A primer on perfect simulation for spatial point processes

This primer provides a self-contained exposition of the case where spatial birth-and-death processes are used for perfect simulation of locally stable point processes. Particularly, a simple dominating coupling from the past (CFTP) algorithm and the CFTP algorithms introduced in [13], [14], and [5] are studied. Some empirical results for the algorithms are discussed. Received: 30 June 2002     

On the Modified Crystalline Stefan Problem with Singular Data

We study the behavior of solutions of the modified Stefan problem in the plane for polygonal interfaces. We are particularly interested in a solution near a singularity of either the loss of a facet or the breaking of a facet. We establish precise regularity results if a facet disappears. We use them to establish the existence of a weak solution with singular data, i.e., when some of the zero-crystalline-curvature facets have zero length.     

Analysis of Threshold Current and Wall-Plug Efficiency of Diode Lasers with Asymmetric Facet Reflectivity

Threshold current and differential quantum efficiency of broad contact lasers with asymmetric facet reflectivity are discussed with the purpose to reveal factors essential for optimisation of the wall-plug efficiency of such lasers. Lasers with low front facet reflectivity and short cavity often exhibit behaviour difficult to explain with a classical theory. More rigorous calculation performed in this work show that differential quantum efficiency is indeed less affected by a change of the front facet reflectivity or cavity length than predicted by such theory. These findings greatly simplify criteria for optimisation of the wall-plug efficiency of broad contact lasers with coated facets.     

CeO2担载Cu纳米粒子电催化CO2还原产乙烯：CeO2不同暴露晶面对催化性能的影响

Fossil fuels are expected to be the major source of energy for the next few decades. However, combustion of nonrenewable resources leads to the release of large quantities of CO₂, the primary greenhouse gas. Notably, the concentration of CO₂ in the atmosphere is increasing annually at an astounding rate. Electrochemical CO₂ reduction (ECR) to value-added fuels and chemicals using electricity from intermittent renewable energy sources is a carbon-neutral method to alleviate anthropogenic CO₂ emissions. Despite the steady progress in the selective generation of C₁ products (CO and formic acid), the production of multi-carbon species still suffers from low selectivity and efficiency. As an ECR product, ethylene (C₂H₄) has a higher energy density than do C₁ species and is an important industrial feedstock in high demand. However, the conversion of CO₂ to C₂H₄ is plagued by low productivity and large overpotential, in addition to the severe competing hydrogen evolution reaction (HER) during the ECR. To address these issues, the design and development of advanced electrocatalysts are critical. Here, we demonstrate fine-tuning of ECR to C₂H₄ by taking advantage of the prominent interaction of Cu with shape-controlled CeO₂ nanocrystals, that is, cubes, rods, and octahedra predominantly covered with (100), (110), and (111) surfaces, respectively. We found that the selectivity and activity of the ECR depended strongly on the exposed crystal facets of CeO₂. The overall ECR Faradaic efficiency (FE) over Cu/CeO₂(110) (FE ≈ 56.7%) surpassed that of both Cu/CeO₂(100) (FE ≈ 51.5%) and Cu/CeO₂(111) (FE ≈ 48.4%) in 0.1 mol·L^-1 KHCO₃ solutions with an H-type cell. This was in stark contrast to the exclusive occurrence of the HER over pure carbon paper, CeO₂(100), CeO₂(110), and CeO₂(111). In particular, the FE toward C₂H₄ formation and the partial current density increased in the sequence Cu/CeO₂(111) < Cu/CeO₂(100) < Cu/CeO₂(110) within applied bias potentials from -1.00 to -1.15 V (vs. the reversible hydrogen electrode), reaching 39.1% over Cu/CeO₂(110) at a mild overpotential (1.13 V). The corresponding values for Cu/CeO₂(100) and Cu/CeO₂(111) were FE_C2H4 ≈ 31.8% and FE_C2H4 ≈ 29.6%, respectively. The C₂H₄ selectivity was comparable to that of many reported Cu-based electrocatalysts at similar overpotentials. Furthermore, the FE for C₂H₄ remained stable even after 6 h of continuous electrolysis. The superior ECR activity of Cu/CeO₂(110) to yield C₂H₄ was attributed to the metastable (110) surface, which not only promoted the effective adsorption of CO₂ but also remarkably stabilized Cu⁺, thereby boosting the ECR to produce C₂H₄. This work offers an alternative strategy to enhance the ECR efficiency by crystal facet engineering.     

Facets for the cut cone I

We study facets of the cut coneC _n , i.e., the cone of dimension 1/2n(n – 1) generated by the cuts of the complete graph onn vertices. Actually, the study of the facets of the cut cone is equivalent in some sense to the study of the facets of the cut polytope. We present several operations on facets and, in particular, a lifting procedure for constructing facets ofC _n+1 from given facets of the lower dimensional coneC _n . After reviewing hypermetric valid inequalities, we describe the new class of cycle inequalities and prove the facet property for several subclasses. The new class of parachute facets is developed and other known facets and valid inequalities are presented.     

Diffeomorphisms with C 1-stably average shadowing

Let M be a closed smooth manifold M, and let f : M → M be a diffeomorphism. In this paper, we consider a nontrivial transitive set Λ of f . We show that if f has the C1-stably average shadowing property on Λ, then Λ admits a dominated splitting.     

A finite volume scheme preserving extremum principle for convection–diffusion equations on polygonal meshes

We propose a nonlinear finite volume scheme for convection–diffusion equation on polygonal meshes and prove that the discrete solution of the scheme satisfies the discrete extremum principle. The approximation of diffusive flux is based on an adaptive approach of choosing stencil in the construction of discrete normal flux, and the approximation of convection flux is based on the second‐order upwind method with proper slope limiter. Our scheme is locally conservative and has only cell‐centered unknowns. Numerical results show that our scheme can preserve discrete extremum principle and has almost second‐order accuracy. Copyright © 2017 John Wiley & Sons, Ltd.     

具有主导晶面的BiOIO3/BiOCl异质结制备与光催化性能

分别以乙二醇/去离子水为溶剂,通过溶剂热/水热法分别制备了具有不同主导晶面的BiOIO₃/{110}BiOCl和BiOIO₃/{001}BiOCl异质结。采用X射线衍射、扫描电子显微镜、能量色散谱和紫外可见漫反射光谱对制备的BiOIO₃/BiOCl光催化剂进行了表征。在可见光照射下,通过对罗丹明 B和苯酚水溶液的光催化降解,考察了 BiOIO₃/BiOCl异质结的光催化活性。结果显示25% BiOIO₃/{110}BiOCl异质结具有最高的光催化效率。BiOIO₃/{110}BiOCl较好的光催化性能是由于其在可见光区较强的光吸收,以及异质结结构和BiOCl所具有的(110)主导晶面有利于光生载流子的分离。超氧自由基(·O₂^-)和空穴(h⁺)是光催化过程中的主要活性物质。此外,根据实验结果探讨了光催化性能增强的机理。     

室温下制备以{211}晶面为主的Ti1-xVxO2薄膜及其可见光催化性能

以金属Ti和V作为靶材,采用直流反应共溅射技术在室温下制备了以{211}晶面为主的锐钛矿相Ti_1-xV_xO₂薄膜,研究了不同V靶功率对Ti_1-xV_xO₂薄膜的薄膜成分、晶相结构和可见光催化性能的影响。研究表明,Ti_1-xV_xO₂薄膜的晶相结构为锐钛矿相,择优取向为(211),而结晶度受V靶功率的影响。随着V靶功率的增加,薄膜中V元素含量逐渐增加,同时,晶粒和沉积速率也逐渐增加。另外,当V靶功率为150 W时,薄膜的表面粗糙度值有一个最大值。V的掺杂导致薄膜的能带间隙变窄,对光的吸收向可见光区偏移,从而有效地改善了薄膜的可见光催化能力。当V靶功率为150 W时,Ti_1-xV_xO₂薄膜的能带间隙值为 2.82 eV,其在2 h的可见光照射下分解了80%的RhB染料。这被归结于能带间隙窄,高能晶面{211}和结晶度高的共同作用。