Physics

Title of thesis:&nbsp;<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;">Rare Events in Reaction-Diffusion Systems
<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;">Subtitle:<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;"> Field-theoretical Approximations and Monte Carlo Simulations<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;">
<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;">Abstract: 
Rare events are events that have near-zero probability of occurring. Despite their apparent irrelevance, when they do occur, they can have substantial, and even catastrophic, repercussions. In this thesis, we study rare events in reaction-diffusion systems, a class of mathematical models which finds various applications in physics and life sciences. In particular, we employ both theoretical and computational methods to determine the tails of the probability distribution describing the state of system.
Firstly, we follow pre-existing literature to derive an equivalent quantum-mechanical description for entirely classical reaction-diffusion systems, called Doi-Peliti formalism. We express the time evolution of the systems as a Feynman path integral, which we then evaluate at the saddle point to obtain a semiclassical approximation for the probability distribution and a closed-form leading-order expression for the tails.
Secondly, we tailor a lesser-known Monte Carlo algorithm for rare probability estimation, called adaptive multilevel splitting, to compute the probability distribution of reaction-diffusion processes. We derive some theoretical results regarding its efficiency, discuss practical implementation choices, and benchmark its performance against well-understood examples.
Finally, we compare the semiclassical approximation to the computational results, determining under which conditions the former succeeds or fails.
Examiner: Johannes Hofmann Supervisor: Johannes Hofmann Opponent: Hanwen Ge
<span style="font-size: 12.0pt; font-family: 'Aptos',sans-serif; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-bidi-font-family: Aptos; color: black; mso-ansi-language: SV; mso-fareast-language: SV; mso-bidi-language: AR-SA;">Location of presentation: <a rel="noopener" href="https://maps.chalmers.se/#495a8bdb-ae0d-4c94-8be5-68240f9a5686" target="_blank" title="Chalmers maps" data-anchor="#495a8bdb-ae0d-4c94-8be5-68240f9a5686">von Bahr, Soliden floor 3</a>

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Presentation of master thesis

Master thesis presentations at Physics

December 18 2024

16:00- 17:00 Edoardo Maria Manoni, MPCAS