Controlling wave propagation through nonlinear engineered granular systems

We study the fundamental dynamic behavior of a special class of ordered granular systems in order to design new, structured materials with unique physical properties. The dynamic properties of granular systems are dictated by the nonlinear, Hertzian, potential in compression and zero tensile strength resulting from the discrete material structure. Engineering the underlying particle arrangement of granular systems allows for unique dynamic properties, not observed in natural, disordered granular media. While extensive studies on 1D granular crystals have suggested their usefulness for a variety of engineering applications, considerably less attention has been given to higher-dimensional systems. The extension of these studies in higher dimensions could enable the discovery of richer physical phenomena not possible in 1D, such as spatial redirection and anisotropic energy trapping. We present experiments, numerical simulation (based on a discrete particle model), and in some cases theoretical predictions for several engineered granular systems, studying the effects of particle arrangement on the highly nonlinear transient wave propagation to develop means for controlling the wave propagation pathways. The first component of this thesis studies the stress wave propagation resulting from a localized impulsive loading for three different 2D particle lattice structures: square, centered square, and hexagonal granular crystals. By varying the lattice structure, we observe a wide range of properties for the propagating stress waves: quasi-1D solitary wave propagation, fully 2D wave propagation with tunable wave front shapes, and 2D pulsed wave propagation. Additionally the effects of weak disorder, inevitably present in real granular systems, are investigated. The second half of this thesis studies the solitary wave propagation through 2D and 3D ordered networks of granular chains, reducing the effective density compared to granular crystals by selectively placing wave guiding chains to control the acoustic wave transmission. The rapid wave front amplitude decay exhibited by these granular networks makes them highly attractive for impact mitigation applications. The agreement between experiments, numerical simulations, and applicable theoretical predictions validates the wave guiding capabilities of these engineered granular crystals and networks and opens a wide range of possibilities for the realization of increasingly complex granular material design.

Metasomatism and magmatic assimilation at a gabbro-limestone contact, Christmas Mountains, Big Bend region, Texas

A composite stock of alkaline gabbro and syenite is intrusive into limestone of the Del Carmen, Sue Peake and Santa Elena Formations at the northwest end of the Christmas Mountains. There is abundant evidence of solution of wallrock by magma but nowhere are gabbro and limestone in direct contact. The sequence of lithologies developed across the intrusive contact and across xenoliths is gabbro, pyroxenite, calc-silicate skarn, marble. Pyroxenite is made up of euhedral crystals of titanaugite and sphene in a leucocratic matrix of nepheline, Wollastonite and alkali feldspar. The uneven modal distribution of phases in pyroxenite and the occurrence' of nepheline syenite dikes, intrusive into pyroxenite and skarn, suggest that pyroxenite represents an accumulation of clinopyroxene "cemented" together by late-solidifying residual magma of nepheline syenite composition. Assimilation of limestone by gabbroic magma involves reactions between calcite and magma and/or crystals in equilibrium with magma and crystallization of phases in which the magma is saturated, to supply energy for the solution reaction. Gabbroic magma was saturated with plagioclase and clinopyroxene at the time of emplacement. The textural and mineralogic features of pyroxenite can be produced by the reaction 2( 1-X) CALCITE + AN_XAB_l-X = (1-X) NEPHELINE+ 2(1-X) WOLLASTONITE+ X ANORTHITE+ 2(1-X) CO₂. Plagioclase in pyroxenite has corroded margins and is rimmed by nepheline, suggestive of resorption by magma. Anorthite and wollastonite enter solid solution in titanaugite. For each mole of calcite dissolved, approximately one mole of clinopyroxene was crystallized. Thus the amount of limestone that may be assimilated is limited by the concentration of potential clinopyroxene in the magma. Wollastonite appears as a phase when magma has been depleted in iron and magnesium by crystallization of titanaugite. The predominance of mafic and ultramafic compositions among contaminated rocks and their restriction to a narrow zone along the intrusive contact provides little evidence for the generation of a significant volume of desilicated magma as a result of limestone assimilation.

Within 60 m of the intrusive contact with the gabbro, nodular chert in the Santa Elena Limestone reacted with the enveloping marble to form spherical nodules of high-temperature calc-silicate minerals. The phases wollastonite, rankinite, spurrite, tilleyite and calcite, form a series of sharply-bounded, concentric monomineralic and two-phase shells which record a step-wise decrease in silica content from the core of a nodule to its rim. Mineral zones in the nodules vary 'with distance from the gabbro as follows:

0-5 m CALCITE + SPURRITE + RANKINITE + WOLLASTONITE
5-16 m CALCITE + TILLEYITE ± SPURRITE + RANKINITE + WOLLASTONITE
16-31 m CALCITE + TILLEYITE + WOLLASTONITE
31-60 m CALCITE + WOLLASTONITE
60-plus CALCITE + QUARTZ

The mineral of a one-phase zone is compatible with the phases bounding it on either side but these phases are incompatible in the same volume of P-T-X_CO2.

Growth of a monomineralio zone is initiated by reaction between minerals of adjacent one-phase zones which become unstable with rising temperature to form a thin layer of a new single phase that separates the reactants and is compatible with both of them. Because the mineral of the new zone is in equilibrium with the phases at both of its contacts, gradients in the chemical potentials of the exchangeable components are established across it. Although zone boundaries mark discontinuities in the gradients of bulk composition, two-phase equilibria at the contacts demonstrate that the chemical potentials are continuous. Hence, Ca, Si and CO₂ were redistributed in the growing nodule by diffusion. A monomineralic zone grows at the expense of an adjacent zone by reaction between diffusing components and the mineral of the adjacent zone. Equilibria between two phases at zone boundaries buffers the chemical potentials of the diffusing species. Thus, within a monomineralic zone, the chemical potentials of the diffusing components are controlled external to the local assemblage by the two-phase equilibria at the zone boundaries.

Mineralogically zoned calc-silicate skarn occurs as a narrow band that separates pyroxenite and marble along the intrusive contact and forms a rim on marble xenoliths in gabbro. Skarn consists of melilite or idocrase pseudomorphs of melili te, one or two . stoichiometric calcsilicate phases and accessory Ti-Zr garnet, perovskite and magnetite. The sequence of mineral zones from pyroxenite to marble, defined by a characteristic calc-silicate, is wollastonite, rankinite, spurrite, calcite. Mineral assemblages of adjacent skarn zones are compatible and the set of zones in a skarn band defines a facies type, indicating that the different mineral assemblages represent different bulk compositions recrystallized under identical conditions. The number of phases in each zone is less than the number that might be expected to result from metamorphism of a general bulk composition under conditions of equilibrium, trivariant in P, T and u_CO2. The "special" bulk composition of each zone is controlled by reaction between phases of the zones bounding it on either side. The continuity of the gradients of composition of melilite and garnet solid solutions across the skarn is consistent with the local equilibrium hypothesis and verifies that diffusion was the mechanism of mass transport. The formula proportions of Ti and Zr in garnet from skarn vary antithetically with that of Si Which systematically decreases from pyroxenite to marble. The chemical potential of Si in each skarn zone was controlled by the coexisting stoichiometric calc-silicate phases in the assemblage. Thus the formula proportion of Si in garnet is a direct measure of the chemical potential of Si from point to point in skarn. Reaction between gabbroic magma saturated with plagioclase and clinopyroxene produced nepheline pyroxenite and melilite-wollastonite skarn. The calcsilicate zones result from reaction between calcite and wollastonite to form spurrite and rankinite.

Grants for Libraries

More and more libraries, museums and cultural institutions rely on fundraising and grant writing to sustain their services, special projects, or new initiatives Since most MLIS programs do not include grant project planning and proposal writing as part of their curriculum, librarians learn the process through trial and error, or continuing education classes. There are numerous books and websites that can assist the novice grant writer. We hope to provide beginners with basic information on the types of grants available, where to look for funding agencies, selected grant writing resources, and a few helpful grant writing hints to get you started. The presentation will be a three-person panel providing a short overview of the areas mentioned above, and discussion of sample grants submitted or received. The overview will be presented in Power Point format with an accompanying handout for each attendee.

Not just another pretty reef: the Gainesville Florida Reef, a satellite of the worldwide Hyperbolic Crochet Coral Reef project: poster presentation

The Gainesville Florida Reef, a satellite of the Worldwide Hyperbolic Crochet Coral Reef, project not only shows the beauty of reefs but serves to: • Foster scientific communication through the visual arts • Raise awareness of the fragility of our coral reefs and the entire ecosystem • Support learning by creating physical models of geometric principles • Connect several areas on campus, including fine arts, mathematics and ecology and environmental sciences through collaboration and mutual interest • Encourage local community and alumni involvement through creating, observing and learning

Tsunamis - a model of their generation and propagation

A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered.

An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model.

Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of non-linear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation.

A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation.

An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally.

The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.

Ecological condition of coastal ocean waters of the northwestern Gulf of Mexico: 2011

In August 2011, the NOAA National Ocean Service (NOS) conducted an assessment of the status of ecological condition of soft-bottom habitat and overlying waters of the continental shelf in the northwestern Gulf of Mexico (GOM). The original sampling design included 50 randomly selected sites from the Mississippi River delta to the U.S./Mexican border, representing a total area of 111,162 square kilometers; however, vessel failures and inclement weather precluded sampling at 16 sites in the western-most part of the study region. Sampling was completed at the remaining 34 sites in offshore waters between the Mississippi River delta and Freeport, Texas, representing an estimated 75,591 square kilometers. Field sampling followed standard methods and indicators applied in prior NOAA coastal studies and EPA’s Environmental Monitoring and Assessment Program (EMAP) and National Coastal Assessment (NCA). A key feature adopted from these studies was the incorporation of a random probabilistic sampling design. Such a design provides a basis for making unbiased statistical estimates of the spatial extent of ecological condition relative to various measured indicators and corresponding thresholds of concern. Indicators included multiple measures of water quality, sediment quality, and biological condition (benthic fauna, fish tissue contaminant levels). Water depths ranged from 13 – 83 m throughout the study area. About 9 % of the area had sediments composed of sands (< 20 % silt+clay), 47 % of the area was composed of intermediate muddy sands (20 – 80 % silt+clay), and 44 % of the sampled area consisted of mud (> 80 % silt+clay). About 50 % of the area (represented by 17 sites) had sediment total organic carbon (TOC) concentrations < 5 mg/g and all of the sites sampled had levels of TOC < 20 mg/g, well below the range associated with potentially harmful effects to benthic fauna (> 50 mg/g). Surface salinities ranged from 23.4 – 36.5 psu, with salinity generally increasing with distance west of the Mississippi River delta. Bottom salinities varied between 31.1 and 36.5 psu, with lowest values occurring at shallow, inner-shelf stations. Surface-water temperatures varied between 29.8 and 31.5 ºC, while near-bottom waters ranged in temperature from 19.4 – 31 ºC. An index of density stratification (Δσt) indicated that portions of coastal shelf waters in the northwestern GOM at the time of this sampling were strongly stratified. Values of Δσt at 19 of the 34 sites sampled in this study (56 % of the study area) ranged from 2.2 to 12.4, which is within the range considered to be indicative of strong vertical stratification (Δσt > 2). Stratification was strongest close to the Mississippi River delta, and decreased with distance west of the delta.

Ecological Condition of Coastal Ocean Waters within Stellwagen Bank National Marine Sanctuary: 2008

In June 2008, the NOAA National Ocean Service (NOS), in conjunction with the EPA National Health and Environmental Effects Laboratory (NHEERL), conducted an assessment of the status of ecological condition of soft-bottom habitat and overlying waters within the boundaries of Stellwagen Bank National Marine Sanctuary (SBNMS). The sanctuary lies approximately 20 nautical miles east of Boston, MA in the southwest Gulf of Maine between Cape Ann and Cape Cod and encompassing 638 square nautical miles (2,181 km2). A total of 30 stations were targeted for sampling using standard methods and indicators applied in prior NOAA coastal studies and EPA’s Environmental Monitoring and Assessment Program (EMAP) and National Coastal Assessment (NCA). A key feature adopted from these studies was the incorporation of a random probabilistic sampling design. Such a design provides a basis for making unbiased statistical estimates of the spatial extent of ecological condition relative to various measured indicators and corresponding thresholds of concern. Indicators included multiple measures of water quality, sediment quality, and biological condition (benthic fauna, fish tissue contaminant levels). Depths ranged from 31 – 137 m throughout the study area. About 76 % of the area had sediments composed of sands (< 20 % silt-clay), 17 % of the area was composed of intermediate muddy sands (20 – 80 % silt-clay), and 7 % of the sampled area consisted of mud (> 80 % siltclay). About 70 % of the area (represented by 21 sites) had sediment total organic carbon (TOC) concentrations < 5 mg/g and all but one site (located in Stellwagen Basin) had levels of TOC < 20 mg/g, which is well below the range potentially harmful to benthic fauna (> 50 mg/g). Surface salinities ranged from 30.6 – 31.5 psu, with the majority of the study region (approximately 80 % of the area) having surface salinities between 30.8 and 31.4 psu. Bottom salinities varied between 32.1 and 32.5 psu, with bottom salinities at all sites having values above the range of surface salinities. Surface-water temperatures varied between 12.1 and 16.8 ºC, while near-bottom waters ranged in temperature from 4.4 – 6.2 ºC. An index of density stratification (Δσt) indicated that the waters of SBNMS were stratified at the time of sampling. Values of Δσt at 29 of the 30 sites sampled in this study (96.7 % of the study area) varied from 2.1 – 3.2, which is within the range considered to be indicative of strong vertical stratification (Δσt > 2) and typical of the western Gulf of Maine in summer. Levels of dissolved oxygen (DO) were confined to a fairly narrow range in surface (8.8 – 10.4 mg/L) and bottom (8.5 – 9.6 mg/L) waters throughout the survey area. These levels are within the range considered indicative of good water quality (> 5 mg/L) with respect to DO. None of these waters had DO at low levels (< 2 mg/L) potentially harmful to benthic fauna and fish.

Ecological condition of coastal ocean waters along the U.S. Mid-Atlantic Bight: 2006

In May 2006, the NOAA National Ocean Service (NOS), in conjunction with the EPA National Health and Environmental Effects Laboratory (NHEERL), conducted an assessment of the status of ecological condition of soft-bottom habitat and overlying waters throughout the mid-Atlantic Bight (MAB) portion of the eastern U.S. continental shelf. The study area encompassed the region from Cape Cod, MA and Nantucket Shoals in the northeast to Cape Hatteras in the south, and was defined using a one nautical mile buffer of the shoreline extended seaward to the shelf break (~100-m depth contour). A total of 50 stations were targeted for sampling using standard methods and indicators applied in prior NOAA coastal studies and EPA’s Environmental Monitoring and Assessment Program (EMAP) and National Coastal Assessment (NCA). A key feature adopted from these studies was the incorporation of a random probabilistic sampling design. Such a design provides a basis for making unbiased statistical estimates of the spatial extent of ecological condition relative to various measured indicators and corresponding thresholds of concern. Indicators included multiple measures of water quality, sediment quality, and biological condition (benthic fauna). Through coordination with the NOAA Fisheries Service/Northeast Fisheries Science Center (NFS/NEFSC), samples of summer flounder (Paralichthys dentatus) also were obtained from 30 winter 2007 bottom-trawl survey stations in overlapping portions of the study area and used for analysis of chemical-contaminant body burdens.