6 papers
First-Passage Times for the Space-Fractional Spectral Fokker-Planck Equation
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +1
We extend the random walk framework to include compounded steps, providing first-passage time (FPT) properties for a new class of superdiffusive processes, which are governed by th…
Causal Discovery via Simultaneous DAG Recovery Using the Angles Space of Directional Dependence Measures
JD Opdyke
Most causal discovery algorithms utilizing a Directed Acyclic Graph (DAG) framework execute sequentially (e.g. constraint-based models) or iteratively (e.g. score-based or function…
A compounded random walk for space-fractional diffusion on finite domains
Christopher N. Angstmann, Daniel S. Han, Bruce I. Henry +2
We formulate a compounded random walk that is physically well defined on both finite and infinite domains, and samples space-dependent forces throughout jumps. The governing evolut…
Finite Time Blowup of Integer- and Fractional-Order Time-Delayed Diffusion Equations
Christopher N. Angstmann, Stuart-James M. Burney, Daniel S. Han +3
In this work, exact solutions are derived for an integer- and fractional-order time-delayed diffusion equation with arbitrary initial conditions. The solutions are obtained using F…
Exact Solutions of Time-Delay Integer- and Fractional-Order Advection Equations
Christopher N. Angstmann, Stuart-James M. Burney, Daniel S. Han +2
Transport phenomena play a vital role in various fields of science and engineering. In this work, exact solutions are derived for advection equations with integer- and fractional-o…
A Stochastic Simulation Method for Fractional Order Compartment Models
Christopher N. Angstmann, Stuart-James M. Burney, Bruce I. Henry +3
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models tha…