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Ordinary Differential Equations and Applied Dynamics Commons™
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- Graphene (2)
- Asymptotics (1)
- Bifurcation (1)
- Boundary value problem (1)
- Buckling (1)
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- Carbon Nanotubes (1)
- Computational (1)
- Coupled differential equations (1)
- Equilibrium Structures (1)
- Interaction forces (1)
- Langevin Model (1)
- Math Model (1)
- Mechanics (1)
- Molecular Dynamics (1)
- Nanostructures (1)
- Optimal control (1)
- Rigid Substrates (1)
- Shallow lake (1)
- Simulation (1)
- Water (1)
- Wetting (1)
Articles 1 - 5 of 5
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith
Buckling Loads Of A Graphene Layer Interacting With Rigid Substrates, Bradley Beckwith
Williams Honors College, Honors Research Projects
The goal of this project is to formulate a model that can predict the buckling of a graphene layer between two rigid substrates. The model will predict the buckling of the graphene layer when it is parallel to the substrates and an edge load is applied to the ends of the layer. Our main focus is to use the model to predict buckling loads given different assumptions for interaction forces between the graphene layer and the substrates. For this project continuum modeling will be used to create a model for the graphene buckling problem. This modeling leads to a total …
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Supercritical And Subcritical Pitchfork Bifurcations In A Buckling Problem For A Graphene Sheet Between Two Rigid Substrates, Jake Grdadolnik
Williams Honors College, Honors Research Projects
In this paper we study a model of the buckling of a sheet of graphene between two rigid substrates. We seek to understand the buckling of the sheet as the substrate separation is varied with a fixed load on each end of the sheet. We write down the expression for total energy of the system and from it derive a 2-point nonlinear boundary-value problem whose solutions are equilibrium configurations of the sheet. We cannot get an explicit solution. Instead, we perform a bifurcation analysis by using asymptotics to approximate solutions on the bifurcating branches near the bifurcation points. The bifurcating …
Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera
Equilibrium Structures And Thermal Fluctuations In Interacting Monolayers, Emmanuel Rivera
Williams Honors College, Honors Research Projects
Coherency strains appear in interacting atomic monolayers due to differing bond lengths, which can arise from different materials or geometries. Examples include extended monolayers interacting with a substrate and the interacting walls of a multi-walled carbon nanotube. These strains can induce various equilibrium configurations, which we will analyze by means of a phenomenological model that incorporates forces from bond stretching and bending within each layer and the weak van der Waals interactions connecting the separate layers. We vary the strengths of each interaction to explore their effects on equilibrium structures, and the specific case of a two-walled carbon nanotube is …
Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans
Understanding The Nature Of Nanoscale Wetting Through All-Atom Simulations, Oliver Evans
Williams Honors College, Honors Research Projects
The spreading behavior of spherical and cylindrical water droplets between 30Å and 100Å in radius on a sapphire surface is investigated using all-atom molecular dynamics simulations for durations on the order of tens of nanoseconds. A monolayer film develops rapidly and wets the surface, while the bulk of the droplet spreads on top of the monolayer, maintaining the shape of a spherical cap. Unlike previous simulations in the literature, the bulk radius is found to increase to a maximum value and receed as the monolayer continues to expand. Simple time and droplet size dependence is observed for monolayer radius and …
Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones
Using A Coupled Bio-Economic Model To Find The Optimal Phosphorus Load In Lake Tainter, Wi, Mackenzie Jones
Williams Honors College, Honors Research Projects
In Dunn County, Wisconsin the lakes suffer from algae blooms due to excess phosphorus runoff. A coupled bio-economic model is studied with the intent of finding the optimal level of phosphorus that should be allowed into the lake depending on certain biologic and economic parameters. We model the algae and phosphorus concentration in the lake over time based off the phosphorus input. Community welfare is modeled by comparing the costs and benefits of phosphorus fertilizer. This model is proposed to find the phosphorus level that maximizes community welfare and then determine how certain environmental and social change initiatives will affect …