Comparisons of RDE inlet dynamics in a linear testing platform and models of varying complexity
Paper describing comparisons between experimental and model predictions of RDE inlet recovery times.
Bedick, Clinton↗
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Results for “Linear dynamics”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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A compute-bound formulation of Galerkin model reduction for linear time-invariant dynamical systems
This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. In conclusion, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.
97 MATHEMATICS AND COMPUTING↗
Quantum Algorithm for Linear Non-unitary Dynamics with Near-Optimal Dependence on All Parameters
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially enhance the accuracy of the recently introduced linear combination of Hamiltonian simulation (LCHS) method [An, Liu, and Lin, Physical Review Letters, 2023]. For the first time, this approach enables quantum algorithms to solve linear differential equations with both optimal state preparation cost and near-optimal scaling in matrix queries on all parameters.
Applied Dynamical Systems↗
Data-Driven Distributed Algorithms for Estimating Eigenvalues and Eigenvectors of Interconnected Dynamical Systems
Here, the paper presents data-driven algorithms to estimate in a distributed manner the eigenvalues, right and left eigenvectors of an unknown linear (or linearized) interconnected dynamic system. In particular, the proposed algorithms do not require the identification of the system model in advance before performing the estimation. As a first step, we consider interconnected dynamical system with distinct eigenvalues. The proposed strategy first estimates the eigenvalues using the well-known Prony method. The right and left eigenvectors are then estimated by solving distributively a set of linear equations. One important feature of the proposed algorithms is that the topology of communication network used to perform the distributed estimation can be chosen arbitrarily, given that it is connected, and is also independent of the structure or sparsity of the system (state) matrix. The proposed distributed algorithms are demonstrated via a numerical example.
97 MATHEMATICS AND COMPUTING↗
Polariton spectra under the collective coupling regime. I. Efficient simulation of linear spectra and quantum dynamics
We outline two general theoretical techniques to simulate polariton quantum dynamics and optical spectra under the collective coupling regimes described by a Holstein–Tavis–Cummings (HTC) model Hamiltonian. The first one takes advantage of sparsity of the HTC Hamiltonian, which allows one to reduce the cost of acting polariton Hamiltonian onto a state vector to the linear order of the number of states, instead of the quadratic order. The second one is applying the well-known Chebyshev series expansion approach for quantum dynamics propagation and to simulate the polariton dynamics in the HTC system; this approach allows us to use a much larger time step for propagation and only requires a few recursive operations of the polariton Hamiltonian acting on state vectors. These two theoretical approaches are general and can be applied to any trajectory-based non-adiabatic quantum dynamics methods. We apply these two techniques with our previously developed Lindblad-partially linearized density matrix approach to simulate the linear absorption spectra of the HTC model system, with both inhomogeneous site energy disorders and dipolar orientational disorders. Our numerical results agree well with the previous analytic and numerical work.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Space-Split Algorithm for Sensitivity Analysis of Discrete Chaotic Systems With Multidimensional Unstable Manifolds
Accurate approximations of the change of a system's output and its statistics with respect to the input are highly desired in computational dynamics. Ruelle's linear response theory provides breakthrough mathematical machinery for computing the linear response of chaotic dynamical systems. In this paper, we propose an algorithm for sensitivity analysis of discrete chaos with an arbitrary number of positive Lyapunov exponents. We combine the concept of perturbation space-splitting, which regularizes Ruelle's original expression, together with measure-based parameterization of the expanding subspace. We use these tools to rigorously derive trajectory-following recursive relations that converge exponentially fast, and construct a memory-efficient Monte Carlo scheme for derivatives of the output statistics. Thanks to the regularization and lack of simplifying assumptions on the system's behavior, our method is immune to the common problems of other popular methods such as the exploding tangent solutions and unphysical shadowing directions. Here, we provide a ready-to-use algorithm, analyze its complexity, and demonstrate several numerical examples of sensitivity computation using physically-inspired low-dimensional systems.
97 MATHEMATICS AND COMPUTING↗
An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra
Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump–probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.
Chemistry↗
Koopman Model Predictive Control for Eco-Driving of Automated Vehicles
In this paper, we develop a data-driven process for building a model predictive control (MPC) for eco-driving of automated vehicles. The process involves performing system identification in which the non-linear vehicle dynamics model is approximated by the Koopman operator, a linear predictor of higher state-dimension, in a data-driven framework. This approach allows us to formulate the eco-driving problem in a constrained quadratic program that leads to a computationally fast MPC. The MPC is then implemented as a closed-loop control of an electric vehicle in numerical simulations for demonstration.
autonomous vehicle↗
Theory of capillary tension and interfacial dynamics of motility-induced phases
The statistical mechanics of equilibrium interfaces has been well-established for over a half century. In the past decade, a wealth of observations have made increasingly clear that a new perspective is required to describe interfaces arbitrarily far from equilibrium. In this work, beginning from microscopic particle dynamics that break time-reversal symmetry, we derive the linear interfacial dynamics of coexisting motility-induced phases. Doing so allows us to identify the athermal energy scale that excites interfacial fluctuations and the nonequilibrium surface tension that resists these excitations. Our theory identifies that, in contrast to equilibrium fluids, this active surface tension contains contributions arising from nonconservative forces which act to suppress interfacial fluctuations and, crucially, is distinct from the mechanical surface tension of Kirkwood and Buff. Here we find that the interfacial stiffness scales linearly with the intrinsic persistence length of the constituent active particle trajectories, in agreement with simulation data. We demonstrate that at wavelengths much larger than the persistence length, the interface obeys surface-area minimizing Boltzmann statistics with our derived nonequilibrium interfacial stiffness playing a role identical to that of equilibrium systems.
36 MATERIALS SCIENCE↗
Potential quantum advantage for simulation of fluid dynamics
Numerical simulation of turbulent fluid dynamics needs to either parametrize turbulence—which introduces large uncertainties—or explicitly resolve the smallest scales—which is prohibitively expensive. Here, we provide evidence through analytic bounds and numerical studies that a potential quantum speedup can be achieved to simulate fluid dynamics using quantum computing. Specifically, we provide a lattice Boltzmann formulation of fluid dynamics for which we give evidence that low-order Carleman linearization is much more accurate than previously believed for these systems. This is achieved via a combination of reformulating the Navier-Stokes nonlinearity (u·$\triangledown$u) to lattice-Boltzmann nonlinearity (u 2 ) and accurately linearizing the dynamical equations, which effectively trades nonlinearity for additional degrees of freedom that add negligible expense in the quantum solver. Based on this, we apply a quantum algorithm for simulating the Carleman-linearized lattice Boltzmann equation and provide evidence that its cost scales logarithmically with system size compared with polynomial scaling in the best known classical algorithms. In this paper, we suggest that a quantum advantage may exist for simulating fluid dynamics, paving the way for simulating nonlinear multiscale transport phenomena in a wide range of disciplines using quantum computing.
42 ENGINEERING↗
Simulating the filamentation of smoothed laser beams with three-dimensional nonlinear dynamics
In a plasma, the ponderomotive force of an inhomogeneous electromagnetic field expels plasma from regions of high intensity. When a laser propagates through a plasma, this force creates density wells that subsequently modify the index of refraction. The beam refracts and focuses into these wells and may filament. In extreme cases, the laser beam will spray due to increasing angular divergence of the beam. The threshold for ponderomotive self-focusing is well established for isolated laser hotspots or speckles. Here, we define a practical threshold for characterizing the filamentation of thousands of speckles that are found in the focal plane of high-power laser beams spatially smoothed with random phase plates as used at high energy and power laser facilities studying inertial confinement fusion. This threshold is tested against three-dimensional simulations of speckled laser light propagating through plasma. Four metrics are applied to assess filamentation: the fraction of power above five times the average intensity, an effective f-number, the mean-squared perpendicular wavenumber, and the fraction of rarefied density with deviation from the initial density exceeding | δn/ n| = 0.1. The speckled beams studied are generated by random phase plates, both with and without additional polarization smoothing, in a parameter regime of relevance to indirect drive experiments. While filamentation has been discussed extensively in the literature, we believe this to be the first published simulation study with three-dimensional nonlinear hydrodynamics that addresses the onset threshold of ponderomotive filamentation and establishes the lengths and time scales necessary to reach a statistical steady state.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Evolution of coupled weakly driven waves in a dissipative plasma
The nonlinear collisional dynamics of coupled driven plasma waves in the presence of background dissipation is studied analytically within kinetic theory. Sufficiently near marginal stability, phase space correlations are poorly preserved and time delays become unimportant. The system is then shown to be governed by two first-order coupled autonomous differential equations of cubic order for the wave amplitudes and two complementary first-order equations for the evolution of their phases. That system of equations can be decoupled and further simplified to a single second-order differential equation of Liénard's type for each amplitude. Numerical solutions for this equation are obtained in the general case, while analytic solutions are obtained for special cases in terms of parameters related to the spacing of the resonances of the two waves in frequency space, e.g., wave lengths and oscillation frequencies. These parameters are further analyzed to find classes of quasi-steady saturation and pulsating scenarios. To classify equilibrium points, local stability analysis is applied, and bifurcation conditions are determined. When the two waves saturate at similar amplitude levels, their combined signal is shown to invariably exhibit amplitude beating and phase jumps of nearly π. In conclusion, the obtained analytical results can be used to benchmark simulations and to interpret eigenmode amplitude measurements in fusion experiments.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Surface coverage dynamics for reversible dissociative adsorption on finite linear lattices
Dissociative adsorption onto a surface introduces dynamic correlations between neighboring sites not found in non-dissociative absorption. We study surface coverage dynamics where reversible dissociative adsorption of dimers occurs on a finite linear lattice. We derive analytic expressions for the equilibrium surface coverage as a function of the number of reactive sites, N, and the ratio of the adsorption and desorption rates. Using these results, we characterize the finite size effect on the equilibrium surface coverage. For comparable N’s, the finite size effect is significantly larger when N is even than when N is odd. Moreover, as N increases, the size effect decays more slowly in the even case than in the odd case. The finite-size effect becomes significant when adsorption and desorption rates are considerably different. These finite-size effects are related to the number of accessible configurations in a finite system where the odd-even dependence arises from the limited number of accessible configurations in the even case. We confirm our analytical results with kinetic Monte Carlo simulations. We also analyze the surface-diffusion case where adsorbed atoms can hop into neighboring sites. As expected, the odd-even dependence disappears because more configurations are accessible in the even case due to surface diffusion.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Validation Framework for Post-Combustion Carbon Capture CFD Simulations
First-principles based computational fluid dynamics (CFD) simulations are proposed as a fundamental tool for investigating solvent-based CO2 absorption in packed columns, due to the ability to accurately represent the underlying non-linear multiscale dynamics. In this work, we employ such models to investigate hydrodynamics of columns with structured by assessing the key hydrodynamic metrics, such as pressure drop and liquid holdup. Our models are validated with experimental data from a specifically designed column for this line of work. The test cases of gas and liquid flowrates and operating conditions were selected through a comprehensive sequential design of experiments approach offered by the CCSI2 toolset.
Panagakos, Grigorios↗
Metastability of stratified magnetohydrostatic equilibria and their relaxation
Motivated by explosive releases of energy in fusion, space and astrophysical plasmas, we consider the nonlinear stability of stratified magnetohydrodynamic equilibria against two-dimensional interchanges of straight magnetic-flux tubes. We demonstrate that, even within this restricted class of dynamics, the linear stability of an equilibrium does not guarantee its nonlinear stability: equilibria can be metastable. We show that the minimum-energy state accessible to a metastable equilibrium under non-diffusive two-dimensional dynamics can be found by solving a combinatorial optimisation problem. These minimum-energy states are, to good approximation, the final states reached by our simulations of destabilised metastable equilibria for which turbulent mixing is suppressed by viscosity. To predict the result of fully turbulent relaxation, we construct a statistical mechanical theory based on the maximisation of Boltzmann's mixing entropy. This theory is analogous to the Lynden-Bell statistical mechanics of collisionless stellar systems and plasma, and to the Robert–Sommeria–Miller theory of two-dimensional vortex turbulence. Our theory reproduces well the results of our numerical simulations for sufficiently large perturbations to the metastable equilibrium.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Multi-Energy Microgrid Planning Considering Heat Flow Dynamics
In this paper, we present a multi-energy microgrid optimal planning method, considering the intra-hour dynamics of the heating system as constraints of the energy dispatch, and consequently of the sizing of the Combined Heat and Power units. The fixed-mass flow rate method and finite difference technique are applied to linearize the dynamic constraints. Moreover, to determine the values of the mass flow rates, a critical scenario representing the slowest heat dynamic process is put forward. Finally, a realistic microgrid case study is presented to illustrate the effect of considering the heat flow dynamics in the overall solution.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Learning-Based Demand Response in Grid Interactive Buildings via Gaussian Processes
This paper presents a predictive controller for a grid-interactive multi-zone building where the temperature dynamics are learned via Gaussian Process (GP) regression. We investigate the development of a learning-based predictive control with two main objectives: (i) continuously learn the temperature dynamics of the building based on data; and, (ii) use the learned dynamics to solve a multi-objective predictive control problem to guarantee occupants' comfort and energy efficiency during normal conditions and demand response events. We leverage the probabilistic non-parametric properties of GPs to estimate the (unknown) non-linear temperature dynamics of the building and to incorporate the uncertainty of those predictions in a multi-objective optimization problem. The GP-based predictive control is solved via a zero-order primal-dual projected-gradient algorithm. We evaluate numerically the performance of the proposed controller using a five-zone commercial building.
demand response↗
Outcomes and Insights From Simplified Analytic Trajectory Optimization for a Tethered Underwater Kite
This letter formulates and solves a periodic trajectory optimization problem for a tethered underwater kite. The goal is to maximize the average mechanical power harvested by the kite. The type of kite considered in this letter extracts electricity from ocean currents by moving cross-current as its reel away from its base station, and consumes electricity to reel back. The problem of optimizing this kite’s trajectory is challenging due to the high dimensionality and nonlinearity of its dynamics. To tackle this challenge, the literature often separates the problem into two subproblems focusing on optimizing the cross-current and the reel-in/reel-out components of the trajectory, respectively, which may be sub-optimal. In contrast, this letter solves for the combined cross-current and reel-in/reel-out trajectory by linearizing the dynamics of the kite around a zero-power reference equilibrium trajectory in spherical coordinates. This allows the trajectory optimization problem to be solved analytically for simple sinusoidal input perturbations from equilibrium. Here we use linear quadratic regulation to enable the nonlinear kite model to track the optimized trajectory. The result is a computationally efficient approach that achieves an attractive Loyd factor of 19.9%, while providing important insights into the nature of the optimal trajectory.
42 ENGINEERING↗