Trace norm estimates for products of integral operators and diffusion semigroups

We give trace norm estimates for products of integral operators and for diffusion semigroups. These are applied to differences of heat semigroups. A natural example of an integral operator with finite trace which is not trace class is given.     

A model for the interaction of near-infrared laser pulses with metal powders in selective laser sintering

A thermal model of the interaction of pulsed near-infrared laser radiation from a Nd:YAG laser was made, taking the measured powder properties such as reflectance, optical penetration depth and thermal conductivity into account. It allows an estimation of the evolution of two different temperatures: the average temperature of the powder (taken over the grains in a volume given by the laser beam diameter and the optical penetration depth) and the temperature distinction within a single grain. It showed that in pulsed mode consolidation can be achieved at much lower average power as the surface of the powder particles are molten but their cores remain at nearly room temperature. This leads to a much lower average temperature and therefore a dramatic decrease in residual thermal stresses in the finished piece. The results of the model were experimentally tested and confirmed. Received: 26 July 2001 / Accepted: 23 November 2001 / Published online: 23 January 2002     

Improved modeling and solution methods for the multi-resource routing problem

This paper presents modeling and solution method improvements for the Multi-Resource Routing Problem (MRRP) with flexible tasks. The MRRP with flexible tasks is used to model routing and scheduling problems for intermodal drayage operations in which two resources (tractors and trailers) perform tasks to transport loaded and empty equipment. Tasks may be either well defined, in which both the origin and the destination of a movement are given, or flexible, in which the origin or the destination is chosen by the model. This paper proposes methods to effectively manage the number of options considered for flexible tasks (either feasible origins for a known destination or feasible destinations for a known origin). This modeling change generates sufficient options to allow for low-cost solutions while maintaining reasonable computational effort. We also propose a new solution method that uses randomized route generation. Computational results from test cases show that these changes improve the quality of solutions by at least 5% in the test cases as compared to methods from previous studies.     

Regularization of some linear ill-posed problems with discretized random noisy data

For linear statistical ill-posed problems in Hilbert spaces we introduce an adaptive procedure to recover the unknown solution from indirect discrete and noisy data. This procedure is shown to be order optimal for a large class of problems. Smoothness of the solution is measured in terms of general source conditions. The concept of operator monotone functions turns out to be an important tool for the analysis.

     

Instability analysis of semiconductor injection lasers with saturable absorption and self-sustained pulsations on the centre manifold

The small-signal analysis of a simple model of three rate equations is performed rigorously by means of both the Routh-Hurwitz theorem and Descartes' sign rule, and the relationship between bistable behaviour and self-sustained pulsations (SSPs) is investigated. Because one eigenvalue of the Jacobian of the model system is always negative, small-amplitude, sinusoidal SSPs can be described in terms of Haken's dressed-mode variables on a two-dimensional centre manifold. Possible simplifications for the switching modelling are also mentioned.     

Microelectromagnet for magnetic manipulation in lab-on-a-chip systems

We demonstrate a simple scheme for fabrication of microelectromagnets consisting of planar spiral coils semi-encapsulated in soft magnetic yokes using conventional microfabrication techniques. The microelectromagnets are suitable for applications operating at frequencies below 250 kHz. Conventional fabrication schemes for planar microelectromagnets typically rely on five mask steps. We allow the current to flow in the soft magnetic yoke and thereby two mask steps are eliminated. We have characterized the electromagnets electrically, the results agree well with theory, and the implications arising from current flowing in the magnetic yoke are discussed. We have integrated the microelectromagnets with microfluidic channels, and demonstrated separation of commercially available magnetic beads from a fluid in a microfluidic system, i.e. a lab-on-a-chip system.     

Empirical minimization

We investigate the behavior of the empirical minimization algorithm using various methods. We first analyze it by comparing the empirical, random, structure and the original one on the class, either in an additive sense, via the uniform law of large numbers, or in a multiplicative sense, using isomorphic coordinate projections. We then show that a direct analysis of the empirical minimization algorithm yields a significantly better bound, and that the estimates we obtain are essentially sharp. The method of proof we use is based on Talagrand's concentration inequality for empirical processes. Research partially supported by NSF under award DMS-0434393. Research partially supported by the Australian Research Council Discovery Porject DP0343616.