Epitaxial Frustration in Deposited Packings of Rigid Disks and Spheres

We use numerical simulation to investigate and analyze the way that rigid disks and spheres arrange themselves when compressed next to incommensurate substrates. For disks, a movable set is pressed into a jammed state against an ordered fixed line of larger disks, where the diameter ratio of movable to fixed disks is 0.8. The corresponding diameter ratio for the sphere simulations is 0.7, where the fixed substrate has the structure of a (001) plane of a face-centered cubic array. Results obtained for both disks and spheres exhibit various forms of density-reducing packing frustration next to the incommensurate substrate, including some cases displaying disorder that extends far from the substrate. The disk system calculations strongly suggest that the most efficient (highest density) packings involve configurations that are periodic in the lateral direction parallel to the substrate, with substantial geometric disruption only occurring near the substrate. Some evidence has also emerged suggesting that for the sphere systems a corresponding structure doubly periodic in the lateral directions would yield the highest packing density; however all of the sphere simulations completed thus far produced some residual "bulk" disorder not obviously resulting from substrate mismatch. In view of the fact that the cases studied here represent only a small subset of all that eventually deserve attention, we end with discussion of the directions in which first extensions of the present simulations might profitably be pursued.Comment: 28 pages, 14 figures; typos fixed; a sentence added to 4th paragraph of sect 5 in responce to a referee's comment

Rigidity and volume preserving deformation on degenerate simplices

Given a degenerate $(n+1)$-simplex in a $d$-dimensional space $M^d$ (Euclidean, spherical or hyperbolic space, and $d\geq n$), for each $k$, $1\leq k\leq n$, Radon's theorem induces a partition of the set of $k$-faces into two subsets. We prove that if the vertices of the simplex vary smoothly in $M^d$ for $d=n$, and the volumes of $k$-faces in one subset are constrained only to decrease while in the other subset only to increase, then any sufficiently small motion must preserve the volumes of all $k$-faces; and this property still holds in $M^d$ for $d\geq n+1$ if an invariant $c_{k-1}(\alpha^{k-1})$ of the degenerate simplex has the desired sign. This answers a question posed by the author, and the proof relies on an invariant $c_k(\omega)$ we discovered for any $k$-stress $\omega$ on a cell complex in $M^d$. We introduce a characteristic polynomial of the degenerate simplex by defining $f(x)=\sum_{i=0}^{n+1}(-1)^{i}c_i(\alpha^i)x^{n+1-i}$, and prove that the roots of $f(x)$ are real for the Euclidean case. Some evidence suggests the same conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr

Locked and Unlocked Chains of Planar Shapes

We extend linkage unfolding results from the well-studied case of polygonal linkages to the more general case of linkages of polygons. More precisely, we consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are hinged together sequentially at rotatable joints. Our goal is to characterize the families of planar shapes that admit locked chains, where some configurations cannot be reached by continuous reconfiguration without self-intersection, and which families of planar shapes guarantee universal foldability, where every chain is guaranteed to have a connected configuration space. Previously, only obtuse triangles were known to admit locked shapes, and only line segments were known to guarantee universal foldability. We show that a surprisingly general family of planar shapes, called slender adornments, guarantees universal foldability: roughly, the distance from each edge along the path along the boundary of the slender adornment to each hinge should be monotone. In contrast, we show that isosceles triangles with any desired apex angle less than 90 degrees admit locked chains, which is precisely the threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof details. (Fixed crash-induced bugs in the abstract.

A software development environment utilizing PAMELA

Hardware capability and efficiency has increased dramatically since the invention of the computer, while software programmer productivity and efficiency has remained at a relatively low level. A user-friendly, adaptable, integrated software development environment is needed to alleviate this problem. The environment should be designed around the Ada language and a design methodology which takes advantage of the features of the Ada language as the Process Abstraction Method for Embedded Large Applications (PAMELA)

Improving Breastfeeding Education Among Hospital Nurses

Breastfeeding is well-documented as the most beneficial method of infant feeding worldwide. There are numerous national initiatives present to improve breastfeeding outcomes. Despite knowledge and health care organization efforts, the recommendations of exclusive breastfeeding through six months of life with continued breastfeeding through one year of age are not being met. The purpose of this DNP project is to determine if a structured self-study educational program on breastfeeding recommendations, the 4th Edition of the Lactation Management Self-Study Modules created by Wellstart International™, provided to hospital nurses on a maternity unit in Central, New York with a Level One nursery, will improve nursing knowledge of appropriate breastfeeding practices, decrease variations in breastfeeding education provided to patients, and improve breastfeeding outcomes for the facility. The research study used a quasi-experimental design to determine how an educational program provided to hospital nurses impacts both their knowledge of breastfeeding as well as the breastfeeding outcomes for the hospital. This DNP project, along with the growing body of literature, supports the need for continued provision of education related to breastfeeding among nurses in direct care of breastfeeding mothers, and expresses a need for further research on this topic to optimize breastfeeding outcomes worldwide

The Ideal Learner: Does Sharing Constructs Elicited from Children at Risk of Exclusion Alter the Perceptions of Teachers Working with Them?

This research explores the constructs that teachers have of students at risk of exclusion from school. To date, little research has explored whether a Personal Construct Psychology (PCP) task to elicit constructs from the students about themselves has the power to alter the teachers’ constructs of said students. Five secondary students in Year 7 or 8, at risk of exclusion, completed a PCP task, Drawing the Ideal Learner (DIL). For each of the students, one teacher who knew the student well was interviewed on two separate occasions using semi-structured interviews. This qualitative social constructionist research utilises a PCP theoretical framework to ascertain whether these teachers believed DIL could provide information to inform them about how best to support the student by developing a shared understanding. In the first interview, teachers were asked about their constructs of the students before the research began and the teacher’s assumptions of their student’s aspirations. At the end of this interview they were shown the student’s DIL. In their second interview, exactly one week later, with varying opportunities for interaction with the students, teachers were asked whether any of their previous constructs about the student had altered in light of new information, including those regarding the student's aspirations. Finally, teachers were asked their views of DIL to elicit previously unknown information from students at risk of exclusion. The outcome of this research highlights the importance of providing students at risk of exclusion with an appropriate tool to elicit their voices about their academic present and future journey, and the importance of sharing this information with school staff who can be instrumental in supporting the students

Algebra versus analysis in the theory of flexible polyhedra

Two basic theorems of the theory of flexible polyhedra were proven by completely different methods: R. Alexander used analysis, namely, the Stokes theorem, to prove that the total mean curvature remains constant during the flex, while I.Kh. Sabitov used algebra, namely, the theory of resultants, to prove that the oriented volume remains constant during the flex. We show that none of these methods can be used to prove the both theorems. As a by-product, we prove that the total mean curvature of any polyhedron in the Euclidean 3-space is not an algebraic function of its edge lengths.Comment: 5 pages, 5 figures; condition (iii) in Theorem 5 is correcte