EAST位形磁流体平衡的模拟

对托卡马克平衡反演数值计算代码EFIT进行了改进,使之适用于EAST装置的磁流体平衡研究.用改进后的平衡反演代码EFIT模拟了EAST装置稳态阶段的偏滤器平衡位形.提出极向场线圈电流作为线性方程组主约束条件,期望位形作为从约束条件,求解非对称电流条件下自由边界平衡问题的方法.结果表明,该方法能较为容易地得到非对称电流条件产生的平衡位形,在非对称电流条件下自由边界平衡计算是收敛的.     

Plasma shape optimization for EAST tokamak using orthogonal method

It is necessary to reduce the currents of poloidal field(PF) coils as small as possible, during the static equilibrium design procedure of Experimental Advanced Superconductive Tokamak(EAST). The quasi-snowflake(QSF) divertor configuration is studied in this paper. Starting from a standard QSF plasma equilibrium, a new QSF equilibrium with 300 kA total plasma current is designed. In order to reduce the currents of PF6 and PF14, the influence of plasma shape on PF coil current distribution is analyzed. A fixed boundary equilibrium solver based on a non-rigid plasma model is used to calculate the flux distribution and PF coil current distribution. Then the plasma shape parameters are studied by the orthogonal method. According to the result, the plasma shape is redefined, and the calculated equilibrium shows that the currents of PF6 and PF14 are reduced by 3.592 kA and 2.773 kA, respectively.     

Two remarks on extremal equilibrium states

First it is shown that each extremal equilibrium state is representable as limit of Gibbs states in finite volumes, and that an analogous statement holds for extremal invariant equilibrium states. Secondly we prove that for negative pair interactions only one equilibrium state exists which minimizes (resp. maximizes) the particle density, but that in general there are more than two extremal invariant equilibrium states with the same particle density. In this context, periodic interactions are studied.     

Hawking-Unruh effect on thermal equilibrium state

It is pointed out that the usual (Gibbs) thermal equilibrium state in Minkowski spacetime is no longer a thermal equilibrium state for a uniformly accelerated observer. Similarly, the thermal equilibrium state in Kruskal spacetime is not a thermal state for a Schwarzschild observer.     

精细平衡气体动理学格式

流体系统在重力作用下，流体压力可与重力相平衡，达到静力平衡状态.常规的有限差分和有限体积方法无法在离散尺度上保持这种平衡态，常常产生虚假速度等非物理现象.通过将重力源项的体积分改写为网格界面值的加权平均，实现离散条件下压力与重力的精细平衡，得到一种Navier-Stokes （NS）方程的精细平衡气体动理学格式.该格式可以在机器精度上精确地保持等温条件下的静力平衡态以及捕捉平衡态附近的小扰动传播.同时，该格式还能求解自然界中更常见的非等温平衡态.此类平衡态除了要求静力平衡还要求热流平衡.利用提出的格式求解NS方程，可以得到静止（机器精度下的零速度）的非等温平衡态，并且密度和温度分布都具有二阶精度.通过多个算例验证格式的有效性，表明该格式可更好地模拟重力场下的温度、密度的分层流动.     

Statistical physics approach to graphical games: local and global interactions

In a graphical game agents play with their neighbors on a graph to achieve an appropriate state of equilibrium. Here relevant problems are characterizing the equilibrium set and discovering efficient algorithms to find such an equilibrium (solution). We consider a representation of games that extends over graphical games to deal conveniently with both local a global interactions and use the cavity method of statistical physics to study the geometrical structure of the equilibria space. The method also provides a distributive and local algorithm to find an equilibrium. For simplicity we consider only pure Nash equilibria but the methods can as well be extended to deal with (approximated) mixed Nash equilirbia.     

Confined colloidal crystals in and out of equilibrium

Recent studies on confined crystals of charged colloidal particles are reviewed, both in equilibrium and out of equilibrium. We focus in particular on direct comparisons of experiments (light scattering and microscopy) with lattice sum calculations and computer simulations. In equilibrium we address buckling and crystalline multilayering of charged systems in hard and soft slit confinement. We discuss also recent crystalline structures obtained for charged mixtures. Moreover we put forward possibilities to apply external perturbations, in order to drive the system out of equilibrium. These include electrolyte gradients as well as the application of shear and electric fields.     

Stability of SIRS system with random perturbations

Epidemiological models with bilinear incidence rate λSI usually have an asymptotically stable trivial equilibrium corresponding to the disease-free state, or an asymptotically stable non-trivial equilibrium (i.e. interior equilibrium) corresponding to the endemic state. In this paper, we consider an epidemiological model, which is an SIRS model with or without distributed time delay influenced by random perturbations. We present the stability conditions of the disease-free equilibrium of the associated stochastic SIRS system.     

Study of equilibrium using collision dynamics

We discuss the possibility of equilibrium (and thermalization) in heavy-ion collisions at intermediate energies within a transport model. This was achieved by dividing the nuclear matter into different collision zones. We find that those nucleons which experience at least ten collisions are close to complete equilibrium whereas others never achieve any equilibrium.     

Self-consistent pseudopotential calculations of the equilibrium properties of bulk and surface Si

A momentum-space formalism is used study the equilibrium properties of bulk and surface Si based on the self-consistent pseudopotential method. The calculated equilibrium lattice constant and the crystal energy are in agreement with experiment. By minimizing the total energy of the system, the equilibrium relaxation for the Si (111) surface was found to be 0.15 Å, in excellent agreement with measurements on the impurity-stabilized relaxed surface.     

Approach to equilibrium for completely positive dynamical semigroups of N-level systems

We give a simple sufficient condition for a completely positive dynamical semigroup of a N-level system to have a unique (invariant) equilibrium state and for every initial state to approach this equilibrium state as t → ∞. We estimate the rate of approach to equilibrium.     

Direct transition from a stable equilibrium to quasiperiodicity in non-smooth systems

The purpose of this Letter is to show how a border-collision bifurcation in a piecewise-smooth dynamical system can produce a direct transition from a stable equilibrium point to a two-dimensional invariant torus. Considering a system of nonautonomous differential equations describing the behavior of a power electronic DC/DC converter, we first determine the chart of dynamical modes and show that there is a region of parameter space in which the system has a single stable equilibrium point. Under variation of the parameters, this equilibrium may collide with a discontinuity boundary between two smooth regions in phase space. When this happens, one can observe a number of different bifurcation scenarios. One scenario is the continuous transformation of the stable equilibrium into a stable period-1 cycle. Another is the transformation of the stable equilibrium into an unstable period-1 cycle with complex conjugate multipliers, and the associated formation of a two-dimensional (ergodic or resonant) torus.     

Analysis of epidemic models with demographics in metapopulation networks

In this paper, two susceptible–infected–susceptible (SIS) epidemic models are presented and analyzed by reaction–diffusion processes with demographics in metapopulation networks. Firstly, an SIS model with constant-inputting is discussed. The model has a disease-free equilibrium, which is locally asymptotically stable when the basic reproduction number is less than unity, otherwise it is unstable. It has an endemic equilibrium, which is globally asymptotically stable. Secondly, in another SIS model, the birth rate is the form of Logistic. Similarly, the stability of disease-free equilibrium and endemic equilibrium is also proved. Finally, numerical simulations are performed to illustrate the analytical results.     

Study of Enol-Keto Tautomerism of N-(2-Hydroxy-1-Naphthylidene)anils

The enol-keto tautomerism of N-(2-hydroxy-1-naphthylidene)anilines was studied. In response to the action of salts (e.g. CaCl₂), in ethanolic solution the equilibrium is shifted extensively in the direction of the keto form; this allows determination of the concentration of the keto form and of the equilibrium constant of the process. In accordance with the Hammett equation, the equilibrium constant varies as a function of the constants a of the substituents on the aniline ring.     

1-羟乙基-3-甲基咪唑氯盐水溶液蒸汽压和凝固特性研究

1-羟乙基-3-甲基咪唑氯盐([HOEtMIM][Cl])是一种亲水性极强的离子液体,与水可以组成吸收式制冷工质对,具有良好的工业应用前景.在制冷工程应用中,离子液体水溶液的低温特性研究非常重要,包括低温段的水溶液蒸汽压数据和凝固特性,而[HOEtMIM][Cl]的相关研究缺乏.本文对水的质量分数分别为17.10%、24.29%、38.03%、49.89%、69.94%,温度范围(278.15K~408.15K)的[HOEtMIM][Cl]水溶液的汽液相平衡进行了测定;并对水的质量分数范围为1.3%~90.0%,温度范围为150K~360K的离子液体水溶液的凝固特性进行了测定,揭示其在低温应用时可能出现的固化问题.获得的蒸汽压及凝固特性数据对该离子液体水溶液应用于制冷系统设计具有重要意义.     

Relaxation properties in classical diamagnetism

It is an old result of Bohr that, according to classical statistical mechanics, at equilibrium a system of electrons in a static magnetic field presents no magnetization. Thus a magnetization can occur only in an out of equilibrium state, such as that produced through the Foucault currents when a magnetic field is switched on. It was suggested by Bohr that, after the establishment of such a nonequilibrium state, the system of electrons would quickly relax back to equilibrium. In the present paper, we study numerically the relaxation to equilibrium in a modified Bohr model, which is mathematically equivalent to a billiard with obstacles, immersed in a magnetic field that is adiabatically switched on. We show that it is not guaranteed that equilibrium is attained within the typical time scales of microscopic dynamics. Depending on the values of the parameters, one has a relaxation either to equilibrium or to a diamagnetic (presumably metastable) state. The analogy with the relaxation properties in the Fermi Pasta Ulam problem is also pointed out.     

Chaotic flows with special equilibria

The European Physical Journal Special Topics - In this review, we categorize chaotic systems with special properties in their equilibrium into eight groups: Systems with no equilibrium (NE),...     

Factors affecting the dimerization of persistent nitrogen‐centered 1‐phenyl urazole radicals to tetrazanes

1‐Phenyl urazole radicals are persistent air‐stable nitrogen‐centered radicals that engage in an equilibrium with the corresponding N―N tetrazane dimers in solution. While the equilibrium typically weakly favors the dimer form, for some 1‐phenyl urazole radicals bearing substituents at the ortho position of the benzene ring, the equilibrium instead strongly favors the dimer form. With the recent surge of interest in the properties and potential applications of heterocyclic radicals, the factors that affect this equilibrium are important to determine. We examined the effect of the extent of ortho substitution (none, 1, or 2 substituents) on the equilibrium by experimentally using variable temperature ¹H nuclear magnetic resonance and UV‐visible spectroscopy in addition to supporting computational investigations at the (U)B3LYP/6‐311G(d,p) level of theory. We confirmed that the equilibrium generally favored the dimer in all cases. However, the equilibrium was more favorable towards dimer formation for urazole radicals substituted with 1 and 2 ortho substituents on the aromatic ring. The activation enthalpies for dissociation of singly substituted dimers were greater than that for dimers without ortho substituents, but lower than that for doubly substituted dimers. The greater preference for dimer formation for the ortho‐substituted urazole radicals is attributed to a greater enthalpic advantage for N―N bond formation. This advantage may be traced to a higher concentration of spin density on the urazole unit of the radicals and a lesser deformation energy required for N―N bond formation.     

Topology of trajectories of the 2D Navier-Stokes equations

In spectral form the 2D incompressible Navier-Stokes equations in a square periodic region will be represented by 430 complex Fourier amplitudes which correspond to isotropic truncation of the upper wave number 16. For small viscosity, we have found five equilibrium states I-V in the entire range of forcing; I-fixed point, II-circle, III-closed orbit, IV-torus, and V-chaos. The fixed-point equilibrium state is the laminar flow. As the forcing passes through a critical value, the fixed point evolves directly to equilibrium state III under a typical multimode forcing. The chaotic transition takes place on a 2-torus-like manifold (equilibrium state IV) which is the product space of a circle and the closed orbit of equilibrium state III, similar to the quasiperiodic 2-torus of Ruelle and Takens. For sufficiently large forcing, the evolution of equilibrium state V is nothing but a simulation of quasistationary 2D turbulence. From the Lyapunov exponents of turbulent flows, we have evaluated the constants in the theoretical results of Foias and his colleagues, which relate the determining mode and fractal dimension with the enstrophy dissipation wave number of 2D turbulence.     

Thermalization of nonequilibrium electron-positron-photon plasmas

Starting from a nonequilibrium configuration we analyze the role of the direct and the inverse binary and triple interactions in reaching thermal equilibrium in a homogeneous isotropic pair plasma. We focus on energies in the range 0.1-10 MeV. We numerically integrate the relativistic Boltzmann equation with the exact QED collisional integrals taking into account all binary and triple interactions. We show that first, when a detailed balance is reached for all binary interactions on a time scale t(k) < or approximately 10(-14) sec, photons and electron-positron pairs establish kinetic equilibrium. Subsequently, when triple interactions satisfy the detailed balance on a time scale t(eq) < or approximately 10(-12) sec, the plasma reaches thermal equilibrium. It is shown that neglecting the inverse triple interactions prevents reaching thermal equilibrium. Our results obtained in the theoretical physics domain also find application in astrophysics and cosmology.