1,089 research outputs found

### 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

### Handling congestion in crowd motion modeling

We address here the issue of congestion in the modeling of crowd motion, in
the non-smooth framework: contacts between people are not anticipated and
avoided, they actually occur, and they are explicitly taken into account in the
model. We limit our approach to very basic principles in terms of behavior, to
focus on the particular problems raised by the non-smooth character of the
models. We consider that individuals tend to move according to a desired, or
spontanous, velocity. We account for congestion by assuming that the evolution
realizes at each time an instantaneous balance between individual tendencies
and global constraints (overlapping is forbidden): the actual velocity is
defined as the closest to the desired velocity among all admissible ones, in a
least square sense. We develop those principles in the microscopic and
macroscopic settings, and we present how the framework of Wasserstein distance
between measures allows to recover the sweeping process nature of the problem
on the macroscopic level, which makes it possible to obtain existence results
in spite of the non-smooth character of the evolution process. Micro and macro
approaches are compared, and we investigate the similarities together with deep
differences of those two levels of description

### 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

### Superspace calculation of the four-loop spectrum in N=6 supersymmetric Chern-Simons theories

Using N=2 superspace techniques we compute the four-loop spectrum of single
trace operators in the SU(2) x SU(2) sector of ABJM and ABJ supersymmetric
Chern-Simons theories. Our computation yields a four-loop contribution to the
function h^2(\lambda) (and its ABJ generalization) in the magnon dispersion
relation which has fixed maximum transcendentality and coincides with the
findings in components given in the revised versions of arXiv:0908.2463 and
arXiv:0912.3460. We also discuss possible scenarios for an all-loop function
h^2(\lambda) that interpolates between weak and strong couplings.Comment: LaTeX, feynmp, 34 pages; v2: typos corrected, formulations improved,
references adde

### Correlation functions of chiral primary operators in perturbative N = 4 SYM

We discuss recent results on two-point functions of chiral primary operatorsin {\cal N}=4 SU(N) supersymmetric Yang-Mills theory. Our results give furthersupport to the belief that such correlators are not renormalized to all ordersin g and to all orders in N

### 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

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