Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Dynamic stiffness”

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.

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

At least 217 records · Page 12

A review of high order strong stability preserving two-derivative explicit, implicit, and IMEX methods

High order strong stability preserving time discretizations ensure the nonlinear non-inner-product strong stability properties of spatial discretizations suited for the stable simulation of hyperbolic PDEs in a wide variety of application areas including fluid dynamics, magnetohydrodynamics, semiconductor devices, electromagnetics, and astrophysics. Over the past decade multiderivative time-stepping have been increasingly used for the time-evolution hyperbolic PDEs, so that the strong stability properties of these methods have become important. In this work we review sufficient conditions for a two-derivative multistage method to preserve the strong stability properties of spatial discretizations in a forward Euler and different conditions on the second derivative. In particular we present the strong stability preserving theory for explicit and implicit two-derivative Runge–Kutta schemes, including a special condition on the second derivative under which these implicit methods may be unconditionally strong stability preserving. This special condition is natural for the stiff component of wide range of plasma physics problems, and can be useful in the context of strong stability preserving implicit-explicit multi-derivative Runge–Kutta schemes, where the time-step restriction is then independent of the stiff term. Lastly, we present the strong stability preserving theory for implicit-explicit multi-derivative general linear methods, and some novel second and third order methods where the time-step restriction is independent of the stiff term.

97 MATHEMATICS AND COMPUTING↗

Origins of Enhanced Ion Transport in Nanostructured Anion-Conducting Polyelectrolytes

Ion-conducting polymer chemistry and microstructure profoundly impact membrane water uptake and ionic conductivity. Water uptake strongly impacts ionic conductivity; yet excess water uptake compromises ion-exchange membrane mechanical properties. Although nanophase separation has been proposed to overcome this trade-off, it is unclear how polymer backbone architecture governs ionic nanostructure and its subsequent impact on water uptake and conductivity. Here, we integrate experiments and molecular dynamics simulations to elucidate the role of backbone chemistry in governing ionic nanostructure, hydration behavior, and ion transport in anion-conducting polyelectrolytes (ACPs). We systematically investigate hydrocarbon polynorbornene (PNB)-based ACPs with three distinct backbone architectures: vinyl-addition polymerization (VAP), ring-opening metathesis polymerization (ROMP), and hydrogenated ROMP. While maintaining comparable ion exchange capacities (IECs) and identical side-chain chemistry, we isolate the effects of backbone structure. We show that nanophase-separated ionic nanostructures originate in the dry state and evolve upon hydration through heterogeneous water uptake, with water preferentially partitioning into ion-rich domains. This nanophase separation arises from a delicate interplay between ionic segregation propensity and the entropic barrier imposed by backbone stiffness. Specifically, flexible backbones intensify attractive ion–ion interactions by reducing the entropic penalty for backbone deformation, promoting nanophase separation, while rigid backbones suppress ionic nanostructure formation. Nanophase-separated ion domains locally concentrate water upon hydration, which in turn enables the connectivity required for fast transport at lower water concentration values. Furthermore, these findings demonstrate that backbone chemistry can be tuned as a design lever to promote nanophase separation and enhance ion transport without excessive water uptake.

Anions↗

Physics Guided Simulation of Electrostatic Discharge: Technical Report

Triboelectrically-charged objects may create threshold sparks, electrostatic discharge (ESD) events, to equilibrate charge between themselves and other relatively charged objects. ESD events exhibit many complex physical phenomena. They are a nexus of several fields of physics with disparate characteristic scales: plasma physics, chemical kinetics, hydrodynamics, circuit models, etc. These scales can span many orders of magnitude from the varied collisions thermalizing information within a plasma on the $\mathcal{O}(fs/ps)$ to the physical size of the plasma channel on the $\mathcal{O}(100µm)$, to the speed of a nonlinear hydrodynamic wave propagating at $\mathcal{O}(µm, ns)$. These threshold ESD events may occur in situations of programmatic importance, delivering energy and power profiles to a “victim load” generating deleterious consequences. To predict and mitigate these consequences we must answer questions about the spark’s energy budget: how much energy goes into producing the spark channel; how much gets radiated away; how much energy is advected away into the hydrodynamics; and how much energy is delivered to a victim load. An ESD simulation toolset has been created and evolved in order to answer these questions. An appropriate, physics guided implementation for simulation can be done by gaining insight into its constituent physics and leveraging that intuition to choose a suitable numerical operator. We examine in detail the chemical kinetics, circuit discharge, and hydrodynamics to deter mine dominant regimes, values, timescales, and interactions to uncover the underlying physical dynamics. We also examine and propose model reduction schemes for high-dimensional chemical kinetics. We use past and current work with experimentally validated and theoretically-verified hydrodynamics to calculate applicability limits of the non-ionizing strong shock limit. We quantify the energy budget from a hydrodynamic perspective and demonstrate that a significant fraction of the stored energy is “earmarked” for hydrodynamic advection as an energy terminus. Lastly, we combine the constituent physics of an ESD event (chemical kinetics, circuit model, and hydrodynamics) into a cohesive, actionable toolset and obtain promising results from an isothermal test case. We then propose a viable, modular evolution of the ESD toolset based upon the performed examination of the physics uncovering dominant physical scales and the stiffness of the compositional differential system.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Fractionation of Lignin for Selective Shape Memory Effects at Elevated Temperatures

We report a facile approach to control the shape memory effects and thermomechanical characteristics of a lignin-based multiphase polymer. Solvent fractionation of a syringylpropane-rich technical organosolv lignin resulted in selective lignin structures having excellent thermal stability coupled with high stiffness and melt-flow resistance. The fractionated lignins were reacted with rubber in melt-phase to form partially networked elastomer enabling selective programmability of the material shape either at 70 °C, a temperature that is high enough for rubbery matrix materials, or at an extremely high temperature, 150 °C. Utilizing appropriate functionalities in fractionated lignins, tunable shape fixity with high strain and stress recovery, particularly high-stress tolerance were maintained. Detailed studies of lignin structures and chemistries were correlated to molecular rigidity, morphology, and stress relaxation, as well as shape memory effects of the materials. The fractionation of lignin enabled enrichment of specific lignin properties for efficient shape memory effects that broaden the materials’ application window. Electron microscopy, melt-rheology, dynamic mechanical analysis and ultra-small angle neutron scattering were conducted to establish morphology of acrylonitrile butadiene rubber (NBR)-lignin elastomers from solvent fractionated lignins.

36 MATERIALS SCIENCE↗

Colloidal Clusters and Networks Formed by Oppositely Charged Nanoparticles with Varying Stiffnesses

Colloidal clusters and gels are ubiquitous in science and technology. Particle softness has a strong effect on interparticle interactions; however, our understanding of the role of this factor in the formation of colloidal clusters and gels is only beginning to evolve. Here, we report the results of experimental and simulation studies of the impact of particle softness on the assembly of clusters and networks from mixtures of oppositely charged polymer nanoparticles (NPs). Experiments were performed below or above the polymer glass transition temperature, at which the interaction potential and adhesive forces between the NPs were significantly varied. Hard NPs assembled in fractal clusters that subsequently organized in a kinetically arrested colloidal gel, while soft NPs formed dense precipitating aggregates, due to the NP deformation and the decreased interparticle distance. Importantly, interactions of hard and soft NPs led to the formation of discrete precipitating NP aggregates at a relatively low volume fraction of soft NPs. A phenomenological model was developed for interactions of oppositely charged NPs with varying softnesses. Furthermore, the experimental results were in agreement with molecular dynamics simulations based on the model. This work provides insight on interparticle interactions before, during, and after the formation of hard–hard, hard–soft, and soft–soft contacts and has impact for numerous applications of reversible colloidal gels, including their use as inks for additive manufacturing.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

Structure-Based Design of Dual Bactericidal and Bacteria-Releasing Nanosurfaces

Here, we report synergistic nanostructured surfaces combining bactericidal and bacteria-releasing properties. A polystyrene-block-poly(methyl methacrylate) (PS-block-PMMA) diblock copolymer is used to fabricate vertically oriented cylindrical PS structures (“PS nanopillars”) on silicon substrates. The results demonstrate that the PS nanopillars (with a height of about 10 nm, size of about 50 nm, and spacing of about 70 nm) exhibit highly effective bactericidal and bacteria-releasing properties (“dual properties”) against Escherichia coli for at least 36 h of immersion in an E. coli solution. Interestingly, the PS nanopillars coated with a thin layer (≈3 nm thick) of titanium oxide (TiO 2 ) (“TiO 2 nanopillars”) show much improved dual properties against E. coli (a Gram-negative bacterium) compared to the PS nanopillars. Moreover, the dual properties emerge against Listeria monocytogenes (a Gram-positive bacterium). To understand the mechanisms underlying the multifaceted property of the nanopillars, coarse-grained molecular dynamics (MD) simulations of a lipid bilayer (as a simplified model for E. coli) in contact with a substrate containing hexagonally packed hydrophilic nanopillars were performed. The MD results demonstrate that when the bacterium–substrate interaction is strong, the lipid heads adsorb onto the nanopillar surfaces, conforming the shape of a lipid bilayer to the structure/curvature of nanopillars and generating high stress concentrations within the membrane (i.e., the driving force for rupture) at the edge of the nanopillars. Membrane rupture begins with the formation of pores between nanopillars (i.e., bactericidal activity) and ultimately leads to the membrane withdrawal from the nanopillar surface (i.e., bacteria-releasing activity). In the case of Gram-positive bacteria, the adhesion area to the pillar surface is limited due to the inherent stiffness of the bacteria, creating higher stress concentrations within a bacterial cell wall. In conclusion, the present study provides insight into the mechanism underlying the “adhesion-mediated” multifaceted property of nanosurfaces, which is crucial for the development of next-generation antibacterial surface coatings for relevant medical applications.

36 MATERIALS SCIENCE↗

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗

Dynamic fracture of glass fiber-reinforced ductile polymer matrix composites and loading rate effect

Here, the dynamic fracture of S-2 glass fiber-reinforced polymer matrix composites (FRPMCs) was investigated in this study. The matrix ductility was improved by a recently developed network topology modification technique via mixing partially reacted substructures (mPRS). The composite material was manufactured and characterized by micro-CT scanning and scanning electron microscopy (SEM). Dynamic single-edge notched bending (d-SENB) experiments were performed on the composites by using a modified split-Hopkinson pressure bar. Each specimen’s fracture process was visualized by ultrafast X-ray imaging. Such in-situ radiography enabled identifying the damage initiation below 50-micron scale and inspecting its propagation through the internal structures of opaque composites, thereby accurately quantifying the composites’ mechanical properties. Furthermore, the identical d-SENB experiments were designed and the digital image correlation (DIC) was employed to monitor the stress wave propagation on the composite specimens. The force and deflection measurements were modified and correlated to the physical damage processes. Besides, quasi-static SENB experiments were conducted to identify the loading rate effects on the composites’ fracture behaviors. The force and deflection history, bending stiffness, energy dissipation, and fracture toughness at different loading rates were quantified and compared. Finally, post-fracture analysis by micro-CT scanning and SEM provided physical observations on the variation of the fracture morphology by different loading rates.

42 ENGINEERING↗

Predicting the viscoplastic response of a crystallizing fluoropolymer using transient network theory

We employ a molecular theory of dynamic polymer networks to describe the viscoplastic response of rubbery FK-800, a thermoplastic copolymer of chlorotrifluoroethylene and vinylidene fluoride, over a broad range of thermal histories. The kinetics of crystallization at different annealing temperatures was modeled using a modified Avrami equation, whose parameters were found to evolve through simple relationships over the full temperature range of the rubbery state. By fitting experimental compression data, we discovered predictable trends for the physical parameters in our mechanical model over its full range of crystallinities (up to ≈20%) and provided insights based on molecular-level physics to justify them. Using this, an end-to-end model was developed to predict the yielding and post-yield behavior of rubbery FK-800 for arbitrary thermal histories. The model successfully predicted the highly nonlinear evolution of characteristic mechanical signatures (stiffness, yield point, post-yield drop) throughout the crystallization process. A statistical analysis of variance test was employed to determine that the measured variations in the mechanical behavior of rubbery FK-800 are primarily dictated by its fractional crystallinity, regardless of its exact thermal history.

36 MATERIALS SCIENCE↗

Parallel Grid-Forming Inverter-Driven Black Start: Power-Hardware-in-the-Loop Validation: Preprint

With power systems encountering increasing deployment levels of inverter-based resources (IBRs), system restoration using grid-forming (GFM) IBRs has gained attention. Engineered to establish grid voltages in the absence of a stiff grid, black-start-capable GFM IBRs are expected to enhance power system resilience by playing a critical role in bottom-up system restoration. This paper experimentally studies the feasibility of the novel approach through power-hardware-in-the-loop (PHIL) testing and validation with a commercial GFM inverter. The PHIL test setup demonstrates an inverter-driven black start of a 5-MW unbalanced distribution feeder where two GFM inverters collectively black start the feeder: one is a commercial hardware GFM inverter interacting through the PHIL interface, and the other is a software GFM emulated by a real-time simulation with full electromagnetic transient (EMT) models. Both GFM inverters are equipped with negative-sequence voltage control to suppress the voltage imbalance resulting from the unbalanced loading, allowing us to study the dynamic interactions between the GFMs with their control parameters unknown. To evaluate the dynamic behavior of the GFM inverters under the entire black-start process, the EMT model of the distribution system details the transformer and motor dynamics to emulate their inrush and startup behaviors. It abstracts conventional grid-connected inverter dynamics, i.e., grid-following inverters. Oscilloscope measurements of the hardware GFM inverter are also presented for critical steps. Takeaways for further study and field deployment are provided.

grid-forming inverter↗

Ionic Interdiffusion at Cathode|Solid-Electrolyte Interface: A Machine Learning–Assisted Multiscale Investigation and Mitigation Strategies

Future lithium batteries are expected to use solid electrolytes to achieve higher energy density and fast charge capabilities. However, most solid electrolytes are thermodynamically unstable against layered oxide cathodes. In this study, the stability of LiCoO2 (LCO) cathode with Li10GeP2S12 (LGPS) solid electrolyte is investigated using ab initio molecular dynamics (AIMD) and machine learning molecular dynamics (MLMD). The propensity of ionic interdiffusion, formation of a passivating interphase layer, and corresponding decay in cell performance is addressed using a continuum model. Large-scale MLMD simulations confirm that the LCO|LGPS interface permits interdiffusion of cobalt (Co) and other ionic species, leading to the formation and growth of a resistive interphase and to dramatic capacity fade even in the first cycle. We examine the literature evidence that incorporating a thin layer of LiNb0.5Ta0.5O3 (LNTO) between LCO and LGPS prevents the interdiffusion of ions. Atomistic simulations suggest that substituting lithium (Li) in LNTO with Co is thermodynamically unfavorable, thereby inhibiting ionic interdiffusion. The stable Nb5+/Ta5+ states form a rigid metal-oxide framework, which consequently also prevents the substitution of niobium (Nb) or tantalum (Ta). However, continuum-level analysis suggests that the higher mechanical stiffness of LNTO can lead to interfacial delamination between the LCO and LNTO. This phenomenon reduces the effectiveness of the protective layer. This paper, therefore, highlights the need to develop novel interlayers that balance low ionic interdiffusion with low mechanical stiffness.

Ncube, Musawenkosi K.↗

Coherent Transfer of Lattice Entropy via Extreme Nonlinear Phononics in Metal Halide Perovskites

Entropy transfer in metal halide perovskites, characterized by significant lattice anharmonicity and low stiffness, underlies the remarkable properties observed in their optoelectronic applications, ranging from solar cells to lasers. The conventional view of this transfer involves stochastic processes occurring within a thermal bath of phonons, where the lattice arrangement and energy flow from higher- to lower-frequency modes. Here, we unveil a comprehensive chronological sequence detailing a conceptually distinct coherent transfer of entropy in a prototypical perovskite CH 3 NH 3 Pbl 3 . The terahertz periodic modulation imposes vibrational coherence into electronic states, leading to the emergence of mixed (vibronic) quantum beat between approximately 3 and 0.3 THz. We highlight a well-structured bidirectional time-frequency transfer of these diverse phonon modes, each developing at different times and transitioning from high to low frequencies from 3 to 0.3 THz, before reversing direction and ascending to around 0.8 THz. First-principles molecular dynamics simulations disentangle a complex web of coherent-phononic coupling pathways and identify the salient roles of the initial modes in shaping entropy evolution at later stages. Capitalizing on coherent entropy transfer and dynamic anharmonicity presents a compelling opportunity to exceed the fundamental thermodynamic (Shockley-Queisser) limit of photoconversion efficiency and to pioneer novel optoelectronic functionalities. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

MFC 5.0: An exascale many-physics flow solver

Many problems of interest in engineering, medicine, and the fundamental sciences rely on high-fidelity flow simulation, making performant computational fluid dynamics solvers a mainstay of the open-source software community. Previous work MFC 3.0 was made a published, documented, and open-source solver via Bryngelson et al. Comp. Phys. Comm. (2021) with numerous physical features, numerical methods, and scalable infrastructure. MFC 5.0 is a significant update to MFC 3.0, featuring a broad set of well-established and novel physical models and numerical methods, as well as the introduction of GPU and APU (or superchip) acceleration. Here, we exhibit state-of-the-art performance and ideal scaling on the first two exascale supercomputers, OLCF Frontier and LLNL El Capitan. Combined with MFC’s single-accelerator performance, MFC achieves exascale computation in practice, and achieved the largest-to-date public CFD simulation at 200 trillion grid points as a 2025 ACM Gordon Bell Prize finalist. New physical features include the immersed boundary method, N-fluid phase change, Euler–Euler and Euler–Lagrange sub-grid bubble models, fluid-structure interaction, hypo- and hyper-elastic materials, chemically reacting flow, two-material surface tension, magnetohydrodynamics (MHD), and more. Numerical techniques now represent the current state-of-the-art, including general relaxation characteristic boundary conditions, WENO variants, Strang splitting for stiff sub-grid flow features, and low Mach number treatments. Weak scaling to tens of thousands of GPUs on OLCF Summit and Frontier and LLNL El Capitan achieves efficiencies within 5% of ideal to over 90% of their respective system sizes. Strong scaling results for a 16-times increase in device count show parallel efficiencies over 90% on OLCF Frontier. MFC’s software stack has undergone further improvements, including continuous integration, which ensures code resilience and correctness through over 300 regression tests; metaprogramming, which reduces code length while maintaining performance portability; and code generation for computing chemical reactions

Computational fluid dynamics↗

Magnetoelastic properties of multiferroic hexagonal ErMnO 3

Here, the strength and dynamics of magnetoelastic coupling through the paramagnetic (PM) – antiferromagnetic (AFM) – ferrimagnetic (FIM) transitions in multiferroic hexagonal ErMnO 3 have been investigated by Resonant Ultrasound Spectroscopy. Elastic stiffening by up to 2% below the PM – AFM transition at 80 K arises from biquadratic coupling between strain and the magnetic order parameter with relaxation times longer than ~10 -6 s for the response of spins to changes in strain. In contrast with YMnO 3 , the PM – AFM transition in ErMnO 3 is accompanied by a peak in acoustic loss immediately below the Néel point which is interpreted in terms of strain relaxation accompanying ordering of spins of Er 3+ at 4b sites. Changes in the magnetic ordering scheme at the AFM – FIM transition near 3 K are accompanied by elastic softening of ~0.03 %. During poling of the low temperature ferrimagnetic structure round magnetic hysteresis loops, small changes in elastic stiffness which arise due to the contribution of piezomagnetic and/or piezoelectric moduli are detected. Contributions of piezoelectric moduli to acoustic resonance frequencies also permit changes in the configuration of ferroelectric domains to be detected in response both to cycling through this transition and to application of a magnetic field. A peak in acoustic loss in the vicinity of 250 K is attributed to strain-mediated pinning/freezing of some aspect of the domain microstructure with an activation energy of ~0.25–0.3 eV. A return to the original elastic properties on heating to temperatures above ~250 K is interpreted in terms of backswitching of domains to the configuration they had at the start. These observations confirm the existence of subtle variations in magnetoelastic coupling behaviour relating to both the magnetic order parameters and magnetic domain structures.

36 MATERIALS SCIENCE↗

Sustainable Shape Memory Elastomers with Reduced Melt Viscosity and Enhanced Stiffness

Melt reactive processing of lignin with nitrile rubber is a promising approach to synthesizing shape memory materials. The strong intramolecular interactions in lignin macromolecular structures, caused by π–π stacking in aromatic rings and hydrogen bonding, often result in large phase separation or low miscibility with rubbers. In this study, we investigated the chemical and molecular characteristics, as well as the stiffness and complex viscosity, of modified kraft lignin melt-reacted with an acrylonitrile/butadiene copolymer containing 41% acrylonitrile (NBR41). To enhance the macromolecular compatibility of kraft lignin with NBR41, kraft lignin was cross-linked with poly(propylene glycol) diglycidyl ether (PPDE) and trimethylolpropane triglycidyl ether (TTE), both rich in epoxy reactive groups capable of forming chemical bonds with hydroxyl and carboxyl groups. Here, our findings demonstrate that the modification of kraft lignin with PPDE and TTE resulted in significantly increased stiffness of the composites. The elastic modulus of NBR41-Kraft lignin-PPDE and NBR41-Kraft lignin-TTE increased by 82 and 162%, respectively. Both the yield strength and Young’s modulus of these two samples showed dramatic improvements. Specifically, the yield strength and Young’s modulus of NBR41-Kraft lignin-TTE increased nearly 4 and 3-fold, respectively, compared to the control sample. Interestingly, despite significant improvements in mechanical properties, the viscosity of NBR41-Kraft lignin-PPDE was substantially lower than that of the control sample. At 210 °C and an angular frequency of 1 rad/s, the complex viscosity of NBR41-Kraft lignin was approximately 100.25 ± 4.77 kPa·s, while that of NBR41-Kraft lignin-PPDE was significantly lower at 56 ± 0.93 kPa·s. These findings were validated through Fourier transform infrared spectroscopy, scanning electron microscopy, dynamic mechanical analysis, thermal characterization, rheological tests, and quasi-elastic neutron scattering techniques.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Medium-Range Ordering in the Ionic Glass Electrolytes LiPON and LiSiPON

In this work, we provide an in-depth structural characterization of the amorphous ionic glasses LiPON and LiSiPON with high Li content. Based on ab initio molecular dynamics simulations, the structure of these materials is an inverted structure with either isolated polyanion tetrahedra or polyanion dimers in a Li+ matrix. Based on neutron scattering data, this type of inverted structure leads to a significant amount of medium-range ordering in the structure, as demonstrated by two sharp diffraction peaks and a periodic structural oscillation in the density function G(r). While this medium-range ordering is commonly observed in liquids and metallic glasses, it has not previously been observed in oxides. On a local scale, adding N and Si increases the number of anion bridges and polyanion dimer structures, leading to higher ionic conductivity. In the medium-range ordering, the addition of Si leads to more disorder in the polyanion substructure but a significant increase in the ordering of the O substructure. Finally, we demonstrate that this inverted structure with medium-range ordering results in a glassy material that is both mechanically stiff and ductile on the nanoscale.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Effectiveness and nonlinear characterization of vibro-impact energy harvesting absorbers in controlling base-excited systems

In this study, model derivations are carried out of a dynamical system under base excitations with a piezoelectric energy harvesting absorber as the tuned-mass-damper. Additionally, amplitude stoppers are included to the absorber in order to create a broadband resonant response, increasing the window of operational use for energy harvesting and system's control. This study is unique in the fact that the energy harvester is coupled to the source of its excitation. A nonlinear reduced-order model is developed using Euler–Lagrange principle and the Galerkin method to accurately estimate the energy harvesting absorber's displacement, harvested power, and the oscillating response of the primary structure. The nonlinear interaction of the energy harvesting absorber and the amplitude stoppers are the focus of this study, where an in-depth investigation of bifurcation points of the primary structure and energy harvesting absorber responses is performed. Due to a transfer of energy between the primary structure and the absorber, it is shown that a soft stopper with stiffness $5 \times {10^3}\,{\text{N}}\;{{\text{m}}^{ - 1}}\,$ has great control of the primary structure with 60% of the uncontrolled amplitude being reduced, as well as an increase of the harvested energy. Medium stoppers with small initial gaps size and hard stoppers do not control the primary structure and show a decrease in the energy harvesting capabilities due to the activation of the nonlinear contact-impact interactions. Finally, these stoppers also generate aperiodic regions due to the possible presence of grazing bifurcations.

36 MATERIALS SCIENCE↗

Order conditions for nonlinearly partitioned Runge-Kutta methods

Recently, a new class of nonlinearly partitioned Runge–Kutta (NPRK) methods was proposed for nonlinearly partitioned systems of autonomous ordinary differential equations y' = F(y, y). The target class of problems are those in which different scales, stiffnesses, or physics are coupled in a nonlinear way, wherein the desired partition cannot be written in a classical additive or component-wise fashion. Here we use a rooted-tree analysis to derive full-order conditions for NPRKM methods, where M denotes the number of nonlinear partitions. Due to the nonlinear coupling and thereby the mixed product differentials, it turns out that the standard node-colored rooted tree analysis used in analyzing ODE integrators does not naturally apply. Instead we develop a new edge-colored rooted-tree framework to address the nonlinear coupling. The resulting order conditions are enumerated, are provided directly for up to fourth order with M = 2 and third order with M = 3, and are related to existing order conditions of additive and partitioned RK methods. We conclude with an example that shows how the nonlinear order conditions can be used to obtain an embedded estimate of the state-dependent nonlinear coupling strength in a dynamical system.

97 MATHEMATICS AND COMPUTING↗