Statistics of the first passage time of Brownian motion conditioned by maximum value or area

We derive the moments of the first passage time for Brownian motion conditioned by either the maximum value or the area swept out by the motion. These quantities are the natural counterparts to the moments of the maximum value and area of Brownian excursions of fixed duration, which we also derive for completeness within the same mathematical framework. Various applications are indicated.Comment: 29 pages, 4 figures include

The first-passage area for drifted Brownian motion and the moments of the Airy distribution

An exact expression for the distribution of the area swept out by a drifted Brownian motion till its first-passage time is derived. A study of the asymptotic behaviour confirms earlier conjectures and clarifies their range of validity. The analysis also leads to a simple closed-form solution for the moments of the Airy distribution.Comment: 13 page

Efficient packing of unit squares in a square

Efficient packing of unit squares in a squar

Electric vehicle charging infrastructure deployment : policy analysis using a dynamic behavioral spatial model

Thesis (S.M. in Technology and Policy)--Massachusetts Institute of Technology, Engineering Systems Division, Technology and Policy Program, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 64-67).The United States government is committed to promoting a market for electric vehicles. To ensure that this electrification program does not result in the same failure that has come be associated with its predecessor programs, Freedom Car and the Partnership for a New Generation of Vehicles, charging infrastructure must be available. At this point, however, it is unclear what the balance will be between industry and government involvement in enabling the distribution of electric vehicle service equipment (EVSE). A number of companies in the private sector have begun initial deployment projects, and municipalities, utilities and other commercial players are beginning to look into the provision of this equipment. However, little is understood about this market where uncertainties about vehicle sales, costs and government support abound. This thesis analyzes the economics of the infrastructure market and explores the internal logic for the companies involved through a dynamic behavioral spatial model to draw policy recommendations for the roles of the government and the private sector in vehicle electrification. Because of the low cost of electricity and high costs of charging infrastructure capital, it will be difficult for EVSE providers to earn a profit selling electricity. Model simulations demonstrate the importance of a public sector infrastructure roll out strategy and investment innovation in the EVSE market toward faster and cheaper charging options. Policies to stimulate electric vehicle adoption must focus on R&D for charging stations and deploying infrastructure.by Michael J. Kearney.S.M.in Technology and Polic

Classical localization and percolation in random environments on trees

We consider a simple model of transport on a regular tree, whereby species evolve according to the drift-diffusion equation, and the drift velocity on each branch of the tree is a quenched random variable. The inverse of the steady-state amplitude at the origin is expressed in terms of a random geometric series whose convergence or otherwise determines whether the system is localized or delocalized. In a recent paper [P. C. Bressloff et al., Phys. Rev. Lett. 77, 5075 (1996)], exact criteria were presented that enable one to determine the critical phase boundary for the transition, valid for any distribution of the drift velocities. In this paper we present a detailed derivation of these criteria, consider a number of examples of interest, and establish a connection with conventional percolation theory. The latter suggests a wider application of the results to other models of statistical processes occurring on treelike structures. Generalizations to the case where the underlying tree is irregular in nature are also considered