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DOE OSTI2025

Investigation of magnetic fluctuations in L-H and H-L transition dynamics on DIII-D

The dynamics of the L-H transition is not fully understood, with many parameters changing the threshold power to enter H-mode and the self-regulation between zonal flows and turbulence in the plasma edge. This paper is primarily a presentation of experimental results for DIII-D L-H and H-L transitions and speculation on the observations made. Power threshold analysis and measurements of pedestal temperatures for these transitions are presented. A comparison is made between an L-H transition and H-L transition of comparable Psep exhibiting oscillatory behaviour, showing symmetry between forward and backward transition dynamics. This paper shows the first observations of magnetic fluctuations during L-H and H-L transitions on DIII-D, and shows that L-H and H-L transitions have similar magnetic fluctuation dynamics. Information geometry analysis has been performed on measurements of plasma density fluctuations, perpendicular plasma velocity fluctuations, and magnetic field fluctuations to investigate the self-regulation and evolution of these variables during the transitions. Perpendicular flow evolution is shown to dominate the transition dynamics in both directions, but self-regulation behaviour is observed between all three variables. A strong correlation between magnetic fluctuation information rate and density fluctuation information rate for these two shots shows the strong influence of magnetic behaviour on both the L-H and H-L transition, and that these transition dynamics necessarily include electromagnetic effects.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Relations between b → cτν decay modes in scalar models

As a consequence of the Ward identity for hadronic matrix elements, we find relations between the differential decay rates of semileptonic decay modes with the underlying quark-level transition b → cτν, which are valid in scalar models. The decay-mode dependent scalar form factor is the only necessary theoretical ingredient for the relations. Otherwise, they combine measurable decay rates as a function of the invariant mass-squared of the lepton pair $q^2$ in such a way that a universal decay-mode independent function is found for decays to vector and pseudoscalar mesons, respectively. This can be applied to the decays $B → D^{\ast}τv, B_s → D^\ast_sτv, B_c → J/ψτv$ and $B → Dτv, B_s → D_sτv, B_c → η_cτv$, with implications for $R(D^{(\ast)}), R(D^{(\ast)}_s), R(J/ψ), R(η_c)$, and $\mathcal{B}(B_c → τv)$. The slope and curvature of the characteristic $q^2$-dependence is proportional to scalar new physics parameters, facilitating their straight forward extraction, complementary to global fits.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2022

Evaluating seasonal and regional distribution of snowfall in regional climate model simulations in the Arctic

In this study, we investigate how the regional climate model HIRHAM5 reproduces the spatial and temporal distribution of Arctic snowfall when compared to CloudSat satellite observations during the examined period of 2007–2010. For this purpose, both approaches, i.e., the assessments of the surface snowfall rate (observation-to-model) and the radar reflectivity factor profiles (model-to-observation), are carried out considering spatial and temporal sampling differences. The HIRHAM5 model, which is constrained in its synoptic representation by nudging to ERA-Interim, represents the snowfall in the Arctic region well in comparison to CloudSat products. The spatial distribution of the snowfall patterns is similar in both identifying the southeastern coast of Greenland and the North Atlantic corridor as regions gaining more than twice as much snowfall as the Arctic average, defined here for latitudes between 66 and 81°N. Excellent agreement (difference less than 1%) in the Arctic-averaged annual snowfall rate between HIRHAM5 and CloudSat is found, whereas ERA-Interim reanalysis shows an underestimation of 45% and significant deficits in the representation of the snowfall rate distribution. From the spatial analysis, it can be seen that the largest differences in the mean annual snowfall rates are an overestimation near the coastlines of Greenland and other regions with large orographic variations as well as an underestimation in the northern North Atlantic Ocean. To a large extent, the differences can be explained by clutter contamination, blind zone or higher resolution of CloudSat measurements, but clearly HIRHAM5 overestimates the orographic-driven precipitation. The underestimation of HIRHAM5 within the North Atlantic corridor south of Svalbard is likely connected to a poor description of the marine cold air outbreaks which could be identified by separating snowfall into different circulation weather type regimes. By simulating the radar reflectivity factor profiles from HIRHAM5 utilizing the Passive and Active Microwave TRAnsfer (PAMTRA) forward-modeling operator, the contribution of individual hydrometeor types can be assessed. Looking at a latitude band at 72–73°N, snow can be identified as the hydrometeor type dominating radar reflectivity factor values across all seasons. The largest differences between the observed and simulated reflectivity factor values are related to the contribution of cloud ice particles, which is underestimated in the model, most likely due to the small sizes of the particles. The model-to-observation approach offers a promising diagnostic when improving cloud schemes, as illustrated by comparison of different schemes available for HIRHAM5.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Drought conditioning of rhizosphere microbiome influences maize water use traits

Background and Aims: Beneficial plant–microbe interactions can improve plant performance under drought; however, we know less about how drought-induced shifts in microbial communities affect plant traits. Methods: We cultivated Zea mays in fritted clay with soil microbiomes originating from contrasting environments (agriculture or forest) under two irrigation treatments (well-watered or water limited). Using this design, we investigated whether water conditioning was carried forward through the microbiome to affect a subsequent plant cohort that was subjected to either a well-watered or water limited treatment. Results: Regardless of the microbiome-origin, plants inoculated with a microbiome from a water limited legacy had traits that allowed them to avoid stress but conserve water. They produced longer roots to explore soil, generated greater soil dissolved organic carbon, potentially stimulating the microbiome, and slower soil water content loss during drought. A well-watered legacy resulted in plants that delayed permanent stomatal closure and higher photosynthetic nitrogen use efficiency. In plants with a forest-originated microbiome, a well-watered legacy and water treatment also resulted in higher rates of photosynthesis and stomatal conductance. Conclusion: These results demonstrate that soil microbiomes can be developed to influence plant drought performance, impacting crop resilience, using short-term microbial conditioning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Aging Mechanisms of Broad Area High-Power ~800nm Laser Diodes

Improved lifetime of high-power broad area laser diodes will enhance their utility for manufacturing, scientific, and medical laser systems. However, factors contributing to gradual degradation of diode laser performance are not fully understood. Here we study the aging mechanisms of ~800 nm aluminum-free laser diodes grown by solid-source MBE. Oxygen was intentionally introduced at three different concentration levels into the quantum well (QW) and waveguide (WG) at concentrations <5×10 15 cm -3 . Diode power, slope efficiency (SE th ), threshold current (I th ), and device parameters such as QW and WG lifetimes were measured at discrete time steps throughout the aging run. The data show that lasing characteristics prior to aging are degraded by oxygen introduction, but the gradual power degradation rate of ~5% over 500 hours at current density 1.74 kA/cm 2 does not change with oxygen concentration. Aging-induced changes in nonradiative lifetimes and threshold were observed for shorter aging times, but stabilized after ~100 hrs. and cannot explain the observed power degradation. This suggests that gradual degradation in these devices is not due to nonradiative recombination at low levels of point defects. The data shows that this degradation results primarily from changes in slope efficiency, and simulation of these results suggests that the power degradation arises from increased intracavity absorption (ICA). Efforts to slow ICA growth, instead of efforts to control low levels of nonradiative recombination centers, may be the most fruitful path forward to improve laser diode lifetime.

42 ENGINEERING↗

DOE OSTI2020

Effects of excess Te on flux inclusion formation in the growth of cadmium zinc telluride when forced melt convection is applied

The presence of second phase defects, particularly flux inclusions of tellurium rich composition, are of great concern for charge collection efficiency in cadmium zinc telluride (CZT) and cadmium telluride (CT) material intended for applications such as radiation detection. These inclusions can distort applied electric field lines within the detector as well as act as trapping centers for charge carriers. Reduction and/or elimination of these inclusions is required to achieve appropriate charge collection efficiencies, especially in detectors of thicknesses greater than 5 mm. These so-called flux inclusions are understood to form as a consequence of constitutional undercooling at the crystal growth interface. In this study, a forced melt convection technique was applied in Vertical Bridgman (VB) melt growth of CZT without reducing imposed growth rates of ~2 mm/hr. Several rotation profiles were tested while adjusting the melt composition from 51.62 to 61.75 atomic percent (at%) Te where the Te concentration was initially increased to improve overall material purity. With forced melt convection, the best inclusion distributions were achieved with highly Te rich melt compositions, far beyond the stoichiometric composition range for the CZT system. Average inclusion diameters were reduced to 2 µm while inclusions greater than 5 µm were essentially eliminated. Composition analyses of these ingots revealed near equilibrium concentrations of Te, even with ingots grown from Te concentrations as high as 61.75 at% Te. In this paper, a recipe for the reduction of inclusions in CZT melt growth is put forward and the implications of this method on our understanding of inclusion formation are discussed.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Human–mouse comparison of the multistage nature of radiation carcinogenesis in a mathematical model

Abstract Mouse models are vital for assessing risk from environmental carcinogens, including ionizing radiation, yet the interspecies difference in the dose response precludes direct application of experimental evidence to humans. Herein, we take a mathematical approach to delineate the mechanism underlying the human–mouse difference in radiation‐related cancer risk. We used a multistage carcinogenesis model assuming a mutational action of radiation to analyze previous data on cancer mortality in the Japanese atomic bomb survivors and in lifespan mouse experiments. Theoretically, the model predicted that exposure will chronologically shift the age‐related increase in cancer risk forward by a period corresponding to the time in which the spontaneous mutational process generates the same mutational burden as that the exposure generates. This model appropriately fitted both human and mouse data and suggested a linear dose response for the time shift. The effect per dose decreased with increasing age at exposure similarly between humans and mice on a per‐lifespan basis (0.72‐ and 0.71‐fold, respectively, for every tenth lifetime). The time shift per dose was larger by two orders of magnitude in humans (7.8 and 0.046 years per Gy for humans and mice, respectively, when exposed at ~35% of their lifetime). The difference was mostly explained by the two orders of magnitude difference in spontaneous somatic mutation rates between the species plus the species‐independent radiation‐induced mutation rate. Thus, the findings delineate the mechanism underlying the interspecies difference in radiation‐associated cancer mortality and may lead to the use of experimental evidence for risk prediction in humans.

Oncology↗

DOE OSTI2025

Numerical schemes for 3-wave kinetic equations: A complete treatment of the collision operator

In our previous work Walton and Tran (2023), numerical schemes for a simplified version of 3-wave kinetic equations, in which only the simple forward-cascade terms of the collision operators are kept, have been successfully designed, especially to capture the long time dynamics of the equation given the multiple blow-up time phenomenon. In this second work in the series, we propose numerical treatments for the complete 3-wave kinetic equations, in which the complete, much more complicated collision operators are fully considered based on a novel conservative form of the equation. Here we then derive an implicit finite volume scheme to solve the equation. The new discretization uses an adaptive time-stepping method which allows for the simulations to be carried to very long times. Our computed solutions are compared with previously derived long-time asymptotic estimates for the decay rate of total energy of time-dependent solutions of 3-wave kinetic equations and found to be in excellent agreement.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Efficient ptychographic phase retrieval via a matrix-free Levenberg-Marquardt algorithm

The phase retrieval problem, where one aims to recover a complex-valued image from far-field intensity measurements, is a classic problem encountered in a range of imaging applications. Modern phase retrieval approaches usually rely on gradient descent methods in a nonlinear minimization framework. Calculating closed-form gradients for use in these methods is tedious work, and formulating second order derivatives is even more laborious. Additionally, second order techniques often require the storage and inversion of large matrices of partial derivatives, with memory requirements that can be prohibitive for data-rich imaging modalities. We use a reverse-mode automatic differentiation (AD) framework to implement an efficient matrix-free version of the Levenberg-Marquardt (LM) algorithm, a longstanding method that finds popular use in nonlinear least-square minimization problems but which has seen little use in phase retrieval. Furthermore, we extend the basic LM algorithm so that it can be applied for more general constrained optimization problems (including phase retrieval problems) beyond just the least-square applications. Since we use AD, we only need to specify the physics-based forward model for a specific imaging application; the first and second-order derivative terms are calculated automatically through matrix-vector products, without explicitly forming the large Jacobian or Gauss-Newton matrices typically required for the LM method. We demonstrate that this algorithm can be used to solve both the unconstrained ptychographic object retrieval problem and the constrained “blind” ptychographic object and probe retrieval problems, under the popular Gaussian noise model as well as the Poisson noise model. We compare this algorithm to state-of-the-art first order ptychographic reconstruction methods to demonstrate empirically that this method outperforms best-in-class first-order methods: it provides excellent convergence guarantees with (in many cases) a superlinear rate of convergence, all with a computational cost comparable to, or lower than, the tested first-order algorithms.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Green AI: Insights Into Deep Learning's Looming Energy Efficiency Crisis

As demands grow to integrate artificial intelligence into every aspect of industry, commerce, and life, deep learning's exploding energy cost has become a looming crisis, making AI systems a salient energy-efficiency challenge. One might expect that doubling a neural network's size would halve its error rate, or at least allow it to achieve greater performance given the same amount of time and energy. I will present clear and substantial scientific evidence which indicates that not only is this intuition wildly wrong, but that neural networks scale so poorly that to increase deep learning performance by only a small fraction can easily require an order of magnitude or more increase in computational resources and energy. Further, the marginal trade-off price of to increase model performance rapidly explodes as performance targets are increased. To address this challenge, I will provide a toolkit of techniques that can be applied today to mitigate the inefficiency of modern deep learning. And, I will conclude by illuminating a practical path forward towards efficient, Green AI.

artificial intelligence↗

DOE OSTI2020

Use of a controlled experiment and computational models to measure the impact of sequential peer exposures on decision making

It is widely believed that one’s peers influence product adoption behaviors. This relationship has been linked to the number of signals a decision-maker receives in a social network. But it is unclear if these same principles hold when the “pattern” by which it receives these signals vary and when peer influence is directed towards choices which are not optimal. To investigate that, we manipulate social signal exposure in an online controlled experiment using a game with human participants. Each participant in the game decides among choices with differing utilities. We observe the following: (1) even in the presence of monetary risks and previously acquired knowledge of the choices, decision-makers tend to deviate from the obvious optimal decision when their peers make a similar decision which we call the influence decision, (2) when the quantity of social signals vary over time, the forwarding probability of the influence decision and therefore being responsive to social influence does not necessarily correlate proportionally to the absolute quantity of signals. To better understand how these rules of peer influence could be used in modeling applications of real world diffusion and in networked environments, we use our behavioral findings to simulate spreading dynamics in real world case studies. We specifically try to see how cumulative influence plays out in the presence of user uncertainty and measure its outcome on rumor diffusion, which we model as an example of sub-optimal choice diffusion. Together, our simulation results indicate that sequential peer effects from the influence decision overcomes individual uncertainty to guide faster rumor diffusion over time. However, when the rate of diffusion is slow in the beginning, user uncertainty can have a substantial role compared to peer influence in deciding the adoption trajectory of a piece of questionable information.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Solar Energy Development on the FSST Reservation

FSST undertook this project to install PV solar with the goal of reducing retail power consumption at 11 Tribal buildings. A combined total of 318kW has been installed over these sites and power savings are being recorded on a regular basis. The Tribe entered into the project with several specific objectives that made this a unique effort. First of all, all of the systems were installed by Tribal maintenance personnel with some technical support. This model had been developed with previous projects that Nebraska Renewable Energy Systems (NRES) had completed and had shown great success. This approach helped to ensure we met the DOE goal of ‘building capacity’ within the Tribe. There was some skepticism about this model in Flandreau at the onset of discussions, but the excellent final results spoke for themselves! A second objective was to overcome the sore lessons that were learned after FSST invested in early deployment of pole mounted solar systems that were not sturdy enough for SD winds. It was a very courageous decision to move forward again with solar pole mounts (and other types) in this very high wind area. We shall report that the Tribe was fully successful in achieving what they set out to do there. The final major objective was to deploy the PV Solar systems in such a way as to integrate them into their surroundings wherever possible. In some cases the mounting choice was clear, but in several locations, the system was designed to be a functional and aesthetically enhancing part of their surroundings. These elevated systems allowed the PV system to act as a shade structure and create useful space under them as well as making power. FSST had these elevated ground mount systems specially designed for our application by Ironridge and were rated for the tough winds of South Dakota (120MPH+).

14 SOLAR ENERGY↗

DOE OSTI2020

Full Concentration Gradient-Tailored Li-Rich Layered Oxides for High-Energy Lithium-Ion Batteries

Lithium-rich layered oxides (LLOs) are prospective cathode materials for next-generation lithium-ion batteries (LIBs), but severe voltage decay and energy attenuation with cycling still hinder their practical applications. In this study, a series of full concentration gradient-tailored agglomerated-sphere LLOs are designed with linearly decreasing Mn and linearly increasing Ni and Co from the particle center to the surface. The gradient-tailored LLOs exhibit noticeably reduced voltage decay, enhanced rate performance, improved cycle stability, and thermal stability. Without any material modifications or electrolyte optimizations, the gradient-tailored LLO with medium-slope shows the best electrochemical performance, with a very low average voltage decay of 0.8 mV per cycle as well as a capacity retention of 88.4% within 200 cycles at 200 mA g –1 . These excellent findings are due to spinel structure suppression, electrochemical stress optimization, and Jahn-Teller effect inhibition. Further investigation shows that the gradient-tailored LLO reduces the thermal release percentage by as much as about 41% when the battery is charged to 4.4 V. This study provides an effective method to suppress the voltage decay of LLOs for further practical utilization in LIBs and also puts forward a bulk-structure design strategy to prepare better electrode materials for different rechargeable batteries.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Demonstrating the β-Ga 2 O 3 Schottky diodes for alpha radiation detection

Schottky barrier diodes were fabricated on (001) monoclinic β-Ga 2 O 3 wafers with low doped epitaxial layers of 7.0 × 10 15 cm −3 . Circular Ni Schottky contacts with area 2 mm 2 were deposited by electron beam evaporation. Devices were characterized electrically by performing forward and reverse current-voltage sweeps with a range of −100 V–2 V, as well as capacitance-voltage sweeps to −30 V. The breakdown voltage was also determined to be −180 V for the devices. Experiments measuring the electrical response from incident X-ray radiation was performed. A response time to X-ray radiation of less than 1 s was recorded and a decay time of approximately 2 s after removing X-ray source, which primarily attribute to X-ray switching on and off time. Energy spectra of alpha particles from a 0.9 μCi 241 Am button source was collected at various voltage biases using devices with the lowest measured leakage current while reverse biased. The total count rate was observed to increase linearly with increasing device bias. In conclusion, the peak channel number was observed to increase with increasing bias with the best resolution of 9.5% at −100 V reverse bias.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2026

Simulation study for particle identification with the dRICH of the ePIC experiment at the EIC

The dual-radiator Imaging Cherenkov detector (dRICH), employing an aerogel and a gas radiator, is a key component of the forward particle identification system for the ePIC experiment at the Electron-Ion Collider (EIC). This study evaluates the dRICH performance using Geant4 simulations in the context of the global ePIC simulation stack, focusing on the optimization of the aerogel radiator and the impact of sensor noise. We compare two aerogel configurations: the initial design (n = 1.019) and the current default (n = 1.026). The latter, characterized by improved optical properties and a higher refractive index, demonstrates enhanced π/K separation at high momenta, effectively extending the operational overlap with the C 2 F 6 gas radiator (n = 1.00076 at 25 °C, as implemented in the simulation software). Additionally, the study investigates the impact of Silicon Photomultiplier (SiPM) dark noise, showing that a 300 kHz noise rate per 3mm x 3mm channel leads to a moderate reduction (approximately 1.5 GeV/c) in the 3σ separation threshold. These results validate the current dRICH design and quantify the purity levels achievable for both radiators under expected experimental conditions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Gravity Well Commercial Economics Assessment: Potential Revenue and Cost: Cooperative Research and Development (Final Report)

In the Gravity Well Revenue Study, we evaluate the potential revenue from energy storage using historical energy-only electricity prices, forward-looking projections of hourly electricity prices, and actual reported revenue. This analysis examines the impact of storage duration and round-trip efficiency, as well as the location of the storage, on storage revenue within the current and projected U.S. power system. We also investigated the impact of round-trip efficiency on storage revenue. We found that the relationship between storage revenue and round-trip efficiency is nonlinear. The value of improved round-trip efficiency declines as round-trip efficiency increases. In the Gravity Well Future Cost Study, we applied learning curves to predict the future cost trajectory of Gravity Wells (GrWs). Two types of analysis were implemented. The first was a bottom-up analysis that used historical learning rates for cost components, such as motors and gearboxes, and cost categories (e.g., engineering and design, etc.) to determine the learning-by-doing based single-factor learning curve. The single factor learning curve expresses the relationship between the cost of GrW and the number of units deployed (or the cumulative capacity). In the second analysis, we predicted future GrW costs via a top-down approach. This approach accounts for historical cost trends in other renewable energy and storage technologies, which have similarities with GrWs. Using a multifactor learning curve that accounts for both intrinsic (cumulative capacity) and extrinsic (the elasticity in the price of steel) factors, we estimated the future cost of GrWs.

25 ENERGY STORAGE↗

DOE OSTI2020

Fermi and Swift Observations of GRB 190114C: Tracing the Evolution of High-energy Emission from Prompt to Afterglow

We report on the observations of gamma-ray burst (GRB) 190114C by the Fermi Gamma-ray Space Telescope and the Neil Gehrels Swift Observatory . The prompt gamma-ray emission was detected by the Fermi GRB Monitor (GBM), the Fermi Large Area Telescope (LAT), and the Swift Burst Alert Telescope (BAT) and the long-lived afterglow emission was subsequently observed by the GBM, LAT, Swift X-ray Telescope (XRT), and Swift UV Optical Telescope. The early-time observations reveal multiple emission components that evolve independently, with a delayed power-law component that exhibits significant spectral attenuation above 40 MeV in the first few seconds of the burst. This power-law component transitions to a harder spectrum that is consistent with the afterglow emission observed by the XRT at later times. This afterglow component is clearly identifiable in the GBM and BAT light curves as a slowly fading emission component on which the rest of the prompt emission is superimposed. As a result, we are able to observe the transition from internal-shock- to external-shock-dominated emission. We find that the temporal and spectral evolution of the broadband afterglow emission can be well modeled as synchrotron emission from a forward shock propagating into a wind-like circumstellar environment. We estimate the initial bulk Lorentz factor using the observed high-energy spectral cutoff. Considering the onset of the afterglow component, we constrain the deceleration radius at which this forward shock begins to radiate in order to estimate the maximum synchrotron energy as a function of time. We find that even in the LAT energy range, there exist high-energy photons that are in tension with the theoretical maximum energy that can be achieved through synchrotron emission from a shock. These violations of the maximum synchrotron energy are further compounded by the detection of very high-energy (VHE) emission above 300 GeV by MAGIC concurrent with our observations. We conclude that the observations of VHE photons from GRB 190114C necessitates either an additional emission mechanism at very high energies that is hidden in the synchrotron component in the LAT energy range, an acceleration mechanism that imparts energy to the particles at a rate that is faster than the electron synchrotron energy-loss rate, or revisions of the fundamental assumptions used in estimating the maximum photon energy attainable through the synchrotron process.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

97 MATHEMATICS AND COMPUTING↗