Effect of Nd3+ concentration on CW and pulsed performance of fiber-coupled diode laser pumped Nd:YVO4 laser at 1064 nm

The effect of Nd³⁺ concentration on the CW and Q-switched laser performances at 1064 nm from Nd: YVO₄ has been studied under diode laser pumping in identical laser configuration. The Nd³⁺ concentrations used were 1, 2 and 3 at.% in YVO₄ crystals. Under the CW operations we have compared the thermal lensing effect, slope efficiencies and also the beam quality at the fourth-order degeneracy configuration. Q-switching was done with the help of an acousto-optic modulator and we have compared the pulses obtained from Nd: YVO₄ laser with different doping concentration. It was found that the 1 at.%-doped crystal is the best, offering highest optical-to-optical conversion efficiency (55%), lowest fractional heat load (24%), highest pulse energy (80 μJ) and shortest pulse width (20 ns). It was also found that there was not much difference in performances for 2 and 3 at.%-doped crystals both in CW and Q-switched configurations.     

A new trust region algorithm for bound constrained minimization

We introduce a new algorithm of trust-region type for minimizing a differentiable function of many variables with box constraints. At each step of the algorithm we use an approximation to the minimizer of a quadratic in a box. We introduce a new method for solving this subproblem, that has finite termination without dual nondegeneracy assumptions. We prove the global convergence of the main algorithm and a result concerning the identification of the active constraints in finite time. We describe an implementation of the method and we present numerical experiments showing the effect of solving the subproblem with different degrees of accuracy.This work was supported by FAPESP (Grants 90-3724-6 and 91-2441-3), CNPq, FINEP, and FAEP-UNICAMP.     

Bound Constrained Smooth Optimization for Solving Variational Inequalities and Related Problems

Variational inequalities and related problems may be solved via smooth bound constrained optimization. A comprehensive discussion of the important features involved with this strategy is presented. Complementarity problems and mathematical programming problems with equilibrium constraints are included in this report. Numerical experiments are commented. Conclusions and directions of future research are indicated.     

On stability and instability criteria for magnetohydrodynamics

It is shown that for most, but not all, three-dimensional magnetohydrodynamic (MHD) equilibria the second variation of the energy is indefinite. Thus the class of such equilibria whose stability might be determined by the so-called Arnold criterion is very restricted. The converse question, namely conditions under which MHD equilibria will be unstable is considered in this paper. The following sufficient condition for linear instability in the Eulerian representation is presented: The maximal real part of the spectrum of the MHD equations linearized about an equilibrium state is bounded from below by the growth rate of an operator defined by a system of local partial differential equations (PDE). This instability criterion is applied to the case of axisymmetric toroidal equilibria. Sufficient conditions for instability, stronger than those previously known, are obtained for rotating MHD. (c) 1995 American Institute of Physics.     

On the determination of elliptic differential and finite difference operators in vector bundles overS 1

For an elliptic differential operatorA overS ¹, , withA _k (x) in END(^r) and as a principal angle, the -regularized determinant Det A is computed in terms of the monodromy mapP _A , associated toA and some invariant expressed in terms ofA _n andA _n–1 . A similar formula holds for finite difference operators. A number of applications and implications are given. In particular we present a formula for the signature ofA whenA is self adjoint and show that the determinant ofA is the limit of a sequence of computable expressions involving determinants of difference approximation ofA.Partially supported by an NSF grant