## Requirements

The MS Symposium started in 2008 to give master’s students the opportunity to give their master’s talk. The benefit of the symposium is that many of the logistics (scheduled room, projectors, and free food) are taken care of for you. Students should invite at least two faculty members to attend their talk. A general invitation will also be sent to the department.

MS Symposium talks are 25 minute presentations on a current topic of interest, which goes beyond what is available in amath courses. Most talks are broken up into twenty minutes of speaking and five minutes for questions. The use of electronic slides is required. Previous topics have come from the scientific literature, are the results of original research, or originate from research or reading projects for classes, and relevant senior theses. A few talks from previous years are provided below.

## Master’s Symposium Dates

Each quarter the graduate program assistant will email students with an opportunity to sign up for a presentation time. During the autumn, winter, and spring quarters there will be a full day Master’s Symposium to allow an opportunity for MS students to give final examination talks. The MS Symposium typically occurs 2 to 3 weeks before the end of a quarter. Dates and times of upcoming MS Symposiums can be found on the Applied Mathematics Event Calendar.

For questions, please email the graduate program assistant.

## Previous MS Symposium Talks

Name | Title | Abstract | Slides |
---|---|---|---|

Lincoln Atkinson | An in-place approach to finding lower-bound counterexamples for small Ramsey numbers | Ramsey theory tells us that once N becomes sufficiently large, the edge-colored complete graph on N vertices, ECCG(N), is guaranteed to contain unicolor complete subgraphs of a certain size. Lower bounds for this threshold are typically established by finding some ECCG(k) for which there are no unicolor complete sugbgraphs of the required size. These counterexamples are often generated “bottom-up” by finding smaller counterexamples (which are presumably easier to find) and extending them. In this talk we will discuss results of trying an “in-place” approach, which starts with a full-size ECCG and repeatedly perturbs it, using various heuristics to efficiently reduce (and hopefully vanish) the number of unicolor subgraphs bigger than a certain size. | (pdf) |

Doug Balcom | Beyond Janus and Epimetheus: Momentum Trading Among Co-Orbiting Satellite Groups | Janus and Epimetheus, a pair of small moons of Saturn, exhibit a behavior unique in the known Solar system: they basically share a common orbital path, and avoid colliding by gravitationally exchanging momentum once every 4 years, just as one of the pair is about to overtake the other. Sasha Malinsky modeled this fascinating system numerically for his presentation at the MS Symposium in March 2011, and explored how altering the bodies’ masses and orbital eccentricities would affect the dynamics. Using Malinsky’s work as a reference, I have constructed a similar model and extended it to simulate hypothetical systems of 3 or more co-orbiting satellites. My talk explores the dynamics and stability of such systems, and how they vary with the number of satellites, their relative masses, and other initial conditions. |
(pdf) |

Mauricio Javier Del Razo Sarmina | Pole dynamics | (pdf) | |

Leah Ganis | The Swinging Spring: Regular and Chaotic Motion | Overview of different types of motion in the elastic pendulum, including chaotic regimes. | (pdf) |

Michael Gostintsev | Aircraft Routing Under The Risk of Detection | The talk will discuss how to find an optimal trajectory for a plane so as to avoid detection by hostile radar systems. Specifically, calculus of variations will be used to minimize a functional with a moveable end point and a non-holonomic constraint. There will also be a constraint on trajectory length. | (pdf) |

Crystal Lee | Mathematical Models of the Evolution of Surface Waves on Deep Water | The cubic nonlinear Schrodinger equation in (2+1)-dimensions (NLS) is used as an approximate model of surface waves on deep water. Many generalizations of NLS have been constructed in hopes of more accurately modeling the underlying physical phenomena. I have developed a Mathematica program that solves NLS numerically and transforms the solution into physical coordinates. This code can be used to compare mathematical predictions with experimental data for a wide variety of surface wave experiments. More specifically, mathematical and experimental results from the use of a solitary wave initial condition are compared. | (pdf) movie 1 movie 2 |

Jessica Lundin | A geophysical inverse problem: Interpolating an ice core depth-age relationship from sparse data |
Often Antarctic ice cores can be dated at only a few discrete depths; however, it is desirable to have a physically based interpolation of the depth-age relationship between the sparse dated points. Piece-wise linear or spline interpolations in the depth-age domain can introduce serious error in the implied accumulation-rate history, because they do not properly account for the variation of dynamical strain with depth due to ice flow, and they do not account for temporal changes in accumulation rate. Our forward problem uses a transient one-dimensional kinematic ice-flow model that produces a depth-age relationship, for specified histories of ice thickness, divide migration, and accumulation rate. We use an inverse method to determine a smooth accumulation-rate history that reproduces the measured depth-age data at a tolerance specified by data uncertainty. In comparison with direct interpolations in the depth-age domain, our inferred accumulation-rate history produces a more physically realistic interpolation of the measured depth-age data, without spurious accumulation-rate events. Here, we produce a continuous depth-age relation for the Siple Dome ice core from layer-counted ages and sparse ages of occluded gases (CH4 and O2), from 98ky to present. Accumulation rate and thinning function pairs vary widely depending on the surface elevation history. Using this kinematic approach, the unique accumulation rate and thinning function pair is not determined. All possible pairs, from different surface elevation and ice divide histories, produce identical depth-age relationships and layer thickness patterns. | (pdf) |

Mark Richards | Melnikov’s method | Theory and application of a perturbative method to determine the existence of chaotic dynamics. | (pdf) |

Konrad Schroder | Developing a Mean-Field Model for Ephaptically Connected Nerve Bundles | Current signal transmission models of nerve fibers are based on the Hodgkins-Huxley experiments on the squid giant axon, assuming no interaction between nearby nerve fibers. We present an improved model that incorporates such an ephaptic interaction, and examine the effects of this connection on the characteristics of the transmitted signal. | (pdf) |

Peizhe Shi | A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition by Lawrence R. Rabiner from Proceedings of the IEEE, vol 77, No 2, February 1989. |
I’m going to talk about hidden Markov model in MS symposium. This model considers a Markov process in which the states are hidden while some signals are observable. The signals, which is also stochastic, come up according to a certain probability distribution corresponding to the underlying states. In this talk, I will describe the model, pose three basis problems of the model and introduce the methods to solve these problems. As you will see, we’ll have some powerful methods to infer the hidden states based on what we see. | (pdf) |

Sam Stapleson | Minimizing Energy Functionals to Model Helical Structures | There has been much research involving helical models. This is especially the case in the area of modeling nucleic acids and other protein structures. By using classical methods from the calculus of variations, one can analyze the properties of these helices and the associated energy densities. This is done by minimizing energy, assumed to depend on curvature and torsion of the curveand their first derivatives. | (ppt) (pdf) (pptx) |

Hallie Torrey | Wave-induced changes in beach profile and porous flow | Understanding the effects of ocean waves on a beach is key to developing research in specialties such as geomorphology, marine ecology, coastal engineering, and groundwater hydrology. Without considering large storms and other natural (or unnatural) phenomena, there are still cyclical changes in tide and storm frequency; for instance, beaches “disappear” in the winter and are “built” in the summer. The erosion/deposition of a beach and the fluid flow within the beach depends, in the least, on properties of the incident waves, properties of the sediment, and the shape of the beach. Small-scale laboratory experiments were carried out to consider the effects of normally incident waves on a beach profile and the dynamics above, under, and at the sediment-water interface. With controlled regular waves, a quasi-steady beach profile was achieved. Dye was used to track both the streamlines within the beach and the dense layers of mixed sand and water. Wells were created to estimate the horizontal pressure gradient in the beach. Research is ongoing, and a source-sink type model is currently under experimental review. | (ppt) (pdf) |

Tom Trogdon | Ostragradskii’s Theorem: Extending The Legendre Transformation | Depending on the application, converting a Lagrangian system to a Hamiltonian system can bring some benefits. Generally, the most important benefit is giving access to a Poisson bracket and thus, better information about conserved quantities. The conversion is straightforward when the Lagrangian depends on the functions and their first derivatives. What do we do when we have higher-order derivatives? That’s where Ostragradskii’s theorem comes in. | (pdf) |

Joy Zhou | Hydraulic Design of Pine Needles | The authors determined the optimal distribution of water transport capacity per given investment in xylem permeability along the needle that either minimizes pressure drop or maximizes needle length. They tested their theory by comparing the hydraulic design of three pine species that differ in needle length. In all three species, the distribution of water transport capacity was similar to their prediction, and the needles of Pinus palustris showed an almost perfect match. | (pdf) |

Laura Zuchlewski | Cicadas | The cicada is an insect that has a dormancy period of either 13 or 17 years, depending on the species. After spending 17 years underground growing, they emerge for 2 weeks as adults to mate and die. Their patterns of emergence can be modeled using differential equations and stochastics. | (pdf) (ppt) |