(Acetato-κO)diaqua­[2-(1H-benzotriazol-1-yl)acetato-κO](1,10-phenanthroline-κ2 N,N′)manganese(II) dihydrate

In the hydrated title complex, [Mn(C8H6N3O2)(CH3CO2)(C12H8N2)(H2O)2]·2H2O, the MnII atom is coordinated by two N atoms from a 1,10-phenanthroline ligand, two water O atoms, a monodentate acetate anion and an O-monodentate 2-(1H-benzotriazol-1-yl)acetate ligand, resulting in a distorted cis-MnN2O4 octa­hedral coordination geometry. The water O atoms are in a trans arrangement and one of them forms an intra­molecular O—H⋯O hydrogen bond to the uncoordinated O atom of the acetate ion. In the crystal, the complex mol­ecules and water mol­ecules are connected by O—H⋯O and O—H⋯N hydrogen bonds to generate a three-dimensional network

Efficient multistep methods for tempered fractional calculus: Algorithms and Simulations

In this work, we extend the fractional linear multistep methods in [C. Lubich, SIAM J. Math. Anal., 17 (1986), pp.704--719] to the tempered fractional integral and derivative operators in the sense that the tempered fractional derivative operator is interpreted in terms of the Hadamard finite-part integral. We develop two fast methods, Fast Method I and Fast Method II, with linear complexity to calculate the discrete convolution for the approximation of the (tempered) fractional operator. Fast Method I is based on a local approximation for the contour integral that represents the convolution weight. Fast Method II is based on a globally uniform approximation of the trapezoidal rule for the integral on the real line. Both methods are efficient, but numerical experimentation reveals that Fast Method II outperforms Fast Method I in terms of accuracy, efficiency, and coding simplicity. The memory requirement and computational cost of Fast Method II are $O(Q)$ and $O(Qn_T)$, respectively, where $n_T$ is the number of the final time steps and $Q$ is the number of quadrature points used in the trapezoidal rule. The effectiveness of the fast methods is verified through a series of numerical examples for long-time integration, including a numerical study of a fractional reaction-diffusion model

Mutual correlation in the shock wave geometry

We probe the shock wave geometry with the mutual correlation in a spherically symmetric Reissner Nordstr\"om AdS black hole on the basis of the gauge/gravity duality. In the static background, we find that the regions living on the boundary of the AdS black holes are correlated provided the considered regions on the boundary are large enough. We also investigate the effect of the charge on the mutual correlation and find that the bigger the value of the charge is, the smaller the value of the mutual correlation will to be. As a small perturbation is added at the AdS boundary, the horizon shifts and a dynamical shock wave geometry forms after long time enough. In this dynamic background, we find that the greater the shift of the horizon is, the smaller the mutual correlation will to be. Especially for the case that the shift is large enough, the mutual correlation vanishes, which implies that the considered regions on the boundary are uncorrelated. The effect of the charge on the mutual correlation in this dynamic background is found to be the same as that in the static background.Comment: 10 page

μ-Oxalato-κ4 O 1,O 2:O 1′,O 2′-bis­[diaqua­(2,2′-bipyridyl-κ2 N,N′)zinc] bis­[2-(1H-benzotriazol-1-yl)acetate] hexa­hydrate

The asymmetric unit of the title compound, [Zn2(C2O4)(C10H8N2)2(H2O)4](C8H6N3O2)2·6H2O, contains one half of the centrosymmetric binuclear cation, one anion and three water mol­ecules. In the cation, the oxalate ligand bridges two ZnII ions in a bis-bidentate fashion, so each ZnII ion is coordinated by two O atoms from the oxalate ligand, two N atoms from two 2,2′-bipyridine ligands and two water mol­ecules in a distorted octa­hedral arrangement. The mean planes of the oxalate and 2,2′-bipyridine ligands form a dihedral angle of 80.0 (1)°. An extensive three-dimensional hydrogen-bonding network formed by classical O—H⋯O and O—H⋯N inter­actions consolidates the crystal packing

Bulk Operator Reconstruction in Topological Tensor Network and Generalized Free Fields

In this paper, we would like to study operator reconstruction in a class of holographic tensor networks describing renormalization group flows studied in arXiv:2210.12127. We study examples of 2d bulk holographic tensor networks constructed from Dijkgraaf-Witten theories and found that for both $\mathbb{Z}_n$ group and $S_3$ group the number of bulk operators behaving like a generalized free field in the bulk scales as the order of the group. We also generalize our study to 3d bulks and found the same scaling for $\mathbb{Z}_n$ theories. However, there is no generalized free field when the bulk comes from more generic fusion categories such as the Fibonacci model.Comment: 11 pages, 3 figure

(E)-N′-(3,4,5-Trimethoxy­benzyl­idene)-2-(8-quinol­yloxy)acetohydrazide methanol solvate

In the title compound, C21H21N3O5·CH4O, the quinoline plane and the benzene ring form a dihedral angle of 3.6 (2)°. The methanol solvent mol­ecule is linked with the acetohydrazide mol­ecule via O—H⋯N and N—H⋯O hydrogen bonds. In the crystal structure, weak inter­molecular C—H⋯O hydrogen bonds help to consolidate the crystal packing, which also exhibits π–π inter­actions, as indicated by short distances of 3.739 (4) Å between the centroids of the aromatic rings

A New Traffic Conflict Measure for Electric Bicycles at Intersections

As electric bicycles (e-bikes) are becoming popular in China, concerns have been raised about their safety conditions. A traffic conflict technique is commonly used in traffic safety analysis, and there are many conflict measures designed for cars. However, e-bikes have high flexibility to change speed and trajectories, which is different from cars, so the conflict measures defined for e-bikes need to be independently explored. Based on e-bike driving characteristics, this paper proposes a new measure, the Integrated Conflict Intensity (ICI), for traffic conflicts involving e-bikes at intersections. It measures the degree of dangerousness of a conflict process, with consideration of both conflict risk and conflict severity. Time to collision is used to measure the conflict risk. Relative kinetic energy is used to measure the conflict severity. ICI can be calculated based on video analysis. The method of determining ICI thresholds for three conflict levels (serious, less serious, and slight) and two conflict types (conflicts between two e-bikes, and conflicts between an e-bike and a car) is put forward based on the questionnaires about safety perception of e-bike riders, which is regarded as the criterion of e-bike safety conditions at intersections. The video recording and a questionnaire survey about conflicts involving e-bikes at intersections have been conducted, and the unified thresholds applicable to different intersections have been determined. It is verified that ICI and its thresholds meet the criterion of e-bike safety conditions. This work is expected to be used in the selection of intersections for safety improvement of e-bike traffic.</p

Formation of Nanofoam carbon and re-emergence of Superconductivity in compressed CaC6

Pressure can tune material's electronic properties and control its quantum state, making some systems present disconnected superconducting region as observed in iron chalcogenides and heavy fermion CeCu2Si2. For CaC6 superconductor (Tc of 11.5 K), applying pressure first Tc increases and then suppresses and the superconductivity of this compound is eventually disappeared at about 18 GPa. Here, we report a theoretical finding of the re-emergence of superconductivity in heavily compressed CaC6. The predicted phase III (space group Pmmn) with formation of carbon nanofoam is found to be stable at wide pressure range with a Tc up to 14.7 K at 78 GPa. Diamond-like carbon structure is adhered to the phase IV (Cmcm) for compressed CaC6 after 126 GPa, which has bad metallic behavior, indicating again departure from superconductivity. Re-emerged superconductivity in compressed CaC6 paves a new way to design new-type superconductor by inserting metal into nanoporous host lattice.Comment: 31 pages, 12 figures, and 4 table