Experimental observations of mode-converted ion cyclotron waves in a tokamak plasma by phase contrast imaging

The process of mode conversion, whereby an externally launched electromagnetic wave converts into a shorter wavelength mode(s) in a thermal plasma near a resonance in the index of refraction, is particularly important in a multi-ion species plasma near the ion cyclotron frequency. Using phase contrast imaging techniques (PCI), mode-converted electromagnetic ion cyclotron waves have been detected for the first time in the Alcator C-Mod tokamak near the H-3He ion-ion hybrid resonance region during high power rf heating experiments. The results agree with theoretical predictions.     

Rotation reversal bifurcation and energy confinement saturation in tokamak Ohmic L-mode plasmas

Direction reversals of intrinsic toroidal rotation have been observed in diverted Alcator C-Mod Ohmic L-mode plasmas following electron density ramps. For low density discharges, the core rotation is directed cocurrent, and reverses to countercurrent following an increase in the density above a certain threshold. Such reversals occur together with a decrease in density fluctuations with 2 cm(-1)≤k(θ)≤11 cm(-1) and frequencies above 70 kHz. There is a strong correlation between the reversal density and the density at which the Ohmic L-mode energy confinement changes from the linear to the saturated regime.     

Integer Optimization on Convex Semialgebraic Sets

Let Y be a convex set in \Re ^k defined by polynomial inequalities and equations of degree at most d ≥ 2 with integer coefficients of binary length at most l . We show that if the set of optimal solutions of the integer programming problem min is not empty, then the problem has an optimal solution of binary length ld ^O(k4) . For fixed k , our bound implies a polynomial-time algorithm for computing an optimal integral solution y ^* . In particular, we extend Lenstra's theorem on the polynomial-time solvability of linear integer programming in fixed dimension to semidefinite integer programming. Received August 3, 1998, and in revised form March 22, 1999.     

Polynomial time approximation schemes for general multiprocessor job shop scheduling

We study preemptive and non-preemptive versions of the general multiprocessor job shop scheduling problem: Given a set of n tasks each consisting of at most μ ordered operations that can be processed on different (possibly all) subsets of m machines with different processing times, compute a schedule (preemptive or non-preemptive, depending on the model) with minimum makespan where operations belonging to the same task have to be scheduled according to the specified order. We propose algorithms for both preemptive and non-preemptive variants of this problem that compute approximate solutions of any positive ε accuracy and run in O(n) time for any fixed values of m, μ, and ε. These results include (as special cases) many recent developments on polynomial time approximation schemes for scheduling jobs on unrelated machines, multiprocessor tasks, and classical open, flow and job shops.     

On the Complexity of Semidefinite Programs

We show that the feasibility of a system of m linear inequalities over the cone of symmetric positive semidefinite matrices of order n can be tested in mn arithmetic operations with -bit numbers, where l is the maximum binary size of the input coefficients. We also show that any feasible system of dimension (m,n) has a solution X such that log||X|| .