Scalar Invariants of surfaces in conformal 3-sphere via Minkowski spacetime

For a surface in 3-sphere, by identifying the conformal round 3-sphere as the projectivized positive light cone in Minkowski 5-spacetime, we use the conformal Gauss map and the conformal transform to construct the associate homogeneous 4-surface in Minkowski 5-spacetime. We then derive the local fundamental theorem for a surface in conformal round 3-sphere from that of the associate 4-surface in Minkowski 5-spacetime. More importantly, following the idea of Fefferman and Graham, we construct local scalar invariants for a surface in conformal round 3-sphere. One distinct feature of our construction is to link the classic work of Blaschke to the works of Bryan and Fefferman-Graham.Comment: 37 page

Neutral silicon interstitials in silicon carbide: a first principles study

International audienceAbstract. The structures and stability of single silicon interstitials in their neutral state are investigated via first principles calculations in 3C- and 4H-SiC. By carefully checking the convergence with Brillouin Zone (BZ) sampling and supercell size we explain the disagreement between previous published results and we show that the split interstitial along direction and tetrahedrally carbon coordinated structure have similar formation energies in the cubic polytype. A new migration mechanism for the silicon interstitial in the neutral state is presented here which could be important for the evolution of defect populations in SiC. For 4H-SiC, the most energetically favourable silicon interstitial is found to be the split interstitial configuration ISisp but situated in the hexagonal layer. The defect formation energies in 4H-SiC are in general larger than those in 3C-SiC, implying that the insertion of silicon interstitial introduces a large lattice distortion to the local coordination environments and affect even the second- or third-nearest neighbours. We also present a comparison between well converged plane waves calculations and calculations with three localized orbital basis sets; one of them, in spite of providing a reasonable description for bulk properties, is clearly not suitable to describe interstitial defects

Deformation modes and ideal strengths of ternary layered Ti2AlC and Ti2AlN from first-principles calculations

Deformation and failure modes were studied for Ti2 AlC and Ti2 AlN by deforming the materials from elasticity to structural instability using the first-principles density functional calculations. We found that the Ti C0.5 Ti N0.5 slabs remain structurally stable under deformations, whereas the weak Ti-Al bonds accommodate deformation by softening and breaking at large strains. The structural stability of the ternary compound is determined by the strength of Ti-Al bond, which is demonstrated to be less resistive to shear deformation than to tension. The ideal stress-strain relationships of ternary compounds are presented and compared with those of the binary materials, TiC and TiN, respectively. For Ti2 AlC and Ti2 AlN, their ideal tensile strengths are comparable to those of the binary counterparts, while the ideal shear strengths yield much smaller values. Based on electronic structure analyses, the low shear deformation resistance is well interpreted by the response of weak Ti-Al bonds to shear deformations. We propose that the low shear strengths of Ti2 AlC and Ti2 AlN originate from low slip resistance of Al atomic planes along the basal plane, and furthermore suggest that this is the mechanism for low hardness, damage tolerance, and intrinsic toughness of ternary layered carbides and nitrides

Carbon dioxide life cycle assessment on urban air mobility in context of emergency medical service

This thesis presents the development of life cycle assessment framework, which includes a series of conceptual models, to evaluate the end-to-end environmental impacts of Urban Air Mobility (UAM) systems, with a specific focus on their application in Emergency Medical Services (EMS) scenarios. The LCA study examines two types of UAM technologies: drones for the delivery of medical supplies and medium-sized electric Vertical Take-off and Landing (eVTOL) aircraft for the transport of medical personnel or patients. The proposed LCA assessment framework incorporates sensitivity analysis modules to account for the uncertainties prevalent in the respective domains. The carbon dioxide emissions in the UAM ecosystem are largely due to the construction and operation of supporting ground infrastructure, as well as the production and operation of unmanned aerial systems, as underscored by this thesis. The analysis reveals that motor production generates the highest environmental impact, while battery-related impacts are uncertain and influenced by flight frequency. Additionally, the study emphasizes the importance of local grid intensity and weather conditions in determining the overall emissions associated with UAM operations. As UAM technologies continue to mature, it is advocated that additional scenario-based and network-level evaluations be carried out. The developed framework in this thesis holds potential for enhancement through improvements in data quality, thereby contributing to a more robust understanding of the environmental implications of UAM in EMS contexts

Snapshot Reinforcement Learning: Leveraging Prior Trajectories for Efficiency

Deep reinforcement learning (DRL) algorithms require substantial samples and computational resources to achieve higher performance, which restricts their practical application and poses challenges for further development. Given the constraint of limited resources, it is essential to leverage existing computational work (e.g., learned policies, samples) to enhance sample efficiency and reduce the computational resource consumption of DRL algorithms. Previous works to leverage existing computational work require intrusive modifications to existing algorithms and models, designed specifically for specific algorithms, lacking flexibility and universality. In this paper, we present the Snapshot Reinforcement Learning (SnapshotRL) framework, which enhances sample efficiency by simply altering environments, without making any modifications to algorithms and models. By allowing student agents to choose states in teacher trajectories as the initial state to sample, SnapshotRL can effectively utilize teacher trajectories to assist student agents in training, allowing student agents to explore a larger state space at the early training phase. We propose a simple and effective SnapshotRL baseline algorithm, S3RL, which integrates well with existing DRL algorithms. Our experiments demonstrate that integrating S3RL with TD3, SAC, and PPO algorithms on the MuJoCo benchmark significantly improves sample efficiency and average return, without extra samples and additional computational resources.Comment: Under revie

Role of Nanolaminated Crystal Structure on the Radiation Damage Tolerance of Ti 3

Nanolaminated Ti3SiC2, a representative MAX phase, shows excellent tolerance to radiation damage. In this paper, first-principles calculations were used to investigate the mechanism of intrinsic point defects in order to explain this outstanding property. Formation energies of intrinsic point defects are calculated and compared; and the results establish a low-energy disorder mechanism in Ti3SiC2. In addition, the migration energy barriers of Si vacancy, Si interstitial, and TiSi antisite yield very low values: 0.9, 0.6, and 0.3 eV, respectively. The intercalation of Si atomic plane between Ti3C2 nanotwinning structures dominates the formation and migration of intrinsic native point defects in Ti3SiC2. The present study also highlights a novel method to improve radiation damage tolerance by developing nanoscale-layered structure which can serve as a sink or rapid recovery channel for point defects

The interplay between thermodynamics and kinetics in the solid-state synthesis of layered oxides.

In the synthesis of inorganic materials, reactions often yield non-equilibrium kinetic byproducts instead of the thermodynamic equilibrium phase. Understanding the competition between thermodynamics and kinetics is a fundamental step towards the rational synthesis of target materials. Here, we use in situ synchrotron X-ray diffraction to investigate the multistage crystallization pathways of the important two-layer (P2) sodium oxides Na0.67MO2 (M = Co, Mn). We observe a series of fast non-equilibrium phase transformations through metastable three-layer O3, O3' and P3 phases before formation of the equilibrium two-layer P2 polymorph. We present a theoretical framework to rationalize the observed phase progression, demonstrating that even though P2 is the equilibrium phase, compositionally unconstrained reactions between powder precursors favour the formation of non-equilibrium three-layered intermediates. These insights can guide the choice of precursors and parameters employed in the solid-state synthesis of ceramic materials, and constitutes a step forward in unravelling the complex interplay between thermodynamics and kinetics during materials synthesis