SEARCH · Engineering Papers

Results for “Non 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.

SourceResearch connectionFrom yearThrough year

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

At least 91 records · Page 5

All sources NASA NTRS DOE OSTI

DOE OSTI2020

Interference of electrical double layers: Confinement effects on structure, dynamics, and screening of ionic liquids

Ionic liquids are widely used as electrolytes in electronic devices in which they are subject to nanoconfinement within nanopores or nanofilms. Because the intrinsic width of an electrical double layer is on the order of several nanometers, nanoconfinement is expected to fundamentally alter the double layer properties. Furthermore, in confined systems, a large portion of the ions are interfacial, e.g., at the electrode interface, leading to significant deviations of electrostatic screening and ion dynamics as compared to bulk properties. In this article, we systematically investigate the interference between electrical double layers for nanoconfined ionic liquids and the resulting influence on the structure, dynamics, and screening behavior. We perform molecular dynamics simulations for the ionic liquids [BMIm + ][BF$^-_4$] and [BMIm + ][PF$^-_6$] confined between two flat electrodes at systematic separation distances between 1.5 nm and 4.5 nm for both conducting and insulating boundary conditions. We find that while ion dynamics is expectedly slower than in the bulk (by ~2 orders of magnitude), there is an unexpected non-linear trend with the confinement length that leads to a local maximum in dynamic rates at ~3.5–4.5 nm confinement. We show that this nonlinear trend is due to the ion correlation that arises from the interference between opposite double layers. We further evaluate confinement effects on the ion structure and capacitance and investigate the influence of electronic polarization of the ionic liquid on the resulting properties. This systematic evaluation of the connection between electrostatic screening and structure and dynamics of ionic liquids in confined systems is important for the fundamental understanding of electrochemical supercapacitors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2022

Off-harmonic optical probing of high intensity laser plasma expansion dynamics in solid density hydrogen jets

Due to the non-linear nature of relativistic laser induced plasma processes, the development of laser-plasma accelerators requires precise numerical modeling. Especially high intensity laser-solid interactions are sensitive to the temporal laser rising edge and the predictive capability of simulations suffers from incomplete information on the plasma state at the onset of the relativistic interaction. Experimental diagnostics utilizing ultra-fast optical backlighters can help to ease this challenge by providing temporally resolved inside into the plasma density evolution. We present the successful implementation of an off-harmonic optical probe laser setup to investigate the interaction of a high-intensity laser at 5.4 x 10 21 W/cm 2 peak intensity with a solid-density cylindrical cryogenic hydrogen jet target of 5μm diameter as a target test bed. The temporal synchronization of pump and probe laser, spectral filtering and spectrally resolved data of the parasitic plasma self-emission are discussed. The probing technique mitigates detector saturation by self-emission and allowed to record a temporal scan of shadowgraphy data revealing details of the target ionization and expansion dynamics that were so far not accessible for the given laser intensity. Plasma expansion speeds of up to (2.3 ± 0.4)x 10 7 m/s followed by full target transparency at 1.4ps after the high intensity laser peak are observed. A three dimensional particle-in-cell simulation initiated with the diagnosed target pre-expansion at -0.2ps and post processed by ray tracing simulations supports the experimental observations and demonstrates the capability of time resolved optical diagnostics to provide quantitative input and feedback to the numerical treatment within the time frame of the relativistic laser-plasma interaction.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Proton Dynamics Scenarios in the Integrable Optics Test Accelerator (IOTA) at Fermilab

The Integrable Optics Test Accelerator (IOTA) at Fermilab provides a versatile platform for studying the interplay of space-charge, impedance, and non-linear optics in high-intensity hadron beams within synchrotrons and storage rings. This report examines the parameters and dynamics of 2.5~MeV proton beam operations in two configurations of the bare IOTA lattice: one for demonstrating Non-linear Integrable Optics with the Danilov-Nagaitsev magnet, and the other for use with electron cooling. We offer order-of-magnitude estimates of the transverse emittance growth rate as a function of beam intensity, highlighting contributions from residual gas scattering, intra-beam scattering, and space-charge effects. Under nominal conditions, the beam lifetime is projected to be less than 7~minutes at low intensity with the current vacuum quality, and fewer than 100,000~turns at high intensity due to strong space-charge effects. The calculations presented here will guide strategies to mitigate emittance growth and inform future IOTA experiments.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Acceleration of Power System Dynamic Simulations Using a Deep Equilibrium Layer and Neural ODE Surrogate

The dominant paradigm for power system dynamic simulation is to build system-level simulations by combining physics-based models of individual components. The sheer size of the system along with the rapid integration of inverter-based resources exacerbates the computational burden of running time domain simulations. Here, in this paper, we propose a data-driven surrogate model based on implicit machine learningspecifically deep equilibrium layers and neural ordinary differential equationsto learn a reduced order model of a portion of the full underlying system. The data-driven surrogate achieves similar accuracy and reduction in simulation time compared to a physics-based surrogate, without the constraint of requiring detailed knowledge of the underlying dynamic models. This work also establishes key requirements needed to integrate the surrogate into existing simulation workflows; the proposed surrogate is initialized to a steady state operating point that matches the power flow solution by design.

Neural ordinary differential equations↗

DOE OSTI2020

A State-Space Model of an Inverter-Based Microgrid for Multivariable Feedback Control Analysis and Design

In this work, a synchronous model for grid-connected and islanded microgrids is presented. The grid-connected model is based on the premise that the reference frame is synchronized with the AC bus. The quadrature component of the AC bus voltage can be cancelled, which allows to express output power as a linear equation for nominal values in the AC bus amplitude voltage. The model for the islanded microgrid is developed by integrating all the inverter dynamics using a state-space model for the load currents. This model is presented in a comprehensive way such that it could be scalable to any number of inverter-based generators using inductor–capacitor–inductor (LCL) output filters. The use of these models allows designers to assess microgrid stability and robustness using modern control methods such as eigenvalue analysis and singular value diagrams. Both models were tested and validated in an experimental setup to demonstrate their accuracy in describing microgrid dynamics. In addition, three scenarios are presented: non-controlled model, Linear-Quadratic Integrator (LQI) power control, and Power-Voltage (PQ/Vdq) droop–boost controller. Experimental results demonstrate the effectiveness of the control strategies and the accuracy of the models to describe microgrid dynamics.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

The Water Table Model (WTM) (v2.0.1): coupled groundwater and dynamic lake modelling

Abstract. Ice-free land comprises 26 % of the Earth's surface and holds liquid water that delineates ecosystems, affects global geochemical cycling, and modulates sea levels. However, we currently lack the capacity to simulate and predict these terrestrial water changes across the full range of relevant spatial (watershed to global) and temporal (monthly to millennial) scales. To address this knowledge gap, we present the Water Table Model (WTM), which integrates coupled components to compute dynamic lake and groundwater levels. The groundwater component solves the 2D horizontal groundwater flow equation using non-linear equation solvers from the C++ PETSc (Portable, Extensible Toolkit for Scientific Computation) library. The dynamic lake component makes use of the Fill–Spill–Merge (FSM) algorithm to move surface water into lakes, where it may evaporate or affect groundwater flow. In a proof-of-concept application, we demonstrate the continental-scale capabilities of the WTM by simulating the steady-state climate-driven water table for the present day and the Last Glacial Maximum (LGM; 21 000 calendar years before present) across the North American continent. During the LGM, North America stored an additional 14.98 cm of sea-level equivalent (SLE) in lakes and groundwater compared to the climate-driven present-day scenario. We compare the present-day result to other simulations and real-world data. Open-source code for the WTM is available on GitHub and Zenodo.

Callaghan, Kerry L. (ORCID:0000000226740838)↗

DOE OSTI2020

The effect of non-linear mutual friction on pulsar glitch sizes and rise times

ABSTRACT Observations of pulsar glitches have the potential to provide constraints on the dynamics of the high density interior of neutron stars. However, to do so, realistic glitch models must be constructed and compared to the data. We take a step towards this goal by testing non-linear models for the mutual friction force, which is responsible for the exchange of angular momentum between the neutron superfluid and the observable normal component in a glitch. In particular, we consider a non-linear dependence of the drag force on the relative velocity between superfluid vortices and the normal component, in which the contributions of both kelvin and phonon excitations are included. This non-linear model produces qualitatively new features, and is able to reproduce the observed bimodal distribution of glitch sizes in the pulsar population. The model also suggests that the differences in size distributions in individual pulsars may be due to the glitches being triggered in regions with different pinning strengths, as stronger pinning leads to higher vortex velocities and a qualitatively different mutual friction coupling with respect to the weak pinning case. Glitches in pulsars that appear to glitch quasi-periodically with similar sizes may thus be due to the same mechanisms as smaller events in pulsars that have no preferred glitch size, but simply originate in stronger pinning regions, possibly in the core of the star.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Uncertainty Error Modeling for Non-Linear State Estimation With Unsynchronized SCADA and µPMU Measurements

Distribution systems of the future smart grid require enhancements to the reliability of distribution system state estimation (DSSE) in the face of low measurement redundancy, unsynchronized measurements, and dynamic load profiles. Micro phasor measurement units (µPMUs) facilitate co-synchronized measurements with high granularity, albeit at an often prohibitively expensive installation cost. Supervisory control and data acquisition (SCADA) measurements can supplement µPMU data, although they are received at a slower sampling rate. Further complicating matters is the uncertainty associated with load dynamics and unsynchronized measurements–not only are the SCADA and µPMU measurements not synchronized with each other, but the SCADA measurements themselves are received at different time intervals with respect to one another. This paper proposes a non-linear state estimation framework which models dynamic load uncertainty error by updating the variances of the unsynchronized measurements, leading to a time-varying system of weights in the weighted least squares state estimator. Case studies are performed on the 33-Bus Distribution System in MATPOWER, using Ornstein–Uhlenbeck stochastic processes to simulate dynamic load conditions.

Cooper, Austin↗

DOE OSTI2020

Extrapolation of thermal conductivity in non-equilibrium molecular dynamics simulations to bulk scale

Predictions of the bulk scale thermal conductivity of solids using non-equilibrium molecular dynamics (MD) simulations have relied on the linear extrapolation of the thermal resistivity versus the reciprocal of the system length in the simulations. Several studies have reported deviation of the extrapolation from linearity near the micro-scale, raising a concern of its applicability to large systems. To investigate this issue, present work conducted extensive MD simulations of silicon with two different potentials (EDIP and Tersoff-II) for unprecedented length scales up to 10.3 μm and simulation times up to 530 ns. For large systems ≥0.35 μm in size the non-linearity of the extrapolation of the reciprocal of the thermal conductivity is mostly due to ignoring the dependence of the thermal conductivity on temperature. To account for such dependence, the present analysis fixes the temperature range for determining the gradient for calculating the thermal conductivity values. However, short systems ≤0.23 μm in size show significant non-linearity in the calculated thermal conductivity values using a temperature window of 500 ± 10 K from the simulations results with the EDIP potential. Since these system sizes are shorter than the mean phonon free path in EDIP (~0.22 μm), the nonlinearity may be attributed to phonon transport. For the MD simulations with the Tersoff-II potential there is no significant non-linearity in the calculated thermal conductivity values for systems ranging in size from 0.05 to 5.4 μm.

42 ENGINEERING↗

DOE OSTI2021

Effects of interaction strength of associating groups on linear and star polymer dynamics

A small number of associating groups incorporated onto a polymer backbone have dramatic effects on the mobility and viscoelastic response of the macromolecules in melts. These associating groups assemble, driving the formation of clusters, whose lifetime affects the properties of the polymers. In this study, we probe the effects of the interaction strength on the structure and dynamics of two topologies, linear and star polymer melts, and further investigate blends of associative and non-associating polymers using molecular dynamics simulations. Polymer chains of approximately one entanglement length are described by a bead–spring model, and the associating groups are incorporated in the form of interacting beads with an interaction strength between them that is varied from 1 to 20 k B T. We find that, for all melts and blends, interaction of a few k B T between the associating groups drives cluster formation, where the size of the clusters increases with increasing interaction strength. These clusters act as physical crosslinkers, which slow the chain mobility. Blends of chains with and without associating groups macroscopically phase separate for interaction strength between the associating groups of a few k B T and above. For weakly interacting associating groups, the static structure function S(q) is well fit by functional form predicted by the random phase approximation where a clear deviation occurs as phase segregation takes place, providing a quantitative assessment of phase segregation.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Dynamic Aperture of the PIP-II Accumulator Ring (PAR)

The Proton Improvement Plan-II (PIP-II) will include a superconducting linear accelerator which will accelerate H- ions to 800MeV, at an intensity never seen before. A proposed PIP-II Accumulator Ring (PAR) can reduce the injection losses to the booster, enhance the ramp up of the Long Baseline Neutrino Facility (LBNF) and support experiments in Dark Sector Physics. When the beam is circulating in PAR at its full intensity, it will then be transferred to the Booster via single turn injection. Strong PAR focusing results in larger phase advances, shorter focal lengths and higher machine tunes, which creates robust beam envelope control. Particles will be able to survive modest excursions from the elliptical phase-space trajectories of linear optics, and any loss of particles would be due to reduced dynamic aperture. The values for tunes and chromaticities are flexible and will continue to evolve as the lattice matures. Since there will be non-linear terms impacting the particles’ trajectories, tracking will include realistic magnetic field errors and installation alignment errors to determine the dynamic aperture as a function of the machine tunes. This will allow us to determine the optimum operating point in phase-space.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

Plasma Lens in Parametric Resonance Ionization Cooling

We present a concept of a plasma lens in a parametric resonance ionization cooling (PIC) for extra cooling of muon colliders. The PIC concept has been developed to overcome most aberrations. However, parasitic non-linear aberrations which is induced in an ionization cooling material still reduce a dynamic aperture of the PIC. The plasma lens generates an azimuthally symmetric focusing field in gas-filled RF cavities that is several orders of magnitude stronger than the conventional superconducting magnets. It allows for reduction of the beam size at the beam expansion points. This reduces the size of the aberrations and therefore greatly simplifies their compensation.

43 PARTICLE ACCELERATORS↗

DOE OSTI2025

Assessing Dynamic Behaviors in Converter- Dominated Power Systems via RMS and EMT Simulations: A Study of Hawaii’s NELHA Microgrid

The transition from conventional power systems to converter-based microgrids has significantly advanced sustainability, clean energy integration, and operational reliability. However, this paradigm shift introduces operational challenges due to the intermittent nature of renewable energy sources and the non-linear characteristics of power electronic loads, inducing voltage fluctuations and harmonic distortions that complicate voltage and frequency regulation. Accurate dynamic modeling is hypothesized to be critical for capturing such effects, enabling reliable simulation and control strategy development. This study introduces an innovative dynamic modeling framework for a real-world converter-based microgrid, utilizing both root mean square (RMS) and electromagnetic transient (EMT) simulation methods. The microgrid was modeled in DIgSILENT PowerFactory, with simulations calibrated against high-resolution field measurements from SEL-735 power quality meters. Results show that RMS simulations effectively characterize steady-state dynamics, while EMT simulations are essential for capturing high-frequency transients and non-linear effects from photovoltaic inverters and variable frequency drives (VFDs). This complementary approach provides a comprehensive understanding of microgrid behavior, providing critical insights for improving simulation accuracy, advancing protection schemes, and improving resilience in future low-inertia power networks.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

Hybrid particle-spectral method for kinetic plasma simulations

A hybrid model for numerical solutions of the Vlasov–Poisson equations is presented, which blends spectral and particle approaches. The model splits the distribution function for plasma species into both spectral and particle representations in the velocity space to combine the advantages of each approach. The spectral representation leverages asymmetrically weighted Hermite basis, whereas the particle representation leverages the particle-in-cell method. Configuration phase space is decomposed with the Fourier method, which is well suited for periodic problems. We derive conservation equations for mass, momentum, and energy for the proposed combined method. It is shown that the coupling error between the two methods is absent in the semi-discrete setting (not taking into account time discretization). Finally, numerical test cases are presented simulating a weak electron beam interaction with plasma, leading to beam–plasma instability. The initially localized electron beam evolved into a highly non-equilibrium distribution function in the velocity space. A small growth rate and the resonance nature of instability make it difficult to obtain accurate solutions for purely particle methods due to noise, which falls as ∼1/Np with a number of particles. At the same time, purely spectral methods may require a large number of modes to capture the highly non-equilibrium state of the evolved beam. We show that the hybrid method is well suited for such problems: it reproduces the linear stage as well as nonlinear dynamics with sufficient accuracy using a highly non-equilibrium distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Polariton spectra under the collective coupling regime. II. 2D non-linear spectra

In our previous work [Mondal et al., J. Chem. Phys. 162, 014114 (2025)], we developed several efficient computational approaches to simulate exciton–polariton dynamics described by the Holstein–Tavis–Cummings (HTC) Hamiltonian under the collective coupling regime. Here, we incorporated these strategies into the previously developed Lindblad-partially linearized density matrix (⁠$\mathscr{L}$-PLDM) approach for simulating 2D electronic spectroscopy (2DES) of exciton–polariton under the collective coupling regime. In particular, we apply the efficient quantum dynamics propagation scheme developed in Paper I to both the forward and the backward propagations in the PLDM and develop an efficient importance sampling scheme and graphics processing unit vectorization scheme that allow us to reduce the computational costs from $\mathscr{O}$($\mathscr{K}$ 2 )$\mathscr{O}$(T 3 ) to $\mathscr{O}$($\mathscr{K}$)$\mathscr{O}$(T 0 ) for the 2DES simulation, where $\mathscr{K}$ is the number of states and T is the number of time steps of propagation. As a result, we further simulated the 2DES for an HTC Hamiltonian under the collective coupling regime and analyzed the signal from both rephasing and non-rephasing contributions of the ground state bleaching, excited state emission, and stimulated emission pathways.

2D non-linear spectra↗

DOE OSTI2023

Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics

Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Diffusion in intact secondary cell wall models of plants at different equilibrium moisture content

Secondary plant cell walls are composed of carbohydrate and lignin polymers, and collectively represent a significant renewable resource. Leveraging these resources depends in part on a mechanistic understanding for diffusive processes within plant cell walls. Common wood protection treatments and biomass conversion processes to create biorefinery feedstocks feature ion or solvent diffusion within the cell wall. X-ray fluorescence microscopy experiments have determined that ionic diffusion rates are dependent on cell wall hydration as well as the ionic species through non-linear relationships. In this work, we use classical molecular dynamics simulations to map the diffusion behavior of different plant cell wall components (cellulose, hemicellulose, lignin), ions (Na + , K + , Cu2 + , Cl - ) and water within a model for an intact plant cell wall at various hydration states (3-30 wt% water). From these simulations, we analyze the contacts between different plant cell wall components with each other and their interaction with the ions. Generally, diffusion increases with increasing hydration, with lignin and hemicellulose components increasing diffusion by an order of magnitude over the tested hydration range. Ion diffusion depends on charge. Positively charged cations preferentially interact with hemicellulose components, which include negatively charged carboxylates. As a result, positive ions diffuse more slowly than negatively charged ions. Measured diffusion coefficients are largely observed to best fit piecewise linear trends, with an inflection point between 10 and 15% hydration. These observations shed light onto the molecular mechanisms for diffusive processes within secondary plant cell walls at atomic resolution.

09 BIOMASS FUELS↗

DOE OSTI2021

Spectroscopy of GR1 centers in synthetic diamonds

We report on the spectroscopic characterization, absorption saturation, and excited-state dynamics of GR1 centers in synthetic diamonds. The non-linear optical measurements reveal an efficient bleaching of the GR1 center’s ground level under ns-pulsed 633 nm excitation. The maxima of absorption and emission cross sections were estimated to be 4.5 × 10 −17 cm 2 and 9 × 10 −17 cm 2 at 630 nm and 780 nm, respectively. The radiative lifetime of the excited level was estimated to be 8.5 ns. The 658 nm probe kinetics uncovered relaxation of 1 T 2 excited level going predominantly to a metastable state with a lifetime of 220 μs. An induced absorption detected with the use of a highly concentrated diamond sample could be due to up-conversion and photoionization processes in additional impurity-vacancy center with absorption at the short-wavelength tail of GR1. The results presented here indicate that synthetic diamonds with GR1 centers could serve as near infrared gain media or passive Q-switchers for laser cavities over the 633–750 nm spectral range. Optimization of the center concentration and the crystal parameters are required to minimize the induced absorption at the lasing wavelengths.

36 MATERIALS SCIENCE↗