The Hughes model for pedestrian dynamics and congestion modelling

In this paper we present a numerical study of some variations of the Hughes model for pedestrian flow under different types of congestion effects. The general model consists of a coupled non-linear PDE system involving an eikonal equation and a first order conservation law, and it intends to approximate the flow of a large pedestrian group aiming to reach a target as fast as possible, while taking into account the congestion of the crowd. We propose an efficient semi-Lagrangian scheme (SL) to approximate the solution of the PDE system and we investigate the macroscopic effects of different penalization functions modelling the congestion phenomena.Comment: 6 page

Flapping states of an el astically anchored wing in a uniform flow

Linear stability analysis of an elastically anchored wing in a uniform flow is investigated both analytically and numerically. The analytical formulation explicitly takes into account the effect of the wake on the wing by means of Theodorsen's theory. Three different parameters non-trivially rule the observed dynamics: mass density ratio between wing and fluid, spring elastic constant and distance between the wing center of mass and the spring anchor point on the wing. We found relationships between these parameters which rule the transition between stable equilibrium and fluttering. The shape of the resulting marginal curve has been successfully verified by high Reynolds number direct numerical simulations. Our findings are of interest in applications related to energy harvesting by fluid-structure interaction, a problem which has recently attracted a great deal of attention. The main aim in that context is to identify the optimal physical/geometrical system configuration leading to large sustained motion, which is the source of energy we aim to extract.Comment: 10 pages, 11 figures, submitted to J. Fluid. Mec

Dueling Federalists: Supreme Court Decisions with Multiple Opinions Citing \u3cem\u3eThe Federalist\u3c/em\u3e, 1986-2007

This Article examines the use of history in legal interpretation through an empirical analysis of one of the most prominent examples of historical evidence in law: citations to The Federalist in Supreme Court Justices\u27 published opinions. In particular, the Article examines a phenomenon that has occurred frequently over the last two decades, but has thus far been virtually ignored: the citation by different Justices to the same historical source (such as The Federalist) to support divergent or opposing historical interpretations of legal meaning. Although the use of historical evidence in constitutional interpretation is itself much debated, The Federalist continues to be cited as binding or persuasive authority by scholars and judges

The Origins and Constitutionality of State Unit Voting in the Electoral College

On November 1, 2000, a Joint Resolution was introduced in Congress proposing a constitutional amendment to change the Article II system of electing the President and Vice President\u27 by abolishing the Electoral College. Acknowledging the fact that there have been more congressionally proposed constitutional amendments on this subject than any other, the sponsoring Senator noted that the issue could become supremely important in a few days, because we have the possibility that the winning candidate for President might not win the popular vote in our country.\u27 One prominent legal scholar has described the mere possibility of such an event as a constitutional accident waiting to happen. Six days later, on election day 2000, the Senator proved to be a prophet (the issue was not fully resolved for over a month). Governor George W. Bush won the presidency with 271 electoral votes, despite Vice President Al Gore tallying more popular votes. The possibility of a split between the electoral vote and the popular vote moved from the province of mere academic speculation to political reality, and the Electoral College debate moved with it to the fore-front of public consciousness. From the media to politicians to scholars, no one seemed without an opinion on whether the Electoral College should be totally discarded, or meticulously preserved. This Note does not attempt to make any judgments on the value of the Electoral College as an institution. Whether as a constitutional procedure the Electoral College ought to be preserved, altered, or eliminated is a question left for other scholars to ad- dress. Instead, this Note analyzes legal issues that would confront any attempt to change the Electoral College by lawsuit or legislation. It will do so by comparing the historical underpinnings of the institution to the legal status of the electoral voting systems currently practiced in the states. The analysis will focus on two separate, but ultimately related, areas of inquiry: (1) the inception of the Electoral College as a product of the Constitutional Convention, and (2) how that origin relates to possible challenges to the winner-take-all allocation of electoral votes, or what is commonly known as the unit rule. This Note examines the Electoral College debate in light of two recent developments: the controversial 2000 election and the decision in Bush v. Gore, and the Supreme Court\u27s recent jurisprudence on state sovereignty. The Constitution leaves the decision on how to allocate its electoral votes completely to the discretion of each state. There are a number of different methods from which the states could choose; an overwhelming majority of states employ the unit rule. This method has become unpopular with many commentators and has been the subject of much criticism. Included in the bill of charges against the method are that it amplifies the effect of the imbalanced allocation of electoral votes, and that it fails to count the votes within a state that were cast for a losing candidate. It is also controversial because it is the mechanism that enhances the possibility of having an electoral vote winner, and hence a president, who received fewer popular votes than the electoral runner- up

Dueling Federalists: Supreme Court Decisions with Multiple Opinions Citing \u3cem\u3eThe Federalist\u3c/em\u3e, 1986-2007

This Article examines the use of history in legal interpretation through an empirical analysis of one of the most prominent examples of historical evidence in law: citations to The Federalist in Supreme Court Justices\u27 published opinions. In particular, the Article examines a phenomenon that has occurred frequently over the last two decades, but has thus far been virtually ignored: the citation by different Justices to the same historical source (such as The Federalist) to support divergent or opposing historical interpretations of legal meaning. Although the use of historical evidence in constitutional interpretation is itself much debated, The Federalist continues to be cited as binding or persuasive authority by scholars and judges

Formation and computational implications of assemblies in neural circuits

In the brain, patterns of neural activity represent sensory information and store it in non-random synaptic connectivity. A prominent theoretical hypothesis states that assemblies, groups of neurons that are strongly connected to each other, are the key computational units underlying perception and memory formation. Compatible with these hypothesised assemblies, experiments have revealed groups of neurons that display synchronous activity, either spontaneously or upon stimulus presentation, and exhibit behavioural relevance. While it remains unclear how assemblies form in the brain, theoretical work has vastly contributed to the understanding of various interacting mechanisms in this process. Here, we review the recent theoretical literature on assembly formation by categorising the involved mechanisms into four components: synaptic plasticity, symmetry breaking, competition and stability. We highlight different approaches and assumptions behind assembly formation and discuss recent ideas of assemblies as the key computational unit in the brain