SEARCH · Engineering Papers

Results for “nonlinear function”

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 649 records · Page 36

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Shadow Lagrangian dynamics for superfluidity

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Metastable Clusters and Competitive Solvation Tune Ion Pairing at Liquid Interfaces

The balance of hydrophobic and hydrophilic interactions underlies emergent phenomena in complex multicomponent chemical systems. Here, we show that a supposedly ‘non–interacting’ nonpolar phase can be used to competitively solvate amphiphilic molecules at an oil/aqueous interface. This solvation, as probed by surface specific nonlinear spectroscopy and simulations, results in a molecularly thin corrugated phase boundary featuring metastable assemblies that alter the hydrogen bonding networks of water and the apparent ‘hard/soft’ descriptors used to describe ionic interactions. We show that competitive solvation enhances amphiphile mobility, opening up otherwise energetically inaccessible complexes that transiently interact with aqueous phase ions. These transient species impact ensemble binding affinities and may represent the molecular agents responsible for aspects of ionic transport and function. In conclusion, the result of this work highlights how seemingly unrelated nonpolar interactions feedback onto aqueous phase chemical phenomena, providing a pathway to tune phase separation and self-assembly to access new reaction pathways using interfaces for a range of chemical and biological systems.

Anions↗

DOE OSTI2024

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. Finally, this paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Transport, correlations, and chaos in a classical disordered anharmonic chain

Here, we explore transport properties in a disordered nonlinear chain of classical harmonic oscillators, and thereby identify a regime exhibiting behavior analogous to that seen in quantum many-body-localized systems. Through extensive numerical simulations of this system connected at its ends to heat baths at different temperatures, we computed the heat current and the temperature profile in the nonequilibrium steady state as a function of system size $\textit{N}$, disorder strength Δ, and temperature $\textit{T}$. The conductivity $κ_N$, obtained for finite length ($\textit{N}$), saturates to a value $κ_∞$ > 0 in the large $\textit{N}$ limit, for all values of disorder strength Δ and temperature $\textit{T}$ > 0. We show evidence that for any Δ > 0 the conductivity goes to zero faster than any power of $\textit{T}$ in the ($\textit{T}$/Δ) → 0 limit, and find that the form $κ_∞$ ~ $e^{{–B|\text{ln}(CΔ/T)|}^{3}}$ fits our data. This form has earlier been suggested by a theory based on the dynamics of multioscillator chaotic islands. The finite-size effect can be $κ_N < κ_∞$ due to boundary resistance when the bulk conductivity is high (the weak disorder case), or $κ_N > κ_∞$ due to direct bath-to-bath coupling through bulk localized modes when the bulk is weakly conducting (the strong disorder case). We also present results on equilibrium dynamical correlation functions and on the role of chaos on transport properties. Finally, we explore the differences in the growth and propagation of chaos in the weak and strong chaos regimes by studying the classical version of the out-of-time-ordered commutator.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2025

Effective Action for Relativistic Hydrodynamics from the Crooks Fluctuation Theorem

A new effective theory framework for fluctuating hydrodynamics in the relativistic regime is derived using standard thermodynamical principles and general properties of nonequilibrium stochastic dynamics. For the first time, we establish clear and concise conditions for ensuring that the resulting effective theories are causal, stable, and well-posed within general relativity. Here, these properties are independent of spacetime foliation and are valid in the full nonlinear regime. Out-of-equilibrium fluctuations are constrained by a relativistically covariant version of the Crooks fluctuation theorem, which determines how the entropy production is distributed even when the system is driven by an external force. This leads to an emerging Z 2 symmetry responsible for imposing fluctuation-dissipation relations for n-point correlation functions, which matches the standard constraints for the Schwinger-Keldysh effective action.

Fluctuation theorems↗

DOE OSTI2025

Modified Andronov-Hopf Oscillator-Based Grid-Forming Converter with Emulated Virtual Cable for Enhanced Power Sharing Performance

Nonlinear oscillator-based grid-forming converters offer superior dynamic and steady-state performance, making them an attractive solution for interconnecting renewable resources. This paper proposes a novel modified Andronov-Hopf oscillator to enhance the operating spectrum and facilitate the integration of renewable energy sources. An inner loop controller based on the Lyapunov energy function is implemented to achieve robust stability and performance, while a virtual cable emulation strategy enables seamless parallel operation. Comprehensive modeling and simulation studies validate the effectiveness of the proposed system, demonstrating its capabilities in addressing diverse operating scenarios, including grid faults, renewable energy fluctuations, and parallel operation. The proposed solution exhibits fast transient response, robust stability, and flexible operation, making it a valuable contribution to the field of renewable energy integration. The results of this study can be used to inform the design and implementation of next-generation grid-forming converters, enabling a more sustainable and reliable energy future. Additionally, the proposed system's ability to operate in both grid-connected and islanded modes makes it an ideal candidate for remote and off-grid renewable energy applications. The proposed solution's scalability and modularity also make it suitable for large-scale renewable energy integration. The proposed system is verified through MATLAB/Simulink and PLECS simulations, demonstrating its effectiveness in ensuring robust and efficient operation.

Andronov-Hopf Oscillator (AHO)↗

DOE OSTI2025

Evolution of Magnetohydrodynamic Turbulence in the Expanding Solar Wind: Residual Energy and Intermittency

We conduct 3D magnetohydrodynamic simulations of decaying turbulence in the context of the solar wind. To account for the spherical expansion of the solar wind, we implement the expanding box model. The initial turbulence comprises uncorrelated counterpropagating Alfvén waves and exhibits an isotropic power spectrum. Our findings reveal the consistent generation of negative residual energy whenever nonlinear interactions are present, independent of the normalized cross helicity σc and compressibility. The spherical expansion facilitates this process. The resulting residual energy is primarily distributed in the perpendicular direction, with S 2 (b) − S 2 (u) ∝ l ⊥ or equivalently –E r ∝ k$^{–2}_{⟂}$. Here S 2 (b) and S 2 (u) are second-order structure functions of magnetic field and velocity respectively. In most runs, S 2 (b) develops a scaling relation S 2 (b) ∝ $l$$^{1/2}_{⊥}$ (E b ∝ k$^{–3/2}_{⟂}$). In contrast, S 2 (u) is consistently shallower than S 2 (b), which aligns with in situ observations of the solar wind. We observe that the higher-order statistics of the turbulence, which act as a proxy for intermittency, depend on the initial σc and are strongly affected by the expansion effect. Generally, the intermittency is more pronounced when the expansion effect is present. Finally, we find that in our simulations, although the negative residual energy and intermittency grow simultaneously as the turbulence evolves, the causal relation between them seems to be weak, possibly because they are generated on different scales.

Interplanetary turbulence↗

DOE OSTI2020

A conservative phase-space moving-grid strategy for a 1D-2V Vlasov–Fokker–Planck Solver

In this work, we develop a conservative configuration- and velocity-space (i.e., phase-space) moving-grid strategy for the Vlasov–Fokker–Planck (VFP) equation in a planar geometry. The velocity-space grid is normalized and shifted in terms of the thermal speed and the bulk-fluid velocity, respectively. The configuration-space grid is moved according to a mesh-motion-partial-differential equation (MMPDE), which equidistributes a monitor function that is inversely proportional to the gradient-length scales of the macroscopic plasma quantities. The resulting inertial terms in the transformed VFP equations are discretized to ensure the discrete conservation of mass, momentum, and energy. To satisfy the discrete conservation theorems in the presence of phase-space mesh motion, we employ the method of discrete nonlinear constraints – explored in previous studies – but the underlying symmetries are determined in a much more efficient manner than before. The conservative grid-adaptivity strategy provides an efficient scheme that resolves important physical structures in the phase-space while controlling the computational complexity at all times. We demonstrate the favorable features of the proposed algorithm through a set of test cases of increasing complexity. The problems test independent components of the algorithms, as well as the integrated capability on settings relevant to inertial confinement fusion.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Weak lensing trispectrum and Kurt-spectra

We introduce two kurt-spectra to probe fourth-order statistics of weak lensing convergence maps. Using state-of-the-art numerical simulations, we study the shapes of these kurt-spectra as a function of source redshifts and smoothing angular scales. We employ a pseudo-Cℓ approach to estimate the spectra from realistic convergence maps in the presence of an observational mask and noise for stage-IV large-scale structure surveys. We compare these results against theoretical predictions calculated using the FFTLog formalism, and find that a simple nonlinear clustering model — the hierarchical ansatz — can reproduce the numerical trends for the kurt-spectra in the nonlinear regime. In addition, we provide estimators for beyond fourth-order spectra where no definitive analytical results are available, and present corresponding results from numerical simulations.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13 C Metabolic Flux Analysis ( 13 C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13 C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13 C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13 C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in “non-gaussian” situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13 C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13 C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P- 13 C MOMA and P- 13 C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

Simulation of Plasma Emission in Magnetized Plasmas

The recent Parker Solar Probe observations of type III radio bursts show that the effects of the finite background magnetic field can be an important factor in the interpretation of data. In the present paper, the effects of the background magnetic field on the plasma-emission process, which is believed to be the main emission mechanism for solar coronal and interplanetary type III radio bursts, are investigated by means of the particle-in-cell simulation method. The effects of the ambient magnetic field are systematically surveyed by varying the ratio of plasma frequency to electron gyrofrequency. The present study shows that for a sufficiently strong ambient magnetic field, the wave–particle interaction processes lead to a highly field-aligned longitudinal mode excitation and anisotropic electron velocity distribution function, accompanied by a significantly enhanced plasma emission at the second-harmonic plasma frequency. For such a case, the polarization of the harmonic emission is almost entirely in the sense of extraordinary mode. On the other hand, for moderate strengths of the ambient magnetic field, the interpretation of the simulation result is less clear. The underlying nonlinear-mode coupling processes indicate that to properly understand and interpret the simulation results requires sophisticated analyses involving interactions among magnetized plasma normal modes, including the two transverse modes of the magneto-active plasma, namely, the extraordinary and ordinary modes, as well as electron-cyclotron-whistler, plasma oscillation, and upper-hybrid modes. At present, a nonlinear theory suitable for quantitatively analyzing such complex-mode coupling processes in magnetized plasmas is incomplete, which calls for further theoretical research, but the present simulation results could provide a guide for future theoretical efforts.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Directional locking effects for active matter particles coupled to a periodic substate

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45° directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ = arctan (p/q) , where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Uncertainty amplification due to density/refractive index gradients in background-oriented schlieren experiments

Here, we theoretically analyze the effect of density/refractive index gradients on the measurement precision of background-oriented schlieren (BOS) experiments by deriving the Cramer–Rao lower bound (CRLB) for the 2D centroid estimation process. A model is derived for the diffraction limited image of a dot viewed through a medium containing density gradients that includes the effect of the experimental parameters such as the magnification and f-number. It is shown using the model that nonlinearities in the density gradient field lead to blurring of the dot image. This blurring amplifies the effect of image noise on the centroid estimation process, leading to an increase in the CRLB and a decrease in the measurement precision. The ratio of position uncertainties of a dot in the reference and gradient images is shown to be a function of the ratio of the dot diameters and dot intensities. We termed this parameter the amplification ratio (A F ), and a methodology for reporting position uncertainties in tracking-based BOS measurements is proposed. The theoretical predictions of the dot position estimation variance from the CRLB are compared to ray tracing simulations, and agreement is obtained. The uncertainty amplification is also demonstrated on experimental BOS images of flow induced by a spark discharge, where it is seen that regions of high amplification ratio correspond to regions of density gradients. This analysis elucidates the dependence of the position uncertainty on density and refractive index gradient-induced distortion parameters, provides a methodology for accounting its effect on uncertainty quantification and provides a framework for optimizing experiment design.

42 ENGINEERING↗

DOE OSTI2023

New static solutions of symmetric $\phi^4$ equation

In this paper, we provide new exact solutions of nonlinear Klein–Gordon ( $\phi^4$) equation in 1 + 1-dimension. For simplicity, we focus on the static equation and ignore the time-dependence. The symmetric $\phi^4$ equation has played an important role in several areas of physics. We obtain several novel non-singular solutions of the symmetric $\phi^4$ model in terms of the Jacobi elliptic functions and compare them with the well-known solutions. Finally, we categorize these solutions in terms of the potential parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A higher-order finite-element implementation of the nonlinear Fokker–Planck collision operator for charged particle collisions in a low density plasma

Collisions between particles in a low density plasma are described by the Fokker–Planck collision operator. In applications, this nonlinear integro-differential operator is often approximated by linearised or ad-hoc model operators due to computational cost and complexity. In this work, we present an implementation of the nonlinear Fokker–Planck collision operator written in terms of Rosenbluth potentials in the Rosenbluth–MacDonald–Judd (RMJ) form. The Rosenbluth potentials may be obtained either by direct integration or by solving partial differential equations (PDEs) similar to Poisson's equation: we optimise for performance and scalability by using sparse matrices to solve the relevant PDEs. We represent the distribution function using a tensor-product continuous-Galerkin finite-element representation and we derive and describe the implementation of the weak form of the collision operator. We present tests demonstrating a successful implementation using an explicit time integrator and we comment on the speed and accuracy of the operator. Finally, we speculate on the potential for applications in the current and next generation of kinetic plasma models.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

X-ray diffraction at the National Ignition Facility

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2 θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2 θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2–7 on the periodic table.

47 OTHER INSTRUMENTATION↗

DOE OSTI2020

High mass and halo resolution from fast low resolution simulations

Generating mocks for future sky surveys requires large volumes and high resolutions, which is computationally expensive even for fast simulations. Here we try to develop numerical schemes to calibrate various halo and matter statistics in fast low resolution simulations compared to high resolution N-body and hydrodynamic simulations. For the halos, we improve the initial condition resolution and develop a halo finder "relaxed-FoF", where we allow different linking lengths for different halo mass and velocity dispersions. We show that our relaxed-FoF halo finder improves the common statistics, such as halo bias, halo mass function, halo auto power spectrum, cross correlation coefficient with the reference halo catalog, and halo-matter cross power spectrum. We also calibrate small-scale velocities of small halos to improve the power spectrum in redshift space. For the matter statistics, we incorporate the potential gradient descent (PGD) method into fast simulations to improve the matter distribution at nonlinear scales. By building a lightcone output, we show that the PGD method significantly improves the weak lensing convergence tomographic power spectrum. With these improvements FastPM is comparable to the high resolution full N-body simulation of the same mass resolution, with two orders of magnitude fewer time steps. These techniques can be used to improve the halo and matter statistics of FastPM simulations for mock catalogs of future surveys such as DESI and LSST.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Thermomagnetic properties of Bi 2 Te 3 single crystal in the temperature range from 55 K to 380 K

Magnetothermoelectric transport provides an understanding of coupled electron-hole-phonon current in topological materials and has applications in energy conversion and cooling. In this paper, we study the Nernst coefficient, the magneto-Seebeck coefficient, and the magnetoresistance of single-crystalline Bi 2 Te 3 under external magnetic field in the range of –3T to 3T and in the temperature range of 55 K to 380 K. Moreau's relation is employed to justify both the overall trend of the Nernst coefficient and the temperature at which this coefficient changes sign. We observe a nonlinear relationship between the Nernst coefficient and the applied magnetic field in the temperature range of 55 K to 255 K. An increase in both the Nernst coefficient and the magneto-Seebeck coefficient is observed as the temperature is reduced which can be attributed to the increased mobility of the carriers at lower temperatures. First-principles density functional theory calculations were carried out to physically model the experimental data including electronic and transport properties. Simulation findings agreed with the experiments and provide a theoretical insight to justify the measurements.

36 MATERIALS SCIENCE↗