Jun 18 – 23, 2023
University of New Brunswick
America/Halifax timezone
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(U*) Numerically Solving Fast-Oscillating Integrals

Jun 19, 2023, 3:00 PM
15m
UNB Tilley Hall (Rm. 5 (max. 70))

UNB Tilley Hall

Rm. 5 (max. 70)

Oral Competition (Undergraduate Student) / Compétition orale (Étudiant(e) du 1er cycle) Theoretical Physics / Physique théorique (DTP-DPT) (DTP) M2-2 Gravity and Cosmology and Astrophysics | Gravité, cosmologie et astrophysique (DPT)

Speaker

Mr Naman Jain (McMaster University)

Description

We use a novel approach to numerically calculate Fast-Oscillating Integrals (FOI) using the Picard-Lefschetz theory. In this theory, analytic oscillatory integrals are converted into sums of convex integrals by deforming the integration domain in the complex plane. Feldbrugge, Pen, and Turok 2019 introduced a new numerical integrator to evaluate the interference effects near caustics in lenses in one dimension. Recent studies have also used this numerical integrator to study lensing of gravitational waves as well, however one shortcoming of the integrator is that it is not optimal. In this work, we optimize the convergence to desired contours in the complex plane and further generalize the algorithm to work for random functions that appear in various physical applications like scintillation of radio signals in astrophysical sources.

Keyword-1 fast oscillating integrals
Keyword-2 picard lefschetz theory

Primary author

Mr Naman Jain (McMaster University)

Co-author

Dr Sergey Sibriyakov (McMaster University)

Presentation materials

There are no materials yet.