A branch and cut approach to the cardinality constrained circuit problem

The Cardinality Constrained Circuit Problem (CCCP) is the problem of finding a minimum cost circuit in a graph where the circuit is constrained to have at most k edges. The CCCP is NP-Hard. We present classes of facet-inducing inequalities for the convex hull of feasible circuits, and a branch-and-cut solution approach using these inequalities. Received: April 1998 / Accepted: October 2000?Published online October 26, 2001     

High Temperature Oxidation of Fe22Cr-alloy

The isothermal and constant heating rate oxidation behaviour of the alloy Fe₇₈Cr₂₂ was examined in air with 1% H₂O and in 7% H₂/93% Ar with 1% or 12% H₂O. The measurements were performed in the temperature range 700–1300°C. The effect of surface treatment prior to oxidation was examined. A Cr₂O₃ scale developed slowly up to900°C. At 1100°C a catastrophic oxidation was observed after heat treatment for 70 h in air with 1% H₂O and in 7% H₂/93% Ar with 12% H₂O. The scale developed in these cases consisted of iron rich oxides such as Fe₂O₃ or FeCr₂O₄, in contrast to the more protective Cr₂O₃ scale seen under other test conditions. Possible causes for the catastrophic oxidation are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Enantiospecific adsorption of cysteine at chiral kink sites on Au(110)-(1 x 2)

Enantiospecific adsorption of cysteine molecules onto chiral kink sites on the Au(110)-(1x2) surface was observed by scanning tunneling microscopy. l- and d-cysteine dimers were found to adopt distinctly different adsorption geometries at S kinks, which can be understood from the need to reach specific, optimum molecule-substrate interaction points. Extended, homochiral domains of l/d-cysteine were furthermore observed to grow preferentially from R/S kinks. The results constitute the first direct, microscopic observation of enantiospecific molecular interaction with chiral sites on a metal single-crystal surface.     

Nanostructured PLD-grown gadolinia doped ceria: Chemical and structural characterization by transmission electron microscopy techniques

The morphology as well as the spatially resolved elemental and chemical characterization of 10 mol% gadolinia doped ceria (CGO10) structures prepared by pulsed laser deposition (PLD) technique are investigated by scanning transmission electron microscopy accompanied with electron energy loss spectroscopy and energy dispersive X-ray spectroscopy. A dense, columnar and structurally inhomogeneous CGO10 film, i.e. exhibiting grain size refinement across the film thickness, is obtained in the deposition process. The cerium M_4,5 edges, used to monitor the local electronic structure of the grains, indicate apparent variation of the ceria valence state across and along the film. No element segregation to the grain boundaries is detected. These results are discussed in the context of solid oxide fuel cell applications.     

Water condensation kinetics on a hydrophobic surface

Employing thermal desorption spectroscopy, we show that the effective probability of water condensation at low water vapor pressure on an octane film is much below unity at 100-120 K. This unusual finding is related to a small binding energy of H2O monomers on octane (approximately equal to 0.08 eV), requiring the formation of critical water clusters for condensation to occur. This results in strong temperature and impingement-rate dependencies of the water condensation rate and a nonlinear uptake as a function of dose time. All these features are rationalized quantitatively by a kinetic model of water condensation.     

The microwave heating of two-dimensional slabs with small Arrhenius absorptivity

The microwave heating of two-dimensional slabs in a long rectangularwaveguide propagating the TE₁₀ mode is examined. The temperaturedependency of the electrical conductivity and the thermal absorptivityis assumed to be governed by the Arrhenius law, while both theelectrical permittivity and the magnetic permeability are assumedconstant. The governing equations are the forced heat equationand the steady-state version of Maxwell's equation while theboundary conditions take into account both convective and radiativeheat loss. Approximate analytical solutions, valid for smallthermal absorptivity, are found for the temperature and theelectric-field amplitude using the Galerkin method. As the Arrheniuslaw is not amenable analytically, it is approximated by a rational-cubicfunction. At the steady state the temperature versus power relationshipis found to be multivalued; at the critical power level thermalrunaway occurs when the temperature jumps from the lower (cool)temperature branch to the upper (hot) temperature branch ofthe solution. In the steady-state limit the approximate analyticalsolutions are compared with the numerical solutions of the governingequations for various special cases. These are the limits ofsmall and large heat loss and an intermediate case involvingradiative heat loss. Results are also presented for a case wheredifferential cooling occurs on the different sides on the slab.An alternative heating scenario, where one end of the waveguideis blocked by a short, is also considered. The approximate solutionsare found for this geometry and compared in the small Biot-numberlimit to Kriegsmann (1997). Also, a control process is presented,which allows thermal runaway to be avoided and the desired finalsteady state to be reached. Various special cases of the feedbackparameters associated with the control process are examined.     

A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs

We propose a branch-and-bound algorithm for solving nonconvex quadratically-constrained quadratic programs. The algorithm is novel in that branching is done by partitioning the feasible region into the Cartesian product of two-dimensional triangles and rectangles. Explicit formulae for the convex and concave envelopes of bilinear functions over triangles and rectangles are derived and shown to be second-order cone representable. The usefulness of these new relaxations is demonstrated both theoretically and computationally.