A Formulation of Noether's Theorem for Fractional Problems of the Calculus of Variations

Fractional (or non-integer) differentiation is an important concept both from theoretical and applicational points of view. The study of problems of the calculus of variations with fractional derivatives is a rather recent subject, the main result being the fractional necessary optimality condition of Euler-Lagrange obtained in 2002. Here we use the notion of Euler-Lagrange fractional extremal to prove a Noether-type theorem. For that we propose a generalization of the classical concept of conservation law, introducing an appropriate fractional operator.Comment: Accepted for publication in the Journal of Mathematical Analysis and Application

Geophysics: Building E5481 decommissioning, Aberdeen Proving Ground

Building E5481 is one of ten potentially contaminated sites in the Canal Creek and Westwood areas of the Edgewood section of Aberdeen Proving Ground examined by a geophysical team from Argonne National Laboratory in April and May of 1992. Noninvasive geophysical surveys, including magnetics, electrical resistivity, and ground-penetrating radar, were conducted around the perimeter of the building to guide a sampling program prior to decommissioning and dismantling. The building is located on the northern margin of a landfill that was sited in a wetland. The large number of magnetic sources surrounding the building are believed to be contained in construction fill that had been used to raise the grade. The smaller anomalies, for the most part, are not imaged with ground radar or by electrical profiling. A conductive zone trending northwest to southeast across the site is spatially related to an old roadbed. Higher resistivity areas in the northeast and east are probably representive of background values. Three high-amplitude, positive, rectangular magnetic anomalies have unknown sources. The features do not have equivalent electrical signatures, nor are they seen with radar imaging

Integrated, flexible, and rapid geophysical surveying

Aberdeen Proving Ground (APG), in the state of Maryland (Figure 1), is currently managing a comprehensive Installation Restoration Program involving more than 360 solid-waste managing units contained within 13 study areas. The Edgewood area and two landfills in the Aberdeen area appear on the National Priority List under the Comprehensive Environmental Response, Compensation, and Liability Act. Therefore, APG has entered into an interagency agreement with the US Environmental Protection Agency to address the listed areas. The West Branch of the Canal Creek area (Figure 1), located within the Edgewood area, is one of the areas that requires a Source Definition Study because there is an ongoing release of volatile organic compounds into the creek. A report prepared by EAI Corporation (1989) included a list of 29 potentially contaminated buildings in the Edgewood area. Sixteen of the buildings contain known contaminants, nine buildings contain unknown contaminants, and four of the buildings are potentially clean. The EAI report recommended that a sampling and monitoring program be established to verify contamination levels in and around each building. Thirteen of the potentially contaminated buildings are in the West Branch of the Canal Creek area and are potential sources of volatile organic compounds. Operations have ceased and the buildings have been abandoned, but processing equipment, sumps, drains, ventilation systems, and underground storage tanks remain. These appurtenances may contain liquid, solid, or vapor contaminants of unknown nature

Unification of Gauge Couplings in the E(6)SSM

We argue that in the two-loop approximation gauge coupling unification in the exceptional supersymmetric standard model can be achieved for any phenomenologically reasonable value of strong gauge coupling at the electroweak scale consistent with the experimentally measured central value.Comment: Parallel talk at SUSY09, Boston, USA, June 2009, 5 page

Further constraints on electron acceleration in solar noise storms

We reexamine the energetics of nonthermal electron acceleration in solar noise storms. A new result is obtained for the minimum nonthermal electron number density required to produce a Langmuir wave population of sufficient intensity to power the noise storm emission. We combine this constraint with the stochastic electron acceleration formalism developed by Subramanian & Becker (2005) to derive a rigorous estimate for the efficiency of the overall noise storm emission process, beginning with nonthermal electron acceleration and culminating in the observed radiation. We also calculate separate efficiencies for the electron acceleration -- Langmuir wave generation stage and the Langmuir wave -- noise storm production stage. In addition, we obtain a new theoretical estimate for the energy density of the Langmuir waves in noise storm continuum sources.Comment: Accepted for publication in Solar Physic

Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and non-tensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.Comment: 18 pages, 12 figures (with subfigures), 1 table. Uses revtex, epsfig,subfigure, and cite. Submitted to PRE. Plots have been bitmapped. High-resolution version is available. Email [email protected] or download from http://rainbow.uchicago.edu/~mbnguyen/research/vm.htm

Using MODFLOW drains to simulate groundwater flow in a karst environment

Modeling groundwater flow in a karst environment is both numerically challenging and highly uncertain because of potentially complex flowpaths and a lack of site-specific information. This study presents the results of MODFLOW numerical modeling in which drain cells in a finite-difference model are used as analogs for preferential flowpaths or conduits in karst environments. In this study, conduits in mixed-flow systems are simulated by assigning connected pathways of drain cells from the locations of tracer releases, sinkholes, or other karst features to outlet springs along inferred flowpaths. These paths are determined by the locations of losing stream segments, ephemeral stream beds, geophysical surveys, fracture lineaments, or other surficial characteristics, combined with the results of dye traces. The elevations of the drains at the discharge ends of the inferred flowpaths are estimated from field data and are adjusted when necessary during model calibration. To simulate flow in a free-flowing conduit, a high conductance is assigned to each drain to eliminate the need for drain-specific information that would be very difficult to obtain. Calculations were performed for a site near Hohenfels, Germany. The potentiometric surface produced by the simulations agreed well with field data. The head contours in the vicinity of the karst features behaved in a manner consistent with a flow system having both diffuse and conduit components, and the sum of the volumetric flow out of the drain cells agreed closely with spring discharges and stream flows. Because of the success of this approach, it is recommended for regional studies in which little site-specific information (e.g., location, number, size, and conductivity of fractures and conduits) is available, and general flow characteristics are desired

A pilgrimage to gravity on GPUs

In this short review we present the developments over the last 5 decades that have led to the use of Graphics Processing Units (GPUs) for astrophysical simulations. Since the introduction of NVIDIA's Compute Unified Device Architecture (CUDA) in 2007 the GPU has become a valuable tool for N-body simulations and is so popular these days that almost all papers about high precision N-body simulations use methods that are accelerated by GPUs. With the GPU hardware becoming more advanced and being used for more advanced algorithms like gravitational tree-codes we see a bright future for GPU like hardware in computational astrophysics.Comment: To appear in: European Physical Journal "Special Topics" : "Computer Simulations on Graphics Processing Units" . 18 pages, 8 figure

Isospin Response of the 4-He Continuum

This research was sponsored by the National Science Foundation Grant NSF PHY-931478

Event by Event Analysis and Entropy of Multiparticle Systems

The coincidence method of measuring the entropy of a system, proposed some time ago by Ma, is generalized to include systems out of equilibrium. It is suggested that the method can be adapted to analyze multiparticle states produced in high-energy collisions.Comment: 13 pages, 2 figure