A proof of anomalous invasion speeds in a system of coupled Fisher-KPP equations

This article is concerned with the rigorous validation of anomalous spreading speeds in a system of coupled Fisher-KPP equations of cooperative type. Anomalous spreading refers to a scenario wherein the coupling of two equations leads to faster spreading speeds in one of the components. The existence of these spreading speeds can be predicted from the linearization about the unstable state. We prove that initial data consisting of compactly supported perturbations of Heaviside step functions spreads asymptotically with the anomalous speed. The proof makes use of a comparison principle and the explicit construction of sub and super solutions

Lattice Design in High-energy Particle Accelerators

This lecture gives an introduction into the design of high-energy storage ring lattices. Applying the formalism that has been established in transverse beam optics, the basic principles of the development of a magnet lattice are explained and the characteristics of the resulting magnet structure are discussed. The periodic assembly of a storage ring cell with its boundary conditions concerning stability and scaling of the beam optics parameters is addressed as well as special lattice insertions such asdrifts, mini beta sections, dispersion suppressors, etc. In addition to the exact calculations that are indispensable for a rigorous treatment of the matter, scaling rules are shown and simple rules of thumb are included that enable the lattice designer to do the first estimates and get the basic numbers 'on the back of an envelope'.Comment: 40 pages, contribution to the CAS - CERN Accelerator School: Advanced Accelerator Physics Course, Trondheim, Norway, 18-29 Aug 2013. arXiv admin note: substantial text overlap with arXiv:1303.651

Workforce Development and the Disadvantaged: New Directions for 2009 and Beyond

Assesses the 1998 Workforce Investment Act's successes and limitations. Outlines the changes needed, such as increasing funding and consolidating programs, for a more effective public workforce training system, especially for the young and hard-to-employ

Reconnecting Young Black Men: What Policies Would Help?

The term "disconnected youth" refers to young people who have been out of school and out of work for considerable periods of time – like a year or more. They are not temporarily "idle" but are fully disconnected from the mainstream worlds of schooling and work. They may be incarcerated or on parole or probation; they might be aging out of foster care or still attached to their nuclear families. But, overwhelmingly, they come from low-income families and often grow up in poor and relatively segregated neighborhoods. Of all racial and gender groups, young black men are by far the most likely to become "disconnected" from school and work. In the year 2000 – when the labor market was very tight – over 17 percent of all young black men between the ages of 16 and 24 were disconnected, while the comparable percentages for other race/gender groups were much lower. Indeed, this figure implies that one out of every six young black men was disconnected from both school and work at that time

Introduction to Transverse Beam Dynamics

In this chapter we give an introduction to the transverse dynamics of the particles in a synchrotron or storage ring. The emphasis is more on qualitative understanding rather than on mathematical correctness, and a number of simulations are used to demonstrate the physical behaviour of the particles. Starting from the basic principles of how to design the geometry of the ring, we review the transverse motion of the particles, motivate the equation of motion, and show the solutions for typical storage ring elements. Following the usual treatment in the literature, we present a second way to describe the particle beam, using the concept of the emittance of the particle ensemble and the beta function, which reflects the overall focusing properties of the ring. The adiabatic shrinking due to Liouville's theorem is discussed as well as dispersive effects in the most simple case.Comment: 19 pages, contribution to the CAS-CERN Accelerator School: Ion Sources, Senec, Slovakia, 29 May - 8 June 2012, edited by R. Bailey, CERN-2013-00

Introduction to Longitudinal Beam Dynamics

This chapter gives an overview of the longitudinal dynamics of the particles in an accelerator and, closely related to that, the issue of synchronization between the particles and the accelerating field. Beginning with the trivial case of electrostatic accelerators, the synchronization condition is explained for a number of driven accelerators like Alvarez linacs, cyclotrons and finally synchrotrons and storage rings, where it plays a crucial role. In the case of the latter, the principle of phase focusing is motivated qualitatively as well as on a mathematically more correct level and the problem of operation below and above the transition energy is discussed. Throughout, the main emphasis is more on physical understanding rather than on a mathematically rigorous treatment.Comment: 15 pages, contribution to the CAS-CERN Accelerator School: Ion Sources, Senec, Slovakia, 29 May - 8 June 2012, edited by R. Bailey, CERN-2013-00

Higher-order Modes and Heating

This chapter gives a basic introduction to the problem of wake fields created in the beam-surrounding environment and the resulting heating effects of machine components. The concepts are introduced and scaling rules derived that are exemplified by several observations from operation of the LHC and other machines.Comment: 14 pages, contribution to the CAS-CERN Accelerator School: Superconductivity for Accelerators, Erice, Italy, 24 April - 4 May 2013, edited by R. Baile