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

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

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

The Monge problem with vanishing gradient penalization: Vortices and asymptotic profile

We investigate the approximation of the Monge problem (minimizing ?????|T(x)???x|d??(x) among the vector-valued maps T with prescribed image measure T_\\#\mu) by adding a vanishing Dirichlet energy, namely ???????|DT|2, where ?????0. We study the ??-convergence as ?????0, proving a density result for Sobolev (or Lipschitz) transport maps in the class of transport plans. In a certain two-dimensional framework that we analyze in details, when no optimal plan is induced by an H1 map, we study the selected limit map, which is a new "special" Monge transport, different from the monotone one, and we find the precise asymptotics of the optimal cost depending on ??, where the leading term is of order ??|log??

A protocol for qualitative and quantitative measurement of endosomal processing using hot spot analysis

A detailed quantification of antigen processing by endosomal compartments provides important information on the pattern of protein fragmentation. Here, we describe a protocol that combines gradient purified endosomes, incubated with antigens, followed by hot spot analysis of MS/MS-sequenced peptides. The analysis identifies differences in endosomal antigen processing by dendritic cells under diverse experimental conditions. For complete details on the use and execution of this protocol, please refer to Clement et al. (2021)

Monge's transport problem in the Heisenberg group

We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group

Predictions for PP-wave string amplitudes from perturbative SYM

The role of general two-impurity multi-trace operators in the BMN correspondence is explored. Surprisingly, the anomalous dimensions of all two-impurity multi-trace BMN operators to order g_2^2\lambda' are completely determined in terms of single-trace anomalous dimensions. This is due to suppression of connected field theory diagrams in the BMN limit and this fact has important implications for some string theory processes on the PP-wave background. We also make gauge theory predictions for the matrix elements of the light-cone string field theory Hamiltonian in the two string-two string and one string-three string sectors.Comment: 46 pages, 12 figures. V3:typos correcte

A Calculation of the plane wave string Hamiltonian from N=4 super-Yang-Mills theory

Berenstein, Maldacena, and Nastase have proposed, as a limit of the strong form of the AdS/CFT correspondence, that string theory in a particular plane wave background is dual to a certain subset of operators in the N=4 super-Yang-Mills theory. Even though this is a priori a strong/weak coupling duality, the matrix elements of the string theory Hamiltonian, when expressed in gauge theory variables, are analytic in the 't Hooft coupling constant. This allows one to conjecture that, like the masses of excited string states, these can be recovered using perturbation theory in Yang-Mills theory. In this paper we identify the difference between the generator of scale transformations and a particular U(1) R-symmetry generator as the operator dual to the string theory Hamiltonian for nonvanishing string coupling. We compute its matrix elements and find that they agree with the string theory prediction provided that the state-operator map is modified for nonvanishing string coupling. We construct this map explicitly and calculate the anomalous dimensions of the new operators. We identify the component arising from the modification of the state-operator map with the contribution of the string theory contact terms to the masses of string states.Comment: 38 pages, Latex; v2: Comparison with string theory changed in light of corrections to string theory results in hep-th/0206073 v3; state-operator map modified; Physical interpretation and conclusions unchange

Comparing strings in AdS(5)xS(5) to planar diagrams: an example

The correlator of a Wilson loop with a local operator in N=4 SYM theory can be represented by a string amplitude in AdS(5)xS(5). This amplitude describes an overlap of the boundary state, which is associated with the loop, with the string mode, which is dual to the local operator. For chiral primary operators with a large R charge, the amplitude can be calculated by semiclassical techniques. We compare the semiclassical string amplitude to the SYM perturbation theory and find an exact agrement to the first two non-vanishing orders.Comment: 16 pages, 4 figures, LaTeX; v2: typos corrected; v3: clarification of boundary conditions at infinity adde