13,191 research outputs found
Architecture of optimal transport networks
We analyze the structure of networks minimizing the global resistance to flow
(or dissipated energy) with respect to two different constraints: fixed total
channel volume and fixed total channel surface area. First, we determine the
shape of channels in such optimal networks and show that they must be straight
with uniform cross-sectional areas. Then, we establish a relation between the
cross-sectional areas of adjoining channels at each junction. Indeed, this
relation is a generalization of Murray's law, originally established in the
context of local optimization. Moreover, we establish a relation between angles
and cross-sectional areas of adjoining channels at each junction, which can be
represented as a vectorial force balance equation, where the force weight
depends on the channel cross-sectional area. A scaling law between the minimal
resistance value and the total volume or surface area value is also derived
from the analysis. Furthermore, we show that no more than three or four
channels meet in one junction of optimal bi-dimensional networks, depending on
the flow profile (e.g.: Poiseuille-like or plug-like) and the considered
constraint (fixed volume or surface area). In particular, we show that sources
are directly connected to wells, without intermediate junctions, for minimal
resistance networks preserving the total channel volume in case of plug flow
regime. Finally, all these results are illustrated with a simple example, and
compared with the structure of natural networks
Continuity and variability in the parental involvement and advocacy beliefs of Latino families of young children
Parental involvement is an important component of children’s school success. Although the literature on parental involvement among Latino families is growing and moving from deficit-based perspectives, very few studies have
examined the parental involvement beliefs and practices of Latino families who vary across demographic and sociocultural lines within the same school community. This qualitative study explored Latino parents’ beliefs about children’s
education, their involvement and advocacy beliefs and practices, and their perceptions of feeling welcome at their children’s school. In-depth interviews were conducted with 12 parents of preschool and kindergarten children who attended a bilingual school. Qualitative descriptive analyses revealed that the majority of parents espoused the cultural value of educación, engaged in learning activities at home, and viewed themselves as living models of behavior for children, regardless of their education or immigrant status. Only first generation immigrant parents made explicit reference to children’s futures. All parents
attributed supportive relationships with school personnel and a bilingual climate as the most important sources of feeling welcome at school. However, parents with more education valued what they perceived as an “open door policy” and were more vocal in critiquing policies. Findings have implications for the development of multicultural competence among teachers and for ways diverse Latino families might develop a shared voice within the school sector.Published versio
On the Representation Theory of Orthofermions and Orthosupersymmetric Realization of Parasupersymmetry and Fractional Supersymmetry
We construct a canonical irreducible representation for the orthofermion
algebra of arbitrary order, and show that every representation decomposes into
irreducible representations that are isomorphic to either the canonical
representation or the trivial representation. We use these results to show that
every orthosupersymmetric system of order has a parasupersymmetry of order
and a fractional supersymmetry of order .Comment: 13 pages, to appear in J. Phys. A: Math. Ge
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