The Linear Ordering Problem Revisited

The Linear Ordering Problem is a popular combinatorial optimisation problem which has been extensively addressed in the literature. However, in spite of its popularity, little is known about the characteristics of this problem. This paper studies a procedure to extract static information from an instance of the problem, and proposes a method to incorporate the obtained knowledge in order to improve the performance of local search-based algorithms. The procedure introduced identifies the positions where the indexes cannot generate local optima for the insert neighbourhood, and thus global optima solutions. This information is then used to propose a restricted insert neighbourhood that discards the insert operations which move indexes to positions where optimal solutions are not generated. In order to measure the efficiency of the proposed restricted insert neighbourhood system, two state-of-the-art algorithms for the LOP that include local search procedures have been modified. Conducted experiments confirm that the restricted versions of the algorithms outperform the classical designs systematically. The statistical test included in the experimentation reports significant differences in all the cases, which validates the efficiency of our proposal.

The forward problem for the electromagnetic Helmholtz equation

157 p.

Shape Optimization for Hypersonic Arc-Wing Missiles

National Natural Science Foundation of China (NO.90916013)

A new solution for the roommate problem: The Q-stable matchings

The aim of this paper is to propose a new solution for the roommate problem with strict preferences. We introduce the solution of maximum irreversibility and consider almost stable matchings (Abraham et al. [2])and maximum stable matchings (Ta [30] [32]). We find that almost stable matchings are incompatible with the other two solutions. Hence, to solve the roommate problem we propose matchings that lie at the intersection of the maximum irreversible matchings and maximum stable matchings, which are called Q-stable matchings. These matchings are core consistent and we offer an effi cient algorithm for computing one of them. The outcome of the algorithm belongs to an absorbing set.

Laser Guiding in the Randomicity of Discrete Surface Strengthening by Arc Discharge

Several discharge areas by laser-guided discharge (LGD) were compared with those by common arc discharge. The randomicity of discharge areas by common arc discharge was controlled by laser guiding on two scales: large scale (the spacing of the discharge areas) and small scale (the inside of the discharge area). The position of the discharge area overlapped completely with a laser focus; therefore, the distribution and surface shape of the discharge areas were controlled. The stochastic movement of anode spot in the discharge area was controlled by laser guiding. As such, the repetitive melting and solidifying of microstructures in the discharge area was constrained. The tempered microstruc- tures in the discharge area were voided, the utilization efficiency of input energy was improved, and the strengthened depth of the discharge areas was increased. The regularity of cross-sectional shape of the discharge area was also improved. The hardness of microstructures in both discharge areas is greater than that of the base material. The highest level of hardness of microstructures in both discharge areas measures above 1000 HV. In summary, the hardness ofmicrostructures in the discharge area by LGD is larger and more discrete than that by common arc discharge.

The stochastic exit problem for dynamical systems

The problem of "exit against a flow" for dynamical systems subject to small Gaussian white noise excitation is studied. Here the word "flow" refers to the behavior in phase space of the unperturbed system's state variables. "Exit against a flow" occurs if a perturbation causes the phase point to leave a phase space region within which it would normally be confined. In particular, there are two components of the problem of exit against a flow:

i) the mean exit time

ii) the phase-space distribution of exit locations.

When the noise perturbing the dynamical systems is small, the solution of each component of the problem of exit against a flow is, in general, the solution of a singularly perturbed, degenerate elliptic-parabolic boundary value problem.

Singular perturbation techniques are used to express the asymptotic solution in terms of an unknown parameter. The unknown parameter is determined using the solution of the adjoint boundary value problem.

The problem of exit against a flow for several dynamical systems of physical interest is considered, and the mean exit times and distributions of exit positions are calculated. The systems are then simulated numerically, using Monte Carlo techniques, in order to determine the validity of the asymptotic solutions.

Modelling Study On The Plasma Flow and Heat Transfer In A Laminar Arc Plasma Torch Operating At Atmospheric and Reduced Pressure

A modelling study is performed to investigate the characteristics of both plasma flow and heat transfer of a laminar non-transferred arc argon plasma torch operated at atmospheric and reduced pressure. It is found that the calculated flow fields and temperature distributions are quite similar for both cases at a chamber pressure of 1.0 atm and 0.1 atm. A fully developed flow regime could be achieved in the arc constrictor-tube between the cathode and the anode of the plasma torch at 1.0 atm for all the flow rates covered in this study. However the flow field could not reach the fully developed regime at 0.1 atm with a higher flow rate. The arc-root is always attached to the torch anode surface near the upstream end of the anode, i.e. the abruptly expanded part of the torch channel, which is in consistence with experimental observation. The surrounding gas would be entrained from the torch exit into the torch interior due to a comparatively large inner diameter of the anode channel compared to that of the arc constrictor-tube.

Topics in bifurcation theory

I. Existence and Structure of Bifurcation Branches

The problem of bifurcation is formulated as an operator equation in a Banach space, depending on relevant control parameters, say of the form G(u,λ) = 0. If dimN(G_u(u_O,λ_O)) = m the method of Lyapunov-Schmidt reduces the problem to the solution of m algebraic equations. The possible structure of these equations and the various types of solution behaviour are discussed. The equations are normally derived under the assumption that G^O_λεR(G^O_u). It is shown, however, that if G^O_λεR(G^O_u) then bifurcation still may occur and the local structure of such branches is determined. A new and compact proof of the existence of multiple bifurcation is derived. The linearized stability near simple bifurcation and "normal" limit points is then indicated.

II. Constructive Techniques for the Generation of Solution Branches

A method is described in which the dependence of the solution arc on a naturally occurring parameter is replaced by the dependence on a form of pseudo-arclength. This results in continuation procedures through regular and "normal" limit points. In the neighborhood of bifurcation points, however, the associated linear operator is nearly singular causing difficulty in the convergence of continuation methods. A study of the approach to singularity of this operator yields convergence proofs for an iterative method for determining the solution arc in the neighborhood of a simple bifurcation point. As a result of these considerations, a new constructive proof of bifurcation is determined.

Plasma-Arc Technology For The Thermal Treatment Of Chemical Wastes

Plasma-arc technology was developed to dispose of chemical wastes from a chemical plant by the Institute of Mechanics, Chinese Academy of Sciences (CAS-IMECH). A pilot plant system with this technology was constructed to destroy two types of chemical wastes. The system included shredding, mixing, and feeding subsystems, a plasma-arc reactor of 150 kW, an off-gas burning subsystem, and a scrubbing subsystem. The additives (CaO, SiO2, and Fe) were added into the reactor to form vitrified slag and capture the hazardous elements. The molten slag was quickly quenched to form an amorphous glassy structure. A direct current (DC) experimental facility of 30kW with plasma-arc technology was also set up to study the pyrolysis process in the laboratory, and the experimental results showed the cooling speed is the most important factor for good vitrified structure of the slag. According to previous tests, the destruction and removal efficiency (DRE) for these chemical wastes was more than 99.999%, and the polychlorinated biphenyls (PCBs) concentration in the solid residues was in the range of 1.28 to 12.9mg/kg, which is far below the Chinese national emission limit for the hazardous wastes. A simplified electromagneto model for numerical simulation was developed to predict the temperature and velocity fields. This model can make satisfactory maximum temperature and velocity distributions in the arc region, as well as the results by the magneto hydrodynamic approach.