Complex Couplings and Simple Springs: Analysis of Model-Form Error for Highly Nonlinear Oscillatory Systems
Explore the source record for details and available documents.
Bandy, Rileigh Jade↗
SEARCH · Engineering Papers
Results for “Nonlinear models”
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.
Coupled Experimental/Computational Investigation of the Dynamics of Interacting Magnetized Plasmas
The interaction, or interpenetration, of magnetized plasmas of different density and/or pressure occurs in a wide variety of natural and man-made systems. Such systems include extragalactic jets propagating into the intergalactic medium, solar coronal mass ejections into background solar wind, compact toroid (CT) fueling of magnetic fusion plasmas, and jets of capsule shell impurities into DT fusion fuel, which can lead to enhanced impurity mix in inertial fusion implosions. These plasmas may take the form of jets, with open, helical magnetic structure, or plasma “bubbles” with closed magnetic fields (B-fields), such as spheromaks or CT’s. Such structures, both open and closed B-field cases, can transport heat, particles and magnetic flux or magnetic helicity into background plasma regions. For example, the origin of extragalactic magnetic fields may be due, at least in part, to transport by astrophysical jets. The goal of this proposed work was to elucidate the detailed plasma and magnetic field dynamics of high-density plasma jets (open B-field) and bubbles (closed B-field) propagating into lower density background magnetized plasma through controlled laboratory experiments and closely coupled nonlinear MHD modeling. These experiments were conducted in the HelCat (Helicon-Cathode) linear plasma device at the University of New Mexico (UNM). Plasma jets and bubbles were launched via an existing compact coaxial plasma gun, mounted on the HelCat device. This gun produced plasmas tens of cm in scale and lasting tens of microseconds, thereby allowing detailed multipoint, space- and time-resolved measurements to be made routinely. The experiments were directly modeled using the extended magnetohydrodynamic (XMHD) PERSEUS code, developed at Cornell University [23,24]. Both experimental and numerical modeling work are ongoing. The main results to date are reported here. Additional supplemental funding for one year (8/1/2019 – 7/31/2020) supported numerical investigation of photoionization processes important in many low temperature plasmas, including the HelCat device. Initial results of this modeling work is also reported.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Harmonic balance based methodology for reduced order modeling to predict response of nonlinear structures
Explore the source record for details and available documents.
Khan, Moheimin Yar↗
Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers
Liquid crystal elastomers (LCEs) are responsive materials that can undergo large reversible deformations upon exposure to external stimuli, such as electrical and thermal fields. Controlling the alignment of their liquid crystals mesogens to achieve desired shape changes unlocks a new design paradigm that is unavailable when using traditional materials. While experimental measurements can provide valuable insights into their behavior, computational analysis is essential to exploit their full potential. Accurate simulation is not, however, the end goal; rather, it is the means to achieve their optimal design. Such design optimization problems are best solved with algorithms that require gradients, i.e., sensitivities, of the cost and constraint functions with respect to the design parameters, to efficiently traverse the design space. In this work, a nonlinear LCE model and adjoint sensitivity analysis are implemented in a scalable and flexible finite element-based open source framework and integrated into a gradient-based design optimization tool. To display the versatility of the computational framework, LCE design problems that optimize both the material, i.e., liquid crystal orientation, and structural shape to reach a target actuated shapes or maximize energy absorption are solved. Multiple parameterizations, customized to address fabrication limitations, are investigated in both 2D and 3D. The case studies are followed by a discussion on the simulation and design optimization hurdles, as well as potential avenues for improving the robustness of similar computational frameworks for applications of interest.
42 ENGINEERING↗
Positron Beam Loading and Acceleration in the Blowout Regime of a Plasma Wakefield Accelerator
Plasma wakefield acceleration in the nonlinear blowout regime has achieved marked milestones in electron beam acceleration, demonstrating high acceleration gradients and energy efficiency while preserving excellent beam quality. However, this regime is deemed unsuitable for achieving positron acceleration of comparable results, which is vital for future compact electron–positron colliders. In this article, we find that an intense positron beam loaded at the back of beam-driven blowout cavity can self-consistently induce the focusing field and flatten the longitudinal wakefield, leading to stable, high-efficiency, and high-quality positron acceleration. This is achieved through the formation of an on-axis electron filament induced by positron beam load, which shapes the plasma wakefield in a distinct way compared to electron beam load in the blowout regime. Via a nonlinear analytic model and numerical simulations, we explain the novel beam loading effects of the interaction between the on-axis filament and the blowout cavity. High-fidelity simulations show that a high-charge positron beam can be accelerated with >20% energy transfer efficiency, ~1% energy spread, and ~1 mm·mrad normalized emittance, while considerably depleting the energy of the drive beam. The concept can also be extended to simultaneous acceleration of electron and positron beams and high transformer ratio positron acceleration as well. This development offers a new route for the application of plasma wakefield acceleration into particle physics.
Science & Technology - Other Topics↗
Parametric Model Order Reduction for Localized Nonlinear Feature Inclusion.
Abstract not provided.
Vlachas, Kostantinos↗
Dynamic Characterization and Performance Evaluation of a 10-kw Power Take-Off with Mechanical Motion Rectifier for Wave Energy Conversion
The power take-off (PTO) is a key component for wave energy converters (WECs). The dynamic properties of the PTO influence the response of the WEC and should be considered when designing the WEC and not oversimplified. In addition, the efficiency as well as the reliability can play an important role on whether the PTO can be suitable for real-world applications. In this paper, a novel compact PTO rated at 10 kW is designed and prototyped, and a comprehensive nonlinear dynamic model is established for the PTO. Through bench testing, the unknown parameters of the dynamic model are characterized and determined. Further verification shows that the model can predict the dynamic performance of the PTO well. In addition, the test results show that the mechanical motion rectifier PTO can achieve good energy transfer efficiency, especially for low-load and low-speed conditions.
bench test↗
Quantum computation of mass gap in an asymptotically free theory
In relativistic field theories, the mass spectrum is given by the difference between the energy of the vacuum and the excited states. Near the continuum limit, the cancellation between these two values leads to loss of precision. We propose a method to extract the mass gap directly using quantum computers and apply it to a particular version of the nonlinear $σ$-model with the correct continuum limit and perform calculations in quantum hardware (at strong coupling) and simulation in classical computers (at weak coupling).
Bedaque, Paulo F. [Maryland U.] (ORCID:00000001521↗
Harmonic balance based methodology for reduced order modeling to predict response of nonlinear structures
Conference paper for ISMA 2024
Khan, Moheimin Yar↗
Theoretical study of various nonlinear phenomena in plasma systems and scaling of magneto-inertial-fusion targets
Plasma physics is an exciting field of study with a wide variety of nonlinear processes that come into play. Examples of such processes include the interaction of small-scale turbulence with large-scale plasma structures and the nonlinear saturation of plasma instabilities, for example those of magneto-hydrodynamical nature. During this Truman LDRD project, I studied a collection of nonlinear problems that are of interest to the field of plasma physics. This LDRD report summarizes four main research accomplishments. First, a new statistical model for describing inhomogeneous drift-wave turbulence inter- acting with zonal flows was developed. This new model includes the effects of nonlinear wave-wave collisions, which are expected to change the spectrum of the underlying DW turbulence and therefore the generation of zonal flows. Second, a new mathematical formalism was proposed to systematically apply the non- linear WKB approximation to general field theories, including those often used in fluid dynamics. This formalism represents an interesting tool for studying physical systems that show an explicit scale separation. Third, a weakly nonlinear model was developed to describe the magneto-Rayleigh-Taylor instability. This instability is of paramount importance to understand as it can reduce the performance of magnetic-inertial-fusion (MIF) platforms. The developed models captures the effects of harmonic generation and saturation of the linear growth of the instability. Finally, a framework was proposed for scaling magneto-inertial fusion (MIF) targets to larger pulsed-power drivers. From this framework, a set of scaling rules were derived that conserve the physical regimes of MIF systems when scaling up in peak current. By doing so, deleterious nonlinear processes that affect MIF performance may be kept at bay.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Connecting relativistic density functional theory to microscopic calculations
The development of systematic effective field theories (EFTs) for nuclear forces and advances in solving the nuclear many-body problem have greatly improved our understanding of dense nuclear matter and the structure of finite nuclei. For global nuclear calculations, density functional theories (DFTs) have been developed to reduce the complexity and computational cost required in describing nuclear systems. However, DFT often makes approximations and assumptions about terms included in the functional, which may introduce systematic uncertainties compared to microscopic calculations using EFTs. In this work, we investigate possible avenues of improving nuclear DFT using nonlinear relativistic mean-field (RMF) theory. We explore the impact of RMF model extensions by fitting the nonlinear RMF model to predictions of nuclear matter and selected closed-shell nuclei using four successful chiral EFT Hamiltonians. We find that these model extensions are impactful and important in capturing the physics present within chiral Hamiltonians, particularly for charge radii and neutron skins of closed-shell nuclei. However, there are additional effects that are not captured within the RMF model, particularly within the isoscalar sector of RMF theory. Additional model extensions and the reliability of the nonlinear RMF model are discussed.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Direct Estimation of Parameters in ODE Models Using WENDy: Weak-Form Estimation of Nonlinear Dynamics
Abstract We introduce the Weak-form Estimation of Nonlinear Dynamics (WENDy) method for estimating model parameters for non-linear systems of ODEs. Without relying on any numerical differential equation solvers, WENDy computes accurate estimates and is robust to large (biologically relevant) levels of measurement noise. For low dimensional systems with modest amounts of data, WENDy is competitive with conventional forward solver-based nonlinear least squares methods in terms of speed and accuracy. For both higher dimensional systems and stiff systems, WENDy is typically both faster (often by orders of magnitude) and more accurate than forward solver-based approaches. The core mathematical idea involves an efficient conversion of the strong form representation of a model to its weak form, and then solving a regression problem to perform parameter inference. The core statistical idea rests on the Errors-In-Variables framework, which necessitates the use of the iteratively reweighted least squares algorithm. Further improvements are obtained by using orthonormal test functions, created from a set of $$C^{\infty }$$ C ∞ bump functions of varying support sizes.We demonstrate the high robustness and computational efficiency by applying WENDy to estimate parameters in some common models from population biology, neuroscience, and biochemistry, including logistic growth, Lotka-Volterra, FitzHugh-Nagumo, Hindmarsh-Rose, and a Protein Transduction Benchmark model. Software and code for reproducing the examples is available at https://github.com/MathBioCU/WENDy .
97 MATHEMATICS AND COMPUTING↗
Nonlinear proper orthogonal decomposition for convection-dominated flows
Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Galaxy bias in the era of LSST: perturbative bias expansions
Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the Rubin Observatory Legacy Survey of Space and Time (LSST) bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Year 10 (Y10) data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian perturbation theory (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. Here, we consider a variety of different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of k max = 0.4 Mpc -1 for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data.
79 ASTRONOMY AND ASTROPHYSICS↗
A Spectacular Viscoelastic Model Calibration for 828/D230/Alox Generated from Legacy Sandia Data
The nonlinear viscoelastic Spectacular model is calibrated to the thermo-mechanical behavior of 828/D230/Alox with an alox volume fraction of 20 %. Legacy experimental data from Sandia’s polymer properties database (PPD) is used to calibrate the model. Based on known densities of the epoxy 828/D230 and the alox filler, the alox volume fractions listed on the PPD were likely reported incorrectly. The alox volume fractions are recalculated here. Using the recalculated alox volume fractions, the PPD contains experimental data for 828/D230/Alox with alox volume fractions of 16 %, 24 %, and 33 %, so the thermo-mechanical behavior at 20 % alox volume fraction is estimated by interpolating between the bounding cases of of 16 % and 24 %. Because the Spectacularmodel can be fairly challenging to calibrate, the calibration procedure is described in detail. Several of the calibration steps involve inverse parameter identification, where an experiment is simulated and parameters are iteratively updated until the model response matches the experimental data. As the PPD does not fully describe all experimental procedures, the experimental simulations use assumed thermal and mechanical loading rates that are typical for the viscoelastic characterization of epoxies. Spectacular uses four independent relaxation functions related to volumetric (ƒ 1 ), shear (ƒ 2 ), thermal strain (ƒ 3 ), and thermal relaxations (ƒ 4 ). The previous SPEC model form, also known as the universal_polymer model, uses two independent relaxation functions related to volumetric and thermal relaxation (ƒ ν = ƒ 1 = ƒ 3 = ƒ 4 ) and shear relaxation (ƒ s = ƒ 2 ). The two constitutive choices are briefly evaluated here, where it is found that the four relaxation function approach of Spectacular was better suited for fitting the coefficient of thermal expansion during both heating and cooling.
36 MATERIALS SCIENCE↗
Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference
Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.
97 MATHEMATICS AND COMPUTING↗
First‐Order Empirical Interpolation Method for Real‐Time Solution of Parametric Time‐Dependent Nonlinear PDEs
ABSTRACT We present a model reduction approach for the real‐time solution of time‐dependent nonlinear partial differential equations (PDEs) with parametric dependencies. A major challenge in constructing efficient and accurate reduced‐order models for nonlinear PDEs is the efficient treatment of nonlinear terms. We address this by unifying the implementation of hyperreduction methods to deal with nonlinear terms. Furthermore, we introduce a first‐order empirical interpolation method (EIM) to provide an efficient approximation of the nonlinear terms in time‐dependent PDEs. We demonstrate the effectiveness of our approach on the Allen–Cahn equation, which models phase separation, and the Buckley–Leverett equation, which describes two‐phase fluid flow in porous media. Numerical results highlight the accuracy, efficiency, and stability of the proposed method compared with both the Galerkin–Newton approach and hyper‐reduced models using the standard EIM.
Nguyen, Ngoc Cuong [Center for Computational Engin↗
ForceGen: End-to-end de novo protein generation based on nonlinear mechanical unfolding responses using a language diffusion model
Through evolution, nature has presented a set of remarkable protein materials, including elastins, silks, keratins and collagens with superior mechanical performances that play crucial roles in mechanobiology. However, going beyond natural designs to discover proteins that meet specified mechanical properties remains challenging. Here, we report a generative model that predicts protein designs to meet complex nonlinear mechanical property-design objectives. Our model leverages deep knowledge on protein sequences from a pretrained protein language model and maps mechanical unfolding responses to create proteins. Via full-atom molecular simulations for direct validation, we demonstrate that the designed proteins are de novo, and fulfill the targeted mechanical properties, including unfolding energy and mechanical strength, as well as the detailed unfolding force-separation curves. Our model offers rapid pathways to explore the enormous mechanobiological protein sequence space unconstrained by biological synthesis, using mechanical features as the target to enable the discovery of protein materials with superior mechanical properties.
59 BASIC BIOLOGICAL SCIENCES↗