Kaitlin Hill

Kaitlin Hill
Wake Forest University | WFU · Department of Mathematics

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14
Publications
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111
Citations

Publications

Publications (14)
Article
We develop a path integral framework for determining most probable paths for a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin–Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we conside...
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We develop a path integral framework for determining most probable paths in a class of systems of stochastic differential equations with piecewise-smooth drift and additive noise. This approach extends the Freidlin-Wentzell theory of large deviations to cases where the system is piecewise-smooth and may be non-autonomous. In particular, we consider...
Article
Full-text available
In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea–ice–ocean–atmosphere system. Observations of the FSD are sparse – traditionally taken via a painstaking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and g...
Article
Full-text available
In sea-ice-covered areas, the sea ice floe size distribution (FSD) plays an important role in many processes affecting the coupled sea-ice-ocean-atmosphere system. Observations of the FSD are spare – traditionally taken via a pain-staking analysis of ice surface photography – and the seasonal and inter-annual evolution of floe size regionally and g...
Article
Full-text available
Women have become better represented in business, academia, and government over time, yet a dearth of women at the highest levels of leadership remains. Sociologists have attributed the leaky progression of women through professional hierarchies to various cultural and psychological factors, such as self-segregation and bias. Here, we present a min...
Preprint
Full-text available
Women have become better represented in business, academia, and government over time, yet a dearth of women at the highest levels of leadership remains. Sociologists have attributed the leaky progression of women through professional hierarchies to various cultural and psychological factors, such as self-segregation and bias. Here, we present a min...
Preprint
Full-text available
The recent widespread thaw of permafrost has led to observations of explosive gas emissions, which expel ice and soil debris and leave behind large craters. This phenomenon appears to be caused by a buildup of pressure from below the permafrost, possibly due to gas released as permafrost melts, followed by a sudden emission of gas through the surfa...
Chapter
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During the workshop on Climate Modeling in Nonsmooth Systems, one of the major discussions involved investigating including more realistic elements, such as fluctuations and time variation, in nonsmooth models that undergo a sudden transition, with an emphasis on conceptual climate models. A number of models were discussed, including the Stommel 19...
Article
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As Arctic sea ice extent decreases with increasing greenhouse gases, there is a growing interest in whether there could be a bifurcation associated with its loss, and whether there is significant hysteresis associated with that bifurcation. A challenge in answering this question is that the bifurcation behavior of certain Arctic energy balance mode...
Article
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Models such as those involving abrupt changes in the Earth's reflectivity due to ice melt and formation often use nonlinear terms (e.g., hyperbolic tangent) to model the transition between two states. For various reasons, these models are often approximated by "simplified" discontinuous piecewise-linear systems that are obtained by letting the leng...
Article
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A definition for the Laplace transform corresponding to the nabla difference operator is given. Several properties of this Laplace transform are established. Further, a definition for the discrete nabla Mittag-Leffler function is provided. Our results are then shown to be robust enough to lead to a practical method for solving initial value problem...
Article
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The dynamics of a predator-prey model with continuous threshold policy harvesting functions on the prey is studied. Theoretical and numerical methods are used to investigate boundedness of solutions, existence of bionomic equilibria, and the stability properties of coexistence equilibrium points and periodic orbits. Several bifurcations as well...
Article
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Under certain conditions, derivatives and differences with respect to boundary conditions are studied for solutions of the discrete boundary value problem, w(m + 2) =f(m, w(m), w(m + 1)), w(m_1) = w_1 and w(m_2) − \sum^r_{i=1} \alpha_i w(\eta_i) = w_2, where m_1 <\eta_1 < \eta_1 +1 < · · · < \eta_r <\eta_ r + 1 <m_2 in Z and \alpha_1, . . . , \alph...

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