A Tutorial on Nonlinear Modal Analysis in Structural Dynamics
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Kuether, Robert J. [Sandia National Laboratories (↗
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A Tutorial on Nonlinear Modal Analysis in Structural Dynamics
Explore the source record for details and available documents.
Kuether, Robert J. [Sandia National Laboratories (↗
Topological Data Analysis for Particulate Gels
Soft gels, formed via the self-assembly of particulate materials, exhibit intricate multiscale structures that provide them with flexibility and resilience when subjected to external stresses. Here, this work combines particle simulations and topological data analysis (TDA) to characterize the complex multiscale structure of soft gels. Our TDA analysis focuses on the use of the Euler characteristic, which is an interpretable and computationally scalable topological descriptor that is combined with filtration operations to obtain information on the geometric (local) and topological (global) structure of soft gels. We reduce the topological information obtained with TDA using principal component analysis (PCA) and show that this provides an informative low-dimensional representation of the gel structure. We use the proposed computational framework to investigate the influence of gel preparation (e.g., quench rate, volume fraction) on soft gel structure and to explore dynamic deformations that emerge under oscillatory shear in various response regimes (linear, nonlinear, and flow). Our analysis provides evidence of the existence of hierarchical structures in soft gels, which are not easily identifiable otherwise. Moreover, our analysis reveals direct correlations between topological changes of the gel structure under deformation and mechanical phenomena distinctive of gel materials, such as stiffening and yielding. In summary, we show that TDA facilitates the mathematical representation, quantification, and analysis of soft gel structures, extending traditional network analysis methods to capture both local and global organization.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Unconventional nonlinear Hall effects in twisted multilayer 2D materials
We present the first investigation of unusual nonlinear Hall effects in twisted multilayer 2D materials. Contrary to expectations, our study shows that these nonlinear effects are not merely extensions of their monolayer counterparts. Instead, we find that stacking order and pairwise interactions between neighboring layers, mediated by Berry curvatures, play a pivotal role in shaping their collective nonlinear optical response. By combining large-scale Real-Time Time-Dependent Density Functional Theory (RT-TDDFT) simulations with model Hamiltonian analyses, we demonstrate a remarkable second-harmonic transverse response in hexagonal boron nitride four-layers, even in cases where the total Berry curvature cancels out. Furthermore, our symmetry analysis of the layered structures provides a simplified framework for predicting nonlinear responses in multilayer materials in general. Our investigation challenges the prevailing understanding of nonlinear optical responses in layered materials and opens new avenues for the design and development of advanced materials with tailored optical properties.
36 MATERIALS SCIENCE↗
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↗
Hybrid Bismuth Halide with Rich Polymorphism and Second Harmonic Generation Response
Hybrid structures have emerged as a promising class of optical materials, due to their ability to couple the robustness of inorganic and the tunability of organic compounds. However, their application in nonlinear optics (NLO) remains limited, largely due to underexplored factors that drive the formation of noncentrosymmetric structures and NLO property characterization. In this work, we explore the formation, structural and temperature polymorphism, and optical properties of the (Et 3 NH) 3 Bi 2 Br 9 composition, which crystallizes as either noncentrosymmetric or centrosymmetric polymorph. Structural analysis showed that the alignment of [Bi 2 Br 9 ] 3– units dictates the symmetry of phases, as well as the nonlinear optical properties, with the triclinic polymorph exhibiting a second harmonic generation (SHG) response both in visible and IR regions (1.29 × KH 2 PO 4 and 0.08 × AgGaS 2 ). Thermal analysis reveals polymorphic phase transitions and low melting points, making them melt-processable and ionic liquid candidates.
36 MATERIALS SCIENCE↗
Using Data Science Tools to Reveal and Understand Subtle Relationships of Inhibitor Structure in Frontal Ring-Opening Metathesis Polymerization
The rate of frontal ring-opening metathesis polymerization (FROMP) using the Grubbs generation II catalyst is impacted by both the concentration and choice of monomers and inhibitors, usually organophosphorus derivatives. Herein we report a data-science-driven workflow to evaluate how these factors impact both the rate of FROMP and how long the formulation of the mixture is stable (pot life). Using this workflow, we built a classification model using a single-node decision tree to determine how a simple phosphine structural descriptor (V bur-near ) can bin long versus short pot life. Additionally, we applied a nonlinear kernel ridge regression model to predict how the inhibitor and selection/concentration of comonomers impact the FROMP rate. Furthermore, the analysis provides selection criteria for material network structures that span from highly cross-linked thermosets to non-cross-linked thermoplastics as well as degradable and nondegradable materials.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Exploring nonlinear Rashba effect and spin Hall conductivity in Janus MXenes W 2 CO 𝑋 (𝑋=S, Se, Te)
Rashba spin-orbit coupling (RSOC) facilitates spin manipulation without relying on an external magnetic field, opening up exciting possibilities for advanced spintronic devices. In this paper, we examine the effects of crystal momentum (𝑘) nonlinearity and anisotropy on the conventional Rashba effect, with a particular focus on their impact on the spin Hall conductivity (SHC) in a newly predicted family of 2D Janus materials, W 2 CO𝑋 (𝑋 =S, Se, Te). Using first-principles density functional theory calculations, we confirm the dynamical and mechanical stability of the studied 2D materials. Strikingly, this materials family exhibits pronounced nonlinear Rashba spin splitting at the Γ point of Brillouin zone near the Fermi level, which cannot be adequately described by the linear-𝑘 Rashba model. Therefore, third-order momentum contributions (𝑘 3 ) must be incorporated into the Rashba Hamiltonian. Our analysis reveals that among the studied systems, W 2 COS exhibits the highest 𝑘 3 contribution of −45.9 eV Å 3 , despite having the lowest linear Rashba constant. Here, a detailed analysis of electronic structure reveals topologically nontrivial behavior in these 2D materials, yielding sizable SHC that is primarily governed by the nonlinear Rashba effect. Notably, these materials also exhibit large spin Hall angle (0.018–2.5 at E 𝐹 ), which is comparable to that of in bulk topological insulators like Bi 2 Se 3 and Bi 2 Te 3 , and surpassing those in narrow bandgap bulk semiconductors GeTe and SnTe, as well as heavy metals such as Pt. Sizable SHC, large spin Hall angles, and the ability to tune SHC via electric fields without altering the topological properties, rooted in the crystal field splitting, underscore the potential of these materials for spintronic applications.
Electronic structure↗
Mapping domain structures near a grain boundary in a lead zirconate titanate ferroelectric film using X-ray nanodiffraction
The effect of an electric field on local domain structure near a 24° tilt grain boundary in a 200 nm-thick Pb(Zr 0.2 Ti 0.8 )O 3 bi-crystal ferroelectric film was probed using synchrotron nanodiffraction. The bi-crystal film was grown epitaxially on SrRuO 3 -coated (001) SrTiO 3 24° tilt bi-crystal substrates. From the nanodiffraction data, real-space maps of the ferroelectric domain structure around the grain boundary prior to and during application of a 200 kV cm −1 electric field were reconstructed. In the vicinity of the tilt grain boundary, the distributions of densities of c -type tetragonal domains with the c axis aligned with the film normal were calculated on the basis of diffracted intensity ratios of c - and a -type domains and reference powder diffraction data. Diffracted intensity was averaged along the grain boundary, and it was shown that the density of c -type tetragonal domains dropped to ∼50% of that of the bulk of the film over a range ±150 nm from the grain boundary. This work complements previous results acquired by band excitation piezoresponse force microscopy, suggesting that reduced nonlinear piezoelectric response around grain boundaries may be related to the change in domain structure, as well as to the possibility of increased pinning of domain wall motion. The implications of the results and analysis in terms of understanding the role of grain boundaries in affecting the nonlinear piezoelectric and dielectric responses of ferroelectric materials are discussed.
36 MATERIALS SCIENCE↗
Accelerating uncertainty quantification in incremental dynamic analysis using dimension reduction-based surrogate modeling
We propose a surrogate modeling framework based on dimension reduction to facilitate the quantification of seismic risk of structural systems in performance-based earthquake engineering. The framework adopts incremental dynamic analysis (IDA) for addressing hazard variability, and promotes significant computational efficiency improvement for propagating epistemic uncertainties associated with the structural models. It utilizes both linear and nonlinear dimension reduction approaches, equipped with inverse mappings, to learn a functional between the input parameter space (e.g., the epistemic uncertainties of the structure) to the high-dimensional output space created through the IDA implementation across different ground motions and seismic intensity levels. Polynomial chaos expansion is adopted as the surrogate model to learn this functional in the reduced space. A nine-story steel moment-resisting frame with uncertain structural properties is used as a testbed. Furthermore, we select the seismic fragility curves as a measure of the structure’s seismic performance, since it provides an estimate of the probability of entering specified damage states for given levels of ground shaking.
42 ENGINEERING↗
Filling data analysis gaps in time-resolved crystallography by machine learning
There is a growing understanding of the structural dynamics of biological molecules fueled by x-ray crystallography experiments. Time-resolved serial femtosecond crystallography (TR-SFX) with x-ray Free Electron Lasers allows the measurement of ultrafast structural changes in proteins. Nevertheless, this technique comes with some limitations. One major challenge is the quality of data from TR-SFX measurements, which often faces issues like data sparsity, partial recording of Bragg reflections, timing errors, and pixel noise. To overcome these difficulties, conventionally, large volumes of data are collected and grouped into a few temporal bins. The data in each bin are then averaged and paired with the mean of their corresponding jittered timestamps. This procedure provides one structure per bin, resulting in a limited number of averaged structures for the entire time interval spanned by the experiment. Therefore, the information on ultrafast structural dynamics at high temporal resolution is lost. This has initiated research for advanced methods of analyzing experimental TR-SFX data beyond the standard binning and averaging method. To address this problem, we use a machine learning algorithm called Nonlinear Laplacian Spectral Analysis (NLSA), which has emerged as a promising technique for studying the dynamics of complex systems. In this work, we demonstrate the power of this algorithm using synthetic x-ray diffraction snapshots from a protein with significant data incompleteness, timing uncertainties, and noise. Our study confirms that NLSA is a suitable approach that effectively mitigates the effects of these artifacts in TR-SFX data and recovers accurate structural dynamics information hidden in such data.
Trujillo, Justin (ORCID:0000000285505360)↗
Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition
We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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)↗
Autonomous Nanoparticle Synthesis Guided by In Situ Multiscale Structural Characterization
Autonomous synthesis platforms promise rapid exploration of vast parameter spaces; yet, integrating in situ structural characterization in closed-loop synthesis optimization remains challenging. We demonstrate a realization of such a closed-loop platform coupled with a droplet-flow microreactor, in situ X-ray scattering methods (SAXS/WAXS), and Gaussian process optimization to synthesize citrate-reduced Au nanoparticles with targeted characteristics. The system efficiently explored ∼19,000 synthesis recipes through 365 experiments, achieving precise control over size (4–60 nm) and polydispersity (σ < 0.11) across large citrate/gold ratios, exceeding traditional synthesis boundaries (1–10). Beyond confirming classical Turkevich–Frens trends, partial-dependence analysis revealed strong nonlinear coupling among precursor, citrate, and pH effects. Combining quantitative SAXS/WAXS analysis with electron microscopy characterization, we uncovered that crystallite size (d c ) and particle size (d) follow d c = 0.18d + β, where synthesis chemistry controls the intercept β while maintaining a universal slope. This parallel-band structure enables independent tuning of crystallite domain size at fixed particle diameter through a combination of chloride, gold precursor, citrate, and pH contributions (cross-validated Spearman ρ = 0.7 ± 0.1). High-resolution electron microscopy shows multiple lattice-fringe orientations within single particles, directly confirming polycrystalline domains and the ability to tune d c at the fixed d. The platform’s validation includes indistinguishable static versus flowing measurements, stable droplet transport at 100 °C, and <5% run-to-run variation, establishing a robust framework for mapping and controlling multiscale nanoparticle structure across expansive chemical spaces. In conclusion, the developed closed-loop platform can be applied to a borad range of nanosyntheis processes.
77 NANOSCIENCE AND NANOTECHNOLOGY↗
Explicit Dynamic Impact Analysis of the Building 3525 Packages
The safe transport and handling of radioactive material containers is critical to ensure the protection of personnel, facilities, and the environment. Accidental drops during handling pose a significant hazard, necessitating robust design and analysis to mitigate potential consequences. This study presents an explicit dynamic impact analysis of two container designs, the Baby Sugarman and the Core Conduction Cooldown Test Facility (CCCTF) Tall Boy, used in Building 3525 at Oak Ridge National Laboratory. The analysis employed nonlinear finite element modeling in LS-DYNA to simulate free-fall impacts from a height of 16.5 ft across eight critical orientations. The study evaluated deformation, strain failure, and shielding integrity under these extreme conditions. Results demonstrated that both designs maintain structural integrity, with no breaches or loss of shielding under specified administrative controls. Notably, a maximum shielding loss of 10 lbs was observed during a top-corner drop, highlighting the need to limit drop heights to less than 1 ft for certain orientations. These findings underscore the effectiveness of engineering controls and design measures in preventing containment breaches and ensuring compliance with safety requirements. This work provides a comprehensive methodology for impact analysis, contributing valuable insights to the field of radioactive materials packaging and transportation safety.
Martinez, Oscar [ORNL] (ORCID:0000000181814046)↗
Investigation of Causal Relationships of the Cross‐Scale Wave Coupling Through Information Theoretical Approach
On 2015 October 2, MMS spacecraft observed an electron micro-injection event near the southern hemispheric high-altitude cusp, coinciding with intense wave activity across several frequency bands. Here, we investigated the MMS magnetic field and plasma during this event to explore cross-scale coupling among the wave modes. Employing the Hilbert-Huang transform, we perform an empirical mode decomposition to extract frequencies and amplitudes of the intrinsic mode functions (IMFs). In this analysis, we establish both linear and nonlinear relationships and examine the information transfer between the IMFs. Notably, the transfer entropy suggests that high frequency ion cyclotron waves may be driven by the mirror mode structures. Our case study effectively demonstrates the utility of the information theory based tools for studying cross-scale wave coupling phenomena.
Rivera, Elmer C. [Andrews University, Berrien Spri↗
Nuclear Materials Packaging, Transportation, and Systems Analysis Group Software Quality Assurance Plan: ANSYS Mechanical Finite Element Analysis Software Version 2023R1
ANSYS Inc. develops and markets engineering simulation software and services used in the aerospace, automotive, manufacturing, electronics, biomedical, energy, defense, and many other industries. ANSYS is dedicated to engineering simulation and is the world’s leading software provider. ANSYS was founded in 1970 and is headquartered in Canonsburg, Pennsylvania. ANSYS provides an engineering analysis tool combining structural, thermal, computational fluid dynamics, acoustic, and electromagnetic simulation capabilities. ANSYS has two main programs, which use the same solvers: (1) Mechanical APDL (ANSYS Design Parametric Language), a Fortran-based coding platform, and (2) ANSYS Workbench, which uses a graphical user interface to aid in finite element analysis implementation. This plan covers both APDL and Workbench. The ANSYS computer program is a large-scale, multipurpose finite element program that can be used to solve several classes of engineering analyses. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses, and various types of field and coupled-field applications. The program contains many special features that allow nonlinearities or secondary effects such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation to be included in the solution. As ANSYS has been developed, other special capabilities such as substructuring, submodeling, random vibration, kinetostatics, kinetodynamics, free convection fluid analysis, acoustics, magnetics, piezoelectrics, coupled-field analysis, and design optimization have been added to the program. These capabilities contribute further to making ANSYS a multipurpose analysis tool for varied engineering disciplines. The ANSYS program has been in commercial use for over 50 years and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil, and steel industries. Additionally, many consulting firms and hundreds of universities have used ANSYS for analysis, research, and educational purposes. ANSYS is recognized worldwide as one of the most widely used and capable programs of its type. Ansys design analysis software is the first created within a quality system with ISO 9001 certification, the internationally accepted quality standard. Product development, testing, maintenance and support processes also meet the United States Nuclear Regulatory Commission's quality requirements, as they have for nearly four decades. The Quality Assurance Service Agreement is suitable for the customers working in the nuclear industry who need to meet specific federal regulations including 10CRF50 Appendix B and provisions of 10CFR21. ANSYS has retained its original International Organization for Standardization (ISO) 9001 accreditation certificate since1995-05-04, It’s current certificate is valid until 2027-05-29.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Multiresolution Quantum Chemistry: Nonlinear Response Properties at the Basis Set Limit
We benchmark the accuracy of Dunning correlation-consistent Gaussian basis sets for computing frequencydependent second-order hyperpolarizabilities relevant to second-harmonic generation (SHG), using multiresolution analysis (MRA) as a reference. Basis set errors are analyzed using a unit-sphere representation of the effective hyperpolarizability vector, enabling direct assessment of directional error structure. We introduce a relative RMS total error metric that integrates directional deviations over the unit sphere and complement it with signed projection errors that distinguish over- and underestimation. Unsupervised clustering based on these signed directional metrics reveals four distinct convergence behaviors across a set of 68 molecules. Unitsphere visualizations of representative systems show that basis set errors are often highly anisotropic and localized along specific bond directions, even when global error measures appear small. Doubly augmented basis sets consistently outperform singly augmented ones, and core-polarization functions are required for uniform convergence in second-row systems. Overall, this work demonstrates that directional analysis combined with clustering provides a robust framework for understanding basis set convergence in nonlinear optical response properties.
Basis sets↗