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Full-Text Articles in Applied Mathematics
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
Examining Bias Against Women In Professional Settings Through Bifurcation Theory, Lauren Cashdan
CMC Senior Theses
When it comes to women in professional hierarchies, it is important to recognize the lack of representation at the higher levels. By modeling these situations we hope to draw attention to the issues currently plaguing professional atmospheres. In a paper by Clifton et. al. (2019), they model the fraction of women at any level in a professional hierarchy using the parameters of hiring gender bias and internal homophily on behalf of the applicant. This thesis will focus on a key theory in Clifton et. al.’s analysis and explain its role in the model, specifically bifrucation analysis. In order to analyze …
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
A Bifurcation Theorem And Applications, Alfonso Castro, Jorge Cossio
All HMC Faculty Publications and Research
In this paper we give a sufficient condition on the nonlinear operator N for a point (λ, u) to be a local bifurcation point of equations of the form u + λL-1(N(u)) = 0, where L is a linear operator in a real Hilbert space, L has compact inverse, and λ ∈ R is a parameter. Our result does not depend on the variational structure of the equation or the multiplicity of the eigenvalue of the linear operator L. Applications are made to systems of differential equations and to the existence of periodic solutions of nonlinear second order …
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
Stability Of Steady Cross-Waves: Theory And Experiment, Seth Lichter, Andrew J. Bernoff
All HMC Faculty Publications and Research
A bifurcation analysis is performed in the neighborhood of neutral stability for cross waves as a function of forcing, detuning, and viscous damping. A transition is seen from a subcritical to a supercritical bifurcation at a critical value of the detuning. The predicted hysteretic behavior is observed experimentally. A similarity scaling in the inviscid limit is also predicted. The experimentally observed bifurcation curves agree with this scaling.