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At least 1,045 records · Page 58

Control of Vibration Systems with Mechanical Motion Rectifier and their Applications to Vehicle Suspension and Ocean Energy Harvester

Vibration control is a large branch in control research, because all moving systems may induce desired or undesired vibration. Due to the limitation of passive system’s adaptability and changing excitation input, vibration control brings the solution to change system dynamic with desired behavior to fulfill control targets. According to preference, vibration control can be separated into two categories: vibration reduction and vibration amplification. Lots of research papers only examine one aspect in vibration control. The thesis investigates the control development for both control targets with two different control applications: vehicle suspension and ocean wave energy converter. It develops control methods for both systems with simplified modeling setup, then followed by the application of a novel mechanical motion rectifier (MMR) gearbox that uses mechanical one-way clutches in both systems. The flow is from the control for common system to the control design for a specifically designed system. In the thesis, active (model predictive control: MPC), semi-active (Skyhook, skyhook-power driven damper: SHPDD, hybrid model predictive control: HMPC), and passive control (Latching Control) methods are developed for different applications or control performance comparison on single system. The thesis also studies about new type of system with switching mechanism, in which other papers do not talk too much and possible control research direction to deal with such complicated system in vibration control. The state-space modeling for both systems are provided in the thesis with detailed model of the MMR gearbox. From the simulation, it can be shown that in the vehicle suspension application, the controlled MMR gearbox can be effective in improving vehicle ride comfort by 29.2% compared to that of the traditional hydraulic suspension. In the ocean wave energy converter, the controlled MMR WEC with simple latching control can improve the power generation by 57% compared to the passive MMR WEC. Besides, the passive MMR WEC also shows its advantage on the passive direct drive WEC in power generation improvement. From the control development flow for the MMR system, the limitation of the MMR gearbox is also identified, which introduces the future work in developing active-MMR gearbox by using an electromagnetic clutch. Some possible control development directions on the active-MMR is also mentioned at the end of the thesis to provide reference for future works.

16 TIDAL AND WAVE POWER↗

Mechanical Properties of Aged A709

A709 plate is in the process of being developed and qualified through a collaboration by Argonne National Laboratory (ANL), Idaho National Laboratory (INL), and Oak Ridge National Laboratory (ORNL). The goal is to qualify A709 plate in Section III, Division 5 of the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code (BPVC). This would permit the construction of A709 plate for fast-reactor structural applications. A tradeoff between creep and creep-fatigue properties was established in prior work. A processing route was identified as providing the optimal balance between creep-rupture and elevated-temperature cyclic properties for the solution annealed condition. This condition, however, resulted in a shorter than desired creep-rupture life. Aging is probed to evaluate its potential at further improving mechanical properties. Aging statically precipitates the solutes in solution prior to service. The processing routes identified as providing the best creep-rupture properties and best balance in mechanical properties are investigated. This report discloses the results from tensile, creep, and elevated-temperature cyclic testing performed at INL on the aged material. The aged properties are compared to solution annealed properties. A709 offers improvement in performance compared to 316H particularly at high temperatures; 316H is a material qualified in Section III, Division 5 of the ASME BPVC. For certain high-temperature fast-reactor design conditions, 316H cannot be used while A709 can.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Ultrasensitive thermo-mechanical bolometer

A thermo-mechanical bolometer includes a substrate and a sensing component mounted on the substrate. The sensing element comprises (a) at least one thermal-actuation component mounted in parallel with the substrate and (b) a strain sensor mounted on the at least one layer of thermal-actuation component. The at least one thermal-actuation component alone or in combination (a) absorbs electromagnetic waves and converts energy from absorbed electromagnetic waves into a change in temperature and (b) converts the change in temperature into a deformation of the at least one layer. The strain sensor comprises a layer of fragments with a gap space between the fragments, wherein the strain sensor senses the deformation or mechanical movement and exhibits a change in electrical resistance in response to the sensed deformation or mechanical movement.

Lin, Yuxuan↗

Autoignition of Premixed Liquefied Petroleum Gas in a Rapid Compression Machine: Experimental Results and Chemical Kinetic Mechanism Reduction

Liquefied petroleum gas (LPG) has many properties that make it an attractive alternative fuel such as lower cost than conventional fuels and an established distribution infrastructure. The development of high efficiency, spark ignited LPG engines is currently limited by engine knock and misfire. The knock and misfire limits are further complicated by the wide range of chemical reactivity in LPG, particularly in international markets. In this study, a rapid compression machine (RCM) was used to characterize the effects of variation in LPG fuel reactivity, equivalence ratio, and exhaust gas recirculation (EGR) on autoignition of LPG/oxidizer/inert/EGR blends. Experiments were conducted with 100% propane (C3H8) and blends of propane with propene, ethane, isobutane, and n-butane. EGR was simulated with mixtures of Ar, CO2, CO, and NO at substitution percentages from 0 to 30 mass percent. Equivalence ratio was varied from 0.75 to 1.5. Ignition delay period under homogeneous autoignition conditions was measured at compressed pressures and temperatures of 23 to 25 bar and 701 to 921 K, respectively. Zero-dimensional simulations of the RCM experiments were performed using Chemkin with several detailed chemical kinetic mechanisms to determine their suitability at predicting ignition delay periods. Multiple reduced chemical kinetic mechanisms were created from the NUIGMech1.1 mechanism to determine the optimal balance between accuracy and computational efficiency for future three-dimensional, time-dependent spark-ignited engine computations.

42 ENGINEERING↗

Study on Emulsification/Demulsification Behavior and Mechanism of Produced Liquid from Polymer Flooding on Alaska North Slope

Heavy oil reservoirs on Alaska North Slope (ANS) are unconsolidated and contain abundant clay minerals, where the first-ever field pilot is currently implemented to validate the use of polymer floods for heavy oil enhanced oil recovery (EOR). The polymer molecules and/or fine clay particles carried with the produced liquid could potentially affect the oil/water separation, which is one of the major concerns for field operators. This dissertation aims to investigate the emulsification behavior of produced liquid, understand the emulsifying mechanism, and seek an adaptive and cost-effective method to treat the produced liquid from polymer flooding. Emulsions were prepared by mechanically mixing the actual heavy oil and the produced water from the pilot site, of which the stability was investigated by bottle test method or multiple light scattering method. Drop size distribution and interfacial properties were measured via microscope and pendant drop technique to probe the stability mechanism further. Results showed that oil-continuous or water-continuous emulsion could be generated depending on the water cut, clay types, clay concentration, and polymer concentration. In the crude oil/water system, the increasing water cut triggered the phase inversion of oil-continuous emulsion to water-continuous emulsion, resulting in faster separation and lower emulsion stability. Whereas, clay particles, no matter added to the oil or water phase, resulted in an unfavorable phase inversion from the loose water-continuous emulsion to the tight oil-continuous emulsion as clay concentration increased. For all four types of clay except Ca-montmorillonite, clay particles added to water led to an earlier phase inversion and higher emulsion stability than that added to the oil. The dual function of polymer on emulsion stability was observed. On the one hand, both sheared and unsheared polymer tended to convert the oil-continuous emulsion formed in either crude oil/water system or complex crude oil/water/clay particle system to the water-continuous emulsion, acting as a weak demulsifier to accelerate the oil/water separation. On the other hand, the addition of polymer to the water-continuous emulsion could result in enhanced emulsion stability, which is primarily attributed to the increased viscosity of the continuous phase and the decreased drop size of the dispersed oil phase. Particularly, the sheared polymer had a weaker ability to stabilize the o/w emulsion than the unsheared polymer due to the lower viscosity of the sheared polymer solution resulting from the breakdown of the polymer macromolecules. As for the chemical demulsification tests, the performance of demulsifiers showed a complex dependency upon the water cut, the shearing intensity, demulsifier type and dosage, and the polymer concentration. A compound emulsion breaker, E12+E18, exhibited the most satisfactory demulsification performance despite the varied test conditions. For severe water-continuous emulsions that might require a multi-fold dosage of demulsifier, a less expensive electrolyte, KCl, was proposed to be used in combination with demulsifier E12+E18 to improve the demulsification performance. In the proposed demulsifier formula, the effectiveness of the commercial demulsifier relied on its destructive effect on the interfacial film, while the efficacy of KCl was mainly dependent on its viscosity reduction effect on the continuous phase. This dissertation illustrates that intermediate layer elimination and water clarification are the major challenges for produced liquid treatment from polymer flooding. It also provides practical and theoretical guidance in advance for the demulsification strategy of the produced liquid from the ongoing first-ever polymer flooding pilot on ANS.

Chang, Hongli↗

Superconducting Magnet System Concept with a Mechanical Energy Transfer in the Magnetic Field

There is an interest to design superconducting magnet systems working in a persistent current mode. These systems continuously generate magnetic field with disconnected power source working like permanent magnet devices. In this paper proposed a magnet system concept based on the direct mechanical energy transfer in the magnetic field. Short circuited superconducting coils do not have current leads and power source. To pump the mechanical energy in the superconducting coil used a magnetizer which magnetically coupled with the coil. The mechanical removing the magnetizer from the magnet induces a persistent current in the superconducting coil which generates the magnetic field. Iron dominated magnet system concept was investigated using OPERA3d code which confirmed a visibility of proposed approach.

43 PARTICLE ACCELERATORS↗

Meshfree Methods for Modeling Chemo-Mechanical Cathode Cracking in Li-Ion Batteries

Through repeated charging and discharging, the electrodes of a Li-ion battery experience cyclic loading causing swelling and contraction due to the movement of lithium, also known as intercalation. This research focuses specifically on the chemo-mechanical cracking in the cathode. Because cathode particles are comprised of many randomly-oriented grains, which have highly anisotropic material properties, the expansion and contraction is very non-uniform. As a result, stress concentrations tend to form between grains, which necessitates the modeling of crack propagation largely along grain boundaries. Chemo-mechanical models are simulated mainly by two methods: the cohesive zone model (CZM) and the continuous damage model (CDM). The CZM is more accurate at capturing the sharp discontinuities of a crack but is very computationally expensive and intractable for large-scale models as a result. Conversely, the CDM is easily computed but not well-suited to easily allow for discontinuous field variables, which are inherent across a crack. This study aims to improve the CDM's ability to capture discontinuous cracks. Current versions of the CDM use the finite element method (FEM), which is one of the most widely used approaches for spatial discretization. This research investigates the use of the Reproducing Kernel Particle Method (RKPM), a meshfree method, for spatial discretization and aims to achieve a chemo-mechanical crack propagation model that achieves both intermediate accuracy and computational time between a CDM and CZM. To gain a better understanding of how the meshfree model compares to the current FEM model in capturing cathode crack propagation, further investigation is needed.

cathode cracking↗

A709 Qualification Plan Update and Mechanical Properties Data Assessment

This report provides a summary of the development effort for the qualification of Alloy 709, an advanced austenitic stainless steel, in the American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel Code, Section III, Division 5, High Temperature Reactors. It provides an assessment of the mechanical properties data generated to date from the tensile, creep, fatigue and creep-fatigue tests of the precipitation-treated Alloy 709 from two commercial heats in plate product form. It was concluded that the mechanical properties of Alloy 709 with the precipitation treatment continued to outperform those of Type 316 stainless steel. This affirms the recommendation to Code qualification this alloy as a replacement for Type 316 stainless steel to support the objective of reducing the construction and operating costs to incentivize advanced reactor deployment. The data also demonstrated that the precipitation treatment is effective in enhancing the creep-fatigue resistance of Alloy 709 while maintaining a significant creep strength advantage over Type 316 stainless steel. This report also provides an update to the test conditions for the creep, fatigue and creep-fatigue test matrices in order to cover the Code Case data package more effectively. Finally, it is recommended to continue the Alloy 709 Code Case Testing Program to develop the data package needed for the determination of the material-specific design parameters for inclusion in the Alloy 709 Code Case.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Microstructural, Corrosion and Mechanical Characterization of Friction-Stir Welded Joints Between Aluminum and Magnesium Alloys

Friction Stir Welding (FSW) of Aluminum-Magnesium (Al-Mg) alloys has garnered increasing attention due to its wide-ranging applications in the automotive and aerospace industries. The microstructural, corrosion, and mechanical properties of FSW Al-Mg welds under selected conditions are critical factors that must be well-investigated to ensure their durability and performance. In this study, electrochemical tests, including Open Circuit Potential (OCP), Linear Polarization Resistance (LPR), Potentiodynamic Polarization Scan (PD), and Electrochemical Impedance Spectroscopy (EIS), have been used to analyze the corrosion resistance of these welds, along with weight loss measurements through cyclic corrosion testing (CCT) and surface evolution via SEM over an 8-week period. Mechanical properties are evaluated through microindentation, nanoindentation, fatigue, and lap-shear tests. The results of the electrochemical tests reveal that the corrosion properties of the center weld zone differ from those of the two base alloys. Indentation tests indicate that the weld zone behaves differently from the base alloys. Surprisingly, the lap shear strength did not decrease significantly even after 8 weeks of cyclic corrosion testing, indicating that the joint prevented any ingress of the electrolyte. Fatigue testing showed that applying an adhesive between the Al and Mg joint improved the fatigue life to some extent, although the corrosion resistance reduced due to the discontinuous bonding of the adhesive layer. Overall, these findings highlight the importance of investigating the corrosion and mechanical properties of FSW Al-Mg welds and provide valuable insights for future modeling works.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Experimental and Numerical Investigations on Dynamic Mechanical Properties of TPMS Structures

Triply Periodic Minimal Surface (TPMS) lattice structures have been of increasing interest due to their light weighting, enhanced mechanical properties, and energy absorption characteristics for automotive and biomedical applications. With the advent of additive manufacturing and geometric modeling software, TPMS lattices with complex geometries can be realized. In this work, TPMS lattice structures were fabricated with PLA using fused filament fabrication (FFF) and their dynamic properties are characterized through drop tower experiments. Although lightweight TPMS lattices are beneficial for their impact absorption capability, most of the existing works are limited to quasi-static compression and dynamic impact tests are rarely performed. The current study investigates the stress-strain and energy absorption characteristics of TPMS lattices through drop tower testing and numerical modeling. Finite element modeling for TPMS lattices is carried out to validate the experimental responses. The mechanical properties, deformation, and failure mechanisms of TPMS lattices under dynamic impact are summarized for potential future applications.

Pokkalla, Deepak↗

A summary of the mechanical properties data developed in FY 2023 by ANL, INL and ORNL to support the data package development for the A709 Code Case

This report provides the status of tensile, creep, fatigue, and creep-fatigue testing to date conducted at Argonne National Laboratory, Idaho National Laboratory, and Oak Ridge National Laboratory to generate the data package required to qualify Alloy 709 in American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section III, Division 5. The Division 5 Class A Alloy 709 Code Case requires data generated from a minimum of three commercial heats. Extensive mechanical properties data have been generated on two commercial heats, and some initial test data have been generated from the third commercial heat. The room temperature tensile test results for the three commercial heats met the specification minimum of the American Society of Mechanical Engineers, Boiler and Pressure Vessel Code, Section II, Part A, SA-213/SA-213M for Grade TP310MoCbN (UNS S31025) seamless tubing. These three commercial heats of Alloy 709 are suitable for generating the code case data.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Image-Based Digital Twin for Assessing the Coupled Electro-Chemo-Mechanical Behavior of Li-Ion Batteries

In energy storage materials, strong electrochemical-mechanical coupling and highly anisotropic material properties contribute to the formation and propagation of micro-cracking during charge/discharge cycling, resulting in reduced performance and service life. In this work, a digital twin is created to investigate the performance of a Li-ion battery cathode and simulate degradation accumulation. Pixel-based model construction is used to represent the complex material geometries from microstructural images supplied by the National Renewable Energy Laboratory (NREL). Because of the expected large deformation and crack opening, the reproducing kernel particle method (RKPM), a meshfree method with discretization at the image pixels, is used to approximate the field variables: electrostatic potential, concentration, and displacement. An interface modified reproducing kernel (IM-RK) is constructed by scaling a smooth kernel function with an interface-distance function to achieve strategic discontinuity types (i.e. weak discontinuities for strain discontinuities and strong discontinuities for cracks) and alleviate Gibbs oscillations near these transition zones. The discrete nature of the images' pixel points is employed throughout the model and approximation construction. The mechanical model is verified using an image-based microstructure under tensile loading. A transient electro-chemo-mechanical coupled simulation is performed to evaluate the potential micro-cracking induced degradation of the battery cathode material subjected to charge/discharge cycling.

battery degradation↗

Novel Mechanisms for the Formation of Dislocation Cell Patterns in BCC Metal

In this study, we present the first simulation results of the formation of dislocation cell wall microstructures in tantalum subjected to shock loading. Dislocation patterns and cell wall formation are important to understanding the mechanical properties of the materials in which they spontaneously arise, and yet the processing and self-assembly mechanisms leading to their formation are poorly understood. By employing transmission electron microscopy and discrete dislocation dynamics, we propose a new mechanism involving coplanar dislocations and pseudo-dipole mixed dislocation arrays that is essential to the pattern formation process. Our large-scale 3D DDD simulations demonstrate the self-organization of dislocation networks into cell walls in deformed BCC metal (tantalum) persisting at strain ε = 20%. The simulation analysis captures several crucial aspects of how the dislocation cell pattern affects metal plasticity, as observed in experiments. Although experimental evidence is inconclusive regarding whether cell wall formation takes place at the shock front, after the shock, during release, or when the sample has had enough time to relax post-recovery, our simulations indicate cell wall formation occurs after the shock and before release. The extended Taylor hardening composite model effectively considers the non-uniform dislocation density when cell walls form and accurately describes the corresponding flow stress.

36 MATERIALS SCIENCE↗

Instrumentation for the In-Core Real-Time Mechanical Testing of Structural Materials (INCREASE) Project

Idaho National Laboratory (INL), in collaboration with the Electric Power Research Institute (EPRI), the Nuclear Regulatory Commission (NRC), the French Atomic and Alternative Energies Commission (CEA), the Joint Research Center (JRC), the Nuclear Research and Consultancy Group (NRG), and the Research Center Rez (CVR), started a Joint Experimental Program (JEEP) project that operates within the Nuclear Energy Agency’s Framework for Irradiation Experiments (FIDES II) program in order to develop capabilities for the in-core real-time mechanical testing of structural materials. This effort will focus on designing a shared capsule capable of housing a variety of in-core mechanical testing instrumentation allowing enhanced experiments for the material science community. The outcome of the project would be high-priority, stress relaxation data for stainless-steel-based materials provided by EPRI and CEA. Stress relaxation is a major phenomenon that contributes to material degradation in nuclear reactor components. Currently, nuclear material stress relaxation is assessed both before and after irradiation, using complex and costly post-irradiation examination (PIE) activities. In-situ data would support the development of precision modeling and simulation of this degradation phenomena and would provide validation and benchmarking for existing models using the PIE data. As part of the U.S. Department of Energy Advanced Sensor and Instrumentation (ASI) program, INL has fabricated and tested out-of-core mechanical test instrumentation. This instrumentation was designed for easy adaptation to the irradiation capsule proposed under this JEEP, and can be deployed to measure real-time stress relaxation under pressurized-water reactor (PWR) conditions. This initial effort will partially serve to replace the testing capabilities lost because of shutting down the Halden Boiling Water Reactor (HBWR). The project would provide these capabilities to the international community via a shared capsule design that is easily adaptable to additional material test reactors. The design features will incorporate expansion to PWR and non-light-water reactor (LWR) environments that will be developed in future work. The capsule and instrumentation will be demonstrated in the Massachusetts Institute of Technology Reactor (MITR) for phase I and the Petten High Flux Reactor (HFR) for phase II irradiations to deliver real-time stress relaxation data on high priority stainless steel structural materials.

36 MATERIALS SCIENCE↗

Mechanical Properties and Interfacial Bonding of Overmolded Polymer Composite Lattice Structures

This study investigates the mechanical properties and interfacial bonding of Polyamide 12 filled with Glass Fiber (PA12/GF) lattice structures overmolded with Nylon 66 (PA66) and Thermoplastic Polyurethane (TPU). The PA12/GF lattices, designed in Gyroid, Isotruss, and Octahedral geometries, were produced using the Selective Laser Sintering (SLS) technique. The thermal characteristics of both the lattice and overmolding materials were analyzed using Differential Scanning Calorimetry (DSC) and Thermogravimetric Analysis (TGA). The mechanical performance and interfacial bonding were evaluated through mechanical testing and microstructural analysis. The results indicate that overmolding improved flexural strength and impact resistance of the PA12/GF lattices. For instance, the plain PA12/GF Isotruss lattice exhibited a flexural strength of 15.5 MPa. By overmolding it with TPU the flexural strength increased by up to 137%, while PA66-overmolding resulted in an increase of 371%, achieving a flexural strength of 73 MPa. In terms of impact resistance, TPU-overmolding improved performance significantly, with an increase of 1800% (Gyroid) compared to the plain lattice. Microstructural analysis revealed good adhesion at the interface, especially when both the lattice and overmolding materials were thoroughly dried prior to the overmolding process to minimize interfacial porosity. This study highlights the potential of using overmolding to enhance lattice structures performance, offering lightweight and cost-efficient solutions for automotive applications.

Talabi, Isaac [ORNL] (ORCID:0000000340215594)↗

Effect of NO on DME-Methanol HCCI Combustion Using a Reduced Chemical Kinetics Mechanism

Methanol is an attractive fuel for the maritime sector due to its wide availability. Its direct use as a fuel, however, is accompanied by challenges such as high latent heat of vaporization and low cetane number. A potential solution to overcome the ignition properties of methanol could be through on-board generation of dimethyl ether (DME) via catalytic dehydration of methanol. The resulting mixture from dehydration can be mixed in with the intake air to generate a homogenous charge compression ignition (HCCI) preburn for subsequent direct injection (DI) mixing controlled compression ignition (MCCI) of neat methanol. Within that context, complementary experimental work found that the influence of combustion residuals on the heat release rate (HRR) was significant, specifically for residual NO. This finding motivated the present computational and kinetic evaluation of the effects of NO on the low (LTHR) and high (HTHR) temperature heat release rates. The strong influence of small quantities of NO on the combustion process of a DME/methanol/H2O mixture (low catalyst or reactor efficiency) necessitated a kinetics-based investigation into this phenomenon. A mechanism sourced from the existing literature with NO had 172 species and 1375 reactions, making it computationally expensive for use. Hence, a mechanism reduction effort was implemented, and a rate constant (k) tuning effort based on sensitivity analysis was needed to validate experimental results using a zero-dimensional engine model in Cantera. The reduced mechanism was able to successfully capture the negligible influence of NO addition on DME HCCI combustion, whereas an advancement in LTHR and HTHR for a DME/methanol/H2O mixture was kinetically confirmed. Reaction pathway analysis showed that addition of NO chemically counteracted the OH sink created by alcohols like methanol, increasing the effectiveness of DME ignition.

Tyrewala, Daanish [ORNL] (ORCID:0000000208599324)↗

On the Order Parameter of the Continuous Phase Transition in the Classical and Quantum Mechanical Limits

The mean field theory is revisited in the classical and quantum mechanical limits. Taking into account the boundary conditions at the phase transition and the third law of the thermodynamics the physical properties of the ordered and disordered phases were reported. The equation for the order parameter predicts the occurrence of a saturation of Ψ 2 = 1 near Θ S , the temperature below the quantum mechanical ground state is reached. The theoretical predictions are also compared with high resolution thermal expansion data of SrTiO 3 monocrystalline samples and other some previous results. An excellent agreement has been found suggesting a universal behavior of the theoretical model to describe continuous structural phase transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Electromagnetic and gravitational interactions from Lagrangian mechanics

Highlights: • Background Maxwell and Einstein fields are universal features of Lagrangian systems. • The Lagrangian function is promoted to a dynamic field. • The Einstein–Maxwell theory is derived from Lagrangian mechanics. Background fields of electromagnetic and gravitational type emerge in the low kinetic energy limit of any regular Lagrangian system and, in particular, in the corresponding limit of any spacetime theory in which the free motion of test particles is described by an unspecified regular Lagrangian. Electromagnetic and gravitational type interactions are therefore a universal feature of low kinetic energy Lagrangian systems. These background interactions can be consistently turned into dynamic Einstein–Maxwell fields by promoting the Lagrangian function to a dynamic scalar field on the tangent bundle of the configuration space. Accordingly, Einstein–Maxwell theory can be deduced from the assumption that the motion of elementary test particles in spacetime is described by Lagrangian mechanics. For higher kinetic energy-type values, identified with the square of the invariant mass of the particle, the Lagrangian induces higher rank interactions that seem however too weak to have been detected in spacetime physics, but which might prove relevant at the Planck scale.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗