Multi-Soliton Solutions and Integrable Discretization for a Coupled Modified Volterra Lattice Equation

In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed.     

内生无限平面网格上基于策略互动的均衡网络结构及吸收集

在内生网络环境下,基于局中人的策略互动研究了均衡网络的结构特性,以及局中人策略选择的倾向性. 在动态进程的同一阶段,规定所有局中人同时进行策略更新,研究了网络生成的连接费用、互动支付等参数之间的相互关系及其对均衡结构或吸收集的影响. 主要贡献是将网络的内生性与无限网格上的策略互动联系在一起,得出不同连接费用水平之下的均衡结构、吸收集的准确特征.     

The characteristics of molten globule states and folding pathways strongly depend on the sequence of a protein

ABSTRACT

The majority of proteins perform their cellular function after folding into a specific and stable native structure. Additionally, for many proteins less compact ‘molten globule’ states have been observed. Current experimental observations show that the molten globule state can show varying degrees of compactness and solvent accessibility; the underlying molecular cause for this variation is not well understood. While the specificity of protein folding can be studied using protein lattice models, current design procedures for these models tend to generate sequences without molten globule-like behaviour. Here we alter the design process so the distance between the molten globule ensemble and the native structure can be steered; this allows us to design protein sequences with a wide range of folding pathways, and sequences with well-defined heat-induced molten globules. Simulating these sequences we find that (1) molten globule states are compact, but have less specific configurations compared to the folded state, (2) the nature of the molten globule state is highly sequence dependent, (3) both two-state and multi-state folding proteins may show heat-induced molten globule states, as observed in heat capacity curves. The varying nature of the molten globules and typical heat capacity curves associated with the transitions closely resemble experimental observations.     

New Feedback Control Model in the Lattice Hydrodynamic Model Considering the Historic Optimal Velocity Difference Effect

A feedback control model of lattice hydrodynamic model is proposed by taking the information of the historic optimal velocity into account for the traffic system. The modern control theory is applied for the linear stability condition with feedback control signal. The result shows that the stability of traffic flow is closely related to the information of the historic optimal velocity. Furthermore, numerical simulations conform that the new feedback control did increase the stability of traffic flow efficiently, which is in accord with theoretical analysis.     

费米气体在调制缺陷晶格中的超流特性

本文研究了费米气体在调制缺陷的一维环形光晶格中的超流特性．在流体动力学模型和两模近似下,整个系统的动力学性质可以等效为单摆模型的哈密顿量,从而得到系统发生超流相变的临界条件ρc ．系统在BEC-BCS整个渡越区中,临界原子数密度将使得系统存在缺陷导致阻尼的正常态之外的另一种状态,即平面波连续穿过缺陷的超流态．系统的超流特性依赖于缺陷的强度、类型以及原子间的相互作用,并且由于缺陷与原子间相互作用的耦合,系统在BCS端更容易维持超流态。     

Possible extinction of Berezinskii–Kosterlitz–Thouless transition by diagonal interactions in the checkerboard lattice

We study the thermodynamics of the classical anisotropic antiferromagnetic Heisenberg model in a checkerboard lattice. The checkerboard lattice is distinguished from the antiferromagnetic square lattice (with coupling constant J) by the presence of a diagonal crossing (coupling constant $J^{\prime }$) in half of the sites. This lattice model is the direct analog of the three-dimensional pyrochlore lattice on a two-dimensional surface. Besides, we considered a single-ion anisotropy D that breaks the $O(3)$ symmetry and contributes to planar spin fields. Since the model is two-dimensional endowed with an $O(2)$ symmetry, a Berezinskii–Kosterlitz–Thouless (BKT) transition is expected to take place. We also investigated the BKT temperature as a function of the coupling constants $J^{\prime }$ and D. The problem is developed through a continuous representation given by the $O(3)$ Nonlinear Sigma Model (NLSM). Computer simulations were also carried out, and the results were in accordance with the analytical model.     

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.     

Thermodynamic and critical properties of an antiferromagnetically stacked triangular Ising antiferromagnet in a field

We study a stacked triangular lattice Ising model with both intra- and inter-plane antiferromagnetic interactions in a field, by Monte Carlo simulation. We find only one phase transition from a paramagnetic to a partially disordered phase, which is of second order and 3D XY universality class. At low temperatures we identify two highly degenerate phases: at smaller (larger) fields the system shows long-range ordering in the stacking direction (within planes) but not in the planes (stacking direction). Nevertheless, crossovers to these phases do not have a character of conventional phase transitions but rather linear-chain-like excitations.     

Spin-1/2 Ising model on a AFM/FM two-layer Bethe lattice in a staggered magnetic field

A bilayer spin-1/2 Ising model consisting of two superposed Bethe lattices with antiferromagnetic/ferromagnetic interactions is studied by the use of exact recursion relations in a pairwise approach in the presence of an external staggered magnetic field. Besides the ground state phase diagrams calculated in different possible planes of the model parameters space, the thermal variations of the order-parameters and the free energy are investigated to obtain the temperature-dependent phase diagrams of the model for different values of the coordination numbers q. Our calculations reveal that depending on the strength of the model parameters, the model exhibits a variety of interesting phase transitions and therefore phase diagrams.     

考虑Soret和Dufour效应的方腔内双扩散自然对流格子Boltzmann模拟

采用格子Boltzmann方法,考虑Soret和Dufour效应,对内置高浓度发热圆的方腔内部双扩散自然对流现象进行数值模拟.高浓度发热圆位于方腔中心,四周壁面均为低温低浓度.在该模型中,用三个独立的LBGK方程分别模拟速度场、温度场和浓度场,并通过Boussinesq近似将它们耦合起来.分析Soret数和Dufour数对方腔内部双扩散自然对流的影响,得到流线图、等温线图、等浓度线图、发热圆表面平均Nusselt数和平均Sherwood数.结果表明：Soret和Dufour效应对方腔内双扩散自然对流影响明显,不能忽略.