夫兰克-赫兹实验中影响板极电流因素浅析

通过公式与绘图比对实验测得的数据,研究电子与氩原子的夫兰克-赫兹实验中不同阴极电压、第一栅极电压、反向电压下,板极电流随加速电压的变化情况。分析板极电流发生变化的规律及原因,观察测得数据及其绘制的夫兰克-赫兹曲线找出对实验研究负向影响最小的阴极电压、第一栅极电压、反向电压的参考数值。     

Synchronization in lattice-embedded scale-free networks

In this work, we study the effects of embedding a system of non-linear phase oscillators in a two-dimensional scale-free lattice. In order to analyze the effects of the embedding, we consider two different topologies. On the one hand, we consider a scale-free complex network where no constraint on the length of the links is taken into account. On the other hand, we use a method recently introduced for embedding scale-free networks in regular Euclidean lattices. In this case, the embedding is driven by a natural constraint of minimization of the total length of the links in the system. We analyze and compare the synchronization properties of a system of non-linear Kuramoto phase oscillators, when interactions between the oscillators take place in these networks. First, we analyze the behavior of the Kuramoto order parameter and show that the onset of synchronization is lower for non-constrained lattices. Then, we consider the behavior of the mean frequency of the oscillators as a function of the natural frequency for the two different networks and also for different values of the scale-free exponent. We show that, in contrast to non-embedded lattices that present a mean-field-like behavior characterized by the presence of a single cluster of synchronized oscillators, in embedded lattices the presence of a diversity of synchronized clusters at different mean frequencies can be observed. Finally, by considering the behavior of the mean frequency as a function of the degree, we study the role of hubs in the synchronization properties of the system.     

A time-dependent Fourier grid Hamiltonian-based formulation of time-dependent multi-configuration Hartree method

We propose a variant of the time-dependent multi-configuration Hartree method within the framework of Fourier grid Hamiltonian method. The workability of the method proposed is demonstrated with a well-known coupled two-mode problem.     

Polarization imaging of multiply-scattered radiation based on integral-vector Monte Carlo method

A new integral-vector Monte Carlo method (IVMCM) is developed to analyze the transfer of polarized radiation in 3D multiple scattering particle-laden media. The method is based on a “successive order of scattering series” expression of the integral formulation of the vector radiative transfer equation (VRTE) for application of efficient statistical tools to improve convergence of Monte Carlo calculations of integrals. After validation against reference results in plane-parallel layer backscattering configurations, the model is applied to a cubic container filled with uniformly distributed monodispersed particles and irradiated by a monochromatic narrow collimated beam. 2D lateral images of effective Mueller matrix elements are calculated in the case of spherical and fractal aggregate particles. Detailed analysis of multiple scattering regimes, which are very similar for unpolarized radiation transfer, allows identifying the sensitivity of polarization imaging to size and morphology.     

Geometric, variational discretization of continuum theories

This study derives geometric, variational discretization of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. Inspired by this framework, we construct a finite-dimensional approximation to the diffeomorphism group and its Lie algebra, thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group. The extension to MHD and complex fluid flow is then made through an appeal to the theory of Euler-Poincaré systems with advection, which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters. Upon deriving a family of structured integrators for these systems, we test their performance via a numerical implementation of the update schemes on a cartesian grid. Among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes.     

Topology and dynamics of attractor neural networks: The role of loopiness

We derive an exact representation of the topological effect on the dynamics of sequence processing neural networks within signal-to-noise analysis. A new network structure parameter, loopiness coefficient, is introduced to quantitatively study the loop effect on network dynamics. A large loopiness coefficient means a high probability of finding loops in the networks. We develop recursive equations for the overlap parameters of neural networks in terms of their loopiness. It was found that a large loopiness increases the correlation among the network states at different times and eventually reduces the performance of neural networks. The theory is applied to several network topological structures, including fully-connected, densely-connected random, densely-connected regular and densely-connected small-world, where encouraging results are obtained.     

On evolutionary spatial heterogeneous games

How cooperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one-parameter payoff matrix. Here, the effects of spatial heterogeneities of the environment and/or asymmetries in the interactions among the individuals are analysed through different extensions of this model. Instead of using the same universal payoff matrix, bimatrix games in which each cell at site (i, j) has its own different ‘temptation to defect’ parameter T(i,j) are considered. First, the case in which these individual payoffs are constant in time is studied. Second, an evolving evolutionary spatial game such that T=T(i,j;t), i.e. besides depending on the position evolves (by natural selection), is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices.     

Gas-phase chemistry of nitrogen trifluoride NF3: structure and stability of its M–NF3 (M=H, Li, Na, K) complexes

The stationary points characterizing the potential energy profiles of the complex processes of the M⁺(M=H, Li, Na, K) and NF₃ were investigated by QCISD and B3LYP in conjunction with the 6-311+G(2d,2p) basis set. The optimized geometries and NBO analysis indicate that the complexes of M⁺(M=Li, Na, K) and NF₃ exist as ion-dipole molecules. But for H⁺ complexes, there are two stable isomers NF₃H⁺ and NF₂⁺–HF. The interaction distances of isomers follow the sequence H⁺< Li⁺< Na⁺< K⁺. The calculated affinity energies of the most stable isomers of H⁺, Li⁺, Na⁺, and K⁺ complexes exceed 20.1 kJ/mol, and these values suggest that the M⁺–NF₃ (M=H, Li, Na, K) complexes could be observed as stable species in gas phase, which supports Fujii's proposal that Li⁺ ion attachment mass spectrometry can serve as a conceivable technique to quantify the emissions of the NF₃.     

Complex networks constructed from irrational number sequences

In this paper, we construct (d,r) networks from sequences of different irrational numbers. In detail, segment an irrational number sequence of length M into groups of d digits which represent the nodes while two consecutive groups overlap by r digits (r=0,1,…,d−1), and the undirected edges indicate the adjacency between two consecutive groups. (3,r) and (4,r) networks are respectively constructed from 14 different irrational numbers and their topological properties are examined. By observation, we find that network topologies change with different values of d, r and even sequence length M instead of the types of irrational numbers, although they share some similar features with traditional random graphs. We make a further investigation to explain these interesting phenomena and propose the identical-degree random graph model. The results presented in this paper provide some insight into distributions of irrational number digits that may help better understanding of the nature of irrational numbers.