Shape maps for second order partial differential equations

We analyse the singularity formation of congruences of solutions of systems of second order PDEs via the construction of \emph{shape maps}. The trace of such maps represents a congruence volume whose collapse we study through an appropriate evolution equation, akin to Raychaudhuri's equation. We develop the necessary geometric framework on a suitable jet space in which the shape maps appear naturally associated with certain linear connections. Explicit computations are given, along with a nontrivial example

Time-dependent kinetic energy metrics for Lagrangians of electromagnetic type

We extend the results obtained in a previous paper about a class of Lagrangian systems which admit alternative kinetic energy metrics to second-order mechanical systems with explicit time-dependence. The main results are that a time-dependent alternative metric will have constant eigenvalues, and will give rise to a time-dependent coordinate transformation which partially decouples the system

Materials Recovery Facilities in the United States Virgin Islands: A Regional Facilities Location Model Study

Continental municipalities have derived many benefits from the economies of scale associated with a regional approach to facilities location and management planning. Centralized solid waste processing facilities is an example. Island communities, however, surrounded by miles of ocean, are constrained to a fragmented approach to the facilities location solution. This research was conducted to determine if the regional paradigm suggested in the literature is applicable to a set of island communities connected by an ocean transportation infrastructure. A linear programming (LP) model, constraints and data requirements were developed and applied to a network of islands. A series of hypothetical material recovery facilities (MRF) location scenarios were studied using actual and projected data obtained for the three-island territory of the U. S. Virgin Islands. In all cases, a significant reduction in capital construction expenditures was realized. For the selected data values in the research, transportation and operating costs increased as expected, but by a surprisingly small amount. This research concludes that the regional approach to economic and environmental facilities planning for island communities is valid. Future research involving larger systems of islands and stochastic processes is suggested

Emma Lazarus: Voice of Liberty

Emma Lazarus is best remembered for her poem, The New Colossus. However, in a recent touring exhibit the visited Drake Memorial Library, her fascinating life and experiences as a Jewish immigrant highlight the late 19th century immigrant experience, much of which is still relevant today. Many groups sought entrance to the United States during Emma’s lifetime for a variety of reasons, from escaping war and famine, to religious persecution, to abject poverty. The outcome for our country was incredibly positive, as these immigrants or their descendants made immeasurable advances for the country in arts, politics and sciences. The United States today continues to be a magnet for those seeking a better life, and as these new immigrants are assimilated into our society, it can have only positive outcomes for our culture as a whole. We must keep in mind that most of us came of immigrant stock, and rather than isolating ourselves or the newcomers, embrace the fresh ideas and news customs they bring with them

Design of Transmission Pipeline Modeling Language

General purpose software design and development involves the repetition of many processes, and the ability to automate these processes is often desired. To formalize a software process, such as modelling pipeline systems that transport fluids, an existing general purpose programming language (GPL) can be extended with its important aspects extracted as a model. However, the complexities and boundaries the programming language places on the ability to concisely and clearly describe the designing and modelling processes of the pipeline configurations can be difficult. The reality is that the library of a typical GPL Application Programmers Interface (API) constitutes class, method, and function names that become available only by object creation and method invocation, and as such cannot express domain concepts effectively. An alternative approach is to develop a language specifically for describing the processes. A language formalism that encourages domain specific development and as a tool for solving the complex problem of efficiently and effectively aiding the pipeline engineer in the design and implementation of pipeline configurations is presented in this paper. The language tool is used on the .Net platform for domain specific software development

A dynamic framework for managing the complexities of risks in megaprojects

The future of mega infrastructure projects is certain - there will be more risks to manage. The challenge is being met through research and innovation combining current approaches with new. This research adopted a dynamic approach through the combination of Analytical Network Process (ANP) and system dynamics (SD) as an innovative methodology known as SDANP to model complexity in megaprojects design and construction. We communicate how the SDANP model could explore problems caused by Social, Technical, Economic, Environmental and Political (STEEP) risks to construction cost, time and performance and provide insights that lead to organizational learning. We proceed to exemplify by means of a real-life case project in the City of Edinburgh and offer suggestions on what front-ended stakeholders could do to improve the management of risks in megaprojects. The results of the application showed that, when compared to traditional risks assessment methods, this SD model with integrated ANP revealed improvements in managing risks according to STEEP risks criteria. The new framework appears to be a superior solution for solving the dynamic complexities of risks during megaproject design and construction. The findings of the study contribute to the project management theoretical development within the field of megaproject management

Tangent bundle geometry induced by second order partial differential equations

We show how the tangent bundle decomposition generated by a system of ordinary differential equations may be generalized to the case of a system of second order PDEs `of connection type'. Whereas for ODEs the decomposition is intrinsic, for PDEs it is necessary to specify a closed 1-form on the manifold of independent variables, together with a transverse local vector field. The resulting decomposition provides several natural curvature operators. The harmonic map equation is examined, and in this case both the 1-form and the vector field arise naturally