The number and degree distribution of spanning trees in the Tower of Hanoi graph

The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribution of the spanning trees in the Hanoi graph. We first establish recursion relations between the number of spanning trees and other spanning subgraphs of the Hanoi graph, from which we find an exact analytical expression for the number of spanning trees of the n-disc Hanoi graph. This result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree. Then, we introduce a vertex labeling which allows to find, for each vertex of the graph, its degree distribution among all possible spanning trees.Postprint (author's final draft

Quantum dot passivation of halide perovskite films with reduced defects, suppressed phase segregation, and enhanced stability

Structural defects are ubiquitous for polycrystalline perovskite films, compromising device performance and stability. Herein, a universal method is developed to overcome this issue by incorporating halide perovskite quantum dots (QDs) into perovskite polycrystalline films. CsPbBr3 QDs are deposited on four types of halide perovskite films (CsPbBr3, CsPbIBr2, CsPbBrI2, and MAPbI3) and the interactions are triggered by annealing. The ions in the CsPbBr3 QDs are released into the thin films to passivate defects, and concurrently the hydrophobic ligands of QDs self-assemble on the film surfaces and grain boundaries to reduce the defect density and enhance the film stability. For all QD-treated films, PL emission intensity and carrier lifetime are significantly improved, and surface morphology and composition uniformity are also optimized. Furthermore, after the QD treatment, light-induced phase segregation and degradation in mixed-halide perovskite films are suppressed, and the efficiency of mixed-halide CsPbIBr2 solar cells is remarkably improved to over 11% from 8.7%. Overall, this work provides a general approach to achieving high-quality halide perovskite films with suppressed phase segregation, reduced defects, and enhanced stability for optoelectronic applications.Peer ReviewedPostprint (author's final draft

Random walks on dual Sierpinski gaskets

We study an unbiased random walk on dual Sierpinski gaskets embedded in d-dimensional Euclidean spaces. We first determine the mean first-passage time (MFPT) between a particular pair of nodes based on the connection between the MFPTs and the effective resistance. Then, by using the Laplacian spectra, we evaluate analytically the global MFPT (GMFPT), i.e., MFPT between two nodes averaged over all node pairs. Concerning these two quantities, we obtain explicit solutions and show how they vary with the number of network nodes. Finally, we relate our results for the case of d = 2 to the well-known Hanoi Towers problem

Dynamic analysis of riverbed evolution: Chengtong Reach of Yangtze Estuary

This paper proposes a new approach to improve the analysis by extensively using the numerical model results. A 2D hydrodynamic model based on the Delft 3D suite is first set up and validated with the field measurement data. The model is then used to examine the hydrodynamic responses of the estuary to the change of local bathymetry or upstream discharge. This approach is applied to the Chengtong Reach of Yangtze Estuary as an example. The net discharge ratio (NDR) is used as an index to demonstrate the trend of channel development. The results show that the net discharge ratios (NDRs) at the main channels of Fujiangsha, Tongzhousha and Langshansha sub-reaches decrease with increase of upstream river discharge in general; however, the NDR at the main channel of Rugaosha sub-reach increases first, and then decreases with increase of upstream river discharge when the river discharge is larger than 45,000 m3/s. This difference is related to the local bathymetry as well as the ebb-dominated or flood dominated characters in those sub-reaches

Effects of the anthropogenic activities on the morphological evolution of the Modaomen Estuary, Pearl River Delta, China

Owing to the intensive human activities, the Modaomen Estuary has been significantly modified since 1950s, which has resulted in considerable changes of hydrodynamics and morphodynamics in the area. In this paper, the effects of the anthropogenic activities on the hydrodynamics and morphological evolution in the estuary at different stages are systematically assessed based on the detailed bathymetric data and field survey. The results show that the human activities have caused the channelization of the enclosed sea area in the Modamen Estuary; fast seaward movement of the mouth bar with high siltation; expansion of the channel volume due to channel deepening. The paper also highlights the main hydrodynamic changes in the estuary, including the rise of the water level; the distinguishing changes of tidal range before and after the 1990s (decrease and increase respectively); as well as the increase of the divided flow ratio. It is found that reclamation is the main factor promoting the transition of nature of the estuary from runoff dominant to runoff and wave dominant, and sand mining activities are mainly to strengthen the tidal dynamic and to low the water level. The results provide useful guidance for better planning of the future developments in the estuary and further research in the area

The number and degree distribution of spanning trees in the Tower of Hanoi graph

The number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph, such as its reliability, communication aspects, synchronization, and so on. However, the practical enumeration of spanning trees and the study of their properties remain a challenge, particularly for large networks. In this paper, we study the number and degree distribution of the spanning trees in the Hanoi graph. We first establish recursion relations between the number of spanning trees and other spanning subgraphs of the Hanoi graph, from which we find an exact analytical expression for the number of spanning trees of the n-disc Hanoi graph. This result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree. Then, we introduce a vertex labeling which allows to find, for each vertex of the graph, its degree distribution among all possible spanning trees

Two-Dimensional Benzobisthiazole-Vinylene-Linked Covalent Organic Frameworks Outperform One-Dimensional Counterparts in Photocatalysis

Vinylene/olefin-linked two-dimensional covalent organic frameworks (v-2D-COFs), featured with vinylene-linked in-plane conjugations, high chemical stabilities, and designable chemical structures, are promising for optoelectronic/photocatalytic applications. Developing v-2D-COFs with superior π-conjugation and optoelectronic properties is meaningful but remains challenging. In this work, we present the crystalline benzobisthiazole-bridged unsubstituted v-2D-COF (v-2D-COF-NS1 and v-2D-COF-NS2) synthesized via a benzothiazole-mediated aldol-type polycondensation. Interestingly, the resultant v-2D-COF exhibits a high chemical stability under both strong acidic (12 M HCl) and basic conditions (saturated KOH) due to the robust vinylene-linked skeletons. Moreover, the electron-deficient thiazole units and 2D π-conjugations endow v-2D-COFs (i.e., v-2D-COF-NS1) a narrow band gap of ∼1.85 eV with a conduction band of −3.65 eV vs vacuum, which are desirable for photocatalytic hydrogen evolution. As such, the v-2D-COF-NS1-based photoelectrode gives a photocurrent up to ∼47 μA cm–2 at 0.3 V vs reversible hydrogen electrode (RHE), which is much higher than the value of the corresponding linear polymer (LP-NS1) and outstanding among the reported COF photoelectrodes. Under a continuous visible light irradiation, v-2D-COF-NS1 generates hydrogen gas with an excellent rate of ∼4.4 mmol h–1 g–1 over 12 h. This work demonstrates the synthesis of unsubstituted v-2D-COFs that intrinsically contain benzobisthiazole-based building blocks and shows great potential in photocatalytic reactions