Merlin Pelz
Welcome to my personal website! I'm a Ph.D. candidate in Applied Mathematics at the University of British Columbia, advised by Prof. Michael J. Ward and Prof. Daniel Coombs. In my work, I'm focusing on further developing mathematical biology with nonlinear dynamics, asymptotic analysis and (S)PDE theory. Specifically, we are currently working on the emergence of symmetry-breaking in compartmental-reaction diffusion systems.
Short CV
Education
| Year | University | Degree | Advisors |
|---|---|---|---|
| 2020 – now | University of British Columbia | Ph.D. (Appl. Mathematics) | Prof. Michael J. Ward & Prof. Daniel Coombs |
| 2017 – 2019 | Technical University of Munich | M.Sc. (Mathematics) | Prof. Mary Silber & Prof. Christian Kühn |
| 2013 – 2017 | University of Bayreuth | B.Sc. (Technomathematics) | Prof. Anton Schiela |
Further Research & Work Experience
Research
Here is a selection of figures to my research. For the corresponding developed theory, please go to the tab Publications. The figures for the 1-D domain were created with Julia and the figures for the 2-D domain with FlexPDE. Intracellular kinetics used are FitzHugh-Nagumo, Gierer-Meinhardt and Rauch-Millonas reaction kinetics.
Symmetry-breaking in periodic 1-D domain with two compartments with FitzHugh-Nagumo kinetics. © Merlin Pelz
Convergence to symmetry-broken state in periodic 1-D domain with two compartments with Rauch-Millonas kinetics. © Merlin Pelz
Convergence to asymmetric state for which one cell is up- and two cells downregulated ("silenced") in periodic 1-D domain with cell Gierer-Meinhardt reaction kinetics. © Merlin Pelz
Bifurcation diagram showing degenerate pitchfork bubble in which stable symmetry-breaking takes place, no-flux 2-D domain with two Rauch-Millonas cells. Hysteresis occurs. © Merlin Pelz
Asymmetric steady-state in no-flux 2-D domain with two diffusion-coupled Gierer-Meinhardt cells. © Merlin Pelz
Numerical experiment: pattern formation in the no-flux 2-D domain with three big and close diffusion-coupled cells with Gierer-Meinhardt reaction kinetics. © Merlin Pelz
Convergence to stochastic attractor after stochastic bifurcation point in periodic 1-D domain with two nonlinearly randomly perturbed Rauch-Millonas cells. © Merlin Pelz
Publications
Articles
2022
Symmetry-Breaking Bifurcations for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities in 2-D by M. P. & Michael J. Ward
The Emergence of Spatial Patterns for Compartmental Reaction Kinetics Coupled by Two Bulk Diffusing Species with Comparable Diffusivities by M. P. & Michael J. Ward
A δf PIC Method with Forward-Backward Lagrangian Reconstructions by Martin Campos Pinto & M. P. & Pierre-Henri Tournier
Talks
2023
SIAM PNW Conference: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DSMB Annual Meeting: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DDynamical Systems in the Life Sciences: invited poster presentation
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DCAIMS Annual Meeting: invited talk
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DSIAM DS23: jumped in
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-DUBC & University of Utah Mathematical Biology Seminar
Title: The Emergence of Spatial Patterns with Diffusion-Coupled Compartments with Activator-Inhibitor Kinetics in 1-D and 2-D
Teaching
| Year | Course | Role |
|---|---|---|
| 2023 | Calculus 2 | Small Class Instructor (4⋅60 students per week) |
| 2022 | Differential Equations for Mechanical Engineers | Tutorial Leader (4⋅30 students per week) |
Contact
For email contact, please use merlinpelz {at} math.ubc.ca.