A new lower bound for the Linear Arrangement of a graph
Juan-José Salazar-González,
Department of Statistics, Operational Research and Computation, University of "La Laguna" (Spain)
Abstract: Minimum Linear Arrangement is a classical basic combinatorial optimization problem from the 1960s, which turns out to be extremely challenging in practice. In particular, for most of its benchmark instances, even the order of magnitude of the optimal solution value is unknown, as testified by the surveys on the problem that contain tables in which the best known solution value often has one more digit than the best known lower bound value. In this talk, we propose a linear-programming based approach to compute lower bounds on the optimum. This allows us, for the first time, to show that the best known solutions are indeed not far from optimal for most of the benchmark instances. This is a join work with Alberto Caprara (Bologna, Italia) and Adam Letchford (Lancaster, U.K.).
A relation between compatibility and hysteresis and its role in the search for new active materials
Richard James,
Department of Aerospace Engineering and Mechanics, University of Minnesota (U.S.A)
Abstract: We present some recent measurements of hysteresis, in materials undergoing big first order phase transformations, that resulted from a systematic program of tuning of the lattice parameters by changing composition. The lattice parameters were tuned so that a certain non generic condition of compatibility between phases was satisfied. An exceptionally sharp drop of size of the hysteresis of the transformation was observed at the special lattice parameters. The data has some fascinating features, including an apparent singularity. We re-examine the origins of hysteresis in light of these measurements, commenting also on the role of defects and pinning, and the use of this kind of tuning to discover "unlikely" new materials. These thoughts lead us to consider hysteresis as arising from an elastic energy barrier associated with the failure of certain conditions of compatibility. We calculate this barrier based on methods of Gamma-convergence, where the small parameter is related to the near satisfaction of this non-generic condition of compatibility. A recent study suggest suggests a tantalizing relation between the emerging alloys with minimum hysteresis and stability of the transformation under cycling. Joint work with Stefan Mueller, Nick Schryvers and Jerry Zhang.
On the motion of a rigid body in a Navier-Stokes liquid under the influence of a time- periodic driving mechanism
Giovanni P. Galdi, Department of Mechanical Engineering, University of Pittsburgh (U.S.A)
Abstract: This talk is devoted to the mathematical investigation of the motion of a rigid body in an infinite Navier-Sokes liquid,under the action of a time-periodic driving mechanism.This latter can be,for example, a time periodic force acting along a given constant direction, or time periodic boundary data. The main objective is to find conditions under which the body is propelled by the driving mechanism, namely, conditions that ensure that the body can cover a given trajectory in a finite time interval. This research is in collaboration with Ana L. Silvestre (IST Lisbon,Portugal).
Mathematical models of fires in street tunnels
Ingo Gasser,
Schwerpunkt Differentialgleichungen und Dynamische Systeme, University of Hamburg (Germany)
Abstract: The following topics will be covered: We discuss various approaches for modelling tunnel fires. We derive a new model and analyse it. Finally, we present numerical simulation on real situations.