Search NASA⌕ Search

SEARCH · Search NASA

Results for “Nonlinear Analysis”

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 541 records · Page 30
All sourcesNASA NTRSDOE OSTI
DOE OSTI2014

Beam-wave interaction behavior of a 35 GHz metal PBG cavity gyrotron

The RF behavior of a 35 GHz photonic band gap (PBG) cavity gyrotron operating in TE{sub 041}-like mode has been presented to demonstrate its single mode operation capability. In this PBG cavity gyrotron, the conventional tapered cylindrical cavity is replaced by a metal PBG cavity as its RF interaction structure. The beam-wave interaction behavior has been explored using time dependent multimode nonlinear analysis as well as through 3D PIC simulation. Metal PBG cavity is treated here similar to that of a conventional cylindrical cavity for the desired mode confinement. The applied DC magnetic field profile has been considered uniform along the PBG cavity length both in analysis as well as in simulation. Electrons energy and phase along the interaction length of the PBG cavity facilitates bunching mechanism as well as energy transfer phenomena from the electron beam to the RF field. The RF output power for the TE{sub 041}-like design mode as well as nearby competing modes have been estimated and found above to 100 kW in TE{sub 041}-like mode with ∼15% efficiency. Results obtained from the analysis and the PIC simulation are found in agreement within 8% variation, and also it supports the single mode operation, as the PBG cavity does not switch into other parasitic modes in considerably large range of varying DC magnetic field, contrary to the conventional cylindrical cavity interaction structure.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Synthesizing Virtual Oscillators to Control Islanded Inverters

Virtual oscillator control (VOC) is a decentralized control strategy for islanded microgrids where inverters are regulated to emulate the dynamics of weakly nonlinear oscillators. Compared to droop control, which is only well defined in sinusoidal steady state, VOC is a time-domain controller that enables interconnected inverters to stabilize arbitrary initial conditions to a synchronized sinusoidal limit cycle. However, the nonlinear oscillators that are elemental to VOC cannot be designed with conventional linear-control design methods. We address this challenge by applying averaging- and perturbation-based nonlinear analysis methods to extract the sinusoidal steady-state and harmonic behavior of such oscillators. The averaged models reveal conclusive links between real- and reactive-power outputs and the terminal-voltage dynamics. Similarly, the perturbation methods aid in quantifying higher order harmonics. The resultant models are then leveraged to formulate a design procedure for VOC such that the inverter satisfies standard ac performance specifications related to voltage regulation, frequency regulation, dynamic response, and harmonic content. Experimental results for a single-phase 750 VA, 120 V laboratory prototype demonstrate the validity of the design approach. They also demonstrate that droop laws are, in fact, embedded within the equilibria of the nonlinear-oscillator dynamics. This establishes the backward compatibility of VOC in that, while acting on time-domain waveforms, it subsumes droop control in sinusoidal steady state.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2016

Proposed Activities to Address Regulatory Gaps and Challenges for Licensing Advanced Reactors Using Seismic Isolation

Over the last decade, particularly since implementation of the certified design regulatory approaches outlined in 10 CFR 52, “Licenses, Certifications, and Approvals for Nuclear Power Plants,” interest has been increasing in the use of seismic isolation (SI) technology to support seismic safety in nuclear facilities. In 2009, the United States (U.S.) Nuclear Regulatory Commission (NRC) initiated research activities to develop new guidance targeted at isolated facilities because SI is being considered for nuclear power plants in the U.S. One product of that research, which was developed around a risk-informed regulatory approach, is a draft NRC NUREG series (NUREG/CR) report that investigates and discusses considerations for use of SI in otherwise traditionally founded large light water reactors (LWRs). A coordinated effort led to new provisions for SI of LWRs in the American Society of Civil Engineers standard ASCE/SEI 4-16, “Seismic Analysis of Safety Related Nuclear Structures.” The risk-informed design philosophy that underpinned development of the technical basis for these documents led to a set of proposed performance objectives and acceptance criteria intended to serve as the foundation for future NRC guidance on the use of SI and related technology. Although the guidance provided in the draft SI NUREG/CR report and ASCE/SEI 4 16 provides a sound basis for further development of nuclear power plant designs incorporating SI, these initial documents were focused on surface-founded or near-surface-founded LWRs and were, necessarily, limited in scope. For example, there is limited information in both the draft NUREG/CR report and ASCE/SEI 4-16 related to nonlinear analysis of soil-structure systems for deeply-embedded reactors, the isolation of components, and the use of vertical isolation systems. Also not included in the draft SI NUREG/CR report are special considerations for licensing of isolated facilities using the certified design approach in 10 CFR 52 and a detailed discussion of seismic probabilistic risk assessments for isolated facilities.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2014

Dust acoustic solitary and shock excitations in a Thomas-Fermi magnetoplasma

The linear and nonlinear properties of dust-acoustic waves are investigated in a collisionless Thomas-Fermi magnetoplasma, whose constituents are electrons, ions, and negatively charged dust particles. At dust time scale, the electron and ion number densities follow the Thomas-Fermi distribution, whereas the dust component is described by the classical fluid equations. A linear dispersion relation is analyzed to show that the wave frequencies associated with the upper and lower modes are enhanced with the variation of dust concentration. The effect of the latter is seen more strongly on the upper mode as compared to the lower mode. For nonlinear analysis, we obtain magnetized Korteweg-de Vries (KdV) and Zakharov-Kuznetsov (ZK) equations involving the dust-acoustic solitary waves in the framework of reductive perturbation technique. Furthermore, the shock wave excitations are also studied by allowing dissipation effects in the model, leading to the Korteweg-de Vries-Burgers (KdVB) and ZKB equations. The analysis reveals that the dust-acoustic solitary and shock excitations in a Thomas-Fermi plasma are strongly influenced by the plasma parameters, e.g., dust concentration, dust temperature, obliqueness, magnetic field strength, and dust fluid viscosity. The present results should be important for understanding the solitary and shock excitations in the environments of white dwarfs or supernova, where dust particles can exist.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2012

Low intensity dust ion-acoustic shock waves due to dust charge fluctuation in a nonextensive dusty plasma

The properties of low intensity dust ion acoustic shock waves are studied in a charge varying dusty plasma with nonextensive electrons. Owing to the departure from the Maxwellian electron distribution to a nonextensive one, the modified electrostatic charging of a spherical dust particle in plasma with ion streaming speed is considered. Based on the weakly nonlinear analysis, a new relationship between the low intensity localized disturbances and nonextensive electrons is derived. It is found that both strength and steepness of shock structures arise as the electrons evolve far from their thermodynamic equilibrium in such plasma with parameter ranges corresponding to Saturn's rings. It is also shown that the ion temperature and population of electrons reduce the possibility of the formation of the shock profile.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

Dissipative dust-acoustic shock waves in a varying charge electronegative magnetized dusty plasma with trapped electrons

The combined effects of an oblique magnetic field and electron trapping on dissipative dust-acoustic waves are examined in varying charge electronegative dusty plasmas with application to the Halley Comet plasma (∼10{sup 4} km from the nucleus). A weakly nonlinear analysis is carried out to derive a modified Korteweg-de Vries-Burger-like equation. Making use of the equilibrium current balance equation, the physically admissible values of the electron trapping parameter are first constrained. We then show that the Burger dissipative term is solely due to the dust charge variation process. It is found that an increase of the magnetic field obliqueness or a decrease of its magnitude renders the shock structure more dispersive.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS1990

Innovative design of composite structures: Axisymmetric deformations of unsymmetrically laminated cylinders loaded in axial compression

The study focuses on the axisymmetric deformation response of unsymmetrically laminate cylinders loaded in axial compression by known loads. A geometrically nonlinear analysis is used. Though buckling is not studied, the deformations can be considered to be the prebuckling response. Attention is directed at three 16 layer laminates: a (90 sub 8/0 sub 8) sub T; a (0 sub 8/90 sub 8) sub T and a (0/90) sub 4s. The symmetric laminate is used as a basis for comparison, while the two unsymmetric laminates were chosen because they have equal but opposite bending-stretching effects. Particular attention is given to the influence of the thermally-induced preloading deformations that accompany the cool-down of any unsymmetric laminate from the consolidation temperature. Simple support and clamped boundary conditions are considered. It is concluded that: (1) The radial deformations of an unsymmetric laminate are significantly larger than the radial deformations of a symmetric laminate, although for both symmetric and unsymmetric laminates the large deformations are confined to a boundary layer near the ends of the cylinder; (2) For this nonlinear problem the length of the boundary layer is a function of the applied load; (3) The sign of the radial deformations near the supported end of the cylinder depends strongly on the sense (sign) of the laminate asymmetry; (4) For unsymmetric laminates, ignoring the thermally-induced preloading deformations that accompany cool-down results in load-induced deformations that are under predicted; and (5) The support conditions strongly influence the response but the influence of the sense of asymmetry and the influence of the thermally-induced preloading deformations are independent of the support conditions.

Hyer, M. W.↗
DOE OSTI2015

The temporal patterns of disease severity and prevalence in schistosomiasis

Schistosomiasis is one of the most widespread public health problems in the world. In this work, we introduce an eco-epidemiological model for its transmission and dynamics with the purpose of explaining both intra- and inter-annual fluctuations of disease severity and prevalence. The model takes the form of a system of nonlinear differential equations that incorporate biological complexity associated with schistosome's life cycle, including a prepatent period in snails (i.e., the time between initial infection and onset of infectiousness). Nonlinear analysis is used to explore the parametric conditions that produce different temporal patterns (stationary, endemic, periodic, and chaotic). For the time-invariant model, we identify a transcritical and a Hopf bifurcation in the space of the human and snail infection parameters. The first corresponds to the occurrence of an endemic equilibrium, while the latter marks the transition to interannual periodic oscillations. We then investigate a more realistic time-varying model in which fertility of the intermediate host population is assumed to seasonally vary. We show that seasonality can give rise to a cascade of period-doubling bifurcations leading to chaos for larger, though realistic, values of the amplitude of the seasonal variation of fertility.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Solving differential equations using deep neural networks

Recent work on solving partial differential equations (PDEs) with deep neural networks (DNNs) is presented. The paper reviews and extends some of these methods while carefully analyzing a fundamental feature in numerical PDEs and nonlinear analysis: irregular solutions. First, the Sod shock tube solution to the compressible Euler equations is discussed and analyzed. This analysis includes a comparison of a DNN-based approach with conventional finite element and finite volume methods, and demonstrates that the DNN is competitive in terms of degrees of freedom required for a given accuracy. Further, the DNN-based approach is extended to consider performance improvements and simultaneous parameter space exploration. Next, a shock solution to compressible magnetohydrodynamics (MHD) is solved for, and used in a scenario where experimental data is utilized to enhance a PDE system that is a priori insufficient to validate against the observed/experimental data. This is accomplished by enriching the model PDE system with source terms that are then inferred via supervised training with synthetic experimental data. The resulting DNN framework for PDEs enables straightforward system prototyping and natural integration of large data sets (be they synthetic or experimental), all while simultaneously enabling single-pass exploration of an entire parameter space.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2013

Collisional drag may lead to disappearance of wave-breaking phenomenon of lower hybrid oscillations

The inhomogeneity in the magnetic field in a cold electron-ion non-dissipative homogeneous plasma leads to the breaking of lower hybrid modes via phase mixing phenomenon [Maity et al. Phys. Plasmas 19, 102302 (2012)]. In this work, we show that an inclusion of collisional drag force in fluid equations may lead to the disappearance of the wave-breaking phenomenon of lower hybrid oscillations. The nonlinear analysis in Lagrangian variables provides an expression for a critical value of damping rate, above which spikes in the plasma density profile may disappear. The critical damping rate depends on the perturbation and magnetic field inhomogeneity amplitudes as well as the ratio of the magnetic field inhomogeneity and perturbation scale lengths.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

Weak turbulence cascading effects in the acceleration and heating of ions in the solar wind

We study the wave-particle interaction and the evolution of electromagnetic waves propagating through a solar-wind-like plasma composed of cold electrons, isotropic protons, and a small portion of drifting anisotropic He{sup +2} (T {sub α} = 6 T {sub ∥α}) and O{sup +6} (T {sub O} = 11 T {sub ∥O}) ions as suggested in Gomberoff and Valdivia and Gomberoff et al., using two approaches. First, we use quasilinear kinetic theory to study the energy transfer between waves and particles, with the subsequent acceleration and heating of ions. Second, 1.5 D (one spatial dimension and three dimensions in velocity space) hybrid numerical simulations are performed to investigate the fully nonlinear evolution of this wave-particle interaction. Numerical results of both approaches show that the temperatures of all species evolve anisotropically, consistent with the time-dependent wave-spectrum energy. In a cascade effect, we observe the emergence of modes at frequencies higher than those initially considered, peaking at values close to the resonance frequencies of O{sup +6} ions (ω ∼ Ω {sub cO}) and He{sup +2} ions (ω ∼ Ω {sub cα}), being the peak due to O{sup +6} ions about three times bigger than the peak associated with He{sup +2} ions. Both the heating of the plasma and the energy cascade were more efficient in the nonlinear analysis than in the quasilinear one. These results suggest that this energy cascade mechanism may participate in the acceleration and heating of the solar wind plasma close to the Sun during fast streams associated with coronal holes.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Spontaneous magnon decays from nonrelativistic time-reversal symmetry breaking in altermagnets

Quasiparticles are central to condensed matter physics, but their stability can be undermined by quantum many-body interactions. Magnons, i.e., quasiparticles in quantum magnets, are particularly intriguing because their properties are governed by both real and spin space. While crystal symmetries may be low, spin interactions often remain approximately isotropic, limiting spontaneous magnon decay. Textbook wisdom holds that collinear Heisenberg magnets follow a dichotomy: ferromagnets host stable magnons, while antiferromagnetic magnons may decay depending on dispersion curvature. Up to now, relativistic spin-orbit coupling and noncollinear order that connect spin space to real space were shown to introduce more complex magnon instability mechanisms. Here, we show that even in nonrelativistic isotropic collinear systems, this conventional dichotomy is disrupted in altermagnets. Altermagnets, a newly identified class of collinear magnets, exhibit compensated spin order with nonrelativistic time-reversal symmetry breaking and even-parity band splitting. Using kinematic analysis, nonlinear spin-wave theory, and quantum simulations, we reveal that even weak band splitting opens a decay phase space, driving quasiparticle breakdown. Additionally, 𝑑-wave altermagnets form a rare “island of stability” at the Brillouin-zone center. Furthermore, our findings establish a quasiparticle stability trichotomy in collinear Heisenberg magnets and position altermagnets as a promising platform for unconventional spin dynamics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Absolute vs Convective Instabilities and Front Propagation in Lipid Membrane Tubes

Here we analyze the stability of biological membrane tubes, with and without a base flow of lipids. Membrane dynamics are completely specified by two dimensionless numbers: the well-known Föppl-von Kármán number Γ and the recently introduced Scriven-Love number SL, respectively quantifying the base tension and base flow speed. For unstable tubes, the growth rate of a local perturbation depends only on Γ, whereas SL governs the absolute versus convective nature of the instability. Furthermore, nonlinear simulations of unstable tubes reveal an initially localized disturbance result in propagating fronts, which leave a thin atrophied tube in their wake. Depending on the value of Γ, the thin tube is connected to the unperturbed regions via oscillatory or monotonic shape transitions-reminiscent of recent experimental observations on the retraction and atrophy of axons. We elucidate our findings through a weakly nonlinear analysis, which shows membrane dynamics may be approximated by a model of the class of extended Fisher-Kolmogorov equations. Our study sheds light on the pattern selection mechanism in axonal shapes by recognizing the existence of two Lifshitz points, at which the front dynamics undergo steady-to-oscillatory bifurcations.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Fragmentation of faceted crystalline wires

The reduction of surface energy is a well-known driving force for the fragmentation of nanowires. Fragmentation can limit the service life of those small low-dimensional building blocks or can be controlled to induce beneficial shape changes. For isotropic surface energy, fragmentation is analogous to the classic Rayleigh-Plateau instability of liquid jets. However, commonly synthesized crystalline nanowires have strongly anisotropic surface energies and exhibit facets coinciding with cusps in the Wulff plot. Depending on growth orientation, different fragmentation behaviors have been seen in nanowires. Using phase-field simulations, we show that fragmentation of faceted nanowires with cubic crystal symmetry may occur by a finite-amplitude nonlinear instability, as opposed to a Rayleigh-Plateau-like linear instability, depending on nanowire growth orientation. Here, we carry out a weakly nonlinear analysis based on sharp interface theory to characterize the faceted nanowire shape corresponding to a surface-energy saddle point. The analysis predicts that the minimum amplitude of a periodic shape perturbation to trigger fragmentation increases with cusp strength but decreases inversely proportionally to the perturbation wavelength for long wavelengths, in good quantitative agreement with phase-field predictions. The results provide the theoretical foundation to predict nanowire stability as a function of length and surface energy in diverse applications.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Rethinking hysteresis in magnetic materials

Abstract Magnetic materials with zero hysteresis are posed to have a significant impact on sustainable energy conversion, electronics, and communication technologies. As the global market for soft magnetic materials continues to expand, driven by increasing demand in renewable energy, automotive, and power transmission sectors, it is important to design magnets that can be cycled under an external field reversibly and rapidly multiple times without a decay in magnetic response. However, designing magnets with small hysteresis has been a challenge because we do not fully understand its origins. In this article, I outline key research efforts investigating the fundamental mechanisms underpinning hysteresis in soft magnets and, highlight recent developments in the use of nonlinear analysis and nucleation barrier methods to predict coercivity in these materials. Graphical abstract

Renuka Balakrishna, Ananya (ORCID:0000000306015257↗