A note on the entropy of mean curvature flow

The entropy of a hypersurface is given by the supremum over all F-functionals with varying centers and scales, and is invariant under rigid motions and dilations. As a consequence of Huisken's monotonicity formula, entropy is non-increasing under mean curvature flow. We show here that a compact mean convex hypersurface with some low entropy is diffeomorphic to a round sphere. We will also prove that a smooth self-shrinker with low entropy is exact a hyperplane.Comment: Accepted for publication in SCIENCE CHINA Mathematic

Block Spin Ground State and 3-Dimensionality of (K,Tl)Fe1.6_{1.6}Se2_2

The magnetic properties and electronic structure of (K,Tl)y Fe1.6 Se2 is studied using first-principles calculations. The ground state is checkerboard antiferromagnetically coupled blocks of the minimal Fe4 squares, with a large block spin moment ~11.2{\mu}B . The magnetic interactions could be modelled with a simple spin model involving both the inter- and intra-block, as well as the n.n. and n.n.n. couplings. The calculations also suggest a metallic ground state except for y = 0.8 where a band gap ~400 - 550 meV opens, showing an antiferromagnetic insulator ground state for (K,Tl)0.8 Fe1.6 Se2 . The electronic structure of the metallic (K,Tl)y Fe1.6 Se2 is highly 3-dimensional with unique Fermi surface structure and topology. These features indicate that the Fe-vacancy ordering is crucial to the physical properties of (K,Tl)y Fe2-x Se2 .Comment: Magnetic coupling constants double checked, journal ref. adde

3D printed neuromorphic sensing systems

Thanks to the high energy efficiency, neuromorphic devices are spotlighted recently by mimicking the calculation principle of the human brain through the parallel computation and the memory function. Various bio-inspired \u27in-memory computing\u27 (IMC) devices were developed during the past decades, such as synaptic transistors for artificial synapses. By integrating with specific sensors, neuromorphic sensing systems are achievable with the bio-inspired signal perception function. A signal perception process is possible by a combination of stimuli sensing, signal conversion/transmission, and signal processing. However, most neuromorphic sensing systems were demonstrated without signal conversion/transmission functions. Therefore, those cannot fully mimic the function provides by the sensory neuron in the biological system. This thesis aims to design a neuromorphic sensing system with a complete function as biological sensory neurons. To reach such a target, 3D printed sensors, electrical oscillators, and synaptic transistors were developed as functions of artificial receptors, artificial neurons, and artificial synapses, respectively. Moreover, since the 3D printing technology has demonstrated a facile process due to fast prototyping, the proposed 3D neuromorphic sensing system was designed as a 3D integrated structure and fabricated by 3D printing technologies. A novel multi-axis robot 3D printing system was also utilized to increase the fabrication efficiency with the capability of printing on vertical and tilted surfaces seamlessly. Furthermore, the developed 3D neuromorphic system was easily adapted to the application of tactile sensing. A portable neuromorphic system was integrated with a tactile sensing system for the intelligent tactile sensing application of the humanoid robot. Finally, the bio-inspired reflex arc for the unconscious response was also demonstrated by training the neuromorphic tactile sensing system

Force/torque and tactile sensors for sensor-based manipulator control

The autonomy of manipulators, in space and in industrial environments, can be dramatically enhanced by the use of force/torque and tactile sensors. The development and future use of a six-component force/torque sensor for the Hermes Robot Arm (HERA) Basic End-Effector (BEE) is discussed. Then a multifunctional gripper system based on tactile sensors is described. The basic transducing element of the sensor is a sheet of pressure-sensitive polymer. Tactile image processing algorithms for slip detection, object position estimation, and object recognition are described