally desired results. With modification (not addressed here), H2OI95 can be used to support SUPCRT92 and similar codes that compute chemical thermodynamic properties of species and reactions over a wide range of temperature and pressure (273.16-1273K and 0-1000 MPa). Version 1.1 of this software calculates an extended set of water properties, including some derivable solely from IAPWS-95, such as the isobaric thermal expansivity and the isothermal compressibility, and still other properties based on supplementary models sanctioned by IAPWS, including the dynamic viscosity, thermal conductivity, surface tension, and static dielectric constant, and various other properties (notably Debye-Hückel parameters) derivable from the dielectric constant and its partial derivatives with respect to temperature and pressure. A coding error in Version 1.0 was identified while testing the implementation of the viscosity model. This error is described in Appendix C. It mainly affects calculation of “higher order” properties such as compressibility and heat capacity near the critical point.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Modeling Sea Ice Effects for Wave Energy Resource Assessments

Wave-generated power has potential as a valuable coastal resource, but the wave climate needs to be mapped for feasibility before wave energy converters are installed. Numerical models are used for wave resource assessments to quantify the amount of available power and its seasonality. Alaska is the U.S. state with the longest coastline and has extensive wave resources, but it is affected by seasonal sea ice that dampens the wave energy and the full extent of this dampening is unknown. To accurately characterize the wave resource in regions that experience seasonal sea ice, coastal wave models must account for these effects. The aim of this study is to determine how the dampening effects of sea ice change wave energy resource assessments in the nearshore. Here, we show that by combining high-resolution sea ice imagery with a sea ice/wave dampening parameterization in an unstructured grid, the Simulating Waves Nearshore (SWAN) model improves wave height predictions and demonstrates the extent to which wave power decreases when sea ice is present. The sea ice parametrization decreases the bias and root mean square errors of wave height comparisons with two wave buoys and predicts a decrease in the wave power of up to 100 kW/m in areas around Prince William Sound, Alaska. The magnitude of the improvement of the model/buoy comparison depends on the coefficients used to parameterize the wave–ice interaction.

16 TIDAL AND WAVE POWER↗
DOE OSTI2023

Analysis of the impact of broad absorption lines on quasar redshift measurements with synthetic observations

ABSTRACT Accurate quasar classifications and redshift measurements are increasingly important to precision cosmology experiments. Broad absorption line (BAL) features are present in 15–20 per cent of all quasars, and these features can introduce systematic redshift errors, and in extreme cases produce misclassifications. We quantitatively investigate the impact of BAL features on quasar classifications and redshift measurements with synthetic spectra that were designed to match observations by the Dark Energy Spectroscopic Instrument (DESI) survey. Over the course of 5 yr, DESI aims to measure spectra for 40 million galaxies and quasars, including nearly three million quasars. Our synthetic quasar spectra match the signal-to-noise ratio and redshift distributions of the first year of DESI observations, and include the same synthetic quasar spectra both with and without BAL features. We demonstrate that masking the locations of the BAL features decreases the redshift errors by about 1 per cent and reduces the number of catastrophic redshift errors by about 80 per cent. We conclude that identifying and masking BAL troughs should be a standard part of the redshift determination step for DESI and other large-scale spectroscopic surveys of quasars.

(galaxies:) quasars: absorption↗
DOE OSTI2026

Development of a coupled experimental–computational approach for engineering optimization of spout-fluidized bed particle coating systems

The design of spout-fluidized bed (SFB) coating systems for nuclear particle fuels typically relies on trial-and-error processes, comprising iterative and time-consuming coating deposition experiments and post-deposition characterization. At an engineering scale, this approach to guided SFB system design is inefficient, highlighting the need for streamlined experimental methodologies which can correlate fluidization conditions to downstream coating outcomes. In this study, we combine time-resolved particle image velocimetry (PIV) with CFD–DEM simulations to benchmark hydrodynamic behavior in a 3D spout-fluidized bed. By exploiting easily accessible optical measurements of particle motion at the bed wall and within the spouting region, we obtain quantitative velocity fields that can be directly compared with model predictions of the occluded bed region, without resorting to complex imaging and characterization techniques such as X-ray or magnetic resonance tomography. Experimental benchmarking reveals strong agreement between CFD–DEM and PIV in the spout and annulus regions, while discrepancies near the wall highlight areas for future model development. Here, the proposed integrated experimental–numerical framework will enable a direct connection between measured variables and numerically predicted fluidization performance of dense, surrogate nuclear particle fuel feedstock such that experimental SFB component design can be rapidly evaluated, informing design decisions for nozzle geometry and operating conditions. Future work will extend this framework by correlating quantified fluidization metrics across nozzle geometries and operating conditions with the resulting coating morphology, microstructure, and uniformity. Establishing these correlations will enable predictive links between hydrodynamic performance and coating quality, providing a rational, scalable basis for optimizing SFB design prior to coating deposition.

CFD/DEM↗
DOE OSTI2020

Digital-analog quantum computation

Digital quantum computing paradigm offers highly desirable features such as universality, scalability, and quantum error correction. However, physical resource requirements to implement useful error-corrected quantum algorithms are prohibitive in the current era of NISQ devices. As an alternative path to performing universal quantum computation, within the NISQ era limitations, we propose to merge digital single-qubit operations with analog multiqubit entangling blocks in an approach we call digital-analog quantum computing (DAQC). Along these lines, although the techniques may be extended to any resource, we propose to use unitaries generated by the ubiquitous Ising Hamiltonian for the analog entangling block and we prove its universal character. Here, we construct explicit DAQC protocols for efficient simulations of arbitrary inhomogeneous Ising, two-body, and M-body spin Hamiltonian dynamics by means of single-qubit gates and a fixed homogeneous Ising Hamiltonian. Additionally, we compare a sequential approach where the interactions are switched on and off (stepwise DAQC) with an always-on multiqubit interaction interspersed by fast single-qubit pulses (banged DAQC). Finally, we perform numerical tests comparing purely digital schemes with DAQC protocols, showing a remarkably better performance of the latter. The proposed DAQC approach combines the robustness of analog quantum computing with the flexibility of digital methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Mind-the-gap - Part III: Doppler velocity measurements from space

Convective motions and hydrometeors microphysical properties are highly sought-after parameters for evaluating atmospheric numerical models. With most of the Earth's surface covered by water, space-borne Doppler radars are ideal for acquiring such measurements at a global scale. While these systems have proven to be useful tools for retrieving cloud microphysical and dynamical properties from the ground, their adequacy, and specific requirements for spaceborne operation still need to be evaluated. Comprehensive forward simulations enable us to assess the advantages and drawbacks of six different Doppler radar architectures currently planned or under consideration by space agencies for the study of cloud dynamics. Radar performance is examined against state-of-the-art numerical model simulations of well-characterized shallow and deep, continental, and oceanic convective cases. Mean Doppler velocity (MDV) measurements collected at multiple frequencies (13, 35 and 94 GHz) provide complementary information in deep convective cloud systems. The high penetration capability of the 13-GHz radar enables to obtain a complete, albeit horizontally under-sampled, view of deep convective storms. The smaller instantaneous field of view (IFOV) of the 35-GHz radar captures more precise information about the location and size of convective updrafts above 5-8 km height of most systems which was determined is the portion of storms where the mass flux peak is typically located. Finally, the lower mean Doppler velocity uncertainty of displaced phase center antenna (DPCA) radars makes them an ideal system for studying microphysics in shallow convection and frontal systems, as well as ice and mixed-phase clouds. It is demonstrated that a 94-GHz DCPA system can achieve retrieval errors as low as 0.05-0.15 mm for raindrop volume-weighted mean diameter and 25% for rime fraction (for a -10 dBZ echo).

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Model Agnostic Bayesian Framework for Online Anomaly/Event Detection in PMU Data

Phasor measurement units (PMU) are integral to the modernization and automation plan of the electric power industry. A PMU data signature contains system-level events (e.g., faults, generation/load change, etc.) and any measurement/device-related errors. Therefore, the reliable and resilient operation of power systems is equivalent to the quality of the PMU data and the situation awareness provided by its data signature. Despite recent progress, current state-of-the-art methods are not fool-proof and have certain limitations tracing an error/abnormality to sensor sub-components and grid systems. This is because of technical challenges imposed by the scarcity of the labeled information, loss of data quality, and non-stationarity of data. In this paper, we consider the online PMU data stream as an output of a stochastic process and pose the anomaly/event detection as a changepoint detection problem dealing with detecting parameter changes in the underlying stochastic processes. The proposed model-agnostic framework relies on: (a) feature extraction utilizing the minimum volume enclosing ellipsoids (MVEE) method from raw PMU observations and (b) a Bayesian framework of changepoint detection. The validity of the proposed methodology is discussed through numerical experiments on real-world utility-scale PMU data.

Hossain, Ramij Raja↗
DOE OSTI2023

Using observational mean-flow data to drive large-eddy simulations of a diurnal cycle at the SWiFT site

Reproducing realistic date- and site-specific unsteady wind conditions in large-eddy simulations is becoming increasingly useful in wind energy. How to run a large-eddy simulation to match observed conditions, however, remains an open research question. One approach that has received considerable attention is mesoscale-to-microscale coupling, in which information about the mesoscale weather, most commonly acquired from a mesoscale numerical weather model, is passed on to a microscale model. In this paper, we demonstrate how the recently developed profile-assimilation technique, a form of mesoscale-to-microscale coupling, can be used to drive large-eddy simulations solely based on observed mean-flow profiles at a single location, bypassing the need for auxiliary mesoscale simulations. The new approach is evaluated for a diurnal cycle at the Scaled Wind Farm Technology site. Observed mean-flow profiles from the ground up to a height of 2 km are reconstructed by aggregating measurements from multiple instruments, and gaps in the data are infilled with natural neighbor interpolation. We perform nine simulations using various forcing approaches to deal with data limitations. The results show that it is indeed possible to drive microscale large-eddy simulation with observations using the profile-assimilation technique, notwithstanding large gaps in virtual potential temperature measurements. However, profile assimilation with vertical smoothing of the error between the desired and actual profiles is required. Without that smoothing, the microscale simulations develop unrealistically high turbulence levels under many situations. Finally, we show that simulated mesoscale data can account for missing observations, although care is needed as both data sources are not necessarily compatible.

17 WIND ENERGY↗
DOE OSTI2021

Learning electric vehicle driver range anxiety with an initial state of charge-oriented gradient boosting approach

This manuscript focuses on the modeling of electric vehicle (EV) driver’s range anxiety, a fear that a vehicle does not have sufficient range, or state of charge (SOC) of the battery pack, to reach its destination and would strand its occupants. Despite numerous research studies on the modeling of charging behaviors, modeling efforts to understand at what battery percentages do EV drivers charge their vehicles, and what are the associated contributing factors, are rather limited. To this end, an ensemble learning model based on gradient boosting is developed. The model sequentially fits new predictors to new residuals of the previous prediction and, then, minimizes the loss when adding the latest prediction. A total of 18 features are defined and extracted from the multisource data, which cover information on driver, vehicles, stations, traffic conditions, as well as spatial-temporal context information of the charging events. The analyzed dataset includes 4.5-year’s charging event log data from 3,096 users and 468 public charging stations in Kansas City Missouri, and the macroscopic travel demand model maintained by the metropolitan planning organization. Here, the result shows the proposed model achieved a satisfactory result with a R square value of 0.54 and root mean square error of 0.14, both better than multiple linear regression model and random forest model. To reduce range anxiety, it is suggested that the priorities of deploying new charging facilities should be given to the areas with higher daily traffic prediction, with more conservative EV users or that are further from residential areas.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2025

Power Flow Geometry and Approximation

Here, the power flow equations are important in numerous power systems problems of practical interest which consider alternating current power flow (ACPF) physics. Perhaps the most well studied being the alternating current optimal power flow problem (ACOPF), seeking to optimize the operation of an electric power system. Due to their non-linearity, problems which include the power flow equations are typically challenging, particularly in optimization. Interestingly, the set of solutions to the power flow equations forms a smooth manifold. As a result, differential geometry can be used to describe and analyze this set of equations. This approach has proven effective in several engineering applications (e.g., solving ACOPF and analyzing the solution space boundary). Central to the success of this approach is an understanding of the power flow manifold's geometry. In this work, we develop the geometric and topological properties of this manifold using concepts from differential geometry. After demonstrating the convenience of this manifold's representation as a function's graph, computational methods are emphasized: we develop retractions, error bounds for linear approximation, and formulas for evaluating the Riemannian metric (including associated objects such as geodesics and the curvature tensor). Scalar curvature and the second fundamental form play a new role in quantifying the quality of linear approximations, like the popular direct current approximation. All functions are implemented in Julia and available in an online repository. Proofs are included for completeness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2026

Accurate Prediction of pKb in Amines: Validation of the CAM-B3LYP/6-311+G(d,p)/SMD Model

Amines play several key roles in chemistry and biology and are involved in numerous industrial processes, often with significant economic impacts. Recently, amines are also garnering interest as catalysts for polymer synthesis and for CO 2 fixation, incentivizing the need to rapidly design and screen new amino compounds. Hence, developing reliable methods to predict their physicochemical properties, e.g., the base dissociation constant (pKb), is pivotal. Here, a density functional theory (DFT)-based approach was employed to compute the pKb of substituted amines, exploring the impact of several key parameters, including (i) the number of explicit water molecules at the reaction center, (ii) the van der Waals (vdW) surface, and (iii) solvent polarizability. In previous work, it was determined that including two explicit water molecules at the reaction center resulted in highly accurate pKb estimates for primary amines. Here, we find that including a third water molecule at the reaction center is essential for accurate pKb for secondary and tertiary amines. The revised methodology was then applied to a wider selection of amines, obtaining a minimum average error (MAE) < 0.4. In conclusion, this result represents an extension of our “easy-to-use method,” a simple and direct DFT approach exploiting CAM-B3LYP/SMD/6-311G+(d,p) to compute pKb without post facto modifications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

A rigorous physics-based enhanced parameter estimation (EPE) methodology for calibration of building energy simulations

Buildings rarely perform as designed/simulated and there are numerous tangible benefits if this gap is reconciled. A new scientifically rigorous yet pragmatic methodology for calibrating building energy simulations - called Enhanced Parameter Estimation (EPE) - is proposed that allows physically relevant parameter estimation rather than a blind force-fit to energy use data. Starting with a rapidly created simulation model, calibration is performed in two stages: (a) building shell calibration with the HVAC system replaced by an ideal system that meets the loads (b) HVAC system calibration with the building shell and all internal loads replaced by a box with only process loads. In the first stage, EPE identifies a small number of high-level heat flows in the energy balance, calculates them with specifically tailored individual driving functions, introduces physically significant parameters to best accomplish energy balance, and, estimates the parameters and their uncertainty bounds. Calibration is thus done with corrective heat flows without any arbitrary tuning of input parameters. Calibration accuracy is enhanced by machine learning of the residual errors. The EPE methodology is demonstrated by means of: a synthetic building and an actual 75,000 sq. ft. building in Pennsylvania. Future work needed for widespread application is discussed.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Isotherm Modeling and Techno-Economic Analysis of Contactor Technologies for New Tetraamine-Appended MOF for NGCC Applications

Recently, a family of tetraamine-functionalized metal-organic frameworks (MOF) has been reported as promising sorbent materials for capturing CO2 from flue gas conditions relevant to natural gas combined cycle (NGCC) applications. The main advantages of these materials are their two-step cooperative CO2 adsorption, which gives rise to unusual two step-shaped CO2 adsorption profiles and their high thermal stability. This work presents the modelling of the two-transition isotherm of the tetraamine-appended MOF, N,N'-bis(3-aminopropyl)-1,4-diaminobutane (3-4-3)-appended Mg2(dobpdc), and the techno-economic analysis (TEA) of carbon capture processes utilizing this sorbent. Due to the unusual isotherm shapes of the experimental CO2 adsorption data for tetraamine-appended Mg2(dobpdc) and the strong nonlinearity of CO2 loading with respect to temperature and pressure, we tested two different models which use logistic functions for representing the different isotherm behaviors in the different pressure ranges. The first model uses the quadratic isotherm model in the low-pressure region, the Langmuir isotherm model in the middle pressure range, and the dual site Langmuir isotherm model in the high-pressure range. To model the transition between regions we used the arctangent functions independent of temperature and the thermal effect was accounted by using the Clausius-Clapeyron relation]. The second model is an extension of the weighted dual-site Langmuir isotherm model presented by Hughes et al.. In this extended model, the dual-site Langmuir isotherm is employed in the three transition regions, using temperature-dependent logistic functions to activate or deactivate the isotherm model in the low, middle, and high-pressure ranges. Both models fit the experimental data quite well with root mean squared errors (RMSE’s) of 0.41 and 0.17 for model 1 and model 2, respectively. Since model 2 resulted in a lower RMSE, it was leveraged for the development of the gas/solid contactor models used by the TEA. Specifically, two different contactor models, an axial-flow fixed bed and moving bed contactor, were developed as part of this work. These models are dynamic, pressure-driven, and consist of mass, energy, and momentum conservation equations. A kinetic model was also developed by performing parameter estimation using experimental fixed bed breakthrough data. These models are then used to simulate CO2 capture processes from the flue gas generated from a ~600 gross MW NGCC power plant. A cost model was developed which considers the capital cost of the reactors and the significant operating costs such as steam and electricity. Using NETL’s Framework for the Optimization and Quantification of Uncertainty of Uncertainty and Surrogates tool (FOQUS), which has the capability of linking models built using numerous modelling platforms with derivative-free optimization solvers, a techno-economic optimization of the carbon capture processes was performed which minimizes the cost of capture.

Caballero, Daison↗
DOE OSTI2025

Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open quantum dynamics in structured thermal environments

In this work, we introduce an efficient method, TTN-HEOM, for exactly calculating the open quantum dynamics for driven quantum systems interacting with highly structured bosonic baths by combining the tree tensor network (TTN) decomposition scheme with the bexcitonic generalization of the numerically exact hierarchical equations of motion (HEOM). The method yields a series of quantum master equations for all core tensors in the TTN that efficiently and accurately capture the open quantum dynamics for non-Markovian environments to all orders in the system–bath interaction. These master equations are constructed based on the time-dependent Dirac–Frenkel variational principle, which isolates the optimal dynamics for the core tensors given the TTN ansatz. The dynamics converges to the HEOM when increasing the rank of the core tensors, a limit in which the TTN ansatz becomes exact. We introduce TENSO, tensor equations for non-Markovian structured open systems, as a general-purpose Python code to propagate the TTN-HEOM dynamics. We implement three general propagators for the coupled master equations: two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive-rank method with a variable memory footprint controlled by the target level of computational error. We exemplify the utility of these methods by simulating a two-level system coupled to a structured bath containing one Drude–Lorentz component and eight Brownian oscillators, which is beyond what can presently be computed using the standard HEOM. Our results show that the TTN-HEOM is capable of simulating both dephasing and relaxation dynamics of driven quantum systems interacting with structured baths, even those of chemical complexity, with an affordable computational cost.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Design of double- and multi-bend achromat lattices with large dynamic aperture and approximate invariants

A numerical method to design nonlinear double- and multi-bend achromat (DBA and MBA) lattices with approximate invariants of motion is investigated. The search for such nonlinear lattices is motivated by Fermilab’s Integrable Optics Test Accelerator (IOTA), whose design is based on an integrable Hamiltonian system with two invariants of motion. While it may not be possible to design an achromatic lattice for a dedicated synchrotron light source storage ring with one or more exact invariants of motion, it is possible to tune the sextupoles and octupoles in existing DBA and MBA lattices to produce approximate invariants. In our procedure, the lattice is tuned while minimizing the turn-by-turn fluctuations of the Courant-Snyder actions J x and J y at several distinct amplitudes, while simultaneously minimizing diffusion of the on-energy betatron tunes. The resulting lattices share some important features with integrable ones, such as a large dynamic aperture, trajectories confined to invariant tori, robustness to resonances and errors, and a large amplitude-dependent tune-spread. Compared to the nominal NSLS-II lattice, the single- and multi-bunch instability thresholds are increased and the bunch-by-bunch feedback gain can be reduced.

43 PARTICLE ACCELERATORS↗