Boundary behaviour of the unique solution to a singular Dirichlet problem with a convection term

AbstractBy Karamata regular variation theory and constructing comparison functions, we derive that the boundary behaviour of the unique solution to a singular Dirichlet problem −Δu=b(x)g(u)+λ|∇u|q, u>0, x∈Ω, u|∂Ω=0, which is independent of λ|∇uλ|q, where Ω is a bounded domain with smooth boundary in RN, λ∈R, q∈(0,2], lims→0+g(s)=+∞, and b is non-negative on Ω, which may be vanishing on the boundary

Magnetic band representations, Fu-Kane-like symmetry indicators and magnetic topological materials

To realize novel topological phases and to pursue potential applications in low-energy consumption spintronics, the study of magnetic topological materials is of great interest. Starting from the theory of nonmagnetic topological quantum chemistry [Bradlyn et al., Nature 547, 298 (2017)], we have obtained irreducible (co)representations and compatibility relations (CRs) in momentum space, and we constructed a complete list of magnetic band (co)representations (MBRs) in real space for other MSGs with anti-unitary symmetries (i.e. type-III and type-IV MSGs). The results are consistent with the magnetic topological quantum chemistry [Elcoro et al., Nat. Comm. 12, 5965 (2021)]. Using the CRs and MBRs, we reproduce the symmetry-based classifications for MSGs, and we obtain a set of Fu-Kane-like formulas of symmetry indicators (SIs) in both spinless (bosonic) and spinful (fermionic) systems, which are implemented in an automatic code - TopMat - to diagnose topological magnetic materials. The magnetic topological materials, whose occupied states can not be decomposed into a sum of MBRs, are consistent with nonzero SIs. Lastly, using our online code, we have performed spin-polarized calculations for magnetic compounds in the materials database and find many magnetic topological candidates.Comment: 6 pages, 3128 pages for the Appendice

Demonstration of Low Voltage and Functionally Complete Logic Operations Using Body-Biased Complementary and Ultra-Thin ALN Piezoelectric Mechanical Switches

This paper reports, for the first time, on the demonstration of low voltage and functionally complete logic elements (NAND and NOR) implemented by using body-biased complementary and ultra-thin (250 nm thick) Aluminum Nitride (AlN) based piezoelectric mechanical switches. This work presents, firstly, the importance of scaling AlN films for the demonstration of ultra-thin AlN switches and, secondly, the implementation of a new actuation scheme based on body biasing to lower the switch threshold voltage. Four of these ultra-thin switches were connected together to synthesize functionally complete MEMS logic gates (NAND and NOR) with a ± 2V swing and a body-bias voltage \u3c 8 V

Quantifying Spatiotemporal Dynamics of Solar Radiation over the Northeast China Based on ACO-BPNN Model and Intensity Analysis

Reliable information on the spatiotemporal dynamics of solar radiation plays a crucial role in studies relating to global climate change. In this study, a new backpropagation neural network (BPNN) model optimized with an Ant Colony Optimization (ACO) algorithm was developed to generate the ACO-BPNN model, which had demonstrated superior performance for simulating solar radiation compared to traditional BPNN modelling, for Northeast China. On this basis, we applied an intensity analysis to investigate the spatiotemporal variation of solar radiation from 1982 to 2010 over the study region at three levels: interval, category, and conversion. Research findings revealed that (1) the solar radiation resource in the study region increased from the 1980s to the 2000s and the average annual rate of variation from the 1980s to the 1990s was lower than that from the 1990s to the 2000s and (2) the gains and losses of solar radiation at each level were in different conditions. The poor, normal, and comparatively abundant levels were transferred to higher levels, whereas the abundant level was transferred to lower levels. We believe our findings contribute to implementing ad hoc energy management strategies to optimize the use of solar radiation resources and provide scientific suggestions for policy planning

Body-Biased Complementary Logic Implemented Using AIN Piezoelectric MEMS Switches

This paper reports on the first implementation of low voltage complementary logic (\u3c 1.5 V) by using body-biased aluminum nitride (AlN) piezoelectric MEMS switches. For the first time, by using opposite body biases the same mechanical switch has been made to operate as both an ntype and p-type (complementary) device. Body-biasing also gives the ability to precisely tune the threshold voltage of a switch. The AlN MEMS switches have shown extremely small subthreshold slopes and threshold voltages as low as 0.8 mV/dec and 30 mV, respectively. Furthermore, this work presents a fully mechanical body-biased inverter formed by two AlN MEMS switches operating at 100 Hz with a ± 1.5 V voltage swing

100 NM Thick Aluminum Nitrade Based Piezoelectric Nano Switches Exhibiting 1 MV Threshold Voltage via Body-Biasing

This paper reports on the first demonstration of aluminum nitride (AIN) piezoelectric logic switches that were fabricated with ultra-thin (100nm) AIN films and exhibit a 1 mV threshold voltage via the body-biasing scheme. The application of a relatively low (\u3c 6 V) fixed potential to the body terminal of a 4-terminal switch has been cycled to \u3e 109 cycles and, although the contact resistance was found to be high (~ 1 MΩ), the nano-films have functioned throughout to show high piezoelectric nano-film reliability