Asymptotics of an optimal compliance-location problem

We consider the problem of placing n small balls of given radius in a certain domain subject to a force f in order to minimize the compliance of the configuration. Then we let n tend to infinity and look at the asymptotics of the minimization problem, after properly scaling the functionals involved, and to the limit distribution of the centres of the balls. This problem is both linked to optimal location and shape optimization problems.Comment: 20 pages with 2 figures; final accepted version (minor changes, some extra details on the positivity assumption on $f$

Optimal transportation with traffic congestion and Wardrop equilibria

In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the notion of traffic intensity, we propose a variant taking into account congestion. This leads to an optimization problem posed on a set of probability measures on a suitable paths space. We establish existence of minimizers and give a characterization. As an application, we obtain existence and variational characterization of equilibria of Wardrop type in a continuous space setting

Long-term planning versus short-term planning in the asymptotical location problem

Given the probability measure $\nu$ over the given region $\Omega\subset \R^n$, we consider the optimal location of a set $\Sigma$ composed by $n$ points \Om in order to minimize the average distance \Sigma\mapsto \int_\Om \dist(x,\Sigma) d\nu (the classical optimal facility location problem). The paper compares two strategies to find optimal configurations: the long-term one which consists in placing all $n$ points at once in an optimal position, and the short-term one which consists in placing the points one by one adding at each step at most one point and preserving the configuration built at previous steps. We show that the respective optimization problems exhibit qualitatively different asymptotic behavior as $n\to\infty$, although the optimization costs in both cases have the same asymptotic orders of vanishing.Comment: for more pictures and some movies as well, see http://www.sissa.it/~brancoli

Laser spectroscopy of cold molecules

This paper reviews the recent results in high-resolution spectroscopy on cold molecules. Laser spectroscopy of cold molecules addresses issues of symmetry violation, like in the search for the electric dipole moment of the electron and the studies on energy differences in enantiomers of chiral species; tries to improve the precision to which fundamental physical constants are known and tests for their possible variation in time and space; tests quantum electrodynamics, and searches for a fifth force. Further, we briefly review the recent technological progresses in the fields of cold molecules and mid-infrared lasers, which are the tools that mainly set the limits for the resolution that is currently attainable in the measurements

Quantitative Comparison of Locomotor Performance in Different Race Walkers

Biomechanics of track and field activities has been investigated by many authors. A literature overview on race walking points out various analyses on: supporting energy (Zarrough et al. 1974), mechanical energy variations (Marchetti et at. 1983), potential versus kinetic energy variations (Ralston and Lukin, 1969), muscular work efficiency (Marchetti et at. 1983), Payne (1979) reported the ground reaction components measured during race walking while some aspects of the related biomechanics were discussed by Boccardi et al. (1978) by displaying a vectorial representation of the ground reaction evolution. As the trainers know well, the primary needs of the race walkers involve something more than a general description of the basic executive mechanism. The athletes have to solve a very complex problem: walk under restrictive Jules for a time varying from 18 to more than 200 minutes at a speed that is usually more than two times higher the threshold at which a man begins running naturally (Cavagna et at., 1977). Such goal is obtained through a proper modification of the normal motor-patterns aimed to the best use of the endurance qualities. By the way, the critical importance of optimal motor efficiency to reduce any possible noisy factor is evident. The aim of this study is to quantify locomotor performances of two homogeneous groups of differently ranked walkers. The vectorial representation of the ground reaction force is used to identify and compare typical biomechanical features associating with the athletic level. A further data processing, including normalization and statistical estimation of the differences between the results from the two groups. leads to a practical and powerful tool for the investigation of motorcoordination and asymmetry in race walking

A Benamou-Brenier approach to branched transport

The problem of branched transportation aims to describe the movement of masses when, due to concavity effects, they have the interest to travel together as much as possible, because the cost for a path of length $\ell$ covered by a mass $m$ is proportional to $m^\alpha\ell$ with $0<\alpha<1$. The optimization of this criterion let branched structures appear and is suitable to applications like road systems, blood vessels, river networks\dots Several models have been employed in the literature to present this transport problem, and the present paper looks at a dynamical one, similar to the celebrated Benamou-Brenier formulation of Kantorovitch optimal transport. The movement is represented by a path $\rho_t$ of probabilities, connecting an initial state $\mu_0$ to a final state $\mu_1$, satisfying the continuity equation \partial_t\rho+\dive_xq=0 together with a velocity field $v$ (with $q=\rho v$ being the momentum). The transportation cost to be minimized is non-convex and finite on atomic measures: $\int_0^1\big(\int_\Omega\rho^{\alpha-1}|q|\,d\#(x)\big)\,dt$

Embedding Branes in Flat Two-time Spaces

We show how non-near horizon, non-dilatonic $p$-brane theories can be obtained from two embedding constraints in a flat higher dimensional space with 2 time directions. In particular this includes the construction of D3 branes from a flat 12-dimensional action, and M2 and M5 branes from 13 dimensions. The worldvolume actions are found in terms of fields defined in the embedding space, with the constraints enforced by Lagrange multipliers.Comment: LaTex, 8 pages. Contribution to the TMR Conference on Quantum aspects of gauge theories, supersymmetry and unification. Paris, 1-7 September 199

Spatial distribution of ions in a linear octopole radio-frequency ion trap in the space-charge limit

We have explored the spatial distribution of an ion cloud trapped in a linear octopole radio-frequency (rf) ion trap. The two-dimensional distribution of the column density of stored silver dimer cations was measured via photofragment-ion yields as a function of the position of the incident laser beam over the transverse cross section of the trap. The profile of the ion distribution was found to be dependent on the number of loaded ions. Under high ion-loading conditions with a significant space-charge effect, ions form a ring profile with a maximum at the outer region of the trap, whereas they are localized near the center axis region at low loading of the ions. These results are explained quantitatively by a model calculation based on equilibrium between the space-charge-induced potential and the effective potential of the multipole rf field. The maximum adiabaticity parameter \eta_max is estimated to be about 0.13 for the high ion-density condition in the present octopole ion trap, which is lower than typical values reported for low ion densities; this is probably due to additional instability caused by the space charge.Comment: 8 pages, 5 figure