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Exceptional points (EPs) have revealed a lot of fundamental physics and promise many important applications. The effect of system nonlinearity on the property of EPs is yet to be well studied. Here, we propose an optical system with nonlinear dissipation to achieve a nonreciprocal EP. Our system consists of a linear whispering-gallery-mode microresonator (WGMR) coupling to a WGMR with nonlinear dissipation. In our system, the condition of EP appearance is dependent on the field intensity in the nonlinear WGMR. Due to the chirality of intracavity field intensity, the EPs and the transmission of the system can be nonreciprocal. Our work may pave the way to exploit nonreciprocal EP for optical information processing.
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CONTEXT: The compounds of the "565" parent ring structure have received much attention from researchers because of their excellent detonation performance. In the present study, 81 derivatives were designed by introducing different substituents based on 6-dinitrophenyl-5,6,7,8-tetrahydro-4-imidazo[4,5-e]furazano[3,4-b] pyrazine (DIOP), which is a compound of the parent ring structure of 565, and the performance of these derivatives, such as the electronic structure, energy gap, heat of formation, and detonation performance, were investigated. Among these energy-containing derivatives, the density ranges from 1.70 to 2.17 g/cm3, the detonation velocity ranges from 8.01 to 10.26 km/s, and the detonation pressure ranges from 27.99 to 49.88 GPa. Through comprehensive analysis of several properties of DIOP derivatives, it was found that the oxygen balance of derivatives with the -ONO2 group was greater than zero and close to zero, while the oxygen balance of derivatives with other groups was almost all less than zero. Among them, G8 (D = 10.1 km/s, P = 47.72 GPa), H8 (D = 10.11 km/s, P = 47.92 GPa), and I8 (D = 10.26 km/s, P = 49.88 GPa) had higher detonation velocity and pressure among all derivatives, and their impact sensitivity was better than RDX. Therefore, three potential high-energy and less sensitive energy-containing derivatives, G8, H8, and I8, were screened out. The intramolecular interactions of the three derivatives were further analyzed, and it was found that there were intensive van der Waals interactions and significant spatial steric effects within the molecules, which had a positive effect on reducing the shock sensitivity of the compounds. Moreover, the three derivatives have a large degree of stacking, which leads to a high density. METHODS: All calculations in this paper are performed using Gaussian16 based on density functional theory. Firstly, the structures of the derivatives were optimized at the level of B3LYP-D3/6-311G**, and then single-site energy calculations were carried out at the level of M06-2X-D3/def2-TZVPP, to reveal the effects of single substituents versus multiple substituents and isomerism on the properties of the DIOP-based energetic derivatives. Multiwfn was used to plot the density of states (DOS) of the derivatives and to calculate the molecular surface electrostatic potential at 0.001 e/Bohr3 electron density, 0.25 Bohr lattice spacing surface.
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CONTEXT: The influence of external electric fields (EEFs) on chemical substances has always been a hot topic in the field of theoretical chemistry research. 2,6-Diamino-3,5-dinitropyrazine-1-oxide (LLM-105) is an energetic material with excellent comprehensive properties and enormous potential for application. This article explores the molecular structure, electronic structure, energy change, frontier molecular orbitals (FMOs) and density of states (DOS), UV-Vis spectra, and infrared spectra of LLM-105 under various electric field conditions. The results indicate that negative EEF can improve the stability of LLM-105, reflected in the initiation of changes in bond length and HOMO-LOMO gap. EEF has a significant impact on the electronic structure of LLM-105. The polarization of the electronic structure brings about a change in total energy, which is reflected in the analysis of energy changes. In addition, the external electric field will cause the frequency of the infrared spectra and the UV-Vis spectra to have different degrees of blue shift. The results of the analysis are helpful to understand the changes of energetic materials under the applied electric field. METHODS: Based on the density functional theory (DFT), the structural optimization and energy calculation were carried out by using B3LYP/6-311G(d, p) and B3LYP/def2-TZVPP methods, respectively. After optimization convergence, vibration analysis was performed without imaginary frequencies to obtain stable configurations. Then, the molecular structure, electronic structure, energy changes, molecular orbital and density of states, UV-Vis spectra, and infrared spectra were analyzed.
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CONTEXT: The crystal and molecular structure, electronic properties, optical parameters, and elastic properties of a 1:2 hexanitrohexaazaisowurtzitane (CL-20)/2-mercapto-1-methylimidazole (MMI) cocrystal under 0 ~ 100 GPa hydrostatic pressure were calculated. The results show that the cocrystal CL-20/MMI undergoes three structural transitions at 72 GPa, 95 GPa, and 97 GPa, respectively, and the structural transition occurs in the part of the MMI compound. Structural mutations formed new bonds S1-S2, C2-C7, and N1C5 at 72GPa, 95 GPa, and 97 GPa, respectively. Similarly, the formation of new bonds is confirmed on the basis of an analysis of the changes in lattice constants, cell volumes, and partial densities of states (PDOS) for S1, S2, C2, C7, N1, and C3 at the corresponding pressures. The optical parameters show that the pressure makes the peaks of various optical parameters of CL-20/MMI larger, and the optical activity is enhanced. The optical parameters also confirm the structural mutation of CL-20/MMI under the corresponding pressure. METHOD: CL-20/MMI was calculated by using the first-principles norm-conservative pseudopotential based on density functional theory (DFT) in the CASTEP software package. For the optimization results, the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is selected to optimize the geometry of the cocrystal in the range of 0-100 GPa. GGA/PBE (Perdew-Burke-Ernzerhof) was selected to relax the cocrystal CL-20/MMI fully without constraints at atmospheric pressure. The sampling scheme in the Brillouin zone [10] is the Monkhorst-Pack scheme, and the number of k-point grids was 2 × 2 × 2. By contrast, this study will use the LDA method to calculate.
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Community detection is a vital task in many fields, such as social networks, and financial analysis, to name a few. The Louvain method, the main workhorse of community detection, is a popular heuristic method based on modularity. But it is difficult for the sequential Louvain method to deal with large-scale graphs. In order to overcome the drawback, researchers have proposed several parallel Louvain methods (Parallel Louvain Method, PLM), which suffer two challenges: (1) latency in the information synchronization and (2) communities swap. To tackle these two challenges, we propose a graph partition algorithm for the parallel Louvain method. Different from existing graph partition algorithms, our graph partition algorithm divides the graph into subgraphs called isolate sets, in which vertices are relatively decoupled from others, and the PLM computes and synchronizes information without delay and communities swap. We first describe concepts and properties of isolate sets. In the second place, we propose an algorithm to divide the graph into isolate sets, which enjoys the same computation complexity as the breadth-first search. Finally, we propose the isolate-set-based parallel Louvain method, which calculates and updates vertices information without latency and communities swap. We implement our method with OpenMP on an 8-cores PC. Experiments on 18 graphs show that our parallel method achieves a maximum 4.62 [Formula: see text] speedup compared with the sequential method, and outputs higher modularity on 14 graphs.