Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “chaotic 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.

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

175 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

A Feynman-Kac based numerical method for the exit time probability of a class of transport problems

The exit time probability, which gives the likelihood that an initial condition leaves a prescribed region of the phase space of a dynamical system at, or before, a given time, is arguably one of the most natural and important transport problems. In this work, we present an accurate and efficient numerical method for computing this probability for systems described by non-autonomous (time-dependent) stochastic differential equations (SDEs) or their equivalent Fokker-Planck partial differential equations. The method is based on the direct approximation of the Feynman-Kac formula that establishes a link between the adjoint Fokker-Planck equation and the forward SDE. The Feynman-Kac formula is approximated using the Gauss-Hermite quadrature rules and piecewise cubic Hermite interpolating polynomials, and a GPU accelerated matrix representation is used to compute the entire time evolution of the exit time probability using a single pass of the algorithm. The method is unconditionally stable, exhibits second order convergence in space, first order convergence in time, and it is straightforward to parallelize. Applications are presented to the advection diffusion of a passive tracer in a fluid flow exhibiting chaotic advection, and to the runaway acceleration of electrons in a plasma in the presence of an electric field, collisions, and radiation damping. Benchmarks against analytical solutions as well as comparisons with explicit and implicit finite difference standard methods for the adjoint Fokker-Planck equation are presented.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Mercury’s Chaotic Secular Evolution as a Subdiffusive Process

Abstract Mercury’s orbit can destabilize, generally resulting in a collision with either Venus or the Sun. Chaotic evolution can causeg 1 to decrease to the approximately constant value ofg 5 and create a resonance. Previous work has approximated the variation ing 1 as stochastic diffusion, which leads to a phenomological model that can reproduce the Mercury instability statistics of secular andN-body models on timescales longer than 10 Gyr. Here we show that the diffusive model significantly underpredicts the Mercury instability probability on timescales less than 5 Gyr, the remaining lifespan of the solar system. This is becauseg 1 exhibits larger variations on short timescales than the diffusive model would suggest. To better model the variations on short timescales, we build a new subdiffusive phenomological model forg 1 . Subdiffusion is similar to diffusion but exhibits larger displacements on short timescales and smaller displacements on long timescales. We choose model parameters based on the behavior of theg 1 trajectories in theN-body simulations, leading to a tuned model that can reproduce Mercury instability statistics from 1–40 Gyr. This work motivates fundamental questions in solar system dynamics: why does subdiffusion better approximate the variation ing 1 than standard diffusion? Why is there an upper bound ong 1 , but not a lower bound that would prevent it from reachingg 5 ?

Astronomy & Astrophysics↗
DOE OSTI2022

Rigorous justification for the space–split sensitivity algorithm to compute linear response in Anosov systems

Ruelle gave a formula for linear response of transitive Anosov diffeomorphisms. Recently, practically computable realizations of Ruelle's formula have emerged that potentially enable sensitivity analysis of certain high-dimensional chaotic numerical simulations encountered in the applied sciences. In this paper, we provide full mathematical justification for the convergence of one such efficient computation, the space–split sensitivity, or S3, algorithm. In S3, Ruelle's formula is computed as a sum of two terms obtained by decomposing the perturbation vector field into a coboundary and a remainder that is parallel to the unstable direction. Such a decomposition results in a splitting of Ruelle's formula that is amenable to efficient computation. Here, we prove the existence of the S3 decomposition and the convergence of the computations of both resulting components of Ruelle's formula.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Fluctuation dynamo in a weakly collisional plasma

The turbulent amplification of cosmic magnetic fields depends upon the material properties of the host plasma. In many hot, dilute astrophysical systems, such as the intracluster medium (ICM) of galaxy clusters, the rarity of particle–particle collisions allows departures from local thermodynamic equilibrium. These departures – pressure anisotropies – exert anisotropic viscous stresses on the plasma motions that inhibit their ability to stretch magnetic-field lines. We present an extensive numerical study of the fluctuation dynamo in a weakly collisional plasma using magnetohydrodynamic (MHD) equations endowed with a field-parallel viscous (Braginskii) stress. When the stress is limited to values consistent with a pressure anisotropy regulated by firehose and mirror instabilities, the Braginskii-MHD dynamo largely resembles its MHD counterpart, particularly when the magnetic field is dynamically weak. If instead the parallel viscous stress is left unabated – a situation relevant to recent kinetic simulations of the fluctuation dynamo and, we argue, to the early stages of the dynamo in a magnetized ICM – the dynamo changes its character, amplifying the magnetic field while exhibiting many characteristics reminiscent of the saturated state of the large-Prandtl-number ( ${Pm}\gtrsim {1}$ ) MHD dynamo. We construct an analytic model for the Braginskii-MHD dynamo in this regime, which successfully matches simulated dynamo growth rates and magnetic-energy spectra. A prediction of this model, confirmed by our numerical simulations, is that a Braginskii-MHD plasma without pressure-anisotropy limiters will not support a dynamo if the ratio of perpendicular and parallel viscosities is too small. This ratio reflects the relative allowed rates of field-line stretching and mixing, the latter of which promotes resistive dissipation of the magnetic field. Finally, in all cases that do exhibit a viable dynamo, the generated magnetic field is organized into folds that persist into the saturated state and bias the chaotic flow to acquire a scale-dependent spectral anisotropy.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Scaling CFB risers: Maintaining microstructure dynamics

Over the years there have been numerous approaches to develop a scaleup methodology for circulating fluidized beds. Many of these past approaches have relied on macroscopic definitions of similitude to define dimensionless groups such as Reynolds number, Froude number, density ratios, and dimensional ratios involving different length scales. These approaches have demonstrated various levels of success, but often fail when used outside the bounds of experimental datasets. The issue with these methods is that they rely on macroscopic similitude with the hopes that those conditions would provide microscopic similitude as it does in single phase systems where the Buckingham Pi techniques have given reasonable success. Two of the main reasons for failure are 1) changing fluidization regimes and 2) changing material properties that result in the material falling into a different Geldart group. Both are certain to change the microstructure (local instantaneous volume solids fraction) and changes to the microstructure affect the interphase transport properties of the reactor system, namely the mass transfer and heat transfer. Here, this work presents a new approach towards scaling based upon maintaining similitude at the microscale. It reviews a novel dimensionless flow regime map developed from analysis of the deterministic chaos parameters and higher order moments to ensure microstructure similitude. The work then examines four cases from the literature to assess the scaling approach used: (1) same particle-different scale risers for Geldart Group B particles, (2) Glicksman scaling of atmospheric circulating fluidized bed combustor, (3) same particle-different scale risers for Geldart Group A particles and (4) Glicksman scaling for pressurized gasification. General findings are that none of the scaling approaches produced directly applicable microstructure similar behavior based upon the chaotic and higher moment analysis. The positive take away is that the approach can define scale conditions that will provide similar microstructure that can be us to predict transport behavior.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear analysis and vibro-impact characteristics of a shaft-bearing assembly

Here this study investigates the nonlinear frequency response of a shaft-bearing assembly with vibro-impacts occurring at the bearing clearances. The formation of nonlinear behavior as system parameters change is examined, along with the effects of asymmetries in the nominal, inherently symmetric system. The primary effect of increasing the forcing magnitude or decreasing the contact gap sizes is the formation of grazing-induced chaotic solution branches occurring over a wide frequency range near each system resonance. The system's nominal setup has very hard contact stiffness and shows no evidence of isolas or superharmonic resonances over the frequency ranges of interest. Moderate contact stiffnesses cause symmetry breaking and introduce superharmonic resonance branches of primary resonances. Even if some primary resonances are not present due to the system's inherent symmetry, their superharmonic resonances still manifest. Branches of quasiperiodic isolas (isolated resonance branches) are also discovered, along with a cloud of isolas near a high-frequency resonance. Parameter asymmetries are found to produce a few significant changes in behavior: asymmetric linear stiffness, contact stiffness, and gap size could affect the behavior of primary resonant frequencies and isolas.

42 ENGINEERING↗
DOE OSTI2022

High Accuracy Indicators of Androgen Suppression Therapy Failure for Prostate Cancer—A Modeling Study

Prostate cancer is a serious public health concern in the United States. The primary obstacle to effective long-term management for prostate cancer patients is the eventual development of treatment resistance. Due to the uniquely chaotic nature of the neoplastic genome, it is difficult to determine the evolution of tumor composition over the course of treatment. Hence, a drug is often applied continuously past the point of effectiveness, thereby losing any potential treatment combination with that drug permanently to resistance. If a clinician is aware of the timing of resistance to a particular drug, then they may have a crucial opportunity to adjust the treatment to retain the drug’s usefulness in a potential treatment combination or strategy. In this study, we investigate new methods of predicting treatment failure due to treatment resistance using a novel mechanistic model built on an evolutionary interpretation of Droop cell quota theory. We analyze our proposed methods using patient PSA and androgen data from a clinical trial of intermittent treatment with androgen deprivation therapy. Our results produce two indicators of treatment failure. The first indicator, proposed from the evolutionary nature of the cancer population, is calculated using our mathematical model with a predictive accuracy of 87.3% (sensitivity: 96.1%, specificity: 65%). The second indicator, conjectured from the implication of the first indicator, is calculated directly from serum androgen and PSA data with a predictive accuracy of 88.7% (sensitivity: 90.2%, specificity: 85%). Our results demonstrate the potential and feasibility of using an evolutionary tumor dynamics model in combination with the appropriate data to aid in the adaptive management of prostate cancer.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Ergodic and nonergodic many-body dynamics in strongly nonlinear lattices

The study of nonlinear oscillator chains in classical many-body dynamics has a storied history going back to the seminal work of Fermi et al. [Los Alamos Scientific Laboratory Report No. LA-1940, 1955 (unpublished)]. Here, we introduce a family of such systems which consist of chains of N harmonically coupled particles with the nonlinearity introduced by confining the motion of each individual particle to a box or stadium with hard walls. The stadia are arranged on a one-dimensional lattice but they individually do not have to be one dimensional, thus permitting the introduction of chaos already at the lattice scale. For the most part we study the case where the motion is entirely one dimensional. We find that the system exhibits a mixed phase space for any finite value of N . Computations of Lyapunov spectra at randomly picked phase space locations and a direct comparison between Hamiltonian evolution and phase space averages indicate that the regular regions of phase space are not significant at large system sizes. While the continuum limit of our model is itself a singular limit of the integrable sinh Gordon theory, we do not see any evidence for the kind of nonergodicity famously seen in the work of Fermi et al. Finally, we examine the chain with particles confined to two-dimensional stadia where the individual stadium is already chaotic and find a much more chaotic phase space at small system sizes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Thermalization at low temperatures via weakly damped multisite baths

We study the thermalization properties of one-dimensional open quantum systems coupled to baths at their boundary. The baths are driven to their thermal states via Lindblad operators, while the system undergoes Hamiltonian dynamics. We specifically consider multisite baths and investigate the extent to which the late-time steady state resembles a Gibbs state at some controllable temperature set by the baths. We study three models: a noninteracting fermion model accessible via free-fermion technology, and two interacting models, the XZ model and the chiral clock model, which are accessible via tensor network methods. We show that, by tuning towards the weak coupling and slow relaxation limits, one can engineer low temperatures in the bulk of the system provided the bath size is big enough. Here, we use this capability to study energy transport in the XZ model at lower temperatures than previously reported. Our work paves the way for future studies of interacting open quantum systems at low temperatures.

1-dimensional spin chains↗
DOE OSTI2021

Mapping the magnetic field in the Taurus/B211 filamentary cloud with SOFIA HAWC + and comparing with simulation

ABSTRACT Optical and infrared polarization mapping and recent Planck observations of the filametary cloud L1495 in Taurus show that the large-scale magnetic field is approximately perpendicular to the long axis of the cloud. We use the HAWC + polarimeter on SOFIA to probe the complex magnetic field in the B211 part of the cloud. Our results reveal a dispersion of polarization angles of 36°, about five times that measured on a larger scale by Planck. Applying the Davis–Chandrasekhar–Fermi (DCF) method with velocity information obtained from Institut de Radioastronomie Millimétrique 30 m C18O(1-0) observations, we find two distinct sub-regions with magnetic field strengths differing by more than a factor 3. The quieter sub-region is magnetically critical and sub-Alfv$\acute{\rm e}$nic; the field is comparable to the average field measured in molecular clumps based on Zeeman observations. The more chaotic, super-Alfv$\acute{\rm e}$nic sub-region shows at least three velocity components, indicating interaction among multiple substructures. Its field is much less than the average Zeeman field in molecular clumps, suggesting that the DCF value of the field there may be an underestimate. Numerical simulation of filamentary cloud formation shows that filamentary substructures can strongly perturb the magnetic field. DCF and true field values in the simulation are compared. Pre-stellar cores are observed in B211 and are seen in our simulation. The appendices give a derivation of the standard DCF method that allows for a dispersion in polarization angles that is not small, present an alternate derivation of the structure function version of the DCF method, and treat fragmentation of filaments.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Integrable symplectic maps with a polygon tessellation

Identifying integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a distinct form of area-preserving (symplectic) mappings derived from the stroboscopic Poincaré cross section of a kicked rotator—an oscillator subjected to an external force periodically switched on in short pulses. The significance of this class of problems extends to various applications in physics and mathematics, including particle accelerators, crystallography, and studies of chaos. Notably, Suris's theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant by exploring piecewise linear transformations on a torus ( T 2 ) and associated systems on the plane ( R 2 ), incorporating arithmetic quasiperiodicity and discontinuities. Introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane or torus. This work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincaré rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of “integrable diffusion,” characterized by infinite and quasirandom hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with suppressed volume occupied by chaotic trajectories, thereby opening doors to potential practical applications. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2022

Multiple origins, one evolutionary trajectory: gradual evolution characterizes distinct lineages of allotetraploid Brachypodium

The “genomic shock” hypothesis posits that unusual challenges to genome integrity such as whole genome duplication may induce chaotic genome restructuring. Decades of research on polyploid genomes have revealed that this is often, but not always the case. While some polyploids show major chromosomal rearrangements and derepression of transposable elements in the immediate aftermath of whole genome duplication, others do not. Nonetheless, all polyploids show gradual diploidization over evolutionary time. To evaluate these hypotheses, we produced a chromosome-scale reference genome for the natural allotetraploid grass Brachypodium hybridum, accession “Bhyb26.” We compared 2 independently derived accessions of B. hybridum and their deeply diverged diploid progenitor species Brachypodium stacei and Brachypodium distachyon. The 2 B. hybridum lineages provide a natural timecourse in genome evolution because one formed 1.4 million years ago, and the other formed 140 thousand years ago. The genome of the older lineage reveals signs of gradual post-whole genome duplication genome evolution including minor gene loss and genome rearrangement that are missing from the younger lineage. In neither B. hybridum lineage do we find signs of homeologous recombination or pronounced transposable element activation, though we find evidence supporting steady post-whole genome duplication transposable element activity in the older lineage. Gene loss in the older lineage was slightly biased toward 1 subgenome, but genome dominance was not observed at the transcriptomic level. We propose that relaxed selection, rather than an abrupt genomic shock, drives evolutionary novelty in B. hybridum, and that the progenitor species’ similarity in transposable element load may account for the subtlety of the observed genome dominance.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Modeling and Experimental Validation of a Direct-Contact Counter-Flow Fluidized Bed Heat Exchanger for Thermal Energy Storage (TES) Applications

Particle-based thermal energy storage (TES) systems are an emerging energy storage technology. The technological advances have reduced costs, making TES more competitive and reliable in the marketplace but an efficient and reliable operation is heavily dependent on coherent heat transfer between air to particles or vice versa. The particle-based TES technologies provide an intermediate system that can store energy for short (0-10 h), long (10-200 h) and seasonal (> 200 h) timescales. The TES systems store energy by converting electricity to thermal energy; electricity can be directly sourced intermittent generation technologies and/or the grid, helping manage peak loads and other mismatches in supply and demand. The overall efficiency of the TES system depends on the performance of system components (particle storage silos and particle transfer mechanism etc.). The particle heat exchanger is one of the key system components that affects the system efficiency. The pressurized fluidized bed heat exchanger (PFB HX) performance is challenging to predict due to the chaotic behavior of particle and fluid interaction. This research presents a computational study of a novel direct-contact, counter-flow and air-to-particles PFB HX, that contributes in advancing the particle-based long-duration TES technologies. For the current analysis an unsteady Eulerian-Eulerian CFD model was developed and validated against experiments performed at the National Laboratory of the Rockies for two particle sizes (600 ..mu..m and 825 ..mu..m ). Following validation, parametric simulations were conducted to evaluate the effects of interphase drag models (Syamlal-O'Brien and Gidaspow), particle size, bed height and the influence of a frictional-viscosity term on hydrodynamics and heat transfer between the air & particles. The key findings from the analysis are: (1) for the studied operating window Syamlal-O'Brien provides superior agreement with measured gas temperatures (errors generally < 10%) while Gidaspow shows large deviations for the coarse particle case; (2) model predictions are most sensitive in the lower 0.2 m above the air distributor where bubble initiation and local mixing dominate interphase heat transfer; (3) representation of the distributor (number of inlet ports) materially affects predicted local mixing and temperature stratification; and (4) the Eulerian-Eulerian framework reproduces bulk thermal trends but shows regime dependent limitations for coarse particles, motivating mesoscale informed closures for scale-up analysis for future studies. These results provide validated guidance for drag selection and distributor design in particle-based thermal energy storage applications. Collectively, the validated model and parametric results quantify key drivers of PHB-HX performance and provide practical guidance for design and optimization. The results provide confidence in the model predictability and provide a step forward to improve on heat exchange performance. The demonstrated performance and modeling approach support the deployment and further development of this novel PHB-HX concept for robust, particle-based long-duration thermal energy storage systems.

25 ENERGY STORAGE↗