Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

煤炭码头船货匹配下泊位动态分配多目标优化模型及算法

本文针对输出型煤炭码头船货匹配下泊位动态分配问题,构建了堆场-取装线-泊位-船舶联合分配优化数学模型,并设计了采用仿真推演策略解码的遗传算法求解。首先,综合考虑船舶、泊位、堆场、取装线、煤种、航道开放时间和装船作业规则等要素,以船舶在港时间最短和作业效率最大为目标建立了相应的多约束多目标优化模型。然后,综合多目标优化、遗传算法以及仿真推演技术,设计了相应的遗传算法求解,包括:组合式编码、采用仿真推演策略的解码方法,追加了具有合法性检查的染色体生成算法,设计了采用多种策略的遗传操作等。最后实例表明,本算法的执行效率高而且优化效果好。     

The ground-state energy of the ±J sping glass. A comparison of various biologically motivated algorithms

We compare various evlutionary strategies to determine the ground-state energy of the ±J spin glass. We show that the choice of different evolution laws is less important than a suitable treatment of the free spins of the system At least one combination of these strategies does not give the correct results, but the ground states of the other different strategies coincide. Therefore we are able to extrapolate the infinit-size ground-state energy for the square lattice to –1.401±0.0015 and for the simple cubic lattice to –1.786±0.004.     

Phase separation of symmetrical polymer mixtures in thin-film geometry

Monte Carlo simulations of the bond fluctuation model of symmetrical polymer blends confined between two neutral repulsive walls are presented for chain lengthN _A=N _B=32 and a wide range of film thicknessD (fromD=8 toD=48 in units of the lattice spacing). The critical temperaturesT _c (D) of unmixing are located by finite-size scaling methods, and it is shown that , wherev ₃0.63 is the correlation length exponent of the three-dimensional Ising model universality class. Contrary to this result, it is argued that the critical behavior of the films is ruled by two-dimensional exponents, e.g., the coexistence curve (difference in volume fraction of A-rich and A-poor phases) scales as , where ₂ is the critical exponent of the two-dimensional Ising universality class ( ₂=1/8). Since for largeD this asymptotic critical behavior is confined to an extremely narrow vicinity ofT _c (D), one observes in practice effective exponents which gradually cross over from ₂ to ₃ with increasing film thickness. This anomalous flattening of the coexistence curve should be observable experimentally.     

Molecular dynamics of cyclic and linear poly(dimethylsiloxanes)

Dielectric spectroscopy (10^–1 Hz to 10⁷ Hz) has been employed to study the molecular dynamics of a series of cyclic and linear polydimethylsiloxanes (PDMS) of various molecular weights ranging from 300 to 10 000 g/mol in the temperature range above the glass transition (from 130 K to 190 K). The observed -relaxation depends strongly on both molecular weight and structure of the samples. For linear PDMS oligomers, the -relaxation shifts towards lower temperatures with decreasing molecular weight in good accordance with the Fox-Flory-model. Cyclic PDMS reveals a qualitatively different molecular weight dependence: for a given temperature the -relaxation time increases with decreasing ring length, but has a maximum for small oligomers (degree of polymerizationn6). The shape of relaxation curves and, with it, the relaxation time distribution is independent from length and architecture of the chains The observed experimental findings are in qualitative agreement with dynamic Monte-Carlo simulations.Dedicated to Prof. E.W. Fischer on the occasion of his 65th birthday Fast macht' das WLF ihn krank, jetzt raucht er wieder, Gott sei Dank! (frei nach Wilhelm Busch)     

Massively time-parallel,approximate simulation of loss queueing systems

A time-parallel simulation obtains parallelism by partitioning the time domain of the simulation. An approximate time-parallel simulation algorithm named GG1K is developed for acyclic networks of loss FCFSG/G/1/K queues. The GG1K algorithm requires two phases. In the first phase, a similar system (i.e. aG/G/1/ queue) is simulated using the GLM algorithm. Then the resultant trajectory is transformed into an approximateG/G/1/K trajectory in the second phase. The closeness of the approximation is investigated theoretically and experimentally. Our results show that the approximation is highly accurate except whenK is very small (e.g. 5) in certain models. The algorithm exploits unbounded parallelism and can achieve near-linear speedup when the number of arrivals simulated is sufficiently large.     

Mechanical properties of twist grain boundaries in Cu

In a previous paper we studied the Young's and shear modulus of a high-angle twist grain boundary (5) in Cu, using the EAM, and related it to the uniaxial strain derivatives of single crystals. In this paper, we discuss elastic properties of ten additional twist grain boundaries, from 8.8–43.6°. The monolayer Young's modulus at each boundary was calculated and found to be 20–50% higher than the bulk value for all eleven boundaries for both csl and type1 structures. The monolayer shear modulus at each boundary was calculated and found to be 93–98% lower than the bulk value for six grain boundaries with csl structure and found to decrease with increasing twist angle. The critical shear stress was also calculated for eleven boundaries with csl structure and found to roughly decrease with increasing twist angle.     

关于模拟法描会聚点电场的讨论

本文论证了“ＱＥ－２”型静电场描迹中模拟聚焦电场的电极在设计上有误的观点。     

Interfacial segregation in Ag-Au,Au-Pd,and Cu-Ni alloys: I. (100) surfaces

Atomistic simulations of segregation to (100) free surface in Ag–Au, Au–Pd, and Cu–Ni alloy systems have been performed for a wide range of temperatures and compositions within the solid solution region of these alloy phase diagrams. In addition to the surface segregation profiles, surface free energies, enthalpies, and entropies were determined. These simulations were performed within the framework of the free energy simulation method, in which an approximate free energy functional is minimized with respect to atomic coordinates and atomic site occupation. The effects of the relaxation with respect to either the atomic positions or the atomic concentrations are discussed. For all alloy bulk compositions (0.05 C 0.95) and temperatures (400 T(K) 1,100) examined, Ag, Au, and Cu segregates to the surface in the Ag–Au, Au–Pd, and Cu–Ni alloy systems, respectively. The present results are compared with several theories for segregation. The resultant segregation profiles in Au–Pd and Ag–Au alloys are shown to be in good agreement with an empirical segregation theory, while in Cu–Ni alloys the disagreement in Ni-rich alloys is substantial. The width of the segregation profile is limited to approximately three to four atomic planes. The surface thermodynamic properties depend sensitively on the magnitude of the surface segregation, and some of them are shown to vary linearly with the magnitude of the surface segregation.     

Environment of the P b center at the Si(111)/oxide interface

We assess several models for the environment of the P _b center (Si dangling bond center) at the interface of Si(111) with its oxide. The comparison of hyperfine constants observed with those predicted using large cluster models favors a local structure in which there is an Si-Si bond within the oxide close to the Si dangling bond. Such Si-Si bonds are also suggested by a number of other experiments and are consistent with the reactive layer model proposed to rationalize a range of oxidation studies.