封闭圆内开缝圆自然对流的非线性特性研究

本文通过数值计算对封闭圆内开缝圆自然对流的非线性特性进行了研究。数值计算以整个流场为计算区域,采用非稳态数学模型和具有QUICK差分格式的SIMPLE算法。计算结果表明,在不同参数下流动和换热存在稳态定常解、周期性振荡解、拟周期性振荡解和非周期性振荡解。稳态定常解的相图是一个点;周期性振荡解的相图是一个极限环,对应功率谱含一个基频及其谐波;拟周期性振荡解的相图为环面,对应功率谱含两个不相关的频率及它们的线性组合频率;非周期性振荡解的功率谱为无规则的宽带连续谱。     

Critical and strong-coupling phases in one- and two-bath spin-boson models

For phase transitions in dissipative quantum impurity models, the existence of a quantum-to-classical correspondence has been discussed extensively. We introduce a variational matrix product state approach involving an optimized boson basis, rendering possible high-accuracy numerical studies across the entire phase diagram. For the sub-Ohmic spin-boson model with a power-law bath spectrum ∝ω(s), we confirm classical mean-field behavior for s<1/2, correcting earlier numerical renormalization-group results. We also provide the first results for an XY-symmetric model of a spin coupled to two competing bosonic baths, where we find a rich phase diagram, including both critical and strong-coupling phases for s<1, different from that of classical spin chains. This illustrates that symmetries are decisive for whether or not a quantum-to-classical correspondence exists.     

Locally ordered regions in the phase transition in the systems with a finite-range correlated quenched disorder

The locally ordered regions (LOR) in the phase transition in disordered systems are studied. There are two parts in this paper. One part is to report our numerical results on the one-dimensional saddle point equation of the Ginzburg-Landau Hamiltonian with random temperature in the presence of an ordering field. The disordered system is modelled as a lattice, on which each cell has a local reduced temperature. The random part of the local reduced temperature is distributed in the Gaussian form. The one-dimensional saddle point equation is solved numerically. The average, the fluctuation and the correlation length of the solution are calculated. The scaling relations for these quantities with the temperature, the ordering field and the disorder strength are derived. The numerical data are fitted with the scaling relations well. Another part is to discuss qualitatively the phase diagram of the finite-range correlated disordered systems. There are two proposed classes for the phase transition in connection with the LOR. One class is described by the percolative scenario, in which the phase transition is inhomogeneous. In the percolative scenario the percolation of the LOR dominates the phase transition. In another class, the phase transition is homogeneous, and can be described by the renormalization group (RG) with replica symmetry breaking (RSB). In the RG with RSB, there is nothing to do with the percolation of LOR. We shall show that these two theories, which seem contradictory, may describe two parts of the whole phase diagram. Whether the phase transition is homogeneous or inhomogeneous depends on the interaction between the LOR. If the interaction between the LOR is strong enough, the phase transition is percolative and inhomogeneous. If the interaction between the LOR is weak, the phase transition is homogeneous. The interaction between the LOR is discussed with the numerical solution on the saddle point equation.     

Phase diagram of a random tiling quasicrystal

We study the phase diagram of a two-dimensional random tiling model for quasicrystals. At proper concentrations the model has 8-fold rotational symmetry. Landau theory correctly gives most of the qualitative features of the phase diagram, which is in turn studied in detail numerically using a transfer matrix approach. We find that the system can enter the quasicrystal phase from many other crystalline and incommensurate phases through first-order or continuous transitions. Exact solutions are given in all phases except for the quasicrystal phase, and for the phase boundaries between them. We calculate numerically the phason elastic constants and entropy density, and confirm that the entropy density reaches its maximum at the point where phason strains are zero and the system possesses 8-fold rotational symmetry. In addition to the obvious application to quasicrystals, this study generalizes certain surface roughening models to two-dimensional surfaces in four dimensions.     

Coupled phase transitions under periodic perturbation

The influence of periodic perturbation on the system of two nonlinear stochastic equations, which model low-frequency pulsations in crisis and transient modes of heat-and-mass transfer with phase transitions, has been investigated by numerical methods. When studying the influence of the periodic perturbation on the system, a researcher should largely take into account the phase diagram. It is shown that nonequilibrium phase transitions from asymmetric cycles of phase trajectories to centrally symmetric ones occur in the absence of noise. These transitions are accompanied by the stochastic resonance response, which enhances as the frequency of the external periodic force decreases.     

Universal critical exponent in class D superconductors

We study a physical system consisting of noninteracting quasiparticles in disordered superconductors that have neither time-reversal nor spin-rotation invariance. This system belongs to class D within the recent classification scheme of random matrix ensembles, and its phase diagram contains three different phases: metallic and two distinct localized phases with different quantized thermal Hall conductances. We find that critical exponents describing different transitions (insulator-to-insulator and insulator-to-metal) are identical within the error of numerical calculations and also find that critical disorder of the insulator-to-metal transition is energy-independent.     

Stretching of a polymer below the theta point

The unfolding of a polymer below the theta point when pulled by an external force is studied both in d=2 on the lattice and in d=3 off the lattice. At T=0 and for finite length chains, it is found that the globule unfolds via multiple steps, corresponding to transitions between different minima, in both cases. In d=3 one of these intermediates is a regular helix. In the infinite length limit, these steps have a qualitative effect only in d=2. The phase diagram in d=2 is determined via the transfer matrix. To rationalize these results, energy-entropy and renormalization group arguments are given.     

Quantum phase analysis of 1D superconducting quantum dot lattice using extended Bose-Hubbard model

We have obtained the quantum phase diagram of a one-dimensional superconducting quantum dot lattice using the extended Bose-Hubbard model for different commensurabilities. We describe the nature of different quantum phases at the charge degeneracy point. We find a direct phase transition from the Mott insulating phase to the superconducting phase for integer band fillings of Cooper pairs. We predict explicitly the presence of two kinds of repulsive Luttinger liquid phases, besides the charge density wave and superconducting phases for half-integer band fillings. We also predict that extended range interactions are necessary to obtain the correct phase boundary of a one-dimensional interacting Cooper system. We have used the density matrix renormalization group method and Abelian bosonization to study our system.     

改进WKB近似的新方法

利用转移矩阵理论，在考虑层间一次反射和转折点处实际相移的基础上，导出了改进的ＷＫＢ公式，数值计算的结果表明本文所得公式的精度远优于传统的ＷＫＢ近似，而且能适用于接近于截止的模式和变化剧烈的折射率分布。     

Nematic-smectic-A-smectic-C multicritical point: An alternative model

A new Landau-type phenomenological free-energy function to describe the nematic-smectic-A transition, smectic-A-smectic-C transition and nematic-smectic-C transition is proposed. The influence of pressure on the these phase transitions is discussed by varying the coupling between various order parameters. The phase diagram of the thermodynamic parameters is studied and a possible nematic-smectic-A-smectic-C bicritical point is predicted. We present a detailed analysis of the different phases that can occur and analyze the question under which conditions a bicritical point is observed in the phase diagram. The obtained topology of the pressure-temperature phase diagram is consistent with experimental results.     

Vibration analysis of liquid-filled pipelines with elastic constraints

In this paper, a transfer matrix method (TMM) in frequency domain considering fluid-structure interaction of liquid-filled pipelines with elastic constraints is proposed. The time-domain equations considering fluid-structure interaction, are transformed into frequency domain by Laplace transformation, and then twelve fourth-order ordinary differential equations and two second-order ordinary differential equations are deduced from the frequency-domain equations. The results of the fourteen frequency-domain equations are assembled into a transfer matrix, which represents the motion of a single pipe section. Combined with point matrices that describe specified boundary conditions, an overall transfer matrix for liquid-filled pipeline system can be assembled. Using the method, all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number. Taking into account the longitudinal vibration, transverse vibration and torsional vibration, the proposed method can be used to analyze the pipelines with bends. Several numerical examples with different constraints are presented here to illustrate the application of the proposed method. The results are validated by measured and simulation data. Through the numerical examples, it is shown that the proposed method is efficient.     

Complete phase diagram of DNA unzipping: eye, Y fork, and triple point

We study the unzipping of double stranded DNA by applying a pulling force at a fraction s (0< or =s < or =1) from the anchored end. From exact analytical and numerical results, the complete phase diagram is presented. The phase diagram shows a strong ensemble dependence for various values of s. In addition, we show the existence of an eye phase and a triple point.     

Stochastic ballistic annihilation and coalescence

We study a class of stochastic ballistic annihilation and coalescence models with a binary velocity distribution in one dimension. We obtain an exact solution for the density which reveals a universal phase diagram for the asymptotic density decay. By universal we mean that all models in the class are described by a single phase diagram spanned by two reduced parameters. The phase diagram reveals four regimes, two of which contain the previously studied cases of ballistic annihilation. The two new phases are a direct consequence of the stochasticity. The solution is obtained through a matrix product approach and builds on properties of a q-deformed harmonic oscillator algebra.     

Phase diagrams of quasispecies theory with recombination and horizontal gene transfer

We consider how transfer of genetic information between individuals influences the phase diagram and mean fitness of both the Eigen and the parallel, or Crow-Kimura, models of evolution. In the absence of genetic transfer, these physical models of evolution consider the replication and point mutation of the genomes of independent individuals in a large population. A phase transition occurs, such that below a critical mutation rate an identifiable quasispecies forms. We show how transfer of genetic information changes the phase diagram and mean fitness and introduces metastability in quasispecies theory, via an analytic field theoretic mapping.     

对称双弹簧振子受迫、有阻尼横振动的混沌行为

对受周期外力驱动的对称双弹簧振子进行了研究,建立了系统的动力学方程,用线性稳定性分析方法讨论了平衡点附近邻域的稳定性,利用数值计算并结合多种分析方法,求解非线性方程和判断解的性质.通过改变系统参数,画出时域图、相图及分岔图等.计算分析和数值实验发现,这个简单的力学系统存在十分丰富的动力学行为(分岔、混沌).理论分析和数值实验结果一致.     

Magnetic states of small cubic particles with uniaxial anisotropy

The lowest energy states in small cubic particles with uniaxial anisotropy are explored as a function of anisotropy strength and particle size. The investigations result in a phase diagram which contains the boundaries between the regions of one, two and three domains (flower, vortex and double vortex states). While the general features of the phase diagram are derived from energy estimates based on domain theory, the details are obtained using numerical micromagnetics. The two-domain and the three-domain phase can be subdivided into subphases. The comparison between different configurations revealed that a twisted vortex configuration with an S-shaped domain wall replaces the symmetric vortex with a straight wall at larger sizes. The three-domain phase contains two subphases which are symmetric with respect to (1 0 0) and (1 1 0) mirror planes, respectively. The transition from two to three domains occurs into the (1 1 0)-three-domain-state (diagonal state). This structure can be described as a configuration with two (quarter-) circular domain walls in two opposing corners. However, this configuration is energetically favored only in a small region within the phase diagram relative to the (1 0 0)-symmetry three-domain state with straight walls (sandwich state).     

Coulomb-frustrated phase separation phase diagram in systems with short-range negative compressibility

Using numerical techniques and asymptotic expansions we obtain the phase diagram of a paradigmatic model of Coulomb-frustrated phase separation in systems with negative short-range compressibility. The transition from the homogeneous phase to the inhomogeneous phase is generically first order in isotropic three-dimensional systems except for a critical point. Close to the critical point, inhomogeneities are predicted to form a bcc lattice with subsequent transitions to a triangular lattice of rods and a layered structure. Inclusion of a strong anisotropy allows for second- and first-order transition lines joined by a tricritical point.     

Phase diagram of the two-channel kondo lattice model in one dimension

Employing the density matrix renormalization group method and strong-coupling perturbation theory, we study the phase diagram of the SU(2)xSU(2) Kondo lattice model in one dimension. We show that, at quarter filling, the system can exist in two phases depending on the coupling strength. The weak-coupling phase is dominated by RKKY exchange correlations, while the strong-coupling phase is characterized by strong antiferromagnetic correlations of the channel degree of freedom. These two phases are separated by a quantum critical point. For conduction-band fillings of less than one-quarter, we find a paramagnetic metallic phase at weak coupling and a ferromagnetic phase at moderate to strong coupling.