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Results for “Geometrically 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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Strain-Modified Raman Responses in Monolayer MoS 2 Nanobubbles Resolved at 5 nm

The formation of nanoscale bubbles is an unavoidable consequence during the transfer of two-dimensional materials onto target substrates, driven by van der Waals interactions at the interface. While often viewed as imperfections, these nanoscale bubbles have garnered considerable scientific interest due to the substantial in-plane strain gradients they induce, which in turn give rise to a variety of intriguing optoelectronic effects, particularly in semiconducting transition metal dichalcogenides. Determining and analyzing the strain distribution within nanobubbles at the nanoscale is crucial for advancing our understanding of these underlying strain-induced effects. Here, we present a high-resolution scanning tunneling microscopy-based tip-enhanced Raman spectroscopic investigation of localized nanoscale strain distribution within the nanobubbles formed between monolayer MoS 2 and Au interface. By employing cryogenic temperature (78 K), we successfully differentiate the nanoscale Raman signatures between nanobubble edge and pristine MoS 2 . We verify a maximum tensile strain of ∽1.15–1.34% at the nanobubble edge, which gradually diminishes toward the center, yielding a cross-sectional strain profile consistent with a doughnut-shaped distribution. Furthermore, we report to achieve ∽5 nm spatial resolution in probing such edge-localized strain within the nanobubble. In addition, comparative average strain analysis of such MoS 2 nanobubbles is conducted via geometric mechanistic analysis such as membrane and nonlinear plate theories, providing key insight into the geometric nature near the bubble edge. Our work provide fundamental information about strain-induced nanoscale chemical understanding of 2D materials on the nanometer scale, paving the way for practical applications of nanobubbles in strain-engineered optoelectronic devices.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

A data-driven approach to construct a quantitative relationship between microstructural features of fatigue cracks and contact acoustic nonlinearity

This study demonstrates the feasibility of a data-driven approach to construct a quantitative relationship between nonlinear acoustic parameters and microstructural features of contact interfaces. The near-surface nonlinearity is measured using dynamic acousto-elastic testing (DAET) with a surface wave probe, while the microstructural features are extracted from scanning electron microscopy (SEM) images of fatigue cracks. Four aluminum alloy samples, each having a fatigue crack are prepared. Six local nonlinearity parameters are measured at different locations along the crack propagation direction. A total of 40 local measurements are acquired. A principal component analysis (PCA) reveals that all six nonlinearity parameters are correlated and hence can be replaced by one principal component (PC). Fifteen crack micro-geometrical features at each measurement point were extracted from the SEM images. Regression analysis is used to relate the PC of the nonlinearity parameters to the microstructural features at the crack interface. We compare three regression models that take variable selection into account: stepwise multiple linear regression (MLR), stepwise principal component regression (PCR), and least absolute shrinkage and selection operator (LASSO). Despite having different principles, the three predictive models identify two features as the most significant in predicting the interface nonlinearity: the crack aperture (opening) distribution and the distance to the crack tip. The differences between the three models and the physical interpretation of the data-driven predictions are discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2026

A tutorial on high-order harmonic generation in atoms, molecules, and condensed matter

This tutorial introduces strong-field-driven high-order harmonics, their experimental generation and characterization techniques, and their main applications including attosecond pulse generation and ultrafast spectroscopy of the target material. We begin from the use of atomic targets, where the first high-order harmonic generation (HHG) experiments were realized in the late 1980s. Then, we briefly discuss the basics of the microscopic generation mechanism and how various steps of the mechanism were exploited in applications such as generating isolated attosecond pulses and probing molecular orbitals. We introduce and describe the standard experimental approaches for condensed phase HHG, where we discuss unique technical challenges of the use of solid-state materials, such as the mitigation of plasma formation and laser damage. We cover the fundamentals of high-harmonic spectroscopy in condensed matter systems, such as wide bandgap dielectrics, semiconductors, liquid media, and 2D-crystals. We provide some examples of rapidly emerging spectroscopic capabilities, such as for probing crystal symmetries, Berry phases, and associated non-trivial topological properties of the source material. Finally, we provide an overview of the research field, including some of the challenges, opportunities, and open questions.

Attosecond pulses↗
DOE OSTI2025

Nonlinear van der Waals Metasurfaces with Resonantly Enhanced Light Generation

Efficient nonlinear wave mixing is of paramount importance for a wide range of applications. However, weak optical nonlinearities pose significant challenges for accessing nonlinear light–matter interaction in compact systems. Here, we experimentally study second harmonic generation in deeply subwavelength 3R-MoS 2 metasurfaces (<λ/13 thick). Our measurements, supported by theoretical analysis, reveal a complex interplay and coupling between geometric resonances, optical extinction, and exciton-driven strong nonlinear susceptibility dispersion. We further demonstrate >150-fold enhancement in second harmonic signal at 740 nm mediated by the A exciton resonance. Additionally, our theoretical studies predict an enhancement of more than 10 6 in second harmonic generation in <100 nm thick structures exhibiting bound states in the continuum resonance. These findings provide insight into accessing and harnessing the unprecedented 3R-MoS 2 nonlinearities at a subwavelength scale, paving the way to ultracompact nonlinear photonic devices.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

Inelastic peridynamic model for molecular crystal particles

The peridynamic theory of solid mechanics is applied to modeling the deformation and fracture of micrometer-sized particles made of organic crystalline material. A new peridynamic material model is proposed to reproduce the elastic–plastic response, creep, and fracture that are observed in experiments. The model is implemented in a three-dimensional, meshless Lagrangian simulation code. In the small deformation, elastic regime, the model agrees well with classical Hertzian contact analysis for a sphere compressed between rigid plates. Under higher load, material and geometrical nonlinearity is predicted, leading to fracture. Finally, the material parameters for the energetic material CL-20 are evaluated from nanoindentation test data on the cyclic compression and failure of micrometer-sized grains.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2018

Quantum Chemical Calculations of the Spectroscopic Properties and Nonlinear Optical Activity of 2,6-Dibromo-3-Chloro-4-Fluoroaniline

The Fourier transform infrared (FT-IR) and Fourier transform Raman (FT-Raman) spectra of 2,6-dibromo-3-chloro-4-fluoroaniline in the solid phase were recorded and analyzed. Quantum chemical calculations of the optimized molecular structure, energies, nonlinear optical (NLO) analysis, molecular surfaces, and vibrational analysis of this substance were performed. The obtained results on the geometric structure and vibrational frequencies were compared with the observed data. The calculated highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) energies also confirm that charge transfer occurs within the molecule. The detailed vibrational assignments were performed using the HF and DFT calculations, and the potential energy distribution (PED) was obtained by the vibrational energy distribution analysis (VEDA4) program. Finally, the effects of the amino, bromo, chloro, and fluoro substituents on the vibrational frequencies were investigated.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2022

Characterization of nonlinear ultrasonic waves behavior while interacting with poor interlayer bonds in large-scale additive manufactured materials

Over the past decades, researchers have developed several nonlinear ultrasonic techniques for quality control of materials commonly used in different applications. Owing to the superior sensitivity of nonlinear ultrasound waves to small defects such as micro-cracks, their applicability in different nondestructive testing (NDT) problems has been investigated in numerous studies. These studies utilize frequency domain analysis to detect the generation of higher harmonics because of the formation of defects in the inspected medium. Frequency domain analysis based on the Fourier transform is a significant approach used in linear systems; however, it may not perform adequately on nonlinear systems. Hence, studies on nonlinear dynamics and physics consider analyzing systems' behavior in the phase-space domain. In contrast to the frequency domain analysis, which can result in information loss, analysis in the phase-space domain retains all the information regarding a system's states. Here, we investigate the nonlinearities induced by poor interlayer bonding in polymer-based additive manufactured parts in the phase-space domain. It is convenient to characterize the nonlinearity in the phase-space domain because it provides a geometrical representation of a system's states. Two types of low quality interlayer bond are considered. The first type is simulated artificially while the second type is manufactured by reducing the bond quality during the printing process. The analysis verified that the received ultrasonic signals exhibit classical nonlinear behavior in the phase-space domain while interacting with simulated poor interlayer bonds. In addition, the results showed that the behavior of ultrasonic waves is amplitude-dependent and evolves into models that have not been previously reported. Furthermore, Largest Lyapunov Exponent (LLE) is used to quantify the behavior of nonlinear ultrasonic waves while interacting with poor interlayer bonds. Using LLE, it was observed that the divergence rate of the phase-space trajectories depends on the amplitude of the excitation. This observation quantitatively proves that nonlinear behavior of ultrasound while interacting with poor interlayer bonds can be amplitude-dependent. The results of both simulated and inherent poor interlayer bond cases showed that LLE can be used as a reliable quantitative damage-sensitive feature to detect and potentially characterize weak bonds, which are difficult to detect using conventional approaches. Additionally, the reported results in the phase-space domain provide a basis for proposing a new mathematical model for ultrasonic waves interacting with poor interlayer bonds.

36 MATERIALS SCIENCE↗
DOE OSTI2026

The impact of optical measurement techniques on measured aerosol particle size distributions

Ambient aerosol particle size distributions measured by the Ultra-High Sensitivity Aerosol Spectrometer (UHSAS) at various sites around the world exhibit modes at optical diameters near 600 nm and 850 nm. These modes are not present in concurrent measurements with the Grimm 11-D Optical Particle Counter (OPC). Here, in this study, we argue that these modes result from the optical measurement technique itself, and we explain why they appear in measurements by the UHSAS but not in those by the Grimm OPC. We construct computer models of the UHSAS and Grimm (“digital UHSAS” and “digital Grimm”) and use these to investigate the size distribution that would result from measurements of artificial aerosol particle size distributions that do not contain modes. The appearance of modes for the structureless incoming size distributions sampled by the digital UHSAS is explained by the nonlinear behavior of partial scattering cross sections of uniform spherical particles as a function of their diameter. The absence of modes in the digital Grimm is explained by the coarser size resolution of that instrument. Detailed analysis of the relationship between optical and geometric diameters for uniform spherical particles reveals two important results. First, these diameters generally have different numerical values for the same particle, and second, the relationship is nonlinear; thus, widths of size bins in terms of optical diameter differ from those in geometric diameter. These results explain the modes observed in the ambient size distributions and highlight concerns with attempts to create a merged size distribution by combining measurements from different instruments.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Calculating RF current condensation with consistent ray-tracing and island heating

Finally, by exploiting the nonlinear amplification of the power deposition of RF waves, current condensation promises new pathways to the stabilization of magnetic islands. We present a numerical analysis of current condensation, coupling a geometrical optics treatment of wave propagation and damping to a thermal diffusion equation solver in the island. Taking into account the island geometry and relativistic damping, previous analytical theory can be made more precise and specific scenarios can be realistically predicted. With this more precise description, bifurcations and associated hysteresis effects could be obtained in an ITER-like scenario at realistic parameter values. Moreover, it is shown that dynamically varying the RF wave launching angles can lead to hysteresis and help to avoid the nonlinear shadowing effect.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Sensitive parameter identification and uncertainty quantification for the stability of pipeline conveying fluid

In this study, several uncertainty quantification and sensitivity analysis methods are used to determine the most sensitive geometric and material input parameters of a cantilevered pipeline conveying fluid when uncertainty is introduced to the system at the onset of instability. The full nonlinear equations of motion are modeled using the extended Hamilton’s principle and then discretized using Galerkin’s method. A parametric study is first performed, and the Morris elementary effects are calculated to obtain a preliminary understanding of how the onset speed changes when each parameter is introduced to a ± 5% uncertainty. Then, four different input uncertainty distributions, mainly, uniform and Gaussian distribution, are chosen to investigate how input distributions affect uncertainty in the output. A convergence analysis is used to determine the number of samples needed to maintain simulation accuracy while saving the most computational time. Then, Monte Carlo simulations are run, and the output distributions for each input distribution at ± 1%, ± 3% and ± 5% input uncertainty range are found and discussed. Additionally, the Pearson correlation coefficients are evaluated for different uncertainty ranges. A final Monte Carlo study is performed in which single parameters are held constant while all others still have uncertainty. Overall, the flow speed at the onset of instability is the most sensitive to changes in the outer diameter of the pipe.

36 MATERIALS SCIENCE↗
DOE OSTI2021

On-chip non-Hermitian optical parametric amplifiers with a large bandwidth

Recently, our groups have introduced the notion of optical parametric amplification based on non-Hermitian phase matching wherein the incorporation of loss can lead to gain in this nonlinear optical process. Previous simulation results using second-order nonlinear optical coupled-mode theory have demonstrated the potential of this technique as an alternative to the stringent phase-matching condition, which is often difficult to achieve in semiconductor platforms. Here we fortify this notion for the case of third-order nonlinearity by considering parametric amplification in silicon nanowires and illustrate the feasibility of these devices by employing rigorous finite-difference time-domain analysis using realistic materials and geometric parameters. Particularly, we demonstrate that by systematic control of the optical loss of the idler in a four-wave mixing process, we can achieve efficient unidirectional energy conversion from the pump to the signal component even when the typical phase-matching condition is violated. Importantly, our simulations show that a signal gain of ∼ <#comment/> 9 d B for a waveguide length of a few millimeters is possible over a large bandwidth of several hundreds of nanometers ( ∼ <#comment/> 600 n m ). This bandwidth is nearly 2 orders of magnitude larger than what can be achieved in the conventional silicon-photonics-based four-wave mixing process.

Ahmed, Asif (ORCID:0000000152234392)↗
DOE OSTI2019

Function Preserving Projection

With function preserving projection (FPP), we aim to address high-dimensional data exploration challenges common in many scientific applications. Instead of preserving the global or local geometric structure of a dataset like traditional dimensionality reduction methods (e.g., principal component analysis, t-stochastic neighborhood embedding), the proposed approach finds a linear projection that reveal interpretable (yet potentially nonlinear) pattern of the properties of interests defined on a highdimensional domain (e.g., simulation yield defined on the input parameter space). The key insight driving FPP is the fact that while non-linear embeddings are difficult to interpret, humans are highly skilled in understanding complex visual patterns. FPP lets users select the complexity of a pattern they consider interpretable, allows to find a joint projection that explains multiple functions, and provides a confidence statistic (akin to a p-value) indicating how salient the resulting pattern is. We demonstrate the efficacy of the proposed method on several synthetic and scientific datasets for both continuous (regression) and discrete (classification) problems of interests and illustrate the scalability of FPP by finding an optimal projection for close to 40 gigabytes in around 10 minutes.

Liu, SHUSEN↗
DOE OSTI2019

Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

42 ENGINEERING↗
DOE OSTI2025

Effects of Central Cut Width on the Dynamical Characteristics of Box Assembly Structure

An investigation into the Box Assembly with Removable Component (BARC) structure is conducted by utilizing computational simulations and experimental structural testing in order to determine the complex dynamical responses instigated by the central cut of the system. Because the dynamics of the BARC system is complex, this study focuses primarily on analyzing the behavior of the box assembly (BA) system. The investigation explores the dynamics of the BA system by varying the central cut widths, ranging from a cut as wide as 0.5” cut to a 0.25” cut system, as well as a 0.1” cut and a system with no cut at all. Experimental testing is performed on each system including a free vibration test using an impact hammer to excite and identify the dominant frequencies of each structure. This testing is followed by pseudo-random vibration tests and swept sinusoidal excitation tests to determine the nonlinear aspects of these systems, such as the possible existence of nonlinear softening, hardening, and/or damping. The results show that nonlinear softening and nonlinear damping are present in each system. The no-cut system demonstrated the highest peak frequencies throughout all the tests, being the most rigid structure. The 0.25” cut system was shown to have the highest peak frequencies among all the cut systems in both the finite elemenet analysis (FEA) and impact testing. This trend did not continue, though, in the random and harmonic testing, possibly due to the added stiffness of the test setup with the slip table and stinger. The results show the importance of accurately measuring the central cut width and how possible geometric uncertainties change the overall dynamical behaviors of complex systems, such as natural characteristics, nonlinear responses, coupling of modes, and oscillating amplitudes.

Padilla, Christopher (ORCID:000900033446732X)↗
DOE OSTI2025

Snap-Through Buckling Pressure Prediction of Spherical Caps: A Comparison of Analytical, Implicit, and Explicit Methods

Snap-through buckling is a nonlinear and dynamic instability that occurs in curved shell structures such as domes, pressure vessels, and aerospace panels. Unlike classical linear buckling, it involves a sudden transition between equilibrium states caused by geometric nonlinearity and rapid strain-to-kinetic energy conversion (Timoshenko & Gere, 1961; Budiansky & Roth, 1962). This study investigates the snap-through behavior of thin spherical caps using both implicit and explicit solvers in ANSYS Workbench. While implicit analysis accurately captures quasi-static response, it struggles with convergence near instability. In contrast, explicit LS-DYNA simulation naturally handles the nonlinear dynamic event with minimal tuning and computational cost.

42 ENGINEERING↗
DOE OSTI2025

Single-Bunch Instabilities Driven by Space Charge During Low-Energy Cooling at Injection in the EIC Hadron Storage Ring

This paper presents a simulation-based study of single-bunch dynamics at the injection energy of 23.8 GeV for protons in the EIC hadron storage ring, focusing on the impact of space-charge–driven instabilities. The analysis demonstrates that at this energy, the proton bunch experiences significant transverse space-charge forces, which can reduce the stability margin in the presence of the geometric and resistive wall impedance. Various collective effects were considered, with particular attention to the nonlinear nature of the transverse space charge. To stabilize the beam, high chromaticity and octupoles were introduced and their effects analyzed using the ELEGANT code. The results provide a quantitative assessment of the stability thresholds and offer guidance for the machine design and operational strategy at injection.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

A Bayesian Multi-fidelity Neural Network to Predict Nonlinear Frequency Backbone Curves

The use of structural mechanics models during the design process often leads to the development of models of varying fidelity. Often low-fidelity models are efficient to simulate but lack accuracy, while the high-fidelity counterparts are accurate with less efficiency. Here, this paper presents a multi-fidelity surrogate modeling approach that combines the accuracy of a high-fidelity finite element model with the efficiency of a low-fidelity model to train an even faster surrogate model that parameterizes the design space of interest. The objective of these models is to predict the nonlinear frequency backbone curves of the Tribomechadynamics Research Challenge benchmark structure which exhibits simultaneous nonlinearities from frictional contact and geometric nonlinearity. The surrogate model consists of an ensemble of neural networks that learn the mapping between low and high-fidelity data through nonlinear transformations. Bayesian neural networks are used to assess the surrogate model's uncertainty. Once trained, the multi-fidelity neural network is used to perform sensitivity analysis to assess the influence of the design parameters on the predicted backbone curves. Additionally, Bayesian calibration is performed to update the input parameter distributions to correlate the model parameters to the collection of experimentally measured backbone curves.

42 ENGINEERING↗
DOE OSTI2023

Nonlinear dynamics, bifurcations, and multi-stability in a vibro-impact system with geometric and multi-segmented freeplay nonlinearities

Freeplay is a common type of piecewise-smooth nonlinearity in dynamical systems, and it can cause discontinuity-induced bifurcations and other behaviors that may bring about undesirable and potentially damaging responses. Prior research has focused on piecewise-smooth systems with two or three distinct regions, but less attention is devoted to systems with more regions (i.e., multi-segmented systems). In this work, numerical analysis is performed on a dynamical system with multi-segmented freeplay, in which there are four stiffness transitions and five distinct regions in the phase space. Here, the effects of the multi-segmented parameters are studied through bifurcation diagram evolution along with induced multi-stable behavior and different bifurcations. These phenomena are interrogated through various tools, such as harmonic balance, basins of attraction, phase planes, and Poincaré section analysis. Results show that among the three multi-segmented parameters, the asymmetry has the strongest effect on the response of the system.

42 ENGINEERING↗