Numerical Calibration of Steiner trees

In this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided

Absolute accuracy in membrane-based ac nanocalorimetry

To achieve accurate results in nanocalorimetry a detailed analysis and understanding of the behavior of the calorimetric system is required. There are especially two system-related aspects that should be taken in consideration: the properties of the empty cell and the effect of the thermal link between sample and cell. Here we study these two aspects for a membrane-based system where heater and thermometer are both in good contact with each other and the center of the membrane. Practical, analytical expressions for describing the frequency dependence of heat capacity, thermal conductance, and temperature oscillation of the system are formulated and compared with measurements and numerical simulations. We finally discuss the experimental conditions for an optimal working frequency, where high resolution and good absolute accuracy are combined

BV Estimates in Optimal Transportation and Applications

In this paper we study the BV regularity for solutions of certain variational problems in Optimal Transportation. We prove that the Wasserstein projection of a measure with BV density on the set of measures with density bounded by a given BV function f is of bounded variation as well and we also provide a precise estimate of its BV norm. Of particular interest is the case f = 1, corresponding to a projection onto a set of densities with an L∞ bound, where we prove that the total variation decreases by projection. This estimate and, in particular, its iterations have a natural application to some evolutionary PDEs as, for example, the ones describing a crowd motion. In fact, as an application of our results, we obtain BV estimates for solutions of some non-linear parabolic PDE by means of optimal transportation techniques. We also establish some properties of the Wasserstein projection which are interesting in their own right, and allow, for instance, for the proof of the uniqueness of such a projection in a very general framework

A two-phase problem with Robin conditions on the free boundary

We study for the first time a two-phase free boundary problem in which the solution satisfies a Robin boundary condition. We consider the case in which the solution is continuous across the free boundary and we prove an existence and a regularity result for minimizers of the associated variational problem. Finally, in the appendix, we give an example of a class of Steiner symmetric minimizers

Magnetocaloric effect in the high-temperature antiferromagnet YbCoC2

The magnetic $H$-$T$ phase diagram and magnetocaloric effect in the recently discovered high-temperature heavy-fermion compound YbCoC$_2$ have been studied. With the increase in the external magnetic field YbCoC$_2$ experiences the metamagnetic transition and then transition to the ferromagnetic state. The dependencies of magnetic entropy change -$\Delta S_m (T)$ have segments with positive and negative magnetocaloric effects for $\Delta H \leq 6$~T. For $\Delta H = 9$~T magnetocaloric effect becomes positive with a maximum value of -$\Delta S_m (T)$ is 4.1 J / kg K and a refrigerant capacity is 56.6 J / kg

Numerical Calibration of Steiner trees

International audienceIn this paper we propose a variational approach to the Steiner tree problem, which is based on calibrations in a suitable algebraic environment for polyhedral chains which represent our candidates. This approach turns out to be very efficient from numerical point of view and allows to establish whether a given Steiner tree is optimal. Several examples are provided