Eternal Sunshine of the Solar Panel

The social dynamics of residential solar panel use within a theoretical population are studied using a compartmental model. In this study we consider three solar power options commonly available to consumers: the community block, leasing, and buying. In particular we are interested in studying how social influence affects the dynamics within these compartments. As a result of this research a threshold value is determined, beyond which solar panels persist in the population. In addition, as is standard in this type of study, we perform equilibrium analysis, as well as uncertainty and sensitivity analyses on the threshold value. We also perform uncertainty analysis on the population levels of each compartment. The analysis shows that social influence plays an important role in the adoption of residential solar panels

“I Got You”: Centering Identities and Humanness in Collaborations Between Mathematics Educators and Mathematicians

Existing literature widely reports on the value of collaborations between mathematicians and mathematics educators, and also how complex those collaborations can be. In this paper, we report on four collaborations that sought to address what mathematics is and who gets to do it. Drawing on the literature and from the careful and intentional work of the collaborators, we offer a framework to capture the richness of those collaborations – one that acknowledges the importance of acknowledging and welcoming the extensive personal and professional experience of each person involved in the collaboration – and a look at how collaborations built with that intentionality and acknowledgment can be impactful for students and institutions and be personally and professionally rewarding for the collaborators

Habitat choice of multiple pollinators in almond trees and its potential effect on pollen movement and productivity: A theoretical approach using the Shigesada–Kawasaki–Teramoto model

California\u27s almond industry, valued at $2.3 billion per year, depends on the pollinator services of honey bees, although pollination by other insects, mainly solitary wild bees, is being investigated as an alternative because of recent declines in the number of honey bee colonies. Our objective is to model the movements of honey bees and determine the conditions under which they will forage in less favorable areas of a tree and its surroundings when other pollinators are present. We hypothesize that foraging in less favorable areas leads to increased movement between trees and increased cross pollination between varieties which is required for successful nut production. We use the Shigesada–Kawasaki–Teramoto model (1979) which describes the density of two species in a two-dimensional environment of variable favorableness with respect to intrinsic diffusions and intra and interspecific interactions of species. The model is applied to almond pollination by honey bees and other pollinators with environmental favorableness based on the distribution of flowers in trees. Using the spectral-Galerkin method in a rectangular domain, we numerically approximated the two-dimensional nonlinear parabolic partial differential system arising in the model. When cross-diffusion or interspecific effects of other pollinators was high, honey bees foraged in less favorable areas of the tree. In the model, high cross-diffusion also resulted in increased activity in honey bees which manifested itself in the field in terms of accelerations, decelerations, and changes in direction, indicating rapid redistribution of densities to an equilibrium state. Empirical analysis of the number of honey bees and other visitors in 2-min intervals to almond trees shows a negative relationship, indicating cross-diffusion effects in nature with the potential to increase movement to a different tree with a more favorable environment, potentially increasing nut production