Suppression of temperature fluctuations and energy barrier generation by velocity shear

First measurements of temperature fluctuations in a region of high velocity shear show that absolute and normalized fluctuation levels are reduced across the shear layer, a result that is consistent with weak parallel electron thermal conduction in the electron temperature dynamics. The concomitant reduction of temperature, density, and electric field fluctuations reduces the anomalous conducted and convected heat fluxes.     

A pressure-jump time-resolved X-ray diffraction study of cubic-cubic transition kinetics in monoolein

In the past two decades, the geometric pathways involved in the transformations between inverse bicontinuous cubic phases in amphiphilic systems have been extensively theoretically modeled. However, little experimental data exists on the cubic-cubic transformation in pure lipid systems. We have used pressure-jump time-resolved X-ray diffraction to investigate the transition between the gyroid QGII and double-diamond QDII phases in mixtures of 1-monoolein in 30 wt % water. We find for this system that the cubic-cubic transition occurs without any detectable intermediate structures. In addition, we have determined the kinetics of the transition, in both the forward and reverse directions, as a function of pressure-jump amplitude, temperature, and water content. A recently developed model allows (at least in principle) the calculation of the activation energy for lipid phase transitions from such data. The analysis is applicable only if kinetic reproducibility is achieved, at least within one sample, and achievement of such kinetic reproducibility is shown here, by carrying out prolonged pressure-cycling. The rate of transformation shows clear and consistent trends with pressure-jump amplitude, temperature, and water content, all of which are shown to be in agreement with the effect of the shift in the position of the cubic-cubic phase boundary following a change in the thermodynamic parameters.     

A network penalty method

We consider the minimum cost network flow problem and describe how the non-linear penalty function methods of Conn and Bartels can be specialized to a combinatorial algorithm for this problem. We report on preliminary computational results which show that this method can require fewer pivots than the simplex method while the amount of work required for each pivot is comparable. The algorithm can be proven finite using a modification of Cunningham's strongly feasible basis pivoting rule.Supported by the Natural Sciences and Engineering Research Council of Canada, and the joint research project Combinatorial Optimization of the Natural Sciences and Engineering Research Council, Canada and the German Research Association (Deutsche Forschungsgemeinschaft, SFB 303).     

Geometry of interpolation sets in derivative free optimization

We consider derivative free methods based on sampling approaches for nonlinear optimization problems where derivatives of the objective function are not available and cannot be directly approximated. We show how the bounds on the error between an interpolating polynomial and the true function can be used in the convergence theory of derivative free sampling methods. These bounds involve a constant that reflects the quality of the interpolation set. The main task of such a derivative free algorithm is to maintain an interpolation sampling set so that this constant remains small, and at least uniformly bounded. This constant is often described through the basis of Lagrange polynomials associated with the interpolation set. We provide an alternative, more intuitive, definition for this concept and show how this constant is related to the condition number of a certain matrix. This relation enables us to provide a range of algorithms whilst maintaining the interpolation set so that this condition number or the geometry constant remain uniformly bounded. We also derive bounds on the error between the model and the function and between their derivatives, directly in terms of this condition number and of this geometry constant.     

A primal-dual trust-region algorithm for non-convex nonlinear programming

A new primal-dual algorithm is proposed for the minimization of non-convex objective functions subject to general inequality and linear equality constraints. The method uses a primal-dual trust-region model to ensure descent on a suitable merit function. Convergence is proved to second-order critical points from arbitrary starting points. Numerical results are presented for general quadratic programs. Received: July 19, 1999 / Accepted: February 1, 2000?Published online March 15, 2000     

A note on using alternative second-order models for the subproblems arising in barrier function methods for minimization

Summary. Inequality constrained minimization problems are often solved by considering a sequence of parameterized barrier functions. Each barrier function is approximately minimized and the relevant parameters subsequently adjusted. It is common for the estimated solution to one barrier function problem to be used as a starting estimate for the next. However, this has unfortunate repercussions for the standard Newton-like methods applied to the barrier subproblem. In this note, we consider a class of alternative Newton methods which attempt to avoid such difficulties. Such schemes have already proved of use in the Harwell Subroutine Library quadratic programming codes {\tt VE14} and {\tt VE19}. Received May 2, 1993/Revised form received February 12, 1994     

Room temperature peierls distortion in small diameter nanotubes

By means of ab initio simulations, we investigate the phonon band structure and electron-phonon coupling in small 4-A diameter nanotubes. We show that both the C(5,0) and C(3,3) tubes undergo above room temperature a Peierls transition mediated by an acoustical long wavelength and an optical q=2k(F) phonon, respectively. In the armchair geometry, we verify that the electron-phonon coupling parameter lambda originates mainly from phonons at q=2k(F) and is strongly enhanced when the diameter decreases. These results question the origin of superconductivity in small diameter nanotubes.