Minimal time problem for discrete crowd models with a localized vector field

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We characterize the minimal time for a discrete crowd model, both for exact and approximate controllability. This leads to an algorithm that computes the control and the minimal time. We finally present a numerical simulation

Controllability and optimal control of the transport equation with a localized vector field

We study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling such system with a control being a Lipschitz vector field on a fixed control set $\omega$. We prove that, for each initial and final configuration, one can steer one to another with such class of controls only if the uncontrolled dynamics allows to cross the control set $\omega$. We also prove a minimal time result for such systems. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in $\omega$ to feed the desired final configuration

Minimal time for the continuity equation controlled by a localized perturbation of the velocity vector field

In this work, we study the minimal time to steer a given crowd to a desired configuration. The control is a vector field, representing a perturbation of the crowd velocity, localized on a fixed control set. We will assume that there is no interaction between the agents. We give a characterization of the minimal time both for microscopic and macroscopic descriptions of a crowd. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control region to feed the desired final configuration. The construction of the control is explicit, providing a numerical algorithm for computing it. We finally give some numerical simulations

A stability result for the diffusion coefficient of the heat operator defined on an unbounded guide

In this article we consider the inverse problem of determining the diffusion coefficient of the heat operator in an unbounded guide using a finite number of localized observations. For this problem, we prove a stability estimate in any finite portion of the guide using an adapted Carleman inequality. The boundary measurements are also realized on the boundary of a larger finite portion of the guide. A special care is required to avoid measurements on the cross-section boundaries which are inside the actual guide. This stability estimate uses a technical positivity assumption. Using arguments from control theory, we manage to remove this assumption for the inverse problem with non homogeneous given boundary conditions

Revisiting the Jurassic Geomagnetic Reversal recorded in the Lesotho Basalt (Southern Africa)

We carried out a detailed and continuous paleomagnetic sampling of the reversed to normal geomagnetic transition recorded by some 60 consecutive flow units near the base of the Lesotho Basalt (183  1 Ma). After alternating field or thermal cleaning the directions of remanence are generally well clustered within flow units. In contrast, the thermal instability of the samples did not allow to obtain reliable paleointensity determinations. The geomagnetic transition is incompletely recorded due to a gap in volcanic activity attested both by eolian deposits and a large angular distance between the field directions of the flows underlying or overlying these deposits. The transition path is noticeably different from that reported in the pioneer work of van Zijl et al. (1962). The most transitional Virtual Geomagnetic Poles are observed after the volcanic hiatus. Once continents are replaced in their relative position 180 Ma ago, the post-hiatus VGP cluster over Russia. However, two successive rebounds from that cluster are found, with VGP reaching repeatedly Eastern Asia coast. Thus, the VGP path is not narrowly constrained in paleolongitude. The decrease in intensity of magnetization as the field deviates from the normal or reversed direction suggests that the decrease in field magnitude during the reversal reached 80-90%. We conclude that although the reversal is of a dipole of much weaker moment than that which existed on average during Cenozoic time, the characteristics of the reversing geodynamo seem to be basically similar.Comment: Paper No GD124 submitted to Geophysical Journal International. Received in original form 20/01/2003, accepted 09/04/200

Knot commensurability and the Berge conjecture

We investigate commensurability classes of hyperbolic knot complements in the generic case of knots without hidden symmetries. We show that such knot complements which are commensurable are cyclically commensurable, and that there are at most $3$ hyperbolic knot complements in a cyclic commensurability class. Moreover if two hyperbolic knots have cyclically commensurable complements, then they are fibered with the same genus and are chiral. A characterisation of cyclic commensurability classes of complements of periodic knots is also given. In the non-periodic case, we reduce the characterisation of cyclic commensurability classes to a generalization of the Berge conjecture.Comment: v3: This version is reorganized with minor errors fixed. Proposition 4.1, Corollary 4.2, and Proposition 5.8 were added. Question 7.2 was upgraded to Theorem 7.2. 30 pages, 1 figur

TECHNOLOGIES THAT TRANSFORM BUSINESS AND RESEARCH: LESSONS FROM THE PAST AS WE LOOK TO THE FUTURE

What are the technologies that will transform business and drive the research agenda for the IS field in the years to come? Which innovations, platforms, and paradigms will become dominant, and which others will ultimately pass into obscurity? In this panel discussion, we will seek answers to these questions from those with a unique and unmatched perspective. The leaders who have witnessed the birth and development of the IS field during the past 40- 50 years will draw on their experiences and their deep knowledge of the field to identify the characteristics of technologies that have changed business in the past. They will also explain how and why today’s innovations will change both research and practice going forward. Their insights have the potential to identify topics for researchers to examine now and in the years to come

Laser-induced plume investigated by finite element modelling and scaling of particle entrainment in laser powder bed fusion

Although metal vaporisation has been observed in several laser processes such as drilling or welding, vapour plume expansion and its induced side effects are not fully understood. Especially, this phenomenon is garnering scientific and industrial interest since recent investigations in laser powder bed fusion (LPBF) have designated metal vaporisation as main source of denudation and powder spattering. The present study aims to provide a new insight on the dynamics of laser-induced vaporisation and to assess the potential of different gases for particle entrainment. A self-consistent finite element model of laser-induced keyhole and plume is thus presented for this purpose, built from a comprehensive literature review. The model is validated with dedicated experimental diagnostics, involving high-speed imaging to measure the ascent velocity of the vapour plume. The transient dynamics of vapour plume is thus quantified for different laser incident intensities and gas flow patterns such as the mushroom-like structure of the vapour plume are analysed. Finally, the model is used as a tool to quantify the entrainment flow expected in LPBF and an analytical model is derived to define a velocity threshold for particle entrainment, expressed in term of background gas properties. Doing so it is possible to predict how denudation evolves when the gaseous atmosphere is changed