The Role of Radical Bridges in Polynuclear Single-Molecule Magnets

Employing radical bridges between anisotropic metal ions has been a viable route to achieve high-performance single-molecule magnets (SMMs). While the bridges have been mainly considered for their ability to promote exchange interactions, the crystal-field effect arising from them has not been taken into account explicitly. This lack of consideration may distort the understanding and limit the development of the entire family. To shed light on this aspect, herein we report a theoretical investigation of a series of N -radical-bridged diterbium complexes. It is found that while promoting strong exchange coupling between the terbium ions, the N -radical induces a crystal field that interferes destructively with that of the outer ligands, and thus reduces the overall SMM behavior. Based on the theoretical results, we conclude that the SMM behavior in this series could be further maximized if the crystal field of the outer ligands is designed to be collinear with that of the radical bridge. This conclusion can be generalized to all exchange-coupled SMMs.     

Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

基于不确定控制理论的最优策略研究

本文在不确定理论的框架下,研究一类带背景状态变量的最优控制模型.在乐观值准则下,利用不确定动态规划的方法,证明了不确定最优性原则,得到最优性方程.作为应用,求解一个固定缴费(DC)型养老金的最优投资策略问题,在乐观值准则下,以工资变量为背景状态变量,建立养老金模型.通过求解不确定最优性方程得到最优投资策略和最优支付率.     

An efficient edge based data structure for the compressible Reynolds-averaged Navier–Stokes equations on hybrid unstructured meshes

An efficient edge based data structure has been developed in order to implement an unstructured vertex based finite volume algorithm for the Reynolds-averaged Navier–Stokes equations on hybrid meshes. In the present approach, the data structure is tailored to meet the requirements of the vertex based algorithm by considering data access patterns and cache efficiency. The required data are packed and allocated in a way that they are close to each other in the physical memory. Therefore, the proposed data structure increases cache performance and improves computation time. As a result, the explicit flow solver indicates a significant speed up compared to other open-source solvers in terms of CPU time. A fully implicit version has also been implemented based on the PETSc library in order to improve the robustness of the algorithm. The resulting algebraic equations due to the compressible Navier–Stokes and the one equation Spalart–Allmaras turbulence equations are solved in a monolithic manner using the restricted additive Schwarz preconditioner combined with the FGMRES Krylov subspace algorithm. In order to further improve the computational accuracy, the multiscale metric based anisotropic mesh refinement library PyAMG is used for mesh adaptation. The numerical algorithm is validated for the classical benchmark problems such as the transonic turbulent flow around a supercritical RAE2822 airfoil and DLR-F6 wing-body-nacelle-pylon configuration. The efficiency of the data structure is demonstrated by achieving up to an order of magnitude speed up in CPU times.     

Prediction of the drag reduction effect of pulsating pipe flow based on machine learning

Prediction of drag reduction effect caused by pulsating pipe flows is examined using machine learning. First, a large set of flow field data is obtained experimentally by measuring turbulent pipe flows with various pulsation patterns. Consequently, more than 7000 waveforms are applied, obtaining a maximum drag reduction rate and maximum energy saving rate of 38.6% and 31.4%, respectively. The results indicate that the pulsating flow effect can be characterized by the pulsation period and pressure gradient during acceleration and deceleration. Subsequently, two machine learning models are tested to predict the drag reduction rate. The results confirm that the machine learning model developed for predicting the time variation of the flow velocity and differential pressure with respect to the pump voltage can accurately predict the nonlinearity of pressure gradients. Therefore, using this model, the drag reduction effect can be estimated with high accuracy.     

A DFT study on mechanisms of CO2 coupling with propargylic alcohols using alkali carbonates

The mechanisms of CO₂ coupling with the propargylic alcohol using alkali carbonates M₂CO₃ (M = Li, Na, K, Cs) have been investigated by means of density functional theory calculations. The calculations reveal that the target product tetronic acid (TA) is yielded through two stages: (a) the formation of the α-alkylidene cyclic carbonate (αACC) intermediate via Cs₂CO₃-mediated carboxylative cyclization of the propargylic alcohol with CO₂, and (b) the conversion of the αACC intermediate with Cs₂CO₃ to produce the cesium salt of the TA. Since the overall kinetic barriers for the two stages are comparable and affordable, the excellent chemoselectivity to the TA should be primarily originated from the high thermodynamic stability of the cesium salt of the TA. Moreover, relative to the TA, the possibility to yield the by-product acyclic carbonate can be excluded due to the both kinetics and thermodynamic inferiority. This result is different from the organic base-mediated reaction. Alternatively, our calculations predict that CsHCO₃ together generated with the cesium salt of the TA might also be an available mediating reagent for the incorporation of CO₂ with the propargylic alcohol. Compared to other alkali carbonates M₂CO₃ (M = Li, Na, K), the stronger basicity of Cs₂CO₃ and the lower ionic potential of cesium ion can raise the effective concentration of the αACC intermediate, and thus the conversion of the αACC intermediate into the cesium salt of the TA can be achieved with high yield.     

Phase transition in the one-dimensional pair-hopping model with unusual one-electron hopping

By modifying the conventional one-electron hopping behavior, we study effects of an occupation-dependent hopping on the ground state of the half-filled one-dimensional pair-hopping model. At weak coupling, the use of bosonization and renormalization-group analysis techniques helps to derive the phase diagram. Such unusual hopping is shown to drive a spin-gap transition and to introduce a new region where the triplet superconducting instability dominates for positively small pair-hopping interaction.