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Results for “Complex dynamical systems”

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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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics

The quantum-classical Liouville equation offers a rigorous approach to nonadiabatic quantum dynamics based on surface hopping type trajectories. However, in practice the applicability of this approach has been limited to short times owing to unfavorable numerical scaling. In this paper we show that this problem can be alleviated by combining it with a formally exact generalized quantum master equation treatment. This allows dramatic improvements in the efficiency of the approach in nonadiabatic regimes, making it computationally tractable to treat the quantum dynamics of complex systems for long times. We demonstrate our approach by applying it to a model of condensed phase charge transfer where our method is shown to be numerically exact in regimes where fewest-switches surface hopping and mean field approaches fail to obtain either the correct rates or long-time populations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Extreme multistability in a memristor-based multi-scroll hyper-chaotic system

In this paper, a new memristor-based multi-scroll hyper-chaotic system is designed. The proposed memristor-based system possesses multiple complex dynamic behaviors compared with other chaotic systems. Various coexisting attractors and hidden coexisting attractors are observed in this system, which means extreme multistability arises. Besides, by adjusting parameters of the system, this chaotic system can perform single-scroll attractors, double-scroll attractors, and four-scroll attractors. Basic dynamic characteristics of the system are investigated, including equilibrium points and stability, bifurcation diagrams, Lyapunov exponents, and so on. In addition, the presented system is also realized by an analog circuit to confirm the correction of the numerical simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Inexact iterative numerical linear algebra for neural network-based spectral estimation and rare-event prediction

Understanding dynamics in complex systems is challenging because there are many degrees of freedom, and those that are most important for describing events of interest are often not obvious. The leading eigenfunctions of the transition operator are useful for visualization, and they can provide an efficient basis for computing statistics, such as the likelihood and average time of events (predictions). Here, we develop inexact iterative linear algebra methods for computing these eigenfunctions (spectral estimation) and making predictions from a dataset of short trajectories sampled at finite intervals. We demonstrate the methods on a low-dimensional model that facilitates visualization and a high-dimensional model of a biomolecular system. Implications for the prediction problem in reinforcement learning are discussed.

Chemistry↗
DOE OSTI2020

GFiRe—Gauge Field integrator for Reheating

We present a new numerical algorithm and code, GFiRe, for solving the nonlinear evolution of Abelian gauge fields coupled to complex scalar fields in homogeneous and isotropic spacetimes. We adopt a hybrid approach to solving the system: the spatial derivatives are discretized using standard Lattice Gauge Field Theory techniques, whereas the time evolution of the fields and scale factor is implemented with explicit, composite, symplectic integrators. An important property of our compound algorithm is that the discretized Gauss constraint is respected exactly, regardless of the order of the symplectic integrator. This remains true even when the background expansion is computed “self-consistently”; that is, when the expansion history is computed using spatial averaged components of the energy momentum tensor in the simulation volume. Hence, our code can also be used in cases where the fields dominate the energy density of the universe, for example, during reheating after inflation. We test the algorithm in scenarios of reheating where the inflaton is a complex scalar field with a potential ∝(2|Φ| 2 - v 2 ) 2 and is coupled to an Abelian gauge field. Tracing the evolution of the system through complex dynamics (including resonant excitation of fields, backreaction, formation of solitons, and changes in the equation of state) in a self-consistently expanding universe, we find the energy conservation violation (<10 -4 ) to be very stable and the Gauss constraint violation (<10 -6 ) to be dominated by differencing noise.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Tailoring Spin-Wave Channels in a Reconfigurable Artificial Spin Ice

Artificial spin ices are ensembles of geometrically arranged interacting nanomagnets that have shown promising potential for the realization of reconfigurable magnonic crystals. Such systems allow for the manipulation of spin waves on the nanoscale and their potential use as information carriers. However, there are presently two general obstacles to the realization of artificial spin-ice-based magnonic crystals: the magnetic state of artificial spin ices is difficult to reconfigure and the magnetostatic interactions between the nanoislands are often weak, preventing mode coupling. We demonstrate, using micromagnetic modeling, that coupling a reconfigurable artificial spin-ice geometry made of weakly interacting nanomagnets to a soft magnetic underlayer creates a complex system exhibiting dynamically coupled modes. These give rise to spin-wave channels in the underlayer at well-defined frequencies, based on the artificial spin-ice magnetic state, which can be reconfigured. Finally, these findings open the door to the realization of reconfigurable magnonic crystals with potential applications for data transport and processing in magnonic-based logic architectures.

25 ENERGY STORAGE↗
DOE OSTI2014

Damage Spreading in Spatial and Small-world Random Boolean Networks

The study of the response of complex dynamical social, biological, or technological networks to external perturbations has numerous applications. Random Boolean Networks (RBNs) are commonly used a simple generic model for certain dynamics of complex systems. Traditionally, RBNs are interconnected randomly and without considering any spatial extension and arrangement of the links and nodes. However, most real-world networks are spatially extended and arranged with regular, power-law, small-world, or other non-random connections. Here we explore the RBN network topology between extreme local connections, random small-world, and pure random networks, and study the damage spreading with small perturbations. We find that spatially local connections change the scaling of the relevant component at very low connectivities ($\bar{K} \ll 1$) and that the critical connectivity of stability $K_s$ changes compared to random networks. At higher $\bar{K}$, this scaling remains unchanged. We also show that the relevant component of spatially local networks scales with a power-law as the system size N increases, but with a different exponent for local and small-world networks. The scaling behaviors are obtained by finite-size scaling. We further investigate the wiring cost of the networks. From an engineering perspective, our new findings provide the key design trade-offs between damage spreading (robustness), the network's wiring cost, and the network's communication characteristics.

Lu, Qiming↗
DOE OSTI2021

Discrete Time-Crystalline Order Enabled by Quantum Many-Body Scars: Entanglement Steering via Periodic Driving

The control of many-body quantum dynamics in complex systems is a key challenge in the quest to reliably produce and manipulate large-scale quantum entangled states. Recently, quench experiments in Rydberg atom arrays [Bluvstein et al. Science 371, 1355 (2021)] demonstrated that coherent revivals associated with quantum many-body scars can be stabilized by periodic driving, generating stable subharmonic responses over a wide parameter regime. We analyze a simple, related model where these phenomena originate from spatiotemporal ordering in an effective Floquet unitary, corresponding to discrete time-crystalline behavior in a prethermal regime. Unlike conventional discrete time crystals, the subharmonic response exists only for Néel-like initial states, associated with quantum scars. We predict robustness to perturbations and identify emergent timescales that could be observed in future experiments. Our results suggest a route to controlling entanglement in interacting quantum systems by combining periodic driving with many-body scars.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Raman Interferometry between Autoionizing States to Probe Ultrafast Wave-Packet Dynamics with High Spectral Resolution

Photoelectron interferometry with femtosecond and attosecond light pulses is a powerful probe of the fast electron wave-packet dynamics, albeit it has practical limitations on the energy resolution. We show that one can simultaneously obtain both high temporal and spectral resolution by stimulating Raman interferences with one light pulse and monitoring the modification of the electron yield in a separate step. Applying this spectroscopic approach to the autoionizing states of argon, we experimentally resolved its electronic composition and time evolution in exquisite detail. Theoretical calculations show remarkable agreement with the observations and shed light on the light-matter interaction parameters. Using appropriate Raman probing and delayed detection steps, this technique enables highly sensitive probing and control of electron dynamics in complex systems.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2020

Multiscale modeling high-order methods and data-driven modeling

Projection-based reduced-order models (ROMs) comprise a promising set of data-driven approaches for accelerating the simulation of high-fidelity numerical simulations. Standard projection-based ROM approaches, however, suffer from several drawbacks when applied to the complex nonlinear dynamical systems commonly encountered in science and engineering. These limitations include a lack of stability, accuracy, and sharp a posteriori error estimators. This work addresses these limitations by leveraging multiscale modeling, least-squares principles, and machine learning to develop novel reduced-order modeling approaches, along with data-driven a posteriori error estimators, for dynamical systems. Theoretical and numerical results demonstrate that the two ROM approaches developed in this work - namely the windowed least-squares method and the Adjoint Petrov - Galerkin method - yield substantial improvements over state-of-the-art approaches. Additionally, numerical results demonstrate the capability of the a posteriori error models developed in this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Climate Forcing & Feedbacks by Fires, Forests, Fossil Energy & Food Production: Observations are Key to Predictions [Slides]

Human emitted GHGs (long lived, cumulative) that trap more heat (IR) and aerosols (short lived, steady) that reflect sunlight (Vis) have altered Earth’s radiation budget and warmed our climate measurably and predictably. Our complex dynamic climate system has trapped 400 ZettaJ (10 21 ) and has many positive feedbacks. Regions are changing at unprecedented rates and crossing thresholds as BAU will lock us into 8.5 W m -2 in 2100.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1986

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought.

Murthy, D. V.↗
NASA NTRS1994

Changes and challenges in the Software Engineering Laboratory

Since 1976, the Software Engineering Laboratory (SEL) has been dedicated to understanding and improving the way in which one NASA organization, the Flight Dynamics Division (FDD), develops, maintains, and manages complex flight dynamics systems. The SEL is composed of three member organizations: NASA/GSFC, the University of Maryland, and Computer Sciences Corporation. During the past 18 years, the SEL's overall goal has remained the same: to improve the FDD's software products and processes in a measured manner. This requires that each development and maintenance effort be viewed, in part, as a SEL experiment which examines a specific technology or builds a model of interest for use on subsequent efforts. The SEL has undertaken many technology studies while developing operational support systems for numerous NASA spacecraft missions.

Pajerski, Rose↗
NASA NTRS1997

The SEL Adapts to Meet Changing Times

Since 1976, the Software Engineering Laboratory (SEL) has been dedicated to understanding and improving the way in which one NASA organization, the Flight Dynamics Division (FDD) at Goddard Space Flight Center, develops, maintains, and manages complex flight dynamics systems. It has done this by developing and refining a continual process improvement approach that allows an organization such as the FDD to fine-tune its process for its particular domain. Experimental software engineering and measurement play a significant role in this approach. The SEL is a partnership of NASA Goddard, its major software contractor, Computer Sciences Corporation (CSC), and the University of Maryland's (LTM) Department of Computer Science. The FDD primarily builds software systems that provide ground-based flight dynamics support for scientific satellites. They fall into two sets: ground systems and simulators. Ground systems are midsize systems that average around 250 thousand source lines of code (KSLOC). Ground system development projects typically last 1 - 2 years. Recent systems have been rehosted to workstations from IBM mainframes, and also contain significant new subsystems written in C and C++. The simulators are smaller systems averaging around 60 KSLOC that provide the test data for the ground systems. Simulator development lasts up to 1 year. Most of the simulators have been built in Ada on workstations. The SEL is responsible for the management and continual improvement of the software engineering processes used on these FDD projects.

Pajerski, Rose S.↗
NASA NTRS1995

What's Happening in the Software Engineering Laboratory?

Since 1976 the Software Engineering Laboratory (SEL) has been dedicated to understanding and improving the way in which one NASA organization the Flight Dynamics Division (FDD) at Goddard Space Flight Center, develops, maintains, and manages complex flight dynamics systems. This paper presents an overview of recent activities and studies in SEL, using as a framework the SEL's organizational goals and experience based software improvement approach. It focuses on two SEL experience areas : (1) the evolution of the measurement program and (2) an analysis of three generations of Cleanroom experiments.

Pajerski, Rose↗
NASA NTRS1987

Mass balances for a biological life support system simulation model

Design decisions to aid the development of future space based biological life support systems (BLSS) can be made with simulation models. The biochemistry stoichiometry was developed for: (1) protein, carbohydrate, fat, fiber, and lignin production in the edible and inedible parts of plants; (2) food consumption and production of organic solids in urine, feces, and wash water by the humans; and (3) operation of the waste processor. Flux values for all components are derived for a steady state system with wheat as the sole food source. The large scale dynamics of a materially closed (BLSS) computer model is described in a companion paper. An extension of this methodology can explore multifood systems and more complex biochemical dynamics while maintaining whole system closure as a focus.

Volk, Tyler↗
DOE OSTI2014

Heterogeneous recurrence monitoring and control of nonlinear stochastic processes

Recurrence is one of the most common phenomena in natural and engineering systems. Process monitoring of dynamic transitions in nonlinear and nonstationary systems is more concerned with aperiodic recurrences and recurrence variations. However, little has been done to investigate the heterogeneous recurrence variations and link with the objectives of process monitoring and anomaly detection. Notably, nonlinear recurrence methodologies are based on homogeneous recurrences, which treat all recurrence states in the same way as black dots, and non-recurrence is white in recurrence plots. Heterogeneous recurrences are more concerned about the variations of recurrence states in terms of state properties (e.g., values and relative locations) and the evolving dynamics (e.g., sequential state transitions). This paper presents a novel approach of heterogeneous recurrence analysis that utilizes a new fractal representation to delineate heterogeneous recurrence states in multiple scales, including the recurrences of both single states and multi-state sequences. Further, we developed a new set of heterogeneous recurrence quantifiers that are extracted from fractal representation in the transformed space. To that end, we integrated multivariate statistical control charts with heterogeneous recurrence analysis to simultaneously monitor two or more related quantifiers. Experimental results on nonlinear stochastic processes show that the proposed approach not only captures heterogeneous recurrence patterns in the fractal representation but also effectively monitors the changes in the dynamics of a complex system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗