Secondary cycle of equilibria in a system with cosymmetry,its creation by bifurcation and impossibility of symmetric treatment of it

A study is reported of the bifurcation of a cycle of equilibria of an autonomous differential equation with cosymmetry in Hilbert space, which is a simulation of the problem of planar filtrational convection of a fluid in a porous medium. The Lyapunov-Schmidt method and perturbation theory are used to find its amplitude and the damping rate of the dominant mode. It is shown that, in the abstract general model, and also in the problem of convection in a rectangular container, this damping rate varies along the cycle of equilibria. Hence, the cycle of equilibria cannot be an orbit of the action of any symmetry group of the given system. (c) 1995 American Institute of Physics.     

Exact Helically Symmetric Plasma Equilibria

The global helically symmetric plasma equilibria are derived as exact solutions to the JFKO equation. The obtained plasma equilibria model astrophysical jets and provide a helically symmetric counterexample to the well-known Parker theorem.     

Bifurcation structures and dominant modes near relative equilibria in the one-dimensional discrete nonlinear Schrödinger equation

We investigate the bifurcation structure of a family of relative equilibria of a ring of seven oscillators described by the discrete nonlinear Schrödinger equation (DNLSE) when the period of these orbits and a suitable defect act as bifurcation parameters. We find a reduced Hamiltonian that gives substantial insight into the dynamics of this system. The convexity of this Hamiltonian at given nonresonant equilibria supports the stability of nearby quasiperiodic solutions. We show that the local loss of convexity in the reduced Hamiltonian is determined by the Hessian of its integrable part in the family of relative equilibria under study. Stable quasiperiodic solutions are studied by considering the power spectral densities of a set of suitable fast and slow actions, whose origin is suggested by the averaging principle. We also show that the return times form an optimal embedding to characterize the system dynamics. We show that the power spectral density of a suitable interference signal, arising from a ring of Bose-Einstein condensates and described by the DNLSE, has a single prominent peak at the breather-like relative equilibria.     

A plasma resistive diffusion model

A self-consistent study of the slow resistive evolution of an axisymmetric toroidal plasma gives rise to a set of transport equations involving one space variable which require input from the solution of a generalized differential equation obtained from the time-differentiated Grad-Shafranov equation. An iterative scheme is presented for the numerical solution of this generalized differential equation which overcomes the problems of the non-standard boundary conditions. As an illustration this method is used to compute the instantaneous diffusion velocity of a class of model toroidal equilibria. A more detailed study is presented of the time evolution of this model in the cylindrical limit in order to illustrate techniques which can be used in a more complete toroidal simulation.     

Closed-loop liquid-liquid equilibria and the global phase behaviour of binary mixtures involving hard-sphere + van der Waals interactions

Calculations of the critical properties of binary mixtures of components of equal size are reported using the Guggenheim equation of state. The calculations are used to determine the global phase diagram of binary mixtures. Type VI phase behaviour is predicted successfully indicating that closed-loop liquid-liquid equilibria can be obtained from hard-sphere + van der Waals interactions. Closed-loop liquid-liquid equilibria occur in the region of the global phase diagram characterized by moderately strong unlike interactions and components with very dissimilar critical temperatures. The Guggenheim equation can predict all experimentally known phase behaviour types. In addition, other hypothetical phase behaviour types are also predicted.     

Analytic Anisotropic Toroidally Axi-symmetric Equilibria with Parallel Flow for Arbitrary Aspect Ratio and Large Triangularity

Though most of the studies on toroidally axi-symmetric equilibria are based on the scalar pressure assumption that leads to the usual Grad-Shafranov equation, the realistic plasma is generally more complicated and plasmas with anisotropic pressure are routinely encountered. On the other hand, effect of plasma flow on tokamak equilibrium has also been attracted much interests historically and there appear some new interests for non-static equilibria For purely toroidal flow case, some exact solutions had been reported before .     

Study of the plasma equilibrium in Damavand tokamak via numerical solution of the Grad-Shafranov equation

In this work we study the Damavand tokamak plasma equilibrium with an elongated ross section and fixed boundary conditions. These equilibria are characterized by three parameters such as elongation, triangularity and magnetic axis shift. An iterative scheme f the moment’s method is used to solve the Grad-Shafranov equation in flux coordinate system. Magnetic flux surface contours and main equilibrium parameters have been btained by applying the geometry and boundary conditions of the Damavand tokamak.     

Thermodynamics and kinetics of indole oligomerization in 0.5 mol L−1 aqueous sulfuric acid: evaluation of some temperature‐dependant parameters

Indole is present in a wide variety of natural compounds with physiological activities, as well as it is a very important intermediate in medicinal and industrial chemistry. For this reason, the evaluation of indole protonation, oligomerization equilibria and the study of the kinetics of dimer and trimer formation in diluted sulfuric acid at various temperatures are of paramount importance because of their practical and scientific implications. Here, we calculate the protonation equilibria by using the literature titration data together with a quantum chemical computational approach, in order to obtain reliable pK_a value of indole from 288 to 313 K. Starting from these calculations, we are able to measure the oligomerization equilibrium constants of indole, their kinetic constants, whose values are dependent of indole pK_a, at different temperatures. Enthalpy and entropy of the reactions are calculated by means of Van't Hoff equation, while the activation parameters of Eyring–Evans–Polanyi equation are evaluated for the whole kinetic constants. Copyright © 2014 John Wiley & Sons, Ltd.     

Linear stability of the spatially homogeneous equilibria of the Vlasov-Poisson system with collisions

In this work we study the stability of the spatially homogeneous solutions of the Vlasov-Poisson system (Vlasov equilibria) when a collision term, in the form of a BGK operator with velocity-dependent collision frequency, is added to the Vlasov equation. Generalizing earlier results, obtained for the same collision model with a constant collision frequency, we find the spectrum and the eigenfunctions of the linear transport operator and derive a new linear dispersion relation for the linearized kinetic equations. Finally, we present some numerical results.     

Non-hydrodynamic modes and general equations of state in lattice Boltzmann equations

The lattice Boltzmann equation is commonly used to simulate fluids with isothermal equations of state in a weakly compressible limit, and intended to approximate solutions of the incompressible Navier–Stokes equations. Due to symmetry requirements there are usually more degrees of freedom in the equilibrium distributions than there are constraints imposed by the need to recover the Navier–Stokes equations in a slowly varying limit. We construct equilibria for general barotropic fluids, where pressure depends only upon density, using the two-dimensional, nine velocity (D2Q9) and one-dimensional, five velocity (D1Q5) lattices, showing that one otherwise arbitrary function in the equilibria must be chosen to suppress instability.     

Magnetohydrostatic Equilibrium with External Gravitational Fields in Symmetric Systems

We present a general formulation for magnetohydrostatic equilibria with external gravitational fields in symmetric systems with one ignorable coordinate, using non-orthogonal coordinate systems. We consider the cases of isothermal as well as adiabatic processes. Analytical exact solutions for the ideal magnetohydrodynamical equilibrium equation are presented for rectangular, cylindrical, and spherical coordinates.     

Interaction of sine-Gordon kinks with defects: phase space transport in a two-mode model

We study a model derived by Fei et al. [Phys. Rev. A 45 (1992) 6019] of a kink solution to the sine-Gordon equation interacting with an impurity mode. The model is a two degree of freedom Hamiltonian system. We investigate this model using the tools of dynamical systems, and show that it exhibits a variety of interesting behaviors including transverse heteroclinic orbits to degenerate equilibria at infinity, chaotic dynamics, and an extremely complex and delicate structure describing the interaction of the kink with the defect. We interpret this in terms of phase space transport theory.     

自由界面轴对称等离子体位形的绝热演化

本文将轴对称等离子体的平衡方程与它对磁面求平均的磁面平均方程相结合,求出了等离子体平衡位形随时间的绝热演化。计算结果与解析的Furth-Yoshikawa定标律符合较好。文中还给出了两种不同类型磁压缩装置的等离子体位形的演化。 关键词：     

An electric bottle for colloids

Particle concentration is a dominant control parameter for colloids and other soft matter systems. We demonstrate a simple technique, "dielectrophoretic equilibrium," implemented as an "electric bottle," a planar capacitor in a larger volume. The uniform field in the capacitor traps particles in this force-free region at a higher density than in the zero field regions outside. We show how the technique measures the equation of state and we initiate and grow colloidal crystals. "Dielectrophoretic equilibria" enable the study of a complete concentration-dependent phase diagram from a single microscopic sample, obviating the previous need for preparing a large number of samples.     

超临界二氧化碳和模型共聚物的相平衡和成核性质研究

在Weeks-Chandler-Andersen （WCA）微扰理论的基础上,建立了一个状态方程,研究了温度和压力以及模型共聚物分子链长对体系相平衡和临界胶束浓度的影响. 关键词： 超临界二氧化碳 模型共聚物 相平衡 临界胶束浓度     

Solitonlike solutions of the Grad-Shafranov equation

A new class of solitonlike solutions is derived for the Grad-Shafranov (GS) equations. A mathematical analogy between the GS equation for MHD equilibria and the cubic Schr?dinger equation for nonlinear wave propagation forms the basis to derive the new class of solutions. The solitonlike solutions are considered for their possible relevance to astrophysics and solar physics problems. We discuss how a solitonlike solution can be generated by a repetitive process of magnetic arcade stretching and plasmoid formation induced by the differential rotation of the solar photosphere or of an accretion disk.     

Elastica hypoarealis

We examine the equilibria of a rigid loop in the plane, characterized by an energy functional quadratic in the curvature, subject to the constraints of fixed length and fixed enclosed area. Whereas the only non self-intersecting equilibrium corresponding to the fixed length constraint is the circle, the area constraint gives rise to distinct equilibria labeled by an integer. These configurations exhibit self-intersections and bifurcations as the area is reduced. In addition, not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but the embedding itself can be expressed as a local function of the curvature. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. Analytical expressions for the energy as a function of the area are obtained in the limiting regimes. Received 18 October 2001 / Received in final form 31 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: capo@fis.cinvestav.mx RID="b" ID="b"e-mail: chryss@nuclecu.unam.mx RID="c" ID="c"e-mail: jemal@nuclecu.unam.mx     

Self-consistent diverted tokamak equilibria with nonzero edge current

The semi-analytical method, previously used to construct model double-null and single-null diverted tokamak equi- libria (Bingren Shi, Plasma Phys. Control Fusion 50 (2008) 085006, 51 (2009) 105008, Nucl. Fusion 51 (2011) 023004), is extended to describe diverted tokamak equilibria with nonzero edge current, including the Pfirsch–Schlüter(PS) cur- rent. The PS current density is expressed in a way suitable to describe a diverted tokamak configuration in the near separatrix region. The model equilibrium is expressed by only two terms of the exact separable solutions of the Grad– Shafranov equation, one of which is governed by a homogeneous ordinary differential equation, and the other by an inhomogeneous one. The particular merits of such a model configuration are that the internal region inside the separa- trix and a suitable scrape-off layer can be simultaneously described by this exact solution. To investigate the physics in the region near the X-point, the magnetic surfaces can be satisfactorily described by approximate hyperbolic curves.     

Admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap

A "parallel current constraint" is derived, that in combination with the Poisson equation allows one to select admissible equilibria of non-neutral plasmas in a Malmberg-Penning trap in the presence of a nonuniform and nonaxisymmetric magnetic field. Asymmetry-induced currents (analogous to the Pfirsch-Schlüter currents in Tokamaks) appearing in a non-neutral plasma even in the absence of magnetic drifts are explicitly computed in the case of a uniformly tilted magnetic field.     

Filamentary plasma eruptions: Results using the non‐linear ballooning model

This paper provides an overview of recent results on two distinct studies exploiting the non‐linear model for ideal ballooning modes with potential applications to edge‐localized modes (ELMs). The non‐linear model for tokamak geometries was developed by Wilson and Cowley in 2004 and consists of two differential equations that characterize the temporal and spatial evolution of the plasma displacement. The variation of the radial displacement along the magnetic field line is described by the first equation, which is identical to the linear ballooning equation. The second differential equation is a two‐dimensional non‐linear ballooning‐like equation, which is often second order in time but can involve a fractional time derivative depending on the geometry. In the first study, the interaction of multiple filamentary eruptions is addressed in a magnetized plasma in a slab geometry. Equally sized filaments evolve independently in both the linear and non‐linear regimes. However, if filaments are initiated with slightly different heights from the reference flux surface, they interact with each other in the non‐linear regime: lower filaments are slowed down and are eventually completely suppressed, while the higher filaments grow faster because of the non‐linear interaction. In the second study, this model of non‐linear ballooning modes is examined quantitatively against experimental observations of ELMs in Mega Amp Spherical Tokamak (MAST) geometries. The results suggest that experimentally relevant results can only be obtained using modified equilibria.