Multiscale geometric mechanics formulations for GFD parameterization.
Abstract not provided.
Eldred, Christopher↗
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Geometric Mechanics Formulations of Momentum-Based Descriptions for Fluids Using Bundle-Valued Differential Forms
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Eldred, Christopher↗
W24-09 Geometric Mechanics Formulations and Structure Preserving Discretizations: An Introductory Course
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Eldred, Christopher↗
Geometric mechanics, (physics-dynamics) coupling and multiscale models
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Eldred, Christopher↗
Differential geometric approaches to momentum-based formulations for fluids [Slides]
This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Constraints on a generalization of geometric quantum mechanics from neutrino and B0-$$ \overline{B^0} $$ oscillations
Abstract Nambu Quantum Mechanics, proposed in Phys. Lett. B536, 305 (2002), is a deformation of canonical Quantum Mechanics in which the manifold over which the “phase” of an energy eigenstate time evolves is modified. This generalization affects oscillation and interference phenomena through the introduction of two deformation parameters that quantify the extent of deviation from canonical Quantum Mechanics. In this paper, we constrain these parameters utilizing atmospheric neutrino oscillation data, andB 0 -$$ \overline{B^0} $$ B 0 ¯ oscillation data from Belle. Surprisingly, the bound from atmospheric neutrinos is stronger than the bound from Belle. Various features of Nambu Quantum Mechanics are also discussed.
Physics↗
Heterogeneous microstructural evolution during hydrodynamic penetration of a high-velocity copper microparticle impacting copper
Microparticle hydrodynamic penetration (HDP) may be associated with the erosion regime in cold spray processing and other high-velocity impact events. Here, in an experimental approach where we can individually launch particles and study the impact sites, we explore copper microparticles impacted on copper substrates at velocities above 900 m/s where HDP begins. We lift cross-sectional lamellae from the impact sites with a focused-ion beam for further microstructural characterization using electron backscatter diffraction and scanning transmission electron microscopy. Due to the gradients of strain, strain rate, and temperature associated with HDP, heterogeneous microstructures result. The structural evolution processes observed include deformation twinning and multiple dislocation-mediated grain recrystallization mechanisms—geometric dynamic recrystallization (gDRX), discontinuous DRX (dDRX), and meta DRX (mDRX). The higher strains at the interface lead to the most significant structural changes and complex mechanisms. In contrast, there is a gradient to more conventional dislocation plasticity away from the interface (on either the particle or substrate side). Here, these microstructural observations are consistent with the deformation map for copper and extend the observations of impact-induced recrystallization across new regimes of behavior.
Cold spray process↗
Time-refraction near the critical angle and angular streaking with attosecond resolution [Invited]
We study the time-refraction of optical waves as they propagate through a time-varying slab and find the frequency shift associated with the abrupt change in the refractive index. We discover a geometrical mechanism responsible for an ultrafast blueshift followed by a redshift, occurring while the refractive index is increased monotonically. Furthermore, we find high sensitivity to incident angles near the traditional critical angle and unravel a new critical angle that varies in time. Finally, we introduce an innovative concept of a streak camera design that utilizes ultrafast nonlinearities in time-varying media and offers attosecond resolution capabilities.
Fruhling, Colton (ORCID:0000000282968802)↗
Quantum and Classical Ergotropy from Relative Entropies
The quantum ergotropy quantifies the maximal amount of work that can be extracted from a quantum state without changing its entropy. Given that the ergotropy can be expressed as the difference of quantum and classical relative entropies of the quantum state with respect to the thermal state, we define the classical ergotropy, which quantifies how much work can be extracted from distributions that are inhomogeneous on the energy surfaces. A unified approach to treat both quantum as well as classical scenarios is provided by geometric quantum mechanics, for which we define the geometric relative entropy. The analysis is concluded with an application of the conceptual insight to conditional thermal states, and the correspondingly tightened maximum work theorem.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Geometric learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity
The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. The difficulty to interpret how these internal variables represent a history of deformation, the lack of direct measurement of these internal variables for calibration and validation, and the weak physical underpinning of those phenomenological laws have long been criticized as barriers to creating realistic models. In this work, geometric machine learning on graph data (e.g. finite element solutions) is used as a means to establish a connection between nonlinear dimensional reduction techniques and plasticity models. Geometric learning-based encoding on graphs allows the embedding of rich time-history data onto a low-dimensional Euclidean space such that the evolution of plastic deformation can be predicted in the embedded feature space. Finally, a corresponding decoder can then convert these low-dimensional internal variables back into a weighted graph such that the dominating topological features of plastic deformation can be observed and analyzed.
42 ENGINEERING↗
In Cell Thermal Creep Frames for Demonstration Project Preparations
The thrust of advanced nuclear reactor demonstrations demands the accelerated qualification of in-core materials to enable licensing processes and developing the performance data. Due to the high-operating temperatures of such reactors, long-term mechanical behavior under constant load is essential to determine the geometrical and mechanical integrity of in-core components during operation and off-normal conditions. Therefore, the thermal creep behavior of neutron-irradiated advanced reactor materials must be determined. The feasibility of using subsize specimens for the irradiation campaigns and the limited available infrastructure challenge the assessment of thermal creep behavior of advanced reactor materials. Therefore, the U.S. Department of Energy Office of Nuclear Energy (DOE-NE) National Reactor Innovation Center (NRIC) prioritizes the development of a thermal creep testing infrastructure for multiple subsize specimens to accelerate the demonstration and deployment of advanced reactor concepts. This report describes the activities for the construction of a thermal creep testing capability at Idaho National Laboratory (INL). The overall project consists of conceptual design, out-of-cell demonstration, and in-cell demonstration phases. During fiscal year (FY)-2021, the team finished the conceptual design of a thermal creep test facility that can test multiple subsize specimens. This conceptual design consisted of the determination of technical and functional requirements, the determination of the design space, and the preparation of the technical drawings. Technical and functional requirements were categorized as required and desired capabilities and the conceptual design was performed to meet all the required capabilities with the flexibility to achieve the desired capabilities. The design space identified the operational capacity of the creep frame for different advanced reactor relevant materials with the consideration of the feasible operation in the hotcell at the Fuels and Applied Science Building (FASB) at INL. Based on the requirements and design space, the multiple specimen creep frame was designed. The official INL engineering drawing process was started and the procurement of materials for construction was initiated. For FY-2022, the out-of-cell demonstration and final installation of the multiple creep frame is planned.
36 MATERIALS SCIENCE↗
Effect of LPBF Processing Parameters on Inconel 718 Lattice Structures: Geometrical Characteristics, Surface Morphology, and Mechanical Properties
Laser Powder Bed Fusion (LPBF) enables the additive manufacturing of complex lattice structures. However, the fabrication of lattice structures via LPBF poses challenges in achieving the intended geometrical accuracy due to their inherent complexity. This study investigates the effects of LPBF processing parameters, specifically laser power and scanning speed, on the geometrical characteristics, surface quality, and mechanical behavior of Inconel 718 lattices structures. The results reveal that processing parameters required for the fabrication of near-full dense structures do not translate effectively to lattice configurations, as variations in energy input influence lattice geometry and surface quality. In this work, strut thickness, open-pore size, open-cell porosity, and surface roughness were measured, and the mechanical properties of the lattices were evaluated under shear loading. The findings indicate that lower energy inputs, achieved by reducing laser power and increasing scanning speed, yield porous structures but lead to mechanical degradation. In contrast, high energy inputs lead to lattices with enhanced strength but result in undesirable open-pore blockage and dimensional inaccuracies. These findings provide insights into tailoring LPBF parameters for dimensional accuracy in lattices and correlating the processing parameters to mechanical performance and surface roughness.
36 MATERIALS SCIENCE↗
Penta-SiCN: A Highly Auxetic Monolayer
We report the negative Poisson’s (NPR) ratio in a two-dimensional (2D) material is a counterintuitive mechanical property that facilitates the development of nanoscale devices with sophisticated functionality. Inspired by the peculiar buckled lower-symmetric, trilayered geometry of pentagonal monolayers, we theoretically predict penta-SiCN, a ternary auxetic metallic monolayer with highly tunable NPR. The penta-SiCN is structurally, thermally, dynamically, and mechanically stable, and sustainable at and beyond room temperature with experimental feasibility. It possesses nontrivial geometrical and mechanical isotropy and relatively moderate thickness. Remarkably, the shorter and quasi sp3-hybridized C–N bond and the rigidity against the strain allow the monolayer to possess a high value of NPR (-0.136), even higher than that of black phosphorene, extendable up to -0.639 by 4% of biaxial stretching. On the other hand, the 2D Young’s modulus of 129.88 N/m decreases to 41.34 N/m at equivalent stretching, indicating relative softening and flexibility. Interestingly, a buckled-to-planar phase transition is identified at 10% biaxial strain before it suffers the fracture at 16%. Additionally, the strong optical anisotropy, absorbance (up to 6.51 x 105 cm -1 ), and presence of plasmon frequency demonstrate its potential application in optomechanical and plasmonics.
36 MATERIALS SCIENCE↗
Dependence of high- Z redeposition on the field-to-surface pitch angle and other sheath parameters in tokamaks
Accurately predicting redeposition is vital for high-Z plasma-facing component (PFC) survivability in magnetic confinement fusion. In this study, we categorize high-Z redeposition into three mechanisms: geometric-driven (prompt), sheath-driven (local), and scrape-off-layer-driven (far) redeposition. To investigate these mechanisms, we employ Monte Carlo transport codes to simulate azimuthally symmetric tungsten source erosion and redeposition in a tokamak. By iteratively analyzing critical parameters, we evaluate redeposition scaling for each mechanism. Specifically, we investigate the impact of magnetic-field-to-PFC pitch angle assumptions on PFC losses into the scrape-off layer. Our findings reveal significant pitch angle sensitivity due to an asymmetric prompt vs local redeposition trade-off. These results enhance our understanding of redeposition phenomena in fusion plasma environments.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Geometric Event-Based Quantum Mechanics
In this work, we propose a special relativistic framework for quantum mechanics. It is based on introducing a Hilbert space for events. Events are taken as primitive notions (as customary in relativity), whereas quantum systems (e.g. fields and particles) are emergent in the form of joint probability amplitudes for position and time of events. Textbook relativistic quantum mechanics and quantum field theory can be recovered by dividing the event Hilbert spaces into space and time (a foliation) and then conditioning the event states onto the time part. Our theory satisfies the full Lorentz symmetry as a ‘geometric’ unitary transformation, and possesses relativistic observables for space (location of an event) and time (position in time of an event).
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Scalable preconditioning for the stabilized contact mechanics problem
We present a family of preconditioning strategies for the contact problem in fractured and faulted porous media. We combine low-order continuous finite elements to simulate the bulk deformation with piecewise constant Lagrange multipliers to impose the frictional contact constraints. This formulation is not uniformly inf-sup stable and requires stabilization. We improve previous work by Franceschini et al. (2020) by introducing a novel jump stabilization technique that requires only local geometrical and mechanical properties. We then design scalable preconditioning strategies that take advantage of the block structure of the Jacobian matrix using a physics-based partitioning of the unknowns by field type, namely displacement and Lagrange multipliers. The key to the success of the proposed preconditioners is a pseudo-Schur complement obtained by eliminating the Lagrange multiplier degrees of freedom, which can then be efficiently solved using an optimal multigrid method. Numerical results, including complex real-world problems, are presented to illustrate theoretical properties, scalability and robustness of the preconditioner. A comparison with other approaches available in the literature is also provided.
58 GEOSCIENCES↗
Geometrically Necessary Dislocation Analysis of Deformation Mechanism for Magnesium under Fatigue Loading at 0 °C
This study focused on the analysis of geometrically necessary dislocation (GND) densities for five selected fine-grained magnesium samples. Among the samples, three were tested under different fatigue-loading conditions at 0 °C, one experienced quasi-static tensile loading at 0 °C, and one represented the as-rolled state. The fatigue-tested samples were chosen according to the relationship between the maximum loading stress of a test and the material’s yield strength. This study provides new insights on the deformation mechanism of fine-grained magnesium at 0 °C. It is observed that the average GND densities were increased by 95~111% for the tested samples when compared with the as-rolled sample. It is especially interesting that there is a significant increase in the average GND density for the sample that experienced the fatigue loading with a low-maximum applied stress, and the maximum applied stress was lower than the material’s yield strength. This observation implies that the grain boundary mediated the dislocation-emission mechanism.
Li, Qizhen↗
An extended numerical manifold method for unsaturated soil-water interaction analysis at micro-scale
To investigate unsaturated soil-water interaction at micro-scale, this work extends the numerical manifold method (NMM) by incorporating a soil-water coupling model considering specific capillary water distribution and capillary force calculation. The soil skeleton is constructed by a soil skeleton generation algorithm with random polygons. To more realistically capture the interaction between soil grains and capillary water, a capillary mechanics-based geometric algorithm is proposed to iteratively calculate the capillary water distribution. The capillary forces corresponding to the capillary water distribution are calculated based on the Young-Laplace equation. The proposed capillary water solving framework is first verified by reproducing the soil-water characteristic curve and the capillary water distribution of an ideal contact-disk model against analytical solutions. To further validate the ability of the capillary water solving framework to predict hydraulic behavior of the real soil, a laboratory test on the Toyoura sand is reproduced numerically. Then an ideal direct shear test is performed to further validate the two-way soil-water coupling procedure, in which a comparison between the numerical and analytical results regarding the shear strength and matric suction is presented. Finally, microscopic hydraulic and compression tests are conducted on two soil specimens with the same porosity and mean grain diameter but different uniformity coefficients. The results elucidate that the extended method is a potential tool to explore unsaturated soil behaviors at micro-scale.
58 GEOSCIENCES↗