Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dynamical”

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 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Emergent facilitation and glassy dynamics in supercooled liquids

In supercooled liquids, dynamical facilitation refers to a phenomenon where microscopic motion begets further motion nearby, resulting in spatially heterogeneous dynamics. This is central to the glassy relaxation dynamics of such liquids, which show super-Arrhenius growth of relaxation timescales with decreasing temperature. Despite the importance of dynamical facilitation, there is no theoretical understanding of how facilitation emerges and impacts relaxation dynamics. Here, we present a theory that explains the microscopic origins of dynamical facilitation. We show that dynamics proceeds by localized bond-exchange events, also known as excitations, resulting in the accumulation of elastic stresses with which new excitations can interact. At low temperatures, these elastic interactions dominate and facilitate the creation of new excitations near prior excitations. Using the theory of linear elasticity and Markov processes, we simulate a model, which reproduces multiple aspects of glassy dynamics observed in experiments and molecular simulations, including the stretched exponential decay of relaxation functions, the super-Arrhenius behavior of relaxation timescales as well as their two-dimensional finite-size effects. The model also predicts the subdiffusive behavior of the mean squared displacement (MSD) on short, intermediate timescales. Furthermore, we derive the phonon contributions to diffusion and relaxation, which when combined with the excitation contributions produce the two-step relaxation processes, and the ballistic–subdiffusive–diffusive crossover MSD behaviors commonly found in supercooled liquids.

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

On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called “lag time”). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5–10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Review of rotating wing dynamic stall: Experiments and flow control

Dynamic stall has been a technical challenge and a fluid dynamical subject of interest for more than fifty years; but in the last decade significant advances have been made in the understanding, prediction, modeling, and control of dynamic stall on rotors. This paper provides a summary of the state of the art of dynamic stall experiments and future directions in the understanding of dynamic stall on rotors. Experimental data sets are discussed, as well the direction of future research for control of dynamic stall. Coordinated testing between airfoils and rotating blades, as well as close integration between computational and experimental studies were found to be productive approaches. Advanced analysis methods, including statistical methods, modal representations, and artificial intelligence methods have led to significant advances in the understanding of dynamic stall. Investigations of dynamic stall control devices have allowed many useful targeted investigations of the transition to separated flow, but have not yet resulted in a commercially implemented device.

42 ENGINEERING↗
DOE OSTI2020

Structural Dynamics in UV Curable Resins Resolved by In Situ 3D Printing X-ray Photon Correlation Spectroscopy

Additive manufacturing (AM) is a promising technique to rapidly produce polymeric materials into complex 3-dimensional (3D) geometries. While AM is widespread and relevant for a range of applications, implementation in industry has outpaced our fundamental understanding of polymer dynamics and structure development during the printing process. Characterization and quantification of such dynamics is necessary to optimize final material properties and design future materials and processes for 3D printing. Here, we utilize X-ray photon correlation spectroscopy (XPCS) to measure spatial and time-resolved, out-of-equilibrium dynamics during direct ink write (DIW) 3D printing. Specifically, we investigate the progression of structural dynamics in a dual cure (UV/thermal) nanocomposite during and directly after printing. As the filament is printed and cured in situ, the relaxation processes of the cross-linking network are measured through the dynamics of inorganic filler particles. The characteristic relaxation time of the dynamics is calculated through the intensity–intensity autocorrelation function g 2 and directly correlated to the printing process parameters, such as printhead velocity and UV light intensity. The time-resolved evolution of nanoscale dynamics follows a power-law dependence as the filament is cured. Additionally, bulk rheological characterizations reveal the macroscopic solidification of the resin, providing correlation of material properties across a wide range of length and time scales. Overall, the measurement of multiscale, out-of-equilibrium dynamics provides insight into the development of structure in polymer nanocomposite filaments during 3D printing and is used to further understand the influence of such parameters on the AM process.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Efficient Phasor-Based Dynamic Volt/VAr and Volt/Watt Analysis of Large Distribution Grid with High Penetration of Smart Inverters

As the penetration of power-electronics based smart inverters (SIs) is increasing in distribution grids, it adds computational challenges in solving dynamic models of large-scale distribution feeders. Voltage and reactive power (Volt/VAr), and voltage and active power (Volt/Watt) dynamics have been analyzed at slower time scales akin to the control of legacy grid devices. However, smart inverters, being power-electronics based devices, can provide dynamic active/reactive power support at a faster time scale, which necessitates Volt/VAr and Volt/Watt dynamics to be analyzed at a faster time scale. The existing dynamic models are overly detailed and computationally intractable for distribution feeders with a large number of inverters. In this context, this proposed work aims towards developing a computationally tractable, scalable, and accurate phasor-based model for dynamic Volt/VAr and Volt/Watt analyses of large distribution systems with high penetration of smart inverters. Case studies demonstrate that the proposed phasor-based model sufficiently captures the Volt/VAr and Volt/Watt dynamics, and is computationally faster by one order of magnitude compared to the average model and by two orders of magnitude compared to the detailed switching model. Case studies also demonstrate the efficacy and scalability of the proposed model in analyzing Volt/VAr and Volt/Watt dynamics of large-scale power networks with hundreds of SIs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

Robust Large-Scale Dynamic Windows using Reversible Metal Electrodeposition

This project funded the study and development of dynamic windows based on reversible metal electrodeposition (RME). Dynamic windows allow user control over light and heat flow into and out of buildings, which offer both advantages in building aesthetics (with worker productivity improvement of 2%) and energy efficiency (up to 20% savings) compared to static controls such as low emissivity coatings and blinds/shades. Despite these advantages, dynamic windows, which traditionally rely on electrochromic metal oxides or conductive organic molecules for light modulation have failed to significantly impact the market due to issues related to cost, color, and optical dynamic range. Dynamic windows based on reversible metal electrodeposition (RME) are an exciting alternative approach and have the potential to overcome the issues associated with traditional technologies. A RME dynamic window is an electrochemical cell that modulates light using the reversible electrodeposition of metal on and off a transparent conducting oxide (TCO), which serves as the working electrode. The electrolyte has nearly colorless metal salts dissolved, and application of a cathodic potential on the TCO reduces the metal cations across the TCO surface to their metallic form, making a thin film that is efficient at blocking out light. A reverse in polarity oxidizes the metal, where it dissolves into solution, returning the window back to transparent. The counter electrode typically employed is a metal mesh, which is used to balance the electrochemical reactions happening on the TCO working electrode. These RME dynamic windows have the largest dynamic range (capable of reaching <<0.1% transmission) with color neutral tinting of any existing technology using solution processed techniques, which positions the technology as a promising candidate to penetrate the residential market. We have successfully scaled up the windows from 25 cm2 to 929 cm 2 , and we have demonstrated significant improvements to both the cycle life (10,000 cycles in a 3-electrode half-cell) and shelf life (>1 month) of our windows. We have published our work in high impact journals (6 published and 2 manuscripts in prep), filed 5 patents, and have incorporated TYNT Technologies to commercialize the technology.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2019

Identification of Performance Shaping Factor Lag and Linger Effects for Dynamic Human Reliability Analysis: Application of Experimental Data

Many researchers have emphasized the importance of dynamic probabilistic safety assessment (PSA), which highlights the necessity of studies for dynamic human reliability analysis (HRA). Dynamic HRA concentrates on a dynamic account of human actions or how performance shaping factors (PSFs) can dynamically modify the human error probability (HEP) over time. In contrast, existing static HRA does not consider human actions as changes over time or event progressions. Accordingly, previous research on dynamic HRA conceptually suggested PSF lag and linger effects to treat dependence between operator actions in dynamic HRA versus existing approaches. As follow-up research, this study attempted to identify PSF lag and linger effects for dynamic HRA on the basis of experimental data. Firstly, mathematical models for PSF lag and linger effects were developed based on a literature survey in the field of biology. Secondly, we analyzed experimental scenarios from a control room study to identify operator actions considered in PSA. Lastly, based on the experimental data, the effect of the stress PSF with lag and linger effects was compared to that without PSF lag and linger effects. This paper concludes with an overall discussion of PSF lag and linger effects based on the relation between the stress PSF and error occurrence.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2025

Enhancing EnergyPlus capabilities to model dynamic building envelopes using python plugin

Nearly half of the energy consumption in the United States is related to buildings, resulting in an urgent need to develop innovative technologies to improve building energy efficiency. Dynamic building envelopes, comprising switchable insulation and thermal energy storage materials, have been proposed recently as a promising solution to reduce buildings' heating and cooling loads by thermally coupling the indoor environment with the ambient environment when beneficial while decoupling them when outdoor conditions are not favorable. Although various related technologies are still underway, the whole-building energy modeling tools, like EnergyPlus, do not have the capability to simulate the transient and dynamic nature of dynamic envelope materials and components to accurately predict their impact on building energy use. The objective of this study is to formulate a method in EnergyPlus simulation engine to model multilayer envelopes, comprising dynamic building materials with variable thermophysical properties, and discuss the changes made to the program using a Python plugin. Furthermore, the thermal performance of the dynamic envelopes using the proposed method is compared and verified with the results from a well-established commercial code, COMSOL Multiphysics. A parametric assessment is also conducted to evaluate the energy efficiency benefits of dynamic envelopes in a single-family residential building, demonstrating total annual energy savings up to 11.6 %, when a dynamic envelope operates alone, and up to 18.2 % when it is combined with a thin layer of phase change material as a thermal storage medium. Finally, a United States wide energy efficiency assessment is presented to showcase the geographical spread of the energy savings. The method designed and implemented in this study provides the researchers with the ability to implement their dynamic insulation methods in EnergyPlus and evaluate the whole building energy impact.

25 ENERGY STORAGE↗
DOE OSTI2024

Site Disorder Drives Cyanide Dynamics and Fast Ion Transport in Li 6 PS 5 CN

Halide argyrodite solid-state electrolytes of the general formula Li 6 PS 5 X exhibit complex static and dynamic disorder that plays a crucial role in ion transport processes. Here, we unravel the rich interplay between site disorder and dynamics in the plastic crystal argyrodite Li 6 PS 5 CN and the impact on ion diffusion processes through a suite of experimental and computational methodologies, including temperature-dependent synchrotron powder X-ray diffraction, AC electrochemical impedance spectroscopy, 7 Li solid-state NMR, and machine learning-assisted molecular dynamics simulations. Sulfide and (pseudo)halide site disorder between the two anion sublattices unilaterally improves long-range lithium diffusion irrespective of the (pseudo)halide identity, which demonstrates the importance of site disorder in dictating bulk ionic conductivity in the argyrodite family. Furthermore, we find that anion site disorder modulates the presence and time scales of cyanide rotational dynamics. Ordered configurations of anions enable fast, quasi-free rotations of cyanides that occur on time scales of 10 11 Hz at T = 300 K. In contrast, we find that cyanide dynamics are slow or frozen in Li 6 PS 5 CN when site disorder between the cyanide and sulfide sublattices is present at T = 300 K. We rationalize the observed differences in cyanide dynamics in the context of elastic dipole interactions between neighboring cyanide anions and local strain induced by the configurations of site disorder that may impact the energetic landscape for cyanide rotational dynamics. Through this study, we find that anion disorder plays a decisive role in dictating the extent and time scales of both lithium ion and cyanide dynamics in Li 6 PS 5 CN.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Efficient fully-coherent quantum signal processing algorithms for real-time dynamics simulation

Simulating the unitary dynamics of a quantum system is a fundamental problem of quantum mechanics, in which quantum computers are believed to have significant advantage over their classical counterparts. One prominent such instance is the simulation of electronic dynamics, which plays an essential role in chemical reactions, non-equilibrium dynamics, and material design. These systems are time-dependent, which requires that the corresponding simulation algorithm can be successfully concatenated with itself over different time intervals to reproduce the overall coherent quantum dynamics of the system. In this paper, we quantify such simulation algorithms by the property of being fully-coherent: the algorithm succeeds with arbitrarily high success probability 1 − δ while only requiring a single copy of the initial state. Here we subsequently develop fully-coherent simulation algorithms based on quantum signal processing (QSP), including a novel algorithm that circumvents the use of amplitude amplification while also achieving a query complexity additive in time t, ln(1/δ), and ln(1/ϵ) for error tolerance ϵ: $Θ‖\mathscr{H}‖|t|+ln(1/ϵ)+ln(1/δ)$. Furthermore, we numerically analyze these algorithms by applying them to the simulation of the spin dynamics of the Heisenberg model and the correlated electronic dynamics of an H2 molecule. Since any electronic Hamiltonian can be mapped to a spin Hamiltonian, our algorithm can efficiently simulate time-dependent ab initio electronic dynamics in the circuit model of quantum computation. Accordingly, it is also our hope that the present work serves as a bridge between QSP-based quantum algorithms and chemical dynamics, stimulating a cross-fertilization between these exciting fields.

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

Ba ( Ti 1 - x , Zr x ) O 3 relaxors: Dynamic ferroelectrics in the gigahertz frequency range

Relaxor ferroelectrics are of great scientific and technological significance as they exhibit large and unusual responses to external stimuli. Their hallmark features are broadness and frequency dispersion of the peak in the temperature dependence of the dielectric constant. Both are believed to originate from the dynamics of polar nanoregions. Here, we apply first-principles-based molecular dynamics to resolve the gigahertz electric response of dynamically poled Ba (Ti 1 - x , Zr x ) O 3 ferroelectric relaxors that remained overlooked so far. We find that (i) the hallmark relaxor features continue to persist even in the dynamically poled structures, but do not necessarily originate from the polar nanoregions dynamics; (ii) dynamically poled samples exhibit polarization aging which leads to the frequency dependence of both remnant polarization and the Curie temperature; (iii) “dynamical” nature of the latter naturally explains the frequency dependence of the dielectric susceptibility maximum in dynamically poled Ba (Ti 1 - x , Zr x) O 3 ; and (iv) incorporation of the polarization aging into dielectric susceptibility expression explains its enhancing contribution in an intuitive way.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Hindered segmental dynamics in associative protein hydrogels studied by neutron spin-echo spectroscopy

Transient binding between associating macromolecules can cause qualitative changes to chain dynamics, including modes of conformational relaxation and diffusion, through tethering effects imparted by long-range connectivity. Here, in this work, the role of binding on short-time segmental dynamics in associative polymer gels is investigated by neutron spin-echo (NSE) measurements on a class of model artificial coiled-coil proteins with a systematically varied architecture, probing timescales of 0.1–130 ns, and length scales close to the molecular radius of gyration. The results illustrate effects of transient cross-linking on chain dynamics on different timescales, manifested in changes in segmental relaxation behavior with variations in strand length, chain concentration, and sticker distribution (endblock- vs midblock-functionalized). In all gels, a short-time cooperative diffusion mode is seen over all wave vectors, analogous to a semidilute solution, with no transitions seen at any known structural length scale. However, the diffusion coefficients are found to decrease with increasing junction density across all gels, with the strand length and number of stickers per chain in each gel appearing to play a relatively minor role. The slowing of cooperative diffusion with junction density contrasts with classical predictions of a greater restoring force for fluctuation dissipation due to the increased elasticity, suggesting additional effects of the coiled-coil junctions such as an enhancement in local viscosity that slows dynamics. Notably, the relaxation rates for all gels can be rescaled by the interjunction spacing inferred from small-angle neutron scattering, where they collapse onto a master curve suggestive of self-similar dynamics even in networks with different strand lengths and chain architectures. On long timescales (but shorter than the junction exchange time), a slowing of network relaxation is observed, resulting in a nondecaying plateau in the spin-echo amplitude attributed to a freezing of chain dynamics due to tethering. A characteristic length scale corresponding to the extent of dynamic fluctuations is estimated for each gel, which appears to be smaller than the interjunction spacing but similar to the correlation blob size of the overlapping strands. The results indicate an important role of transient binding on molecular-scale dynamics in associative polymer gels, even on timescales shorter than the junction exchange time, in addition to its effects on long-range self-diffusion previously observed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Dynamic Cooling on Contemporary Quantum Computers

We study the problem of dynamic cooling whereby a target qubit is cooled at the expense of heating up N − 1 further identical qubits by means of a global unitary operation. A standard back-of-the-envelope high-temperature estimate establishes that the target qubit temperature can be dynamically cooled by at most a factor of 1 / N . Here we provide the exact expression for the minimum temperature to which the target qubit can be cooled and reveal that there is a crossover from the high initial temperature regime, where the scaling is 1 / N , to a low initial temperature regime, where a much faster scaling of 1 / N occurs. This slow, 1 / N scaling, which was relevant for early high-temperature NMR quantum computers, is the reason dynamic cooling was dismissed as ineffectual around 20 years ago; the fact that current low-temperature quantum computers fall in the fast, 1 / N scaling regime, reinstates the appeal of dynamic cooling today. We further show that the associated work cost of cooling is exponentially more advantageous in the low-temperature regime. We discuss the implementation of dynamic cooling in terms of quantum circuits and examine the effects of hardware noise. We successfully demonstrate dynamic cooling in a three-qubit system on a real quantum processor. Since the circuit size grows quickly with N , scaling dynamic cooling to larger systems on noisy devices poses a challenge. We therefore propose a suboptimal cooling algorithm, whereby relinquishing a small amount of cooling capability results in a drastically reduced circuit complexity, greatly facilitating the implementation of dynamic cooling on near-future quantum computers. Published by the American Physical Society2024

Physics↗
DOE OSTI2022

Bacterial community dynamics explain carbon mineralization and assimilation in soils of different land-use history

Soil dwelling microorganisms are key players in the terrestrial carbon cycle, driving both the degradation and stabilization of soil organic matter. Bacterial community structure and function vary with respect to land use; yet the ecological drivers of this variation remain poorly described and difficult to predict. For this work, we conducted a multi-substrate DNA-stable isotope probing experiment across cropland, old-field, and forest habitats to link carbon mineralization dynamics with the dynamics of bacterial growth and carbon assimilation. We tracked the movement of 13 C derived from five distinct carbon sources as it was assimilated into bacterial DNA over time. We show that carbon mineralization, community composition, and carbon assimilation dynamics all differed with respect to land use. We also show that microbial community dynamics affect carbon assimilation dynamics and are associated with soil DNA content. Soil DNA yield is easy to measure and may be useful in predicting microbial community dynamics linked to soil carbon cycling. Soil dwelling microorganisms are key players in the terrestrial carbon cycle, driving both the degradation and stabilization of soil organic matter. Microbial communities vary with respect to land use, but we still have an incomplete understanding of how variation in community structure links to variation in community function. DNA stable isotope probing (DNA-SIP) is a high-resolution method that can identify specific microbial taxa that assimilate carbon in situ. We conducted a large-scale multi-substrate DNA-SIP experiment to explore differences in bacterial activity across land-use regimes. We show that microbial community dynamics vary with land use, that these dynamics are linked to soil carbon cycling, and that they are associated with easily measured soil properties.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Progressive Dynamics for Cloth and Shell Animation

We propose Progressive Dynamics, a coarse-to-fine, level-of-detail simulation method for the physics-based animation of complex frictionally contacting thin shell and cloth dynamics. Progressive Dynamics provides tight-matching consistency and progressive improvement across levels, with comparable quality and realism to high-fidelity, IPC-based shell simulations [Li et al. 2021] at finest resolutions. Together these features enable an efficient animation-design pipeline with predictive coarse-resolution previews providing rapid design iterations for a final, to-be-generated, high-resolution animation. In contrast, previously, to design such scenes with comparable dynamics would require prohibitively slow design iterations via repeated direct simulations on high-resolution meshes. We evaluate and demonstrate Progressive Dynamics's features over a wide range of challenging stress-tests, benchmarks, and animation design tasks. Here Progressive Dynamics efficiently computes consistent previews at costs comparable to coarsest-level direct simulations. Its matching progressive refinements across levels then generate rich, high-resolution animations with high-speed dynamics, impacts, and the complex detailing of the dynamic wrinkling, folding, and sliding of frictionally contacting thin shells and fabrics.

Computer Science↗
DOE OSTI2021

Photo-Switching of Protein Dynamical Collectivity

We examine changes in the picosecond structural dynamics with irreversible photobleaching of red fluorescent proteins (RFP) mCherry, mOrange2 and TagRFP-T. Measurements of the protein dynamical transition using terahertz time-domain spectroscopy show in all cases an increase in the turn-on temperature in the bleached state. The result is surprising given that there is little change in the protein surface, and thus, the solvent dynamics held responsible for the transition should not change. A spectral analysis of the measurements guided by quasiharmonic calculations of the protein absorbance reveals that indeed the solvent dynamical turn-on temperature is independent of the thermal stability/photostate however the protein dynamical turn-on temperature shifts to higher temperatures. This is the first demonstration of switching the protein dynamical turn-on temperature with protein functional state. The observed shift in protein dynamical turn-on temperature relative to the solvent indicates an increase in the required mobile waters necessary for the protein picosecond motions, that is, these motions are more collective. Melting-point measurements reveal that the photobleached state is more thermally stable, and structural analysis of related RFP’s shows that there is an increase in internal water channels as well as a more uniform atomic root mean squared displacement. These observations are consistent with previous suggestions that water channels form with extended light excitation providing O2 access to the chromophore and subsequent fluorescence loss. We report that these same channels increase internal coupling enhancing thermal stability and collectivity of the picosecond protein motions. The terahertz spectroscopic characterization of the protein and solvent dynamical onsets can be applied generally to measure changes in collectivity of protein motions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Process-oriented evaluation of quasi-stationary Rossby waves and their impact on surface air temperature extremes in dynamical downscaling over North America

Quasi-stationary Rossby waves are a crucial component of the general circulation and play a significant role in regional water and energy cycles, as well as in extreme events. However, process-oriented evaluation for Rossby waves is rarely performed for dynamical downscaling simulations. To close this gap, we evaluate three classes of dynamical downscaling approaches, with a focus on quasi-stationary Rossby waves and their impact on surface air temperature over North America during Northern Hemisphere summer. The three classes of models differ in the way large-scale forcing is provided: a limited-area model (LAM) constrained only by lateral boundary conditions, represented by RegCM4 from the North American branch of the Coordinated Regional Downscaling Experiment (NA-CORDEX), a LAM with spectral nudging to maintain consistency in large-scale dynamics with the forcing data, represented by the Weather Research and Forecasting (WRF) model simulation in NA-CORDEX, and a global variable-resolution model with smoothly varying grid spacings, represented by the Community Atmosphere Model version 5.4, with the Model for Prediction Across Scales (MPAS) as its dynamical core (CAM-MPAS). With no constraints on the atmospheric dynamics, CAM-MPAS exhibits several mean biases in the upper-level circulations over the Pacific Coast region: a weaker subtropical jet, a northward-shifted mid-latitude jet, and an overestimated southerly flow. With the lateral boundary constraint alone, RegCM4 also exhibits weaker jets and overestimated southerly winds off the West Coast. Rossby ray theory reveals that those wind biases direct incoming Rossby waves northward. The erroneously routed Rossby waves distort the relationship between the accumulation of wave activity over the US West Coast and surface temperature anomalies over the Southern Great Plains, which emerges approximately 4 d after the convergence of wave-activity flux in the ERA-Interim reanalysis. Furthermore, the response of heatwaves to the extreme wave activity flux is not reproduced by the two models, a serious drawback as a dynamical downscaling framework is expected to connect large-scale forcing to local-scale phenomena. The WRF model employing spectral nudging is largely free from the aforementioned problems. A pair of sensitivity simulations suggests that spectral nudging is the key to improving the dynamics of quasi-stationary Rossby waves and their impact on surface air temperature. Our results also demonstrate the effectiveness of Rossby wave diagnostics that allow for realistic background flows for assessing the credibility of dynamical downscaling over North America, where incoming Rossby waves propagate through complex circulation patterns before traveling across the continent.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Data-driven modeling and control of dynamical systems using Koopman and Perron-Frobenius operators

This dissertation studies the data-driven modeling and control problem of nonlinear systems by exploiting the linear operator theoretic framework involving Koopman and Perro-Frobenius operator. A systematic linear-operator based controller design procedure has been established, which can be used to solve a variety of nonlinear control problems, including feedback stabilization using control Lyapunov functions, optimal quadratic regulation using Koopman eigenfunctions and convex optimization formulation of optimal control problem using P-F and Koopman operator approximation. As the core of data-driven modeling, we first propose a new algorithm for the finite-dimensional approximation of the linear transfer Koopman and Perron-Frobenius operator from time-series data. We argue that the existing approach for the finite-dimensional approximation of these transfer operators such as Dynamic Mode Decomposition (DMD) and Extended Dynamic Mode Decomposition (EDMD) do not capture two important properties of these operators, namely positivity and Markov property. The algorithm we propose preserves these two properties. We call the proposed algorithm as naturally structured DMD (NSDMD) since it retains the inherent properties of these operators. Naturally structured DMD algorithm leads to a better approximation of the steady-state dynamics of the system regarding computing Koopman and Perron- Frobenius operator eigenfunctions and eigenvalues. However, preserving positivity property is critical for capturing the real transient dynamics of the system. This positivity property of the transfer operators and it's finite-dimensional approximation play an important role for controller and estimator design of nonlinear systems. To solve the feedback stabilization problem for nonlinear control systems, we tried to take advantage of the Koopman operator framework. The Koopman operator approach provides a linear representation for a nonlinear dynamical system and a bilinear representation for a nonlinear control system. The problem of feedback stabilization of a nonlinear control system is then transformed to the stabilization of a bilinear control system. We propose a control Lyapunov function (CLF)-based approach for the design of stabilizing feedback controllers for the bilinear system. The search for finding a CLF for the bilinear control system is formulated as a convex optimization problem. This leads to a schematic procedure for designing CLF-based stabilizing feedback controllers for the bilinear system and hence the original nonlinear system. Another advantage of the proposed controller design approach outlined in this dissertation is that it does not require explicit knowledge of system dynamics. In particular, the bilinear representation of a nonlinear control system in the Koopman eigenfunction space can be obtained from time-series data. Next, we study the optimal quadratic regulation problem for nonlinear systems. The linear operator theoretic framework involving the Koopman operator is used to lift the dynamics of nonlinear control system to an infinite-dimensional bilinear system. The optimal quadratic regulation problem for nonlinear system is formulated in terms of the finite-dimensional approximation of the bilinear system. A convex optimization-based approach is proposed for solving the quadratic regulator problem for bilinear system. We applied a variety of examples and compared the simulation results between our framework and conventional LQR control using linearized model. For more general optimal control problems, we provide a density-function based convex formulation for the optimal control problem of the nonlinear system. The convex formulation relies on the duality result in the stability theory of a dynamical system involving density function and Perron-Frobenius operator. The optimal control problem is formulated as an infinite-dimensional convex optimization program. The finite-dimensional approximation of the optimization problem relies on the recent advances made in the data-driven computation of the Koopman operator, which is dual to the Perron-Frobenius operator. Simulation results are presented to demonstrate the application of the developed framework.

Huang, Bowen↗