## Poster Session 4

#### Presentation Title

A Simplified Model of Surface Tension Induced Folding

#### Faculty Mentor

Nicholas Brubaker

#### Start Date

23-11-2019 10:45 AM

#### End Date

23-11-2019 11:30 AM

220

poster 4

Poster

#### Subject Area

physical_mathematical_sciences

#### Abstract

Optimization problems frequently appear in everyday life and in most physical situations there is a limiting constraint involved. For this project, we built a mathematical model that will accurately predict when a paper structure will fold onto itself after a drop of water has started to evaporate from within it. Due to the physicality of the system, the volume of the drop acts as a constraint. By scaling down to a two-dimensional cross-section, we analyzed the relationship between the angles with respect to their vertical axes and constructed a model to measure the energy that is emitted from the changing positions. By using a combination of the method of Lagrange Multipliers and creating a matrix of second derivatives of our model, we composed a modified eigenvalue problem. Through further analysis, we were able to determine the minimum amount of energy required to move the structure into its desired state. For our future work, we hope to continue analyzing this model with varied parameters to further understand the physical implications of this structure.

#### Share

COinS

Nov 23rd, 10:45 AM Nov 23rd, 11:30 AM

A Simplified Model of Surface Tension Induced Folding

220

Optimization problems frequently appear in everyday life and in most physical situations there is a limiting constraint involved. For this project, we built a mathematical model that will accurately predict when a paper structure will fold onto itself after a drop of water has started to evaporate from within it. Due to the physicality of the system, the volume of the drop acts as a constraint. By scaling down to a two-dimensional cross-section, we analyzed the relationship between the angles with respect to their vertical axes and constructed a model to measure the energy that is emitted from the changing positions. By using a combination of the method of Lagrange Multipliers and creating a matrix of second derivatives of our model, we composed a modified eigenvalue problem. Through further analysis, we were able to determine the minimum amount of energy required to move the structure into its desired state. For our future work, we hope to continue analyzing this model with varied parameters to further understand the physical implications of this structure.