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The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity (2023)
Journal Article

We study the dynamics of the non-local Lotka-Volterra system ut=Duuxx+u(1-φ - u-αv), vt=Dvvxx+v(1-φ - v-βu), where a star denotes the spatial convolution and the kernel φ is a top hat function. We initially focus on the case of small, equal diffusivi... Read More about The non-local Lotka-Volterra system with a top hat kernel - Part 1: dynamics and steady states with small diffusivity.

A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem (2023)
Journal Article

High demand for components with complex geometries at macro and micro levels drives the development of additive manufacturing (AM). However, the scientific basis for designing energy beam scanning strategies (e.g. beam scanning speed, beam path, beam... Read More about A rational approach to beam path planning in additive manufacturing: the inverse heat placement problem.

The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics (2023)
Journal Article

In this paper, we consider the classical Riemann problem for a generalized Burgers equation, u t + h α ( x ) u u x = u x x , $$\begin{equation*} u_t + h_{\alpha }(x) u u_x = u_{xx}, \end{equation*}$$ with a spatially dependent, nonlinear sound speed,... Read More about The Riemann problem for a generalized Burgers equation with spatially decaying sound speed. I Large‐time asymptotics.