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Formal studies of models of concurrency are usually focused on two major models: Interleaving abstraction (Bergstra, 2001; Milner, 1990) and partially ordered causality (Diekert and Rozenberg, 1995; Jensen, 1997; Reisig, 1998). Although very mature, these models retain a known limitation: Neither of them can model the “not later than” relationship effectively, which causes problems with specifying priorities, error recovery, time testing, inhibitor nets, etc. See for reference: Best and Koutny (1992); Janicki (2008); Janicki and Koutny (1995); Juhas et al. (2006); Kleijn and Koutny (2004). A solution, proposed independently (in this order) in (Lamport, 1986; Gaifman and Pratt, 1987) and (Janicki and Koutny, 1991), suggests to model concurrent behaviours by an ordered structure, i.e. a triple (X, R1, R2), where X is the set of event occurrences, and R1 and R2 are two binary relations on X. The relation R1 is interpreted as “causality”, i.e. an abstraction of the “earlier than” relationship, and R2 is interpreted as “weak causality”, an abstraction of the “not later than” relationship. For ordered structures’ model, the following two kinds of relational structures are of special importance: stratified order structures (SO-structures) and interval order structures (IO-structures). The SO-structures can fully model concurrent behaviours when system executions (operational semantics) are described in terms of stratified orders, while the IO-structures can fully model concurrent behaviours when system executions are described in terms of interval orders (Janicki, 2008; Janicki and Koutny, 1997). It was argued in (Janicki and Koutny, 1993), and also implicitly in a 1914 Wiener’s paper Wiener (1914), that any execution that can be observed by a single observer must be an interval order. Thus, IO-structures provide a very definitive model of concurrency. However, the theory of IO-structures remains far less developed than its simpler counterpart - the theory of SO-structures. One of the most important concepts lying at the core of partial orders and algebraic structures theory is the concept of transitive closure of relations. The equivalent of transitive closure for SO-structures, called <>-closure, has been proposed in (Janicki and Koutny, 1995) and consequently used in (Janicki and Koutny, 1995; Juhas et al., 2006; Kleijn and Koutny, 2004) and others. However, a similar concept for IO-structures has not been proposed. In this thesis we define that concept. We introduce the transitive closure for IO-structures, called the []-closure. We prove that it has same properties as the standard transitive closure for partial orders and []-closure for SO-structures (published in Janicki and Zubkova (2009); Janicki et al. (2009)), and provide some comparison of different versions of transitive closure used in various relational structures. Some properties of another recently introduced *-closure (Janicki et al., 2013) are also discussed. / Thesis / Master of Science (MSc)

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The abundance of forgiveness research has advanced scientific knowledge of the construct. Its multifaceted nature, however, has created specialization and domain-dependent research (e.g., close-relationship vs. non-relationship forgiveness). The current paper argues that a comprehensive framework that could be applied across domains is needed. The general principles perspective (Higgins, 1990, 1999), which identifies mechanisms that explain both chronic and situational variance, was used as a framework for forgiveness, specifically the mechanisms of accessibility and need for closure. Two studies tested the principles, a two-part study (N = 244 and 78, respectively) and an online survey (N = 214). The two-part study tested chronic accessibility for forgiveness (Accessibility Study One) within the context of the religiosity-forgiveness relationship (an area that has previously produced complex and contradictory results) and both the chronic and situational influence of need for closure (Need for Closure Study). The online survey was designed to test both situational and chronic accessibility (Accessibility Study Two) by priming half of the participants with religious words. Students from a large, Mid-Atlantic university participated. For accessibility, it was proposed that religious individuals would have higher chronic accessibility for forgiveness, because of the emphasis religions place on it; similarly, it was proposed that increasing accessibility for religiosity would increase situational accessibility for forgiveness. Results supported a weak, positive relationship between religiosity and chronic accessibility for forgiveness; however, increased accessibility did not relate to likelihood to forgive future transgressions. For situational accessibility, the religious prime did not successfully influence accessibility for religiosity; thus, situational accessibility could not be tested. For need for closure, it was proposed that forgiveness requires some comfort with uncertainty in order to engage in the process. Therefore, chronic need for closure was expected to negatively relate to likelihood to forgive future transgressions. Results replicated this previously found relationship. For situational need for closure, manipulated through perceived time limitations, it was proposed that it would interact with chronic forgiveness to predict likelihood to forgive, because as need for closure increases so too does automaticity. Forgiveness is arguably an automatic response for someone high in chronic forgiveness. Results did not support the interaction effect. In general, the project supported the chronic influence of the principles but did not support the situational. The limitations of the current project necessitate further inquiry for clarification, though some conclusions are suggested. Results suggest that motivations may be more influential than cognitions in forgiveness, that forgiveness research may require more highly contextualized models, and thus that the potential advantages of a comprehensive framework will require more sophisticated theoretical and empirical work. / Ph. D.

If we adjoin the cube root of a cube free rational integer <i>m</i> to the rational numbers we construct a cubic field. If we adjoin the cube roots of distinct cube free rational integers <i>m</i> and <i>n</i> to the rational numbers we construct a bicubic field. The number theoretic invariants for the cubic fields and their normal closures are well known. Some work has been done on the units, classnumbers and other invariants of the bicubic fields and their normal closures by Parry but no method is available for calculating those invariants. This dissertation provides an algorithm for calculating the number theoretic invariants of the bicubic fields and their normal closure. Among these invariants are the discriminant, an integral basis, a set of fundamental units, the class number and the rank of the 3-class group. / Ph. D.

The integrity of nearly all engineering structures are threatened by the presence of cracks. Structural failure occurs if a crack larger than a critical size exists. Although most well designed structures initially contain no critical cracks, subcritical cracks can grow to failure under fatigue loading, called fatigue crack growth (FCG). Because it is impossible or impractical to prevent subcritical crack growth in most applications, a damage tolerant design philosophy was developed for crack sensitive structures. Design engineers have taken advantage of the FCG threshold concept to design for long fatigue lives. FCG threshold (DKth) is a value of DK (crack-tip loading), below which no significant FCG occurs. Cracks are tolerated if DK is less than DKth. However, FCG threshold is not constant. Many variables influence DKth including microstructure, environment, and load ratio. The current research focuses on load ratio effects on DKth and threshold FCG. Two categories of load ratio effects are studied here: extrinsic and intrinsic. Extrinsic load ratio effects operate in the crack wake and include fatigue crack closure mechanisms. Intrinsic load ratio effects operate in the crack-tip process zone and include microcracking and void production. To gain a better understanding of threshold FCG load ratio effects (1) a fatigue crack closure model is developed to consider the most likely closure mechanisms at threshold, simultaneously, and (2) intrinsic load ratio mechanisms are identified and modeled. An analytical fatigue crack closure model is developed that includes the three closure mechanisms considered most important at threshold (PICC, RICC, and OICC). Crack meandering and a limited amount of mixed-mode loading are also considered. The rough crack geometry, approximated as a two-dimensional sawtooth wave, results in a mixed-mode crack-tip stress state. Dislocation and continuum mechanics concepts are used to determine mixed-mode crack face displacements. Plasticity induced crack closure is included by modifying an existing analytical model, and an oxide layer in the crack mouth is modeled as a uniform layer. Finite element results were used to verify the analytical solutions for crack-tip stress intensity factor and crack face displacements. These results indicate that closure for rough cracks can occur at two locations: (1) at the crack-tip, and (2) at the asperity nearest the crack-tip. Both tip contact and asperity contact must be considered for rough cracks. Tip contact is more likely for high Kmax levels, thick oxide layers, and shallow asperity angles, a. Model results indicate that closure mechanisms combine in a synergistic manner. That is, when multiple closure mechanisms are active, the total closure level is greater than the sum of individual mechanisms acting alone. To better understand fatigue crack closure where multiple closure mechanisms are active (i.e. FCG threshold), these interactions must be considered. Model results are well supported by experimental data over a wide range of DK, including FCG threshold. Closure-free load ratio effects were studied for aluminum alloys 2024, 7050, and 8009. Alloys 7050 and 8009 were selected because load ratio effects at FCG threshold are not entirely explained by fatigue crack closure. It is believed that closure-free load ratio mechanisms occur in these alloys. Aluminum alloy 2024 was selected for study because it is relatively well behaved, meandering most load ratio effects are explained by fatigue crack closure. A series of constant Kmax threshold tests on aluminum alloys were conducted to eliminate fatigue crack closure at threshold. Even in the absence of fatigue crack closure load ratio (Kmax) effects persist, and are correlated with increased crack-tip damage (i.e. voids) seen on the fatigue crack surfaces. Accelerated FCG was observed during constant Kmax threshold testing of 8009 aluminum. A distinct transition is seen the FCG data and is correlated with a dramatic increase in void production seen along the crack faces. Void production in 8009 aluminum is limited to the specimen interior (plane-strain conditions), promoting crack tunneling. At higher values of Kmax (+_ 22.0 MPaà m), where plane-stress conditions dominate, a transition to slant cracking occurs at threshold. The transition to slant cracking produces an apparent increase in FCG rate with decreasing DK. This unstable threshold behavior is related to constraint conditions. Finally, a model is developed to predict the accelerated FCG rates, at higher Kmax levels, in terms of crack-tip damage. The effect of humidity (in laboratory air) on threshold FCG was studied to ensure that environmental effects at threshold were separated from load ratio effects. Although changes in humidity were shown to strongly affect threshold FCG rates, this influence was small for ambient humidity levels (relative humidity between 30% and 70%). Transient FCG behavior, following an abrupt change in humidity level, indicated environmental damage accumulated in the crack-tip monotonic plastic zone. Previous research implies that hydrogen (a component of water vapor) is the likely cause of this environmental damage. Analysis suggests that bulk diffusion is not a likely hydrogen transport mechanism in the crack-tip monotonic plastic zone. Rather, dislocation-assisted diffusion is presented as the likely hydrogen transport mechanism. Finally, the (extrinsic) fatigue crack closure model and the (intrinsic) crack-tip damage model are put in the context of a comprehensive threshold model. The ultimate goal of the comprehensive threshold model is to predict fatigue lives of cyclically loaded engineering components from (small) crack nucleation, through FCG, and including failure. The models developed in this dissertation provide a basis for a more complete evaluation of threshold FCG and fatigue life prediction. The research described in this dissertation was performed at NASA-Langley Research Center in Hampton, Virginia. Funding was provided through the NASA GSRP program (Graduate Student Researcher Program, grant number NGT-1-52174). / Ph. D.

After 17 years in service, a 3 ft by 3 ft closure pour section of an Interstate 81 (I-81) bridge deck failed by punching through near Marion, Virginia. Visual inspection noted that there was considerable corrosion on some of the reinforcing bars in the vicinity of the construction joint, while other failure bars had little or no corrosion. Sections of the bridge deck were cut and delivered to Virginia Tech for further investigation. It was clear from an initial investigation that shrinkage of the deck concrete had caused the construction joints to open and thereby allow water and chlorides to enter the joint. In addition, it was observed that several bars across the closure pour construction joints had suffered significant section loss due to corrosion, but it was not clear if fatigue and strength failure of the reinforcing bars were also contributing factor in the closure pour failure. To study the problem four fatigue tests and five strength tests performed. The specimens included six slab strips cut from the I-81 bridge deck, with the 3-ft closure pour included, and three additional specimens that were cast in the laboratory to represent a base line for performance. A three-point loading setup was used for both fatigue and strength tests. However, for the final strength and fatigue tests, a jacking system was designed and implemented in an effort to open the closure pour construction joints to simulate the open joints of the I-81 bridge. The objectives of this research program are to provide a better understanding of the closure pour failure mechanism, develop inspection procedures for Virginia Department of Transportation (VDOT) to assess its bridge inventory containing similar construction joints, and to develop recommendations for future construction of similar construction joints. / Master of Science

This project defines a decision support system developed to permit the user to perform a cost - benefit analysis for any military installation cited for closure, relocation, or privatization. The procedure recognizes both the economic costs and strategic benefits of a feasible solution. Though the cost estimates for a particular study may vary in magnitude, the economic portion of the model must focus on the net savings to the tax payer. Detailed cost estimates for each alternative have been developed at a level so that sensitivity analysis can be performed on any of the input parameters. Individual cost elements have been summed to yield the net cost increase / decrease to the United States tax payer. The resultant cost figures were converted to an economic score. The paper also describes a effective method to evaluate the benefits derived from implementing various alternatives. By incorporating a group participative process using multivoting and the Dunn-Rankin technique, the values resulting fro m benefits have yielded a benefits score. The Brown-Gibson model, which considers both subjective and objective measures, was used to depict the combination of economic and benefit scores to provide an overall cost - benefit score. A graphical illustrat ion of the cost - benefit tradeoffs serves as a useful tool in assessing the risk associated with a decision. The results of the analysis have supported the Department of the Navy's decision to privatize the Naval Air Warfare Center Aircraft Division, Indianapolis, IN. The Department of Defense is considering alternatives for many military installations, this process will facilitate those decisions. / Master of Science

The purpose of the study was to document and examine the experiences and perspectives of students and staff who were affected by the closure of Mount Rogers Combined School in 2010. Mount Rogers Combined School was established in Grayson County, Virginia, by the concerted efforts of volunteers and community members who valued education and considered schooling a top priority for the area. The original four-room school was built of rocks and housed grades 1 through 11, taught by four teachers, one of whom also served as the principal (Grayson County School Board [GCSB], 1993). In 1990, it was the smallest school in the Commonwealth of Virginia (United States Department of Agriculture, 1990). A review of early education in Virginia and early education in Grayson County is documented to place the study in historical context. A brief history of Grayson County is also included in this paper. The qualitative case study documents the experiences and perspectives of the students and staff who went through the school's closure. Both primary and secondary sources were used to complete the study including interviews of students and staff who worked at or attended the school, reviews of official records and documents found in archives, examination of personal manuscripts, inspection of artifacts, and study of general histories. School divisions close and consolidate schools to improve instructional programs for students, offset student enrollment declines, provide adequate facilities for learning, and for economic savings. Communication, developing relationships, transportation, extracurricular activities and course offerings are variables that should be considered when planning a school closure. While transportation and changes in relationships are particular challenges, the overall benefits for former staff members include better access to more resources and professional development opportunities. Former students tend to adapt better than staff members when schools close due to more course offerings and access to a broader range of extracurricular activities. The findings are aligned with the literature that was reviewed for the study. / Ed. D.

Cells interact with their immediate fibrous extracellular matrix (ECM); alignment of which has been shown influence metastasis. Specifically, intra-vital imaging studies on cell invasion from tumor-matrix interface and wounds along aligned fibers describe invasion to occur as singular leader (tip) cells, or as collective mass of a few chain or multiple tip cells. Recapitulation of these behaviors in vitro promises to provide new insights in how, when and where cells get the stimulus to break cell-cell junctions and ensue invasion by migrating along aligned tracks. Using Spinneret based Tunable Engineered Parameters (STEP) technique, we fabricated precise layout of suspended fibers of varying diameters (300, 500 and 1000 nm) mimicking ECM dimensions, which were interfaced with cell monolayers to study invasion. We demonstrated that nanofiber diameter and their spacing were key determinants in cells to invade either as singularly, chains of few cells or multiple-chains collectively. Through time-lapse microscopy, we reported that singular cells exhibited a peculiar invasive behavior of recoiling analogous to release of a stretched rubber band; detachment speed of which was influenced with fiber diameter (250, 425 and 400 µm/hr on small, medium and large diameter fibers respectively). We found that cells initiated invasion by putting protrusion on fibers; dynamics of which we captured using a contrasting network of mismatched diameters deposited orthogonally. We found that vimentin, a key intermediate filament upregulated in cancer invasion localized within a protrusion only when the protrusion had widened at the base, signifying maturation. To develop a comprehensive picture of invasion, we also developed strategies to quantify migratory speeds and the forces exerted by cells on fibers. Finally, we extended our findings of cell invasion to report a new wound healing assay to examine gap closure. We found that gaps spanned by crosshatch network of fibers closed faster than those on parallel fibers and importantly, we reported that gaps of 375 µm or larger did not close over a 45-day period. In summary, the methods and novel findings detailed from this study can be extended to ask multiple sophisticated hypotheses in physiologically relevant phenomenon like wound healing, morphogenesis, and cancer metastasis. / Ph. D. / Disease phenomenon like cancer invasion and wound healing have a myriad of things in common including cell migration and the ability of cells to remodel their immediate environment. Often times these singular or group migratory events of cells are initiated and directed by peculiar cells called tip/leader cells that explore cellular environment and make room for migration. While research in the last few decades has yielded a tremendous wealth of information as to how biochemical factors influence their behavior, our understanding of how the biophysical properties of the environment affect their behavior is in its infancy. This lack of understanding can somewhat be attributed to the difficulty in fabricating mechanically welldefined substrate systems that can be tailored to recapture these invasive episodes in a controlled setting outside of a living organism. In this study, we utilize a novel Spinneret based Tunable Engineered Parameters (STEP) technique to fabricate mechanically tunable nanofibers that show close resemble to native cellular environment. Cells were made to interact with these fibers and it was shown for the first time that factors like fiber spacing, diameter and topography can significantly affect the types of leader cells and their trajectory. Furthermore, once these cells come out of the simulated tumors/wounds, their migratory behaviors were still affected by mechanical properties of the fibers. Similarly, we also showed for the first time that the ability of the gaps to close in simulated wound healing settings could be significantly dependent on size, shape, and properties of fibers. These findings offer a novel outlook to our current understanding of single and collective cell behavior and how the biophysical properties of the native cellular environment can affect these behaviors. This can not only expand our understanding of how this invasive episodes occur, but also help us come up with preventive measures to inhibit such episodes for a better prognosis of diseases like cancer and chronic wounds.