Tootfinder

This https://arxiv.org/abs/2311.04443 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrodinger equations
The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrodinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on …

Self Supervised Learning for Improved Calibrationless Radial MRI with NLINV-Net
Moritz Blumenthal, Chiara Fantinato, Christina Unterberg-Buchwald, Markus Haltmeier, Xiaoqing Wang, Martin Uecker
https://arxiv.org/abs/2402.06550

Self Supervised Learning for Improved Calibrationless Radial MRI with NLINV-Net
Purpose: To develop a neural network architecture for improved calibrationless reconstruction of radial data when no ground truth is available for training. Methods: NLINV-Net is a model-based neural network architecture that directly estimates images and coil sensitivities from (radial) k-space data via non-linear inversion (NLINV). Combined with a training strategy using self-supervision via data undersampling (SSDU), it can be used for imaging problems where no ground truth reconstructions a…

This https://arxiv.org/abs/2307.05292 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_nli…

Self-similarity of rogue wave generation in gyrotrons: Beyond the Peregrine breather
Within the framework of numerical simulations, we study the gyrotron dynamics under conditions of a significant excess of the operating current over the starting value, when the generation of electromagnetic pulses with anomalously large amplitudes (``rogue waves'') can be realized. The averaged shape of high-power pulses is shown to be very close to the celebrated Peregrine breather. At the same time, we demonstrate that the relation between peak power and duration of rogue waves is self-simil…

This https://arxiv.org/abs/2403.01667 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reaction-diffusion models of biological invasion: Open source computational tools, key concepts and analysis
This review provides open-access computational tools that support a range of mathematical approaches to analyse three related scalar reaction-diffusion models used to study biological invasion. Starting with the classic Fisher-Kolmogorov (Fisher-KPP) model, we illustrate how computational methods can be used to explore time-dependent partial differential equation (PDE) solutions in parallel with phase plane and regular perturbation techniques to explore invading travelling wave solutions moving…

A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping
Arthur Barbosa, Najib Kacem, Noureddine Bouhaddi
https://arxiv.org/abs/2403.05176

A design methodology for nonlinear oscillator chains enabling energy localization tuning and soliton stability enhancement with optimal damping
In this paper, the vibration energy localization in coupled nonlinear oscillators is investigated, based on the creation of standing solitons. The main objective is to establish a design methodology for mechanical lattices using the Nonlinear Schrödinger Equation (NLSE) as a guide strategy, even in the presence of damping. A three-dimensional diagram is used to illustrate stable parameter regions for damped stationary solitons. Moreover, an analysis of the influence of the number of oscillator…

This https://arxiv.org/abs/2403.01667 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reaction-diffusion models of biological invasion: Open source computational tools, key concepts and analysis
This review provides open-access computational tools that support a range of mathematical approaches to analyse three related scalar reaction-diffusion models used to study biological invasion. Starting with the classic Fisher-Kolmogorov (Fisher-KPP) model, we illustrate how computational methods can be used to explore time-dependent partial differential equation (PDE) solutions in parallel with phase plane and regular perturbation techniques to explore invading travelling wave solutions moving…

This https://arxiv.org/abs/2403.01667 has been replaced.
link: https://scholar.google.com/scholar?q=a

Reaction-diffusion models of biological invasion: Open source computational tools, key concepts and analysis
This review provides open-access computational tools that support a range of mathematical approaches to analyse three related scalar reaction-diffusion models used to study biological invasion. Starting with the classic Fisher-Kolmogorov (Fisher-KPP) model, we illustrate how computational methods can be used to explore time-dependent partial differential equation (PDE) solutions in parallel with phase plane and regular perturbation techniques to explore invading travelling wave solutions moving…