SEARCH · Search NASA
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.
Conditions are described which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. It was found that when the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.
Diffusion models (DMs) are a class of generative machine learning methods that sample a target distribution by transforming samples of a trivial (often Gaussian) distribution using a learned stochastic differential equation. In standard DMs, this is done by learning a “score function” that reverses the effect of adding diffusive noise to the distribution of interest. Here we consider the generalisation of DMs to lattice systems with discrete degrees of freedom, and where noise is added via Markov chain jump dynamics. We show how to use tensor networks (TNs) to efficiently define and sample such “discrete diffusion models” (DDMs) without explicitly having to solve a stochastic differential equation. We show the following: (i) by parametrising the data and evolution operators as TNs, the denoising dynamics can be represented exactly; (ii) the auto-regressive nature of TNs allows to generate samples efficiently and without bias; (iii) for sampling Boltzmann-like distributions, TNs allow to construct an efficient learning scheme that integrates well with Monte Carlo. We illustrate this approach to study the equilibrium of two models with non-trivial thermodynamics, the d = 1 constrained Fredkin chain and the d = 2 Ising model. Published by the American Physical Society 2025
We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (fluctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and find that the systematic bias is of the order of 0.065 eV/Å (~1.2 × 10 -3 E h / a 0 ) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is sufficiently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.
The dynamic response of a nonlinear, single degree of freedom structural system subjected to a physically white noise parametric excitation is investigated. The Ito stochastic calculus is employed to derive a general differential equation for the moments of the response coordinates. The differential equations of moments of any order are found to be coupled with higher order moments. A non-Gaussian closure scheme is developed to truncate the moment equations up to fourth order. The statistical of the stationary response are computed numerically and compared with analytical solutions predicted by a Gaussian closure scheme and the stochastic averaging method. It is found that the computed results exhibit the jump phenomenon which is typical of the characteristics of deterministic nonlinear systems. In addition, the numerical algorithm leads to multiple solutions all of which give positive mean squares. However, two of these solutions are found to violate the properties of high order moments. One solution preserves the moments properties and demonstrates that the system achieves a stationary response.
The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.
The Active Flexible Wing Project is a collaborative effort between the NASA Langley Research Center and Rockwell International. The objectives are the validation of methodologies associated with mathematical modeling, flutter suppression control law development and digital implementation of the control system for application to flexible aircraft. A flutter suppression control law synthesis for this project is described. The state-space mathematical model used for the synthesis included ten flexible modes, four control surface modes and rational function approximation of the doublet-lattice unsteady aerodynamics. The design steps involved developing the full-order optimal control laws, reducing the order of the control law, and optimizing the reduced-order control law in both the continuous and the discrete domains to minimize stochastic response. System robustness was improved using singular value constraints. An 8th order robust control law was designed to increase the symmetric flutter dynamic pressure by 100 percent. Preliminary results are provided and experiences gained are discussed.
It has been recently established that particle dynamics in the magnetotail geometry can be described as a nonintegrable Hamiltonian system with well-defined entry and exit regions through which stochastic orbits can enter and exit the system after repeatedly crossing the equatorial plane. It is shown that the phase space regions occupied by orbits of different numbers of equatorial crossings or different exit modes are separated by fractal boundaries. The fractal boundaries in an entry region for stochastic orbits are examined and the capacity dimension is determined.
Reliability analysis techniques developed for robotics are applied to a six-DOF (degree-of-freedom) visual positioning system. The task is to measure an object's pose and then grip the object reliably subject to time and accuracy constraints. Errors due to pixel truncation in the stadimetric vision system, forward kinematic and inverse kinematic uncertainties, and joint position and velocity noise are stochastically modeled. Simulation results for PUMA 500 kinematic and dynamic characteristics are presented.
The paper presents conditions which guarantee that the control strategies adopted by N players constitute an efficient solution, an equilibrium, or a core solution. The system dynamics are described by an Ito equation, and all players have perfect information. When the set of instantaneous joint costs and velocity vectors is convex, the conditions are necessary.
In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.
Non-conservative processes play a fundamental role in plasticity and are behind important macroscopic phenomena such as creep, dynamic strain aging, loop raft formation, etc. In the most general case, vacancy-induced dislocation climb is the operating unit mechanism. While dislocation/vacancy interactions have been modeled in the literature using a variety of methods, the approaches developed rely on continuum descriptions of both the vacancy population and its fluxes. However, there are numerous situations in physics where point defect populations display heterogeneous concentrations and/or non-smooth kinetics. Here, a kinetic Monte Carlo (kMC) approach for modeling vacancy transport in response to arbitrary stress fields is used. Vacancies are treated as point particles and are coupled to the dislocation substructure representing a deformed material via an advection term defined by the local stress gradients. The stress fields and the dislocation substructure are evolved using a discrete dislocation dynamics (DDD) module. To extend the coupled model to the treatment of large systems, we have implemented it in the massively-parallel DDD code ParaDiS. To avoid numerical incompatibilities associated with merging deterministic (DDD) and stochastic (kMC) integration algorithms, we cast the entire elasto-plastic-diffusive problem within a single stochastic framework, taking advantage of a parallel kMC algorithm to evolve the system as a single event-driven process. The large-scale implementation enables the study of the evolution of a variety of dislocation-defect scenarios governed by non-conservative transport kinetics. After carrying out an exhaustive numerical and computational analysis of our parallel algorithm, we show results that emphasize situations where inhomogeneous vacancy dynamics are of relevance, and compare discrete kinetics to continuum solutions for several cases.
Stochastic quantum trajectories, such as pure state evolutions under unitary dynamics and random measurements, offer a crucial ensemble description of many-body open system dynamics. Recent studies have highlighted that individual quantum trajectories also encode essential physical information. Prominent examples include measurement-induced phase transitions, where a pure quantum state corresponding to fixed measurement outcomes (trajectories) exhibits distinct entanglement phases, depending on the measurement rate. However, direct observation of this effect is hindered by an exponential postselection barrier, whereby the probability of realizing a specific trajectory is exponentially small. We propose a deterministic method to efficiently prepare quantum trajectories in polynomial time using imaginary time evolution and, thus, overcome this fundamental challenge. Here, we demonstrate that our method applies to a certain class of quantum states, and argue that universal approaches do not exist for any quantum trajectories. Our result paves the way for experimentally exploring the physics of individual quantum trajectories at scale and enables direct observation of certain postselection-dependent phenomena.
Decentralized stochastic control is characterized by being decentralized in that the information to one controller is not the same as information to another controller. The system including the information has a stochastic or uncertain component. This complicates the development of decision rules which one determines under the assumption that the system is deterministic. The system is dynamic which means the present decisions affect future system responses and the information in the system. This circumstance presents a complex problem where tools like dynamic programming are no longer applicable. These difficulties are discussed from an intuitive viewpoint. Particular assumptions are introduced which allow a limited theory which produces mechanizable affine decision rules.
The underlying philosophy and motivation of the optimal projection/maximum entropy (OP/ME) stochastic modeling and reduced control design methodology for high order systems with parameter uncertainties are discussed. The OP/ME design equations for reduced-order dynamic compensation including the effect of parameter uncertainties are reviewed. The application of the methodology to several Large Space Structures (LSS) problems of representative complexity is illustrated.
Supercomputer optimizations for a computational method of solving stochastic, multibody, dynamic programming problems are presented. The computational method is valid for a general class of optimal control problems that are nonlinear, multibody dynamical systems, perturbed by general Markov noise in continuous time, i.e., nonsmooth Gaussian as well as jump Poisson random white noise. Optimization techniques for vector multiprocessors or vectorizing supercomputers include advanced data structures, loop restructuring, loop collapsing, blocking, and compiler directives. These advanced computing techniques and superconducting hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations, by permitting the solution of large multibody problems. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random aerospace fluctuations.
A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.
The problem of determining the limiting performance characteristics of mechanical systems subject to random input is studied. A review is presented of the classical work in the optimal design of stochastic systems. Some recent results of stochastic optimal control theory are employed. The solution to the limiting performance problem is formulated in both the frequency and time domains. Both formulations require substantial, burdensome computations when applied to large scale systems.
Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.