An integral-representation result for continuum limits of discrete energies with multi-body interactions

We prove a compactness and integral-representation theorem for sequences of families of lattice energies describing atomistic interactions defined on lattices with vanishing lattice spacing. The densities of these energies may depend on interactions between all points of the corresponding lattice contained in a reference set. We give conditions that ensure that the limit is an integral defined on a Sobolev space. A homogenization theorem is also proved. The result is applied to multibody interactions corresponding to discrete Jacobian determinants and to linearizations of Lennard-Jones energies with mixtures of convex and concave quadratic pair-potentials

Wave mitigation in ordered networks of granular chains

We study the propagation of stress waves through ordered 2D networks of granular chains. The quasi-particle continuum theory employed captures the acoustic pulse splitting, bending, and recombination through the network and is used to derive its effective acoustic properties. The strong wave mitigation properties of the network predicted theoretically are confirmed through both numerical simulations and experimental tests. In particular, the leading pulse amplitude propagating through the system is shown to decay exponentially with the propagation distance and the spatial structure of the transmitted wave shows an exponential localization along the direction of the incident wave. The length scales that characterized these exponential decays are studied and determined as a function of the geometrical properties of the network. These results open avenues for the design of efficient impact mitigating structures and provide new insights into the mechanisms of wave propagation in granular matter.Comment: submitted to Journal of the Mechanics and Physics of Solid

An Intellectual Framework for Assessing Agricultural Climate Adaptation Combining Stakeholder Engagement and Process Based Modeling: Lower Boise River Basin, Idaho

The impacts of climate change have significant implications for agricultural yields and water use. Previous studies have focused on impacts of climatic factors on crop phenology and yields, with little consideration of local farm management strategies that might mitigate some of these negative effects. Further, the inclusion of stakeholders is commonly left out of many biophysical studies of agricultural landscapes. Therefore, there is considerable uncertainty in the future of regional agroecosystems. In this study, we adopt a social-ecological systems perspective to develop an intellectual framework for assessing agricultural climate adaptation. With research questions focused in both biophysical and social science, we utilize a process-based crop simulation model and stakeholder meetings to examine agricultural response to climate change and adaptations that mitigate for climate change effects. This study advances our understanding of future climate effects on local agriculture, and provides a framework to include local variables into process-based modelling methods. A regional assessment of baseline (1980–2015) and future (2015–2099) yields and water use for four irrigated crops in the Lower Boise River Basin (LBRB) of southwestern Idaho was conducted using a stakeholder informed model. Six different future climate scenarios, ranging in precipitation and temperature, were applied to our model to understand the potential degree to which climate change might affect yields, hydrologic fluxes, and planting date. Analysis of crop yields in most climate scenarios show a slight to moderate decrease in wheat and corn yields by 2100, while alfalfa and sugarbeets stay the same or moderately increase in more mild scenarios. Next, we identify potential concerns with the current irrigation season, which starts on April 1. Under all climate scenarios, our model predicts the growing season to start earlier in the year based on ET estimates and planting dates. This has major implications for future water policy, as the current irrigation season may need to be redefined to allow for early season irrigation in the coming decades. Our results, along with continued communication and iterative stakeholder engagement in the LBRB, can lead to adaptive solutions and policy changes in the agricultural sector. This research highlights the usefulness of combining local information with biophysical models that aim to understand agricultural systems, and can therefore be adjusted to other regions

Classroom Teachers and School-Based Mental Health Professionals: A Multi-Case Study

The purpose of this qualitative, multiple-case study was to understand the pedagogy and attitudes of teachers when faced with the presence of school-based mental health professionals in the classrooms in two schools in southwestern Virginia. Semi-structured interviews, with open-ended questions, document analysis, and participant observations were utilized to collect data. The theory that guided this study was Bandura’s (1993) theory of perceived self-efficacy as it related to an individual teacher’s sense of how capable he or she is of creating an environment conducive to learning. The research centered around understanding how a teacher addresses necessary changes to pedagogy and attitude, given the deviations in the dynamics of the classroom. Three research questions in this study addressed the role of school-based mental health service presence in schools on teachers’ classroom practices and approaches, and more specifically, pedagogy and attitudes toward the classroom environment and students. The data collection occurred at one high school in the Virginia Mountains region. The schools chosen for this study were currently collaborating with school-based mental health programs. Data consisted of interviews, classroom observations, and document analysis. The results of this study provided information on the attitude and pedagogy of the participants as they experienced teaching with School-Based Mental Health professionals in the classroom. The empirical, theoretical, and practical implications were also discussed

Starling flock networks manage uncertainty in consensus at low cost

Flocks of starlings exhibit a remarkable ability to maintain cohesion as a group in highly uncertain environments and with limited, noisy information. Recent work demonstrated that individual starlings within large flocks respond to a fixed number of nearest neighbors, but until now it was not understood why this number is seven. We analyze robustness to uncertainty of consensus in empirical data from multiple starling flocks and show that the flock interaction networks with six or seven neighbors optimize the trade-off between group cohesion and individual effort. We can distinguish these numbers of neighbors from fewer or greater numbers using our systems-theoretic approach to measuring robustness of interaction networks as a function of the network structure, i.e., who is sensing whom. The metric quantifies the disagreement within the network due to disturbances and noise during consensus behavior and can be evaluated over a parameterized family of hypothesized sensing strategies (here the parameter is number of neighbors). We use this approach to further show that for the range of flocks studied the optimal number of neighbors does not depend on the number of birds within a flock; rather, it depends on the shape, notably the thickness, of the flock. The results suggest that robustness to uncertainty may have been a factor in the evolution of flocking for starlings. More generally, our results elucidate the role of the interaction network on uncertainty management in collective behavior, and motivate the application of our approach to other biological networks.Comment: 19 pages, 3 figures, 9 supporting figure

Solitary waves in a chain of repelling magnets

We study experimentally, numerically, and theoretically the dynamics of a one dimensional array of repelling magnets. We demonstrate that such systems support solitary waves with a profile and propagation speed that depend on the amplitude. The system belongs to the kind of nonlinear lattices studied in [Friesecke and Matthies, Physica D 171, 211–220 (2002)] and exhibits a sech^2 profile in the low energy regime and atomic scale localization in the high energy regime. Such systems may find potential applications in the design of novel devices for shock absorption, energy localization and focusing. Furthermore, due to the similarity of the magnetic potential with the potentials governing atomic forces, the system could be used for a better understanding of important problems in physics and chemistry

Tailoring Stress Waves in 2-D Highly Nonlinear Granular Crystals: Simulations and Experiments

We study the propagation of elastic stress waves in two-dimensional highly nonlin-ear granular crystals composed of square packings of spheres with and without cylindrical intruders, via experiments and numerical simulations. By varying the intruder material, we show the ability to alter the propagating wave front characteristics. Experiments agree well with dis-crete particle simulations

Using A Nursing History Web Site With Today's Nursing Students

Recognizing the importance of nursing history, an interdisciplinary team at Appalachian State University created a North Carolina Nursing History Web site (http://nursinghistory.appstate.edu/). The Web site can be used for teaching undergraduate and graduate nursing and other health professions students