Steady-state fully noninductive current driven by electron cyclotron waves in a magnetically confined plasma

A steady-state, fully noninductive plasma current has been sustained for the first time in a tokamak using electron cyclotron current drive only. In this discharge, 123 kA of current have been sustained for the entire gyrotron pulse duration of 2 s. Careful distribution across the plasma minor radius of the power deposited from three 0. 5-MW gyrotrons was essential for reaching steady-state conditions. With central current drive, up to 153 kA of current have been fully replaced transiently for 100 ms. The noninductive scenario is confirmed by the ability to recharge the Ohmic transformer. The dependence of the current drive efficiency on the minor radius is also demonstrated.     

Modulated periodic stokes waves in deep water

Modulated deep-water 1D Stokes waves are considered experimentally and theoretically. Wave trains are modulated in a controlled fashion and their evolution is recorded. Data from repeated laboratory experiments are reproducible near the wave maker, but diverge away from the wave maker. Numerical integration of a perturbed nonlinear Schrodinger equation and an associated linear spectral problem indicate that under suitable conditions modulated periodic Stokes waves evolve chaotically. Sensitive spectral evolution in the neighborhood of homoclinic manifolds of the unperturbed nonlinear Schrodinger equation is found.     

Positive solutions for systems of nonlinear eigenvalue problems for functional differential equations

Values of?λ?are determined for which there exist positive solutions of the system of functional differential equations, u″?+?λa(t)f(v _t )?=?0,v″?+?λb(t)g(u _t )?=?0, for 0?t?u(s)?=?v(s)?=?φ(s), ?r?≤?s?≤?0, and the boundary conditions u(0)?=?v(0)?=?φ(0)?=?u(1)?=?v(1)?=?0. A Guo–Krasnosel'skii fixed point theorem is applied.     

Uniqueness implies existence for (n,p) boundary value problems

The uniqueness of solutions of certain boundary value problems implies their existence for the nth order nonlinear ordinary differential equation y⁽ⁿ⁾=f(x,y,y^',y^'',....,y^(n-1)) This existence is established by using shooting methods and yields results for (n,p) boundary value problems.     

Open problem and conjectures,countably many solutions for a bvp on a measure chain

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Geometric Satake, Springer correspondence and small representations

For a simply-connected simple algebraic group $G$ over $\mathbb C $ , we exhibit a subvariety of its affine Grassmannian that is closely related to the nilpotent cone of $G$ , generalizing a well-known fact about $GL_n$ . Using this variety, we construct a sheaf-theoretic functor that, when combined with the geometric Satake equivalence and the Springer correspondence, leads to a geometric explanation for a number of known facts (mostly due to Broer and Reeder) about small representations of the dual group.     

Existence and multiplicity for positive solutions of a second-order multi-point discrete boundary value problem

We investigate the existence and multiplicity of positive solutions for a system of nonlinear second-order difference equations with multi-point boundary conditions.