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At least 343 records · Page 19

A Proposal for Standardized MMOD Shielding for Robotic Spacecraft

NASA robotic spacecraft are required to assess the potential for small debris induced failure for all disposal-critical components. Additional shielding might then be necessary in order to meet the acceptable risk requirement for the overall mission. Traditionally this requirement had been met with little or no additional shielding. Since the introduction of a high density debris population in ORDEM 3.0, some missions, especially those in higher portions of Low Earth Orbit, have needed additional MMOD-specific shielding in order for the mission to meet the requirement. This is a costly design effort when performed late in the project life cycle, which adds unexpected mass to the spacecraft components during the integration phase, and could disrupt thermal management.A proposal is discussed to develop a more cost-effective approach to MMOD-shielding, which can be employed earlier in the hardware design phase. The development and adoption of standardized shielding assemblies allows early tailoring of the shielding around a component, so that the mass is accounted for, as well as the small particle penetration risk, at a point in the design phase when the cost and schedule impact are more manageable. A set of several assemblies can be developed with a range of protection thresholds, in order to control mass where less shielding is needed. Such shielding assemblies would be developed in collaboration with blanket assembly specialists and thermal control engineers to ensure manufacturability and thermal performance challenges are known and acceptable. One clear benefit of such an approach is that hypervelocity testing can be performed on each of the standard shield assemblies to refine and confirm their performance prior to use.The challenges inherent in designing supplemental MMOD shielding will be discussed, including variations in the orbital debris environment and performance prediction. The benefits of a standardized shielding approach and example applications will also be presented.

Hull, Scott M.↗

A Proposal for Standardized MMOD Shielding for Robotic Spacecraft

NASA robotic spacecraft are required to assess the potential for small debris induced failure for all disposal-critical components. Additional shielding might then be necessary in order to meet the acceptable risk requirement for the overall mission. Traditionally this requirement had been met with little or no additional shielding. Since the introduction of a high density debris population in ORDEM 3.0, some missions, especially those in higher portions of Low Earth Orbit, have needed additional MMOD-specific shielding in order for the mission to meet the requirement. This is a costly design effort when performed late in the project life cycle, which adds unexpected mass to the spacecraft components during the integration phase, and could disrupt thermal management. A proposal is discussed to develop a more cost-effective approach to MMOD-shielding, which can be employed earlier in the hardware design phase. The development and adoption of standardized shielding assemblies allows early tailoring of the shielding around a component, so that the mass is accounted for, as well as the small particle penetration risk, at a point in the design phase when the cost and schedule impact are more manageable. A set of several assemblies can be developed with a range of protection thresholds, in order to control mass where less shielding is needed. Such shielding assemblies would be developed in collaboration with blanket assembly specialists and thermal control engineers to ensure manufacturability and thermal performance challenges are known and acceptable. One clear benefit of such an approach is that hypervelocity testing can be performed on each of the standard shield assemblies to refine and confirm their performance prior to use.The challenges inherent in designing supplemental MMOD shielding will be discussed, including variations in the orbital debris environment and performance prediction. The benefits of a standardized shielding approach and example applications will also be presented.

Hull, Scott M.↗

Thermal barrier coatings for gas turbine and diesel engines

The present state of development of thin thermal barrier coatings for aircraft gas turbine engines and thick thermal barrier coatings for truck diesel engines is assessed. Although current thermal barrier coatings are flying in certain gas turbine engines, additional advances will be needed for future engines. Thick thermal barrier coatings for truck diesel engines have advanced to the point where they are being seriously considered for the next generation of engine. Since coatings for truck engines is a young field of inquiry, continued research and development efforts will be required to help bring this technology to commercialization.

Miller, Robert A.↗

Fuel Property Effects on Knock Propensity and Thermal Efficiency in a Direct-Injection Spark-Ignition Engine

Engine knock remains one of the major barriers to further improvement in thermal efficiency of Direct-Injection Spark-Ignition (DISI) engines. While Research Octane Number and Motor Octane Number are often used as standard rating methods for knock resistance of fuels, the impacts of other fuel properties on knock propensity in modern engines such as heat of vaporization (HoV) and laminar flame speed (LFS) require better understanding in order to co-optimize fuels and engine designs to achieve higher thermal efficiency and lower CO2 emission. In the present study, computational fluid dynamics (CFD) is used to model a boosted DISI engine with a focus on knock prediction and fuel property effects. A level-set G-equation model is employed to capture turbulent premixed combustion, and is coupled with a transported Livengood-Wu (L-W) integral approach to predict autoignition in the unburnt region. A criterion associated with the L-W integral is developed to accurately predict knock onset and knock-limited spark-advance. This model is then applied to a sensitivity analysis of HoV and LFS on knock tendency and thermal efficiency. The pressure-temperature trajectory framework is applied and extended to study the fuel effects on auto-ignition process in the engine. An existing efficiency-based merit function, which is derived from experiments for boosted SI engines, is evaluated and improved based on the current CFD results.

DISI↗

Aerospace Ceramic Materials: Thermal, Environmental Barrier Coatings and SiC/SiC Ceramic Matrix Composites for Turbine Engine Applications

Ceramic materials play increasingly important roles in aerospace applications because ceramics have unique properties, including high temperature capability, high stiffness and strengths, excellent oxidation and corrosion resistance. Ceramic materials also generally have lower densities as compared to metallic materials, making them excellent candidates for light-weight hot-section components of aircraft turbine engines, rocket exhaust nozzles, and thermal protection systems for space vehicles when they are being used for high-temperature and ultra-high temperature ceramics applications. Ceramic matrix composites (CMCs), including non-oxide and oxide CMCs, are also recently being incorporated in gas turbine engines for high pressure and high temperature section components and exhaust nozzles. However, the complexity and variability of aerospace ceramic processing methods, compositions and microstructures, the relatively low fracture toughness of the ceramic materials, still remain the challenging factors for ceramic component design, validation, life prediction, and thus broader applications. This ceramic material section paper presents an overview of aerospace ceramic materials and their characteristics. A particular emphasis has been placed on high technology level (TRL) enabling ceramic systems, that is, turbine engine thermal and environmental barrier coating systems and non-oxide type SiC/SiC CMCs. The current status and future trend of thermal and environmental barrier coatings and SiC/SiC CMC development and applications are described.

Thermal Barrier Coatings↗

Development of Integrated Thermal Fluids Modeling Capability for MSRs

The DOE Nuclear Energy Advanced Modeling and Simulation (NEAMS) program supports a full range of computational thermal fluids analysis capabilities and code developments for a broad class of light-water and advanced reactor concepts. The research and development approach under thermal fluids technical area synergistically combines three length and time scales in a hierarchal multi-scale approach. To demonstrate the feasibility and capabilities of a multi-scale thermal fluids capability using these codes, a key joint effort has been pursued to develop an integrated system-and engineering-scale thermal fluids analysis capability with the MOOSE-based codes, through integration of SAM and Pronghorn, both based on the MOOSE framework. This report summarizes the progress in developing an integrated system- and engineering-scale thermal fluids analysis capability based on SAM and Pronghorn for molten salt reactors (MSRs), which gained significant interest in recently years. Two coupling approaches were studied, i.e. separate domain or domain-segregated coupling approach and the domain-overlapping approach. A series of coupled multi-physics models have been developed for a common reference molten salt fast reactor (MSFR) concept, ranging from standalone SAM system model to integrated SAM-Pronghorn-Griffin models. Both the steady state and the transient simulations are performed to the state-of-the-art simulation capabilities of NEAMS software suite in MSFR system applications. This report also covers further development and testing of the gas transport model in SAM for MSR modeling support. The presence of noncondensable gas in MSR systems would have strong impacts on fission gas removal and transport of noble metals throughout the system. Fission products removed through the off-gas system can also impact reactivity and can act as an additional point of heat removal. To ensure that the gas transport model is adequately tested, the supported modeling capabilities and features of SAM were identified, and a suite of tests were developed to test the model for each identified feature. Validation and UQ testing were also performed for the model and demonstrated that the buoyancy term, which was originally developed using non-salt/helium gas experimental data, can capture the experimental gas bubble velocity and diameter to within experimental and code uncertainty. An existing MSRE model was also modified in this work to include the gas transport model and to demonstrate the gas model behavior for realistic conditions of interest.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Thermal energy transformer

For use in combination with a heat engine, a thermal energy transformer is presented. It is comprised of a flux receiver having a first wall defining therein a radiation absorption cavity for converting solar flux to thermal energy, and a second wall defining an energy transfer wall for the heat engine. There is a heat pipe chamber interposed between the first and second walls having a working fluid disposed within the chamber and a wick lining the chamber for conducting the working fluid from the second wall to the first wall. Thermal energy is transferred from the radiation absorption cavity to the heat engine.

Berdahl, C. M.↗

Development and Demonstration of a Fuel-Efficient, Class 8 Tractor & Trailer Engine System (SuperTruck II)

Navistar presents the SuperTruck II (ST II) Final Report to the Unites States Department of Energy (US DOE), which covers the five Budget Periods (BPs) from 10-1-2016 through 6-30-2022. For ST II, Navistar built on the achievements of the SuperTruck I (ST I) Program as a catalyst to continue critical research, design and development, testing, and operations to reach the ambitious goals of the ST II project. This approach allowed Navistar to continue contributing to the essential needs of our nation for safe, efficient, and cost-effective delivery of goods and services, as we reduced negative environmental effects and improved operational productivity. This document contains information specified in DOE F 4600.2, Final Scientific/Technical Report DOE F 241.3, B. SCIENTIFIC/TECHNICAL REPORTS, explaining how we met and exceeded program requirements. Throughout this Final Report, Navistar extracted information from documents prepared during the project that represent our management, design and development, building, and testing efforts to meet and exceed SuperTruck II project goals. Navistar followed Plan requirements to achieve / exceed Project Objectives: a) >100% improvement in vehicle freight efficiency (FE) (on ton-MPG basis) relative to 2009 baseline with stretch goal of 140% improvement [actual: 170%); b) >55% engine brake thermal efficiency (BTE) demonstrated in operational engine at a 65-mph cruise point on a dynamometer – ≥31% increase from 2009 baseline [actual: 55.20% of combined BTE) ; and c) development and implementation of commercially cost effective technologies (in terms of a simple payback). Technology selection / development path focused on developing technologies applicable for production within 3-year approach, while ensuring technology readiness and cost of ownership for end users. The Program was organized into five budget periods: Requirements / Technology Assessment and Initial Hardware Testing; Technology Development and Concept Readiness Demonstration; Technology Finalization and Validation Tractor / Trailer Fabrication, Integration and Commissioning Demonstration; and Fuel Economy (FE) and Brake Thermal Efficiency (BTE) and Program Completion. Leadership was provided by DOE, with tasks performed by laboratories (Argonne National Laboratory, Lawrence Livermore National Laboratory); partners at Bosch, TPI, Dana, and J.B. Hunt; , and support from University of Michigan and Clemson University. Navistar lead this team with Principal Investigator / Contracting Officer; Project Manager (PM); Vehicle, Engine, and Aftertreatment Engineers; Finance Manager, Technical Program Leads, and Legal/IP; and other key personnel. Work also included personnel in risk management; funding / budget / finance. Work involved analysis, development, testing, and down selection of individual/system engine, aftertreatment, and vehicle technologies, with integration of selected technologies into a prototype vehicle for demonstration of fuel-efficiency gain. Work also included component/integrated system level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. As ST II progressed, Navistar performed computer-based modeling / simulations of technologies focused on the primary operational areas: Engine, Aftertreatment, and Vehicle. During the ST II Program, the COVID Virus outbreak unexpectedly challenged by the effects of, which affected staffing, scheduling, design, supplies, availability of materials, production procedures, and testing. The DOE responded by extending the program by three quarters to ensure that project tasks were completed for this vital project. Focus continued on analyzing, developing, testing, and down selecting individual-/system-level engine and vehicle technologies for integration of the final selected technologies into a prototype vehicle that would demonstrate fuel-efficiency gains made possible through these technologies. This included component/integrated system-level development of truck and trailer aerodynamics, base engine efficiency, advanced aftertreatment, combustion efficiency, waste heat recovery, solar power, distributed and intelligent vehicle power, hybrid powertrain, reduced rolling resistance, weight reduction, idle reduction, and driver feedback. Throughout the program, function, reliability, and performance at all levels were ensured through testing. Proof of this approach was demonstrated in multiple, on-road demonstrations: Scenario A (Flatland) Fuel Economy, Scenario B (Hilly) Fuel Economy, and City Cycle Tests. Other benefits derived from ST II included new/improved products, publications, patents, and next-step capabilities related to electric/hydrogen vehicles and autonomous driving.

Zukouski, Russ↗

A Thermal Radiation Modulation Platform by Emissivity Engineering with Graded Metal–Insulator Transition

Thermal radiation from a black body increases with the fourth power of absolute temperature (T 4 ), an effect known as the Stefan-Boltzmann law. Typical materials radiate heat at a portion of this limit, where the portion, called integrated emissivity (ε int ), is insensitive to temperature (|dε int /dT| ≈ 10 -4 °C -1 ). The resultant radiance bound by the T 4 law limits the ability to regulate radiative heat. Here, an unusual material platform is shown in which ε int can be engineered to decrease in an arbitrary manner near room temperature (|dε int /dT| ≈ 8 × 10 -3 °C -1 ), enabling unprecedented manipulation of infrared radiation. As an example, ε int is programmed to vary with temperature as the inverse of T 4 , precisely counteracting the T 4 dependence; hence, thermal radiance from the surface becomes temperature-independent, allowing the fabrication of flexible and power-free infrared camouflage with unique advantage in performance stability. In this work, the structure is based on thin films of tungsten-doped vanadium dioxide where the tungsten fraction is judiciously graded across a thickness less than the skin depth of electromagnetic screening.

36 MATERIALS SCIENCE↗

Thermal Conductivity and Elastic Modulus Evolution of Thermal Barrier Coatings under High Heat Flux Conditions

Laser high heat flux test approaches have been established to obtain critical properties of ceramic thermal barrier coatings (TBCs) under near-realistic temperature and thermal gradients that may he encountered in advanced engine systems. Thermal conductivity change kinetics of a thin ceramic coating were continuously monitored in real time at various test temperatures. A significant thermal conductivity increase was observed during the laser simulated engine heat flux tests. For a 0.25 mm thick ZrO2-8%Y2O3 coating system, the overall thermal conductivity increased from the initial value of 1.0 W/m-K to 1. 15 W/m-K, 1. 19 W/m-K and 1.5 W/m-K after 30 hour testing at surface temperatures of 990C, 1100C, and 1320C. respectively. Hardness and modulus gradients across a 1.5 mm thick TBC system were also determined as a function of laser testing time using the laser sintering/creep and micro-indentation techniques. The coating Knoop hardness values increased from the initial hardness value of 4 GPa to 5 GPa near the ceramic/bond coat interface, and to 7.5 GPa at the ceramic coating surface after 120 hour testing. The ceramic surface modulus increased from an initial value of about 70 GPa to a final value of 125 GPa. The increase in thermal conductivity and the evolution of significant hardness and modulus gradients in the TBC systems are attributed to sintering-induced micro-porosity gradients under the laser-imposed high thermal gradient conditions. The test techniques provide a viable means for obtaining coating data for use in design, development, stress modeling, and life prediction for various thermal barrier coating applications.

Zhu, Dongming↗

Tests of NASA ceramic thermal barrier coating for gas-turbine engines

A two-layer thermal barrier coating system with a bond coating of nickel-chromium-aluminum-yttrium and a ceramic coating of yttria-stabilized zirconia was tested for corrosion protection, thermal protection and durability. Full-scale gas-turbine engine tests demonstrated that this coating eliminated burning, melting, and warping of uncoated parts. During cyclic corrosion resistance tests made in marine diesel fuel products of combustion in a burner rig, the ceramic cracked on some specimens. Metallographic examination showed no base metal deterioration.

Liebert, C. H.↗

Lunar Thermal Wadis and Exploration Rovers: Outpost Productivity and Participatory Exploration

The presentation introduces the concept of a thermal wadi, an engineered source of thermal energy that can be created using native material on the moon or elsewhere to store solar energy for use by various lunar surface assets to survive the extremely cold environment of the lunar night. A principal benefit of this approach to energy storage is the low mass requirement for transportation from Earth derived from the use of the lunar soil, or regolith, as the energy storage medium. The presentation includes a summary of the results of a feasibility study involving the numerical modeling of the performance of a thermal wadi including a manufactured thermal mass, a solar energy reflector, a nighttime thermal energy reflector and a lunar surface rover. The feasibility study shows that sufficient thermal energy can be stored using unconcentrated solar flux to keep a lunar surface rover sufficiently warm throughout a 354 hour lunar night at the lunar equator, and that similar approaches can be used to sustain surface assets during shorter dark periods that occur at the lunar poles. The presentation includes descriptions of a compact lunar rover concept that could be used to manufacture a thermal wadi and could alternatively be used to conduct a variety of high-value tasks on the lunar surface. Such rovers can be produced more easily because the capability for surviving the lunar night is offloaded to the thermal wadi infrastructure. The presentation also includes several concepts for operational scenarios that could be implemented on the moon using the thermal wadi and compact rover concepts in which multiple affordable rovers, operated by multiple terrestrial organizations, can conduct resource prospecting and human exploration site preparation tasks.

Sacksteder, Kurt↗

Ultimate Suppression of Thermal Transport in Amorphous Silicon Nitride by Phononic Nanostructure.

Engineering the thermal conductivity of amorphous materials is highly essential for the thermal management of future electronic devices. Here, we demonstrate the impact of ultrafine nanostructuring on the thermal conductivity reduction of amorphous silicon nitride (a-Si3N4) thin films, in which the thermal transport is inherently impeded by the atomic disorders. Ultrafine nanostructuring with feature sizes below 20 nm allows us to fully suppress contribution of the propagating vibrational modes (propagons), leaving only the diffusive vibrational modes (diffusons) to contribute to thermal transport in a-Si3N4. A combination of the phonon-gas kinetics model and the Allen-Feldmann theory reproduced the measured results without any fitting parameters. The thermal conductivity reduction was explained as extremely strong diffusive boundary scattering of both propagons and diffusIons. These findings give rise to substantial tunability of thermal conductivity of amorphous materials, which enables us to provide better thermal solutions in microelectronic devices.

Tambo, Naoki↗

Evaluation of thermal processing and properties of 422 martensitic stainless steel for replacement of 4140 steel in diesel engine pistons

The thermal and mechanical properties of martensitic stainless steel 422 were evaluated for suitability as a drop-in replacement for 4140 steel in next generation heavy-duty diesel engine (HDDE) pistons. The time and temperature of the austenitization and tempering steps were studied to achieve optimum materials performance in piston applications, including the balance of thermal and mechanical properties and resistance to long-term thermal aging. Reducing the tempering temperature from 700 to 600 °C caused a substantial increase in elevated temperature strength from 25 to 600 °C, but had no significant influence on thermal conductivity, suggesting that thermal conductivity in 422 is dominated largely by composition and distribution of alloying elements and mostly independent of the sub-grain structure size and precipitate size. Compared to the current HDDE piston alloy 4140, 422 exhibits substantially higher elevated temperature strength and lower thermal conductivity, the latter which will cause 422 to operate at higher temperatures in pistons, possibly requiring a piston redesign to take advantage of the improved high temperature strength of 422. Piston material selection and alloy design strategies with potential to mitigate some of the shortcomings of martensitic stainless steels, such as 422, as drop-in replacements are discussed.

36 MATERIALS SCIENCE↗

Enhancing Thermal Transport in Polymeric Composites Via Engineered Noncovalent Filler–Polymer Interactions

Understanding thermal transport mechanisms in polymeric composites allows us to expand the boundaries of thermal conductivity in them, either increasing it for more efficient heat dissipation or decreasing it for better thermal insulation. But, these mechanisms are not fully understood. Systematic experimental investigations remain limited. Practical strategies to tune the interfacial thermal resistance (ITR) between fillers and polymers and the thermal conductivity of composites remain elusive. Here, we studied the thermal transport in representative polymer composites, using polyethylene (PE) or polyaniline (PANI) as matrices and graphite as fillers. PANI, with aromatic rings in its backbone, interacts with graphite through strong noncovalent π–π stacking interactions, whereas PE lacks such interactions. We can then quantify how π–π stacking interactions between graphite and polymers enhance thermal transport in composites. PE/graphite and PANI/graphite composites with the same 1.5% filler volume fractions show a ∼22.82% and ∼34.85% enhancement in thermal conductivity compared to pure polymers, respectively. Calculated ITRs in PE/graphite and PANI/graphite are ~6 x 10 -8 m 2 KW -1 and ~1 x 10 -8 m 2 KW -1 , respectively, highlighting how π–π stacking interactions reduce ITR. Molecular dynamics (MD) simulations suggest that π–π stacking interactions between PANI chains and graphite surfaces enhance alignment of PANI's aromatic rings with graphite surfaces. This allows more carbon atoms from PANI chains to interact with graphite surfaces at a shorter distance compared to PE chains. Finally, our work indicates that tuning the π–π stacking interactions between polymers and fillers is an effective approach to reduce the ITR and enhance the thermal conductivity of composites.

atoms↗

Heat engine requirements for advanced solar thermal power systems

Requirements and constraints are established for power conversion subsystems, including heat engine, alternator and auxiliaries, of dish concentrator solar thermal power systems. In order to be competitive with conventional power systems, it is argued that the heat engine should be of less than 40 kW rated output, in a subsystem with an efficiency of at least 40% at rated output and at least 37% at half power. An interval between major overhauls of 50,000 hours is also desirable, along with minor maintenance and lubrication not more than four times a year requiring no more than one man-hour each time, and optimal reliability. Also found to be important are the capability for hybrid operation using heat from a solar receiver, fuel-fired combustor or both simultaneously, operation at any attitude, stability to transients in input power and output loading, operation at ambient temperatures from -30 to 50 C, and compatibility with environmental and safety requirements. Cost targets include a price of $180/kWe, and operation, maintenance and replacement costs averaging $0.001/kWh for 30 years of operation.

Jaffe, L. D.↗

Investigation of Thermal High Cycle and Low Cycle Fatigue Mechanisms of Thick Thermal Barrier Coatings

Thick thermal barrier coating systems in a diesel engine experience severe thermal low cycle fatigue (LCF) and high cycle fatigue (HCF) during engine operation. In this paper, the mechanisms of fatigue crack initiation and propagation in a ZrO2-8wt.% Y2O3 thermal barrier coating, under simulated engine thermal LCF and HCF conditions, are investigated using a high power CO2 laser. Experiments showed that the combined LCF/HCF tests induced more severe coating surface cracking, microspallation and accelerated crack growth, as compared to the pure LCF test. Lateral crack branching and the ceramic/bond coat interface delaminations were also facilitated by HCF thermal loads, even in the absence of severe interfacial oxidation. Fatigue damages at crack wake surfaces, due to such phenomena as asperity/debris contact induced cracking and splat pull-out bending during cycling, were observed especially for the combined LCF/HCF tests. It is found that the failure associated with LCF is closely related to coating sintering and creep at high temperatures, which induce tensile stresses in the coating after cooling. The failure associated with HCF process, however, is mainly associated with a surface wedging mechanism. The interaction between the LCF, HCF and ceramic coating creep, and the relative importance of LCF and HCF in crack propagation are also discussed based on the experimental evidence.

Zhu, Dongming↗

Investigation of Thermal High Cycle and Low Cycle Fatigue Mechanisms of Thick Thermal Barrier Coatings

Thick thermal barrier coating systems in a diesel engine experience severe thermal low cycle fatigue (LCF) and high cycle fatigue (HCF) during engine operation. In this paper, the mechanisms of fatigue crack initiation and propagation in a ZrO2-8wt% Y2O3 thermal barrier coating, under simulated engine thermal LCF and HCF conditions, are investigated using a high power CO2 laser. Experiments showed that the combined LCF-HCF tests induced more severe coating surface cracking, microspallation and accelerated crack growth, as compared to the pure LCF test. Lateral crack branching and the ceramic/bond coat interface delaminations were also facilitated by HCF thermal loads, even in the absence of severe interfacial oxidation. Fatigue damage at crack wake surfaces, due to such phenomena as asperity/debris contact induced cracking and splat pull-out bending during cycling, was observed especially for the combined LCF-HCF tests. It is found that the failure associated with LCF is closely related to coating sintering and creep at high temperatures, which induce tensile stresses in the coating after cooling. The failure associated with HCF process, however, is mainly associated with a surface wedging mechanism. The interaction between the LCF, HCF and ceramic coating creep, and the relative importance of LCF and HCF in crack propagation are also discussed based on the experimental evidence.

Zhu, Dongming↗