Finite Element Methods for a Model for Full Waveform Acoustic Logging

A model is defined to simulate the propagation of waves in aradially symmetric, isotropic, composite system consisting ofa fluid-filled well bore ^f through a fluid-saturated poroussolid ^p. Biot's equations of motion are chosen to describe thepropagation of waves in ^p, while the standard equation of motionfor compressible inviscid fluids is used for ^f, with appropriateboundary conditions at the contact surface between ^f and ^p.Also, absorbing boundary conditions for the artificial boundariesof ^p are derived for the model, their effect being to make themtransparent for waves arriving normally First, results on the existence and uniqueness of the solutionof the differential problem are given and then a discrete-time,explicit finite element procedure is defined and analysed, withfinite element spaces suited for radially symmetric problemsbeing used for the spatial discretisation.     

Modelling,simulation, animation,and real-time control (MoSART) for a class of electromechanical systems: a system-theoretic approach

This paper describes an interactive modelling, simulation, animation, and real-time control (MoSART) environment for a class of ‘cart-pendulum’ electromechanical systems that may be used to enhance learning within differential equations and linear algebra classes. The environment is useful for conveying fundamental mathematical/systems concepts through computer-aided analysis, design, graphical visualization, and 3D animation. Referred to as Cart-Pendulum Control3D-Lab1Control3D-Lab-short for control 3D animation laboratory. The author to whom correspondence should be addressed., the environment is based on Microsoft Windows/Visual C++/Direct-3D and MATLAB/Simulink2MATLAB and Simulant are trademarks of The Masterworks, Inc.. Pull-down menus provide access to systems/models/control laws, exogenous signals, parameters, animation models and visual indicators, a suite of (easy-to-modify) Simulant diagrams containing models and control laws, MATLAB m-files for detailed analysis and design, and detailed documentation for each of the above. Three blocks enable animation, joystick inputs, and real-time animation within Simulant. Examples are presented to illustrate the utility of the environment as a valuable tool for analysing/visualizing the above class of electromechanical systems and for enhancing mathematics instruction.     

The Saffman-Taylor problem for an extremely shear-thinning fluid

We consider a steady flow driven by pushing a finger of gasinto a highly shear-thinning power-law fluid, with exponentn, in a Hele-Shaw channel. We formulate the problem in termsof the streamfunction , which satisfies the p-Laplacian equation (with ), and investigate travelling wave solutions in the large-n (extreme shear-thinning) limit.We take a Legendre transform of the free-boundary problem for, which reduces it to a linear problem on a fixed domain. The solution to this problem is foundby using matched asymptotic expansions and the resulting shapeof the finger deduced (being, to leading order, a semi-infinitestrip). The nonlinear problem for the streamfunction is alsotreated using matched asymptotic expansion in the physical plane.The finger-width selection problem is briefly discussed in termsof our results.     

Molecular properties from conformational ensembles. 1. Dipole moments of molecules with multiple internal rotations

We present a novel method for constructing the stable conformational space of small molecules with many rotatable bonds that uses our iterative stochastic elimination (ISE) algorithm, a robust stochastic search method capable of finding ensembles of best solutions for large combinatorial problems. To validate the method, we show that ISE reproduces the best conformers found in a fully exhaustive search, as well as compare computed dipole moments to experimental values, based on molecular ensembles and their Boltzmann distributions. Results were also compared to the alternative molecular dynamics and simulated annealing methods. Our results clarify that many low energy conformations may be required to reproduce molecular properties, while single low energy conformers or ensembles of low energy conformers cannot account for the experimental properties of flexible molecules. Whereas ISE well reproduces conformations that are not separated by very large energy barriers, it has not been successful in reproducing conformations of strained molecules.     

Observation of free-electron-laser-induced collective spontaneous emission (superfluorescence)

We have observed and characterized 501.6 nm collective spontaneous emission (superfluorescence) following 1s(2) → 1s3p excitation of helium atoms by 53.7 nm free-electron laser radiation. Emitted pulse energies of up to 100 nJ are observed, corresponding to a photon number conversion efficiency of up to 10%. We observe the peak intensity to scale as ρ(2) and the emitted pulse width and delay to scale as ρ(-1), where ρ is the atom number density. Emitted pulses as short as 1 ps are observed, which corresponds to a rate around 75,000 times faster than the spontaneous 1s3p → 1s2s decay rate. To our knowledge, this is the first observation of superfluorescence following pumping in the extreme ultraviolet wavelength region, and extension of the technique to the generation of extreme ultraviolet and x-ray superfluorescence pulses should be straightforward by using suitable atomic systems and pump wavelengths.     

Assessment of Temporal Variability Trends for Inorganic Parameters in Ground Water

Abstract

The passage of environmental legislation in the United States has dramatically increased ground-water monitoring in the vicinity of point sources such as abandoned waste disposal sites, operational waste disposal sites, and municipal landfills. Even though these programs require sufficient sampling to define background conditions as part of the site characterization process, there is still a general absence of quantitative information on the magnitude and periodicity of temporal fluctuations for inorganic constituents in ground water. This paper presents an approach that has been used to develop an initial characterization of these temporal trends.

A search if on-going site investigation reports identified 18 facilities across the United States that had monthly monitoring data at a frequency of at least monthly for a period of one and a half years or longer (15 RCRA-C hazardous waste disposal facilities with monthly data for a period of 2–3 years, 2 research monitoring locations with biweekly monitoring data for a period of one and a half years, and a precious metal mining operation with daily monitoring data for a limited number of parameters for a period of one and a half years). The data from these site investigations were used to describe the temporal variability of several ground-water constituents including pH, specific conductance, sulfate, sodium, chloride, alkalinity, silica, iron, and manganese. An assessment of these data suggests that the magnitude of temporal ground-water fluctuations are on the order of 20 percent of the average concentration for chloride, 10 percent of the average concentration for sodium, manganese and specific conductance, 5 percent of the average concentration for alkalinity and pH, and essentially zero for silica. The apparent periodicities of these temporal fluctuations ranged from 40 weeks to approximately 2 years. The magnitude and periodicities in ground water are substantially smaller than those that have been reported and documented for the same constituents in surface waters. These differences are due to the fact that sunlight and wind, two energy factors that drive temporal cycles in surface water, do not exert a similar influence on the environmental chemistry of ground-water constituents.     

HUMIC MACROMOLECULES IN NATURAL WATERS

Abstract

Humic substances are the major organic constituents of soils and sediments. They also occur in small concentrations in natural surface waters and groundwaters. They form through the breakdown of plant and animal tissues by chemical and biological processes that tend to produce complex chemical structures that are more stable than the original material from which they were derived. One of the more important characteristics of humic substances is their ability to form water-soluble and water-insoluble complexes with metal ions and hydrous oxides and to interact with clay minerals and various organic compounds such as alkanes, fatty acids, and toxic organic substances such as pesticides.     

Inner-shell excitation spectroscopy and fragmentation of small hydrogen-bonded clusters of formic acid after core excitations at the oxygen K edge

Inner-shell excitation spectra and fragmentation of small clusters of formic acid have been studied in the oxygen K-edge region by time-of-flight fragment mass spectroscopy. In addition to several fragment cations smaller than the parent molecule, we have identified the production of HCOOH.H+ and H3O+ cations characteristic of proton transfer reactions within the clusters. Cluster-specific excitation spectra have been generated by monitoring the partial ion yields of the product cations. Resonance transitions of O1s(C[double bond]O/OH) electrons into pi(CO)* orbital in the preedge region were found to shift in energy upon clusterization. A blueshift of the O1s(C[double bond]O)-->pi(CO)* transition by approximately 0.2 eV and a redshift of the O1s(OH)-->pi(CO)* by approximately 0.6 eV were observed, indicative of strong hydrogen-bond formation within the clusters. The results have been compared with a recent theoretical calculation, which supports the conclusion that the formic-acid clusters consist of the most stable cyclic dimer andor trimer units. Specifically labeled formic acid-d, HCOOD, was also used to examine the core-excited fragmentation mechanisms. These deuterium-labeled experiments showed that HDO+ was formed via site-specific migration of a formyl hydrogen within an individual molecule, and that HD2O+ was produced via the subsequent transfer of a deuterium atom from the hydroxyl group of a nearest-neighbor molecule within a cationic cluster. Deuteron (proton) transfer from the hydroxyl site of a hydrogen-bond partner was also found to take place, producing deuteronated HCOOD.D+ (protonated HCOOH.H+) cations within the clusters.