漏阈值系统的自组织临界性:近平均场的动力学影响及其对地震、神经生物学和预测方面的意义

阈值系统被看作是自然界中某些最重要的非线性自组织系统,包括地震断层系统、神经网络、超导和半导体、互联网以及政治、社会和生态系统。所有这些系统都具有与时、空、强相关的动力学,且都典型地显示了时空尺度的多重性。我们在两种不同尺度上讨论地震阈值系统自组织的物理学问题(1)“微观”的实验室尺度,来自模拟结果的考虑导致了动力学方程,这些方程可以推导从滑动实验中得到的结果;(2)“宏观”的地震断层系统尺度,强相关地震断层系统的物理学可以通过应用定义在希尔伯特本征态空间有关的态向量来理解。所有的这些系统中,长程相关导致局部各态历经动力学的存在。耗损效应的存在导致了“漏阈值”动力学的出现,它等同于一个控制与背景涨落尺度有关的成核事件尺度的新的标度场的出现。在宏观地震断层尺度的框架下,这些作为一种预报未来地震活动方法的观念显示出了比较大的希望。

Spontaneous U(1) Symmetry Breaking in Coupled Bose System

Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.

Novel Quantum Phases of Ultracold Bosonic Atoms in Honeycomb Optical Lattice

We study the quantum phase transition of ultracold atoms in the honeycomb optical lattice. The Hamiltonian of ultracold bosonic atoms in the honeycomb optical lattice is derived. We take the mean-field approximation and further solve the Hamiltonian with the numerical diagonalization method. We obtain the phase diagram and find that the Mort-insulator （MI）, density wave （DW） and modulated superfluid （MS） phases appear. Furthermore, the phase diagram is analyzed according to the order parameter and the average number of particles.

Statistical Properties of Multispecies Competition Ecosystems Subjected to Dichotomous Noises

We investigate statistical properties of multispecies competition ecosystems subjected to both symmetric and asymmetric dichotomous noises. The expression of the stationary probability distribution function （SPDF） is analytically derived by means of mean-field approximation, and verified by stochastic simulations. The results indicate that： （i） A noise amplitude （a0）, a noise autocorrelation time （τ0） and a noise symmetry parameter （k） all can affect the SPDF; （ii） There is an optimal τ0, which makes the mean value of population density be maximal, near which a transition takes place, i.e., the stationary mean value of species density （（x）st） suddenly falls to a lower constant, （iii） As k decreases, the maximum of （x）xt and the optimal 70 increase. The parameter planes of TO -- a20 and τ0- k for the transition are plotted.

Applicability of Mean Field Approximation to Numerical Experiments of Thermal Convection during the Cooling Period of Lake Biwa

This paper describes the applicability of a stochastic model to the numerical experiments of thermal convection carried out under the condition of the northern part of Lake Biwa, Shiga Prefecture, Japan. It was shown in the previous study that the temporal changes of vertical water temperature distributions during the cooling period between September and February can be reproduced by a simple 3D-CFD model. It was also pointed out that the spatial distributions of cooled water body sinking to the bottom due to water surface cooling represent similar features of forest gap distribution, which can be clarified by a stochastic model. The basic features of numerical experiments on thermal convection such as the spatial distribution of cooled water body are firstly shown with several cooling rates at water surface. Then, a stochastic model, which was originally introduced to explain forest gap dynamics, is shown with its MFA （mean field approximation） as first approximation of stochastic model. It is pointed out through the comparison of theoretical results by MFA with tuned model constants to numerical experiments that MFA with some refinement can be applicable to reproduce the basic features of simulated results to some extent, although further investigations are required to clarify the applicability of the model to more detailed mechanism of thermal convection such as size distribution of cooled water body, phase change of flow pattern, etc..

Relation between the E(5) symmetry and the interacting boson model beyond the mean-field approximation

In a unified algebraic scheme,we investigate the relation between the E(5) symmetry and the interacting boson model beyond the mean-field level.The results indicate that the E(5) symmetry is actually in between the critical point of the U(5)-O(6) transition and the O(6) limit but it is fairly close to the former based on the phase diagram of the interacting boson model at the large boson number limit.In addition,an algebraic Hamiltonian of the E(5)-β2n model is proposed.

β-decay studies approaching the N=20 island of inversion with a new shell-model Hamiltonian

β-decay properties of N=18-22,Z=10-14 nuclei are analyzed with a new shell-model Hamiltonian using the Gogny densitydependent interaction.The Gogny force which has been widely and successfully used in mean-field theory can provide reasonable two-body matrix elements for cross-shell calculations.The log f t values andβ-decay level schemes are systematically studied using the D1S-Gogny interaction and compared with the SDPF-M results and experimental data.It is shown that the new Hamiltonian provides reliable results forβ-decay along with subtle level schemes for this region.Shell-model calculations with Gogny interaction can lead to a successful description of nuclei in and around the N=20 island of inversion and supplements experiment where sufficient data are not available.

Mean field study of a propagation-turnover lattice model for the dynamics of histone marking

We present a mean field study of a propagation-tumover lattice model, which was proposed by Hodges and Crabtree [Proc. Nat. Acad. Sci. 109, 13296 （2012）] for understanding how posttranslational histone marks modulate gene expression in mammalian ceils. The kinetics of the lattice model consists of nucleation, propagation and turnover mechanisms, and exhibits second-order phase transition for the histone marking domain. We showed rigorously that the dynamics essentially depends on a non-dimensional parameter k = k＋/k-, the ratio between the propagation and turnover rates, which has been observed in the simulations. We then studied the lowest order mean field approximation, and observed the phase transition with an analytically obtained critical parameter. The boundary layer analysis was utilized to investigate the structure of the decay profile of the mark density. We also studied the higher order mean field approximation to achieve sharper estimate of the critical transition parameter and more detailed features. The comparison between the simulation and theoretical results shows the validity of our theory.

Influence of Density-Dependent Coupling Constants on Equation of State of Infinite Symmetric Nuclear Matter

In the mean field approximation of nonlinear relativistic a-ω-p model, we have studied the influence of density-dependent coupling constants between nucleons and mesons on the equation of state （EOS） of infinite symmetric nuclear matter in different conditions. We find that the EOS of nuclear matter will become stiffer as e, d in the self- interaction of σ meson increase when the coeffcients except aω in Гω, in which the opposite occurs, are fixed. On the other hand, greater values of aσ, bσ, cσ, aω, dω and smaller values of dσ, bω, cω will lead to stiffer EOS ifc and d are fixed. Besides, greater values of Гω lead to stiffer EOS in high density region for the EOS with same incompressibility coefficient at saturation density.