New Planar P-time Computable Six-Vertex Models and a Complete Complexity Classification

We discover new P-time computable six-vertex models on planar graphs beyond Kasteleyn's algorithm for counting planar perfect matchings. We further prove that there are no more: Together, they exhaust all P-time computable six-vertex models on planar graphs, assuming #P is not P. This leads to the following exact complexity classification: For every parameter setting in ${\mathbb C}$ for the six-vertex model, the partition function is either (1) computable in P-time for every graph, or (2) #P-hard for general graphs but computable in P-time for planar graphs, or (3) #P-hard even for planar graphs. The classification has an explicit criterion. The new P-time cases in (2) provably cannot be subsumed by Kasteleyn's algorithm. They are obtained by a non-local connection to #CSP, defined in terms of a "loop space". This is the first substantive advance toward a planar Holant classification with not necessarily symmetric constraints. We introduce M\"obius transformation on ${\mathbb C}$ as a powerful new tool in hardness proofs for counting problems.Comment: 61 pages, 16 figures. An extended abstract appears in SODA 202

Sensor Scheduling with Intelligent Optimization Algorithm Based on Quantum Theory

The particle swarm optimization (PSO) algorithm superiority exists in convergence rate, but it tends to get stuck in local optima. An improved PSO algorithm is proposed using a best dimension mutation technique based on quantum theory, and it was applied to sensor scheduling problem for target tracking. The dynamics of the target are assumed as linear Gaussian model, and the sensor measurements show a linear correlation with the state of the target. This paper discusses the single target tracking problem with multiple sensors using the proposed best dimension mutation particle swarm optimization (BDMPSO) algorithm for various cases. Our experimental results verify that the proposed algorithm is able to track the target more reliably and accurately than previous ones

Density Functional Theory Analysis of Surface Structures of Spinel LiNi0.5Mn1.5O4 Cathode Materials

First-principle calculation was employed to investigate the surface stability for (100), (110) and (111) low index facets of LiNi0.5Mn1.5O4 (LNMO) crystallographic structures with a P4332 space group and phase transitions at the surface regions of Ni0.5Mn1.5O4. The calculated surface energies of (100) and (111) facets with Li-terminations are 1.39 and 1.40 eV, respectively, indicating that both these facets of the LNMO are stable according to the calculation results. Defect formation energies and diffusion barriers of Ni and Mn in surface facets of the Ni0.5Mn1.5O4 are much lower than those in the bulk. This suggests that the Ni and Mn ions in the surface regions of the LNMO easily occupy the tetrahedral Li-positions during delithiation process, which supports the experimental results and explains the surface structure changes of the LNMO upon delithiation

Composites of Piezoelectric Materials and Silicon as Anode for Lithium Ion Batteries

Group IVA elements (Si, Ge and Sn) are promising candidates for the anode materials of lithium ion batteries (LIBs) due to their large theoretical specific capacities. However, serious problems of pulverization and capacity degradation resulted from the huge volume changes during charge/discharge operations hindered their successful applications as the anode materials in the LIBs. In this work, diffusion behaviors of Li ions in Si(100) and Si(111) slabs with a piezoelectric field applied perpendicularly to the surfaces were investigated using density functional theory. Results showed that the diffusivity of the Li in Si can be significantly enhanced by applying the electric field generated from the piezoelectric material. This finding can explain well the recent experimental observations in which improved electrochemical performance was obtained using Si/carbon nanotube/BaTiO3 as the anode for the LIBs. New generation of anode composite materials can be designed based on this idea and the piezoelectric material is used not only to accommodate the volume variation of active materials of Si, but also to enhance the charging rate of the LIBs

Adsorption and Diffusion of Sodium on Graphene with Grain Boundaries

Effects of grain boundaries (GBs) in graphene on adsorption and diffusion of sodium were investigated using first principle calculations. Results showed that the presence of GBs in graphene enhanced the adsorption of sodium, with their adsorption energies in the range of -1.32~-0.79 eV, which were lower than the value of -0.67 eV for sodium adsorbed on pristine graphene. The diffusion energy barriers were in the range of 0.09 to 0.35 eV when sodium was diffused along GBs of graphene, whereas they were decreased when sodium was gradually diffused into the GBs. Results showed that graphene with GBs had a larger energy storage capacity for sodium than the pristine one, indicating that it can be used as a good anode material for sodium ion batteries

Rhenium Doping Induced Structural Transformation in Mono-layered MoS2 with Improved Catalytic Activity for Hydrogen Evolution Reaction

This paper reports a new design methodology to improve catalytic activities of catalysts based on two-dimensional transition metal dichalcogenides through elemental doping which induces structural transformations. Effects of rhenium (Re) doping on structural stability/phase transformation and catalytic activity of mono-layered trigonal prismatic (2H) MoS2 were investigated using density functional theory as one example. Results show that 2H-Mo1-xRexS2 transforms into 1T'-Mo1-xRexS2MoS2 as the value of x is larger than 0.4, and the transfer of the electron from Re to Mo is identified as the main reason for this structural transformation. The 1T'-Mo1-xRexS2 shows a good catalytic activity for the hydrogen evolution reaction when 0.75≤x≤0.94