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A parametric study of slow dynamic nonlinear elasticity with comparisons to models

Several phenomenological models that aspire to quantitative description of anomalous nonlinear mesoscopic elasticity are reviewed and compared with laboratory measurements. This class of nonlinearity, best known perhaps for slow dynamics and aging, is seen widely in imperfectly consolidated granular solids but is not well understood. Typical slow dynamic tests show that a modest conditioning oscillatory "pump" strain depresses material stiffness, which then recovers like the logarithm of time after conditioning ceases. Several phenomenological models based on physical arguments have been proposed that predict the material stiffness response to arbitrary pump strain histories during conditioning and recovery. Approximate closed form and numerical solutions to the models are presented that predict the quantitative influence of three key pump parameters: the pump's strain amplitude, the pump's strain rate, and the pump’s duration. Laboratory measurements on Berea sandstone, concrete and a confined single aluminum bead find that slow dynamic responses are linear in pump strain and independent of pump frequency. Measurements also show that, after pump-off, stiffness recovers over times far longer than the pump duration. These observations and others are compared to model predictions. One of the considered models, based on a picture of fast brittle damage and slow healing, successfully matches all these behaviors.

36 MATERIALS SCIENCE

The role of fast and slow dynamics in nonlinear resonant ultrasound spectroscopy of consolidated granular materials

Abstract Elastic nonlinearity observed in consolidated granular media can be attributed to the combination of slow and fast effects, which give rise to hysteresis and relaxation of both modulus and damping after the sample is perturbed. A consequence is a high level of complexity in the measurements of the sample linear and nonlinear elastic parameters. The results of experiments are dependent on the experimental protocol that is adopted to measure the relevant quantities and it is hard to quantify parameters with accuracy and repeatability. Here we focus on examining Nonlinear Resonant Ultrasound Spectroscopy, showing experimentally the role of slow dynamics in the process and quantifying/discussing its influence on the quantification of nonlinearity. We also propose a model to describe the process, which shows that different contributions to nonlinearity (e.g., classical and hysteretic) could be due to physical features (defects) relaxing with different relaxation times.

Science & Technology - Other Topics

A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II

Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.

36 MATERIALS SCIENCE

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue

Customizable wave tailoring nonlinear materials enabled by bilevel inverse design

Abstract Passive wave transformation via nonlinearity is ubiquitous in settings from acoustics to optics and electromagnetics. It is well known that different nonlinearities yield different effects on propagating signals, which raises the question of “what precise nonlinearity is the best for a given wave tailoring application?” In this work, considering a one-dimensional spring-mass chain connected by polynomial springs (a variant of the Fermi-Pasta-Ulam-Tsingou system), we introduce a bilevel inverse design method which couples the shape optimization of structures for tailored constitutive responses with reduced-order nonlinear dynamical inverse design. We apply it to two qualitatively distinct problems—minimization of peak transmitted kinetic energy from impact, and pulse shape transformation—demonstrating our method’s breadth of applicability. For the impact problem, we obtain two fundamental insights. First, small differences in nonlinearity can drastically change the dynamic response of the system, from severely under- to outperforming a comparative linear system. Second, the oft-used strategy of impact mitigation via “energy locking” bistability can be significantly outperformed by our optimal nonlinearity. We validate this case with impact experiments and find excellent agreement. This study establishes a framework for broader passive nonlinear mechanical wave tailoring material design, with applications to computing, signal processing, shock mitigation, and autonomous materials.

Science & Technology - Other Topics

Learning Nonlinear Reduced Models from Data with Operator Inference

This review discusses Operator Inference, a nonintrusive reduced modeling approach that incorporates physical governing equations by defining a structured polynomial form for the reduced model, and then learns the corresponding reduced operators from simulated training data. The polynomial model form of Operator Inference is sufficiently expressive to cover a wide range of nonlinear dynamics found in fluid mechanics and other fields of science and engineering, while still providing efficient reduced model computations. The learning steps of Operator Inference are rooted in classical projection-based model reduction; thus, some of the rich theory of model reduction can be applied to models learned with Operator Inference. This connection to projection-based model reduction theory offers a pathway toward deriving error estimates and gaining insights to improve predictions. Furthermore, through formulations of Operator Inference that preserve Hamiltonian and other structures, important physical properties such as energy conservation can be guaranteed in the predictions of the reduced model beyond the training horizon. This review illustrates key computational steps of Operator Inference through a large-scale combustion example.

Mechanics

Quantum control of Hubbard excitons

Quantum control of the many-body wavefunction is a central challenge in quantum materials research, as it could yield a precise control knob to manipulate emergent phenomena. Floquet engineering, the coherent dressing of quantum states with periodic non-resonant optical fields, has become an important strategy for quantum control. Most applications to solid-state systems have targeted weakly interacting or single-ion states, leaving the manipulation of many-body wavefunctions largely unexplored. Here, in this work, we use Floquet engineering to achieve quantum control of a strongly correlated Hubbard exciton in the one-dimensional Mott insulator Sr 2 CuO 3 . A nonresonant midinfrared optical field coherently dresses the exciton wavefunction, driving its rotation between bright and dark states. We use resonant third-harmonic generation to quantify ultrafast π/2 rotations on the Bloch sphere spanned by these exciton states. Our work advances the quest towards programmable control of correlated states and exciton-based quantum sensing.

36 MATERIALS SCIENCE

Characterizing and modeling the mechanical behavior of an anion exchange membrane for carbon capture applications

A new direct air capture (DAC) technology uses a moisture swing (MS) process with anion exchange membranes, potentially offering a more energy-efficient way to remove CO₂ from the air. In this MS process, the membrane absorbs CO₂ as it dries and releases it when water is added. Understanding the mechanical behavior of these membranes is essential for improving the design and efficiency of DAC systems and prolonging sorbent lifetime. This study tested one anion exchange membrane, Fumasep’s FAA-3, under mechanical loading and various temperature and humidity conditions to measure its swelling, stiffness, strength, plastic deformation, and stress relaxation. Experimental results were used to identify a mechanical model for FAA-3 that can be used to predict the material’s nonlinear viscous behavior under various loads and environments. Unlike prior studies that assumed linear elastic behavior, this work incorporates humidity-dependent swelling, thermal expansion, and nonlinear viscoelasticity of FAA-3 in both the experiments and the model.

Direct air capture

Semi-Dynamic Leach Testing of Densified Silicon-based Iodine Waste Forms

Iodine waste forms (IWF) require a conceptual corrosion release model (CCRM) to provide iodine (I) release rates for performance modeling nuclear waste disposal repositories. To develop a CCRM, an understanding of the corrosion mechanisms of the IWF are required along with data from consistent test methods to parameterize the model. The present study has advanced both areas by providing and assessing the corrosion resistance of IWF types based on their processing history in minor variations of semi-dynamic leach tests. The test included a series of semi-dynamic leach tests using monolithic IWFs in deionized water (leachant). Several experiments were conducted under alternate test conditions with changes to temperature, leachant replacement, leachant pH, leachant volume, masking, and surface finish to elucidate if varying these conditions impacted IWF corrosion behavior. Tests were conducted on two classes of IWFs: (1) I-bearing silver-mordenite (AgZ) materials processed by hot isostatic pressing (HIP) at different temperatures, pressures, sizes, and times; and (2) I-bearing silver-functionalized silica aerogels (SFA) processed by either HIP or spark plasma sintering (SPS). The corrosion susceptibility of AgZ samples was influenced by HIP temperature and pressure. The SPS SFAs retained I far better than HIP SFAs. Additional findings in this study include: (1) The iodine dissolution rate decreased with decreasing temperature, (2) a common ion effect may occur and slow dissolution of the host phase if the leachant is not regularly replaced, (3) pH controls the dissolution rate, and (4) the iodine dissolution rate slows with extended test time (up to 224 days). Based on this work, these parameters should thus be represented when developing a CCRM.

corrosion

Lagrange-Remap strategy for multi-material fluid-solid simulations using compressive limiters

In the present work, the Lagrange-Remap strategy proposed in [1] is extended to multi-material fluid-solid simulations. Both hypo-elastic and hyper-elastic material models are considered to describe the mechanical behavior of the solids. In practice, the deviatoric stress tensor (for hypo-elastic materials) and the left Cauchy-Green tensor (for isotropic hyper-elastic materials) are remapped, while the use of compressive limiters effectively reduces numerical diffusion during the remapping step. The simplicity of this diffuse interface approach is emphasized in the context of multi-material fluid-solid simulations. A series of Lagrange-Remap test cases, involving both solids and fluids, are conducted and compared with reference Lagrangian simulations, demonstrating the robustness and accuracy of the overall numerical strategy.

Compressive limiters

Elastic Modulus Measurement at High Temperatures for Miniature Ceramic Samples Using Laser Micro-Machining and Thermal Mechanical Analyzer

In this paper, we demonstrate a method of measuring the flexural elastic modulus of ceramics at an intermediate (~millimeter) scale at high temperatures. We used a picosecond laser to precisely cut microbeams from the location of interest in a bulk ceramic. They had a cross-section of approximately 100 μm × 300 μm and a length of ~1 cm. They were then tested in a thermal mechanical analyzer at room temperature, 500 °C, 800 °C, and 1100 °C using the four-point flexural testing method. We compared the elastic moduli of high-purity Al2O3 and AlN measured by our method with the reported values in the literature and found that the difference was less than 5% for both materials. This paper provides a new and accurate method of characterizing the high-temperature elastic modulus of miniature samples extracted from representative/selected areas of bulk materials.

Chemistry

Nonlinear reversal of photoexcitation on the attosecond time scale improves ultrafast X-ray diffraction images

The complex refractive index of a material governs its light-matter interactions, with intense light fields enabling tailored nonlinear optical responses. In the X-ray regime, rapid photoionization limits the potential of nonlinear techniques by inducing irreversible electronic damage. Here we demonstrate that intense, sub-femtosecond X-ray pulses, shorter than typical Auger decay times, can partially reverse photoexcitation via stimulated emission near atomic resonances. By analyzing thousands of coherent diffraction patterns and ion spectra from neon nanoparticles exposed to sub-fs and 15-fs pulses, we observe enhanced X-ray diffraction alongside reduced energy absorption for sub-fs pulses. Theoretical modeling attributes this to dynamics akin to Rabi flopping that prolong the lifetime of resonant states and suppress electronic bleaching. These findings suggest that ultrashort, intense X-ray pulses enable active control of X-ray refractive index and damage pathways, opening avenues for improved high-resolution imaging and nonlinear spectroscopy in complex nanoscale systems.

Ulmer, Anatoli [Universität Hamburg (Germany)] (OR

Photon–photon chemical thermodynamics of frequency conversion processes in highly multimode systems

Abstract Frequency generation in highly multimode nonlinear optical systems is inherently a complex process, giving rise to an exceedingly convoluted landscape of evolution dynamics. While predicting and controlling the global conversion efficiencies in such nonlinear environments has long been considered impossible, here, we formally address this challenge even in scenarios involving a very large number of spatial modes. By utilizing fundamental notions from optical statistical mechanics, we develop a universal theoretical framework that effectively treats all frequency components as chemical reactants/products, capable of undergoing optical thermodynamic reactions facilitated by a variety of multi-wave mixing effects. These photon–photon reactions are governed by conservation laws that directly determine the optical temperatures and chemical potentials of the ensued chemical equilibria for each frequency species. In this context, we develop a comprehensive stoichiometric model and formally derive an expression that relates the chemical potentials to the optical stoichiometric coefficients, in a manner akin to atomic/molecular chemical reactions. This advancement unlocks new predictive capabilities that can facilitate the optimization of frequency generation in highly multimode photonic arrangements, surpassing the limitations of conventional schemes that rely exclusively on nonlinear optical dynamics. Notably, we identify a universal regime of Rayleigh–Jeans thermalization where an optical reaction at near-zero optical temperatures can promote the complete and entropically irreversible conversion of light to the fundamental mode at a target frequency. Our theoretical results are corroborated by numerical simulations in settings where second-harmonic generation, sum-frequency generation and four-wave mixing processes can manifest.

Optics

Nonlinear Loss Engineering in Near‐Zero‐Index Bulk Materials

Transparent conducting oxides (TCOs) show unprecedented optical nonlinearities in the near infrared wavelength range, where the real part of their linear refractive index approaches zero. More specifically, the Kerr nonlinearities of these materials have sparked widespread attention due to their magnitude and speed. However, due to the absorptive nature of these nonlinear processes, it is of fundamental interest to further investigate the imaginary component of the nonlinear index. The present work studies the nonlinear optical absorption properties of aluminium‐doped zinc oxide (AZO) thin films in their near‐zero‐index (NZI) spectral window. It is found that the imaginary part of the refractive index is reduced under optical excitation such that the field penetration depth more than doubles. An optically induced shift of the NZI bandwidth of ≈120 nm for a pump intensity of 1.3 TW cm −2 is also demonstrated. Looking into the optically induced spectral redistribution of the probe signal, local net gain is recorded, which is ascribed to a nonlinear adiabatic energy transfer. The present study adds key information about the fundamental interplay between real and imaginary nonlinear indices in NZI media, while advancing parametric amplification as viable direction for loss compensation.

36 MATERIALS SCIENCE

Novel Zwitterionic Polyurethane-in-Salt Electrolytes with High Ion Conductivity, Elasticity, and Adhesion for High-Performance Solid-State Lithium Metal Batteries

This study presents a novel polymer-in-salt (PIS) zwitterionic polyurethane-based solid polymer electrolyte (zPU-SPE) that offers high ionic conductivity, strong interaction with electrodes, and excellent mechanical and electrochemical stabilities, making it promising for high-performance all solid-state lithium batteries (ASSLBs). The zPU-SPE exhibits remarkable lithium-ion (Li+) conductivity (3.7 × 10⁻⁴ S cm−1 at 25 °C), enabled by exceptionally high salt loading of up to 90 wt.% (12.6 molar ratio of Li salt to polymer unit) without phase separation. It addresses the limitations of conventional SPEs by combining high ionic conductivity with a Li+ transference number of 0.44, achieved through the incorporation of zwitterionic groups that enhance ion dissociation and transport. The high surface energy (338.4 J m−2) and elasticity ensure excellent adhesion to Li anodes, reducing interfacial resistance and ensuring uniform Li+ flux. When tested in Li||zPU||LiFePO₄ and Li||zPU||S/C cells, the zPU-SPE demonstrated remarkable cycling stability, retaining 76% capacity after 2000 cycles with the LiFePO4 cathode, and achieving 84% capacity retention after 300 cycles with the S/C cathode. Molecular simulations and a range of experimental characterizations confirm the superior structural organization of the zPU matrix, contributing to its outstanding electrochemical performance. The findings strongly suggest that zPU-SPE is a promising candidate for next-generation ASSLBs.

Wang, Kun

Calibration of the Nonlinear Viscoelastic SPECtacular Model for 828-CTBN/DEA/GMB and 828/Z/AlOx

Nonlinear viscoelastic model calibrations are developed for two filled epoxies: an adduct of Epon 828 DGEBA and CTBN cross-linked with diethanolamine (DEA) filled with glass microballoons, called 828-CTBN/DEA/GMB, and Epon 828 DGEBA cross-linked with Ancamine Z and filled with alumina, called 828/Z/AlOx. The thermo-mechanical responses of these materials are represented using the SPECtacular constitutive model, an extension of the Simplified Potential Energy Clock (SPEC) model. The model couples

Cundiff, Kenneth Noel [Sandia National Laboratorie