Calculation of Neutral Beam Injected Torque and Its Effective Tangency Major Radius for EAST

Toroidal rotation has been recognized to have significant effects on the transport and magnetohydrodynarnic（MHD） stability of tokamak plasmas.Neutral beam injection（NBI） is the most effective rotation generation method on current,tokamak devices.To estimate the effective injected torque of the first neutral beam injection system on EAST,a simplified analytic method was derived.Calculated beam torque values were validated by those obtained from the NUBEAM code simulation.According to the results,for the collisional torque,the effective tangential radius for torque deposition is close to the beam tangency major radius.However,due to the dielectric property of tokamak plasma,the equivalent tangency major radius of the J×B torque is equal to the average major radius of the magnetic flux surface.The results will be useful for the research of toroidal momentum confinement and the experimental analysis of momentum transport related with NBI on EAST.

Viability for a class of semilinear differential equations of retarded type

Let X be a Banach space, A ： D（A） X → X the generator of a compact C0- semigroup S（t） ： X → X, t ≥ 0, D a locally closed subset in X, and f ： （a, b） × X →X a function of Caratheodory type. The main result of this paper is that a necessary and sufficient condition in order to make D a viable domain of the semilinear differential equation of retarded type u＇（t） = Au（t） ＋ f（t, u（t - q））, t ∈ [to, to ＋ T], with initial condition uto = φ ∈C（[-q, 0]; X）, is the tangency condition lim infh10 h^-1d（S（h）v（O）＋hf（t, v（-q））; D） = 0 for almost every t ∈ （a, b） and every v ∈ C（[-q, 0]; X） with v（0）, v（-q）∈ D.

New bifurcations of basin boundaries involving Wada and a smooth Wada basin boundary

This paper demonstrates and analyses double heteroclinic tangency in a three-well potential model, which can produce three new types of bifurcations of basin boundaries including from smooth to Wada basin boundaries, from fractal to Wada basin boundaries in which no changes of accessible periodic orbits happen, and from Wada to Wada basin boundaries. In a model of mechanical oscillator, it shows that a Wada basin boundary can be smooth.

On Types of Isolated KKT Points in Polynomial Optimization

Let f be a real polynomial function with n variables and S be a basic closed semialgebraic set in R^(n).In this paper,the authors are interested in the problem of identifying the type(local minimizer,maximizer or not extremum point)of a given isolated KKT point x^(*)of f over S.To this end,the authors investigate some properties of the tangency variety of f on S at x^(*),by which the authors introduce the definition of faithful radius of f over S at x^(*).Then,the authors show that the type of x^(*)can be determined by the global extrema of f over the intersection of S and the Euclidean ball centered at x^(*)with a faithful radius.Finally,the authors propose an algorithm involving algebraic computations to compute a faithful radius of x*and determine its type.

Equivalent Conditions of Dominated Splitting for Volume-Preserving Diffeomorphisms

We discuss the equivalent conditions of dominated splitting for conservative diffeomorphisms in C^1 topology.