Plasma ions dynamics in the wake of a short laser pulse

A new physical effect of a plasma channel formation by the ponderomotive force of a wakefield generated by a laser pulse with a length of the order of the electron plasma wavelength is discussed. For a narrow pulse, wherein the width is less than c/omega(pe) ( omega(pe) and c are the plasma frequency and light velocity, respectively), the channel has an annular form with on-axis density maximum. The depth of the channel increases with the distance from the pulse until the phase mixing arises and the wake starts to break. The linear fluid theory is used to obtain the scaling for wave-breaking conditions. The results of numerical simulations for high intensity laser pulses are in good agreement with theoretical predictions.     

Measurements of O2-broadening and -shifting parameters of water vapor spectral lines in the second hexad region

Oxygen pressure induced broadening and shifting coefficients for water vapor absorption lines in the 8600–9010 cm⁻¹ region have been measured and calculated. The spectra were recorded with a Bruker IFS 125HR spectrometer at a spectral resolution of 0.01 cm⁻¹ for lines with angular moment of the upper states up to 10. Calculations of line broadening and shifting coefficients are performed using a semi-empirical approach. The method is based on the impact theory of broadening, and includes the correction factors whose parameters can be determined by fitting the broadening or shifting coefficients to the experimental data. The comparison of our calculations with the experimental values argues that the semi-empirical method is quite acceptable for the determination of the water vapor absorption line profile parameters.     

Observation of the decay B- → D(s)((*)+) K- ℓ- ν(ℓ)

We report the observation of the decay B- → D(s)((*)+) K- ?- ν(?) based on 342 fb(-1) of data collected at the Υ(4S) resonance with the BABAR detector at the PEP-II e+ e- storage rings at SLAC. A simultaneous fit to three D(s)(+) decay chains is performed to extract the signal yield from measurements of the squared missing mass in the B meson decay. We observe the decay B- → D(s)((*)+) K- ?- ν(?) with a significance greater than 5 standard deviations (including systematic uncertainties) and measure its branching fraction to be B(B- → D(s)((*)+) K- ?- ν(?)) = [6.13(-1.03)(+1.04)(stat)±0.43(syst)±0.51(B(D(s)))]×10(-4), where the last error reflects the limited knowledge of the D(s) branching fractions.     

Stabilized SQP revisited

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve superlinear convergence in situations when the Lagrange multipliers associated to a solution are not unique. Within the framework of Fischer (Math Program 94:91–124, 2002), the key to local superlinear convergence of sSQP are the following two properties: upper Lipschitzian behavior of solutions of the Karush-Kuhn-Tucker (KKT) system under canonical perturbations and local solvability of sSQP subproblems with the associated primal-dual step being of the order of the distance from the current iterate to the solution set of the unperturbed KKT system. According to Fernández and Solodov (Math Program 125:47–73, 2010), both of these properties are ensured by the second-order sufficient optimality condition (SOSC) without any constraint qualification assumptions. In this paper, we state precise relationships between the upper Lipschitzian property of solutions of KKT systems, error bounds for KKT systems, the notion of critical Lagrange multipliers (a subclass of multipliers that violate SOSC in a very special way), the second-order necessary condition for optimality, and solvability of sSQP subproblems. Moreover, for the problem with equality constraints only, we prove superlinear convergence of sSQP under the assumption that the dual starting point is close to a noncritical multiplier. Since noncritical multipliers include all those satisfying SOSC but are not limited to them, we believe this gives the first superlinear convergence result for any Newtonian method for constrained optimization under assumptions that do not include any constraint qualifications and are weaker than SOSC. In the general case when inequality constraints are present, we show that such a relaxation of assumptions is not possible. We also consider applying sSQP to the problem where inequality constraints are reformulated into equalities using slack variables, and discuss the assumptions needed for convergence in this approach. We conclude with consequences for local regularization methods proposed in (Izmailov and Solodov SIAM J Optim 16:210–228, 2004; Wright SIAM J. Optim. 15:673–676, 2005). In particular, we show that these methods are still locally superlinearly convergent under the noncritical multiplier assumption, weaker than SOSC employed originally.     

Mathematical Programs with Vanishing Constraints: Optimality Conditions,Sensitivity, and a Relaxation Method

We consider a class of optimization problems with switch-off/switch-on constraints, which is a relatively new problem model. The specificity of this model is that it contains constraints that are being imposed (switched on) at some points of the feasible region, while being disregarded (switched off) at other points. This seems to be a potentially useful modeling paradigm, that has been shown to be helpful, for example, in optimal topology design. The fact that some constraints “vanish” from the problem at certain points, gave rise to the name of mathematical programs with vanishing constraints (MPVC). It turns out that such problems are usually degenerate at a solution, but are structurally different from the related class of mathematical programs with complementarity constraints (MPCC). In this paper, we first discuss some known first- and second-order necessary optimality conditions for MPVC, giving new very short and direct justifications. We then derive some new special second-order sufficient optimality conditions for these problems and show that, quite remarkably, these conditions are actually equivalent to the classical/standard second-order sufficient conditions in optimization. We also provide a sensitivity analysis for MPVC. Finally, a relaxation method is proposed. For this method, we analyze constraints regularity and boundedness of the Lagrange multipliers in the relaxed subproblems, derive a sufficient condition for local uniqueness of solutions of subproblems, and give convergence estimates. Research of the first author was supported by the Russian Foundation for Basic Research Grants 07-01-00270, 07-01-00416 and 07-01-90102-Mong, and by RF President’s Grant NS-9344.2006.1 for the support of leading scientific schools. The second author was supported in part by CNPq Grants 301508/2005-4, 490200/2005-2 and 550317/2005-8, by PRONEX-Optimization, and by FAPERJ.     

Some Optimization Reformulations of the Extended Linear Complementarity Problem

We consider the extended linear complementarity problem (XLCP) introduced by Mangasarian and Pang [22], of which the horizontal and vertical linear complementarity problems are two special cases. We give some new sufficient conditions for every stationary point of the natural bilinear program associated with XLCP to be a solution of XLCP. We further propose some unconstrained and bound constrained reformulations for XLCP, and study the properties of their stationary points under assumptions similar to those for the bilinear program.