Numerical conservative solutions of the Hunter--Saxton equation

In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws

Enhancing Departments and Graduate Education in Geography

This paper describes the development, implementation, and preliminary outcomes of Enhancing Departments and Graduate Education (EDGE) in Geography, a multi-year project begun in 2005 to study the process of professional development in graduate geography in the U.S and sponsored by the National Science Foundation. As a research and action project responding to the needs of graduate geography programs, EDGE seeks to provide academic geographers with an empirical perspective of disciplinary as well as interdisciplinary and generic skills that M.A./M.S. and Ph.D. students develop as a result of graduate education. Related objectives are to understand how disciplinary skills are applied by geography graduates once they enter the professional workforce in both academic and non-academic professional settings, and to gauge the extent graduate programs are sufficiently preparing geography graduates for those careers. We begin by summarizing the research goals and design of EDGE, highlighting the roles and contributions of geographers and educational researchers, and noting the interplay and synergy between disciplinary and interdisciplinary methodologies and practices. To date, research has focused on: 1) assessing contemporary workforce competencies in professional geography and 2) examining the role of department climate and culture on student experience and faculty development within masters and doctoral programs. Although the EDGE research efforts are still underway, we present some preliminary research findings and discuss the implications of those outcomes for professional development in geography and related social and environmental sciences. Also discussed is the complementary nature of discipline-based and interdisciplinary professional development efforts

Magnetic translation and Berry's phase factor through adiabatically rotating a magnetic field

For a spin subjected to an adiabatically changing magnetic field, the solid angle result as embodied by a rotation operator is the only path-dependent factor in the quantum evolution operator. For a charged particle, the infinite degeneracy calls for a rigorous investigation. We find that in this case, it is the product of the rotation operator and a path-ordered magnetic translation operator that enters into the evolution operator and determines the geometric phase. This result agrees with the fact that the instantaneous hamiltonian is invariant under magnetic translation as well as rotation. Experimental verification of the result is proposed.Comment: Submitted to Physics Letters A in November 1999. This paper finds the relation between the solid angle result and the magnetic translation operator. Author of Ref[5] should be J. Zak. It was changed by the publishing editor of Phys.Letts.A 275(2000)473 and the change was erroneously followed in the previous versio

Computer graphics for management: An abstract of capabilities and applications of the EIS system

The Executive Information Services (EIS) system, developed as a computer-based, time-sharing tool for making and implementing management decisions, and including computer graphics capabilities, was described. The following resources are available through the EIS languages: centralized corporate/gov't data base, customized and working data bases, report writing, general computational capability, specialized routines, modeling/programming capability, and graphics. Nearly all EIS graphs can be created by a single, on-line instruction. A large number of options are available, such as selection of graphic form, line control, shading, placement on the page, multiple images on a page, control of scaling and labeling, plotting of cum data sets, optical grid lines, and stack charts. The following are examples of areas in which the EIS system may be used: research, estimating services, planning, budgeting, and performance measurement, national computer hook-up negotiations