arXiv subjects

Laura Huynh

Publications and source records attributed to Laura Huynh.

3 recordsLinked to original sources

arXiv2026

Nonlinear Inverse Iterations for Spin-Orbit Coupled Quantum Gases

This work concerns the computation of ground states of two-component spin-orbit coupled Bose-Einstein condensates (SO-coupled BECs), modelled by a coupled nonlinear eigenvalue problem of Gross-Pitaevskii type. Spin-orbit coupling gives rise to fascinating phenomena, including supersolid-like phases with spatially modulated densities. However, in such complex settings, conventional numerical approaches, such as generalized inverse iterations or gradient descent, often converge very slowly. To overcome this issue, we apply the concept of the J-method [E.~Jarlebring, S.~Kvaal, W.~Michiels. SIAM~J.~Sci.~Comput.~36-4,~2014] to construct a nonlinear inverse iteration scheme whose convergence can be accelerated through spectral shifting, analogous to techniques used for linear eigenproblems. For a fixed shift parameter, we establish local linear convergence rates determined by spectral gaps in the neighbourhood of each quasi-unique ground state. With adaptively chosen shifts, superlinear convergence is observed, which we verify through numerical experiments.

math.NA↗

arXiv2025

Metric-driven numerical methods

In this paper, we explore the concept of metric-driven numerical methods as a powerful tool for solving various types of multiscale partial differential equations. Our focus is on computing constrained minimizers of functionals - or, equivalently, by considering the associated Euler-Lagrange equations - the solution of a class of eigenvalue problems that may involve nonlinearities in the eigenfunctions. We introduce metric-driven methods for such problems via Riemannian gradient techniques, leveraging the idea that gradients can be represented in different metrics (so-called Sobolev gradients) to accelerate convergence. We show that the choice of metric not only leads to specific metric-driven iterative schemes, but also induces approximation spaces with enhanced properties, particularly in low-regularity regimes or when the solution exhibits heterogeneous multiscale features. In fact, we recover a well-known class of multiscale spaces based on the Localized Orthogonal Decomposition (LOD), now derived from a new perspective. Alongside a discussion of the metric-driven approach for a model problem, we also demonstrate its application to simulating the ground states of spin-orbit-coupled Bose-Einstein condensates.

math.NA↗

arXiv2023

Bubble Cloud Characteristics and Ablation Efficiency in Dual-Frequency Intrinsic Threshold Histotripsy

Histotripsy is a non-thermal focused ultrasound ablation method that destroys tissue through the generation and activity of acoustic cavitation. Intrinsic threshold histotripsy generates bubble clouds when the dominant negative pressure phase of a single-cycle pulse exceeds an intrinsic threshold of ~25-30 MPa. The ablation efficiency is dependent upon the size and density of bubbles within the bubble cloud. This work investigates the effects of dual-frequency pulsing schemes on the bubble cloud behavior and ablation efficiency in intrinsic threshold histotripsy. A modular histotripsy transducer applied dual-frequency histotripsy pulses to tissue phantoms with a 1:1 pressure ratio from 500 kHz and 3 MHz frequency elements and varying the 3 MHz pulse arrival relative to the arrival of the 500 kHz pulse (-100 ns, 0 ns, and +100 ns). High-speed optical imaging captured cavitation effects to characterize bubble cloud and individual bubble dynamics. Lesion formation and ablation efficiency were also investigated in red blood cell (RBC) phantoms. Results showed that the single bubble and bubble cloud size for dual-frequency cases were intermediate to published results for the component single frequencies of 500 kHz and 3 MHz. Bubble cloud size and dynamics were also shown to be altered by the arrival time of the 3 MHz pulse relative to the 500 kHz pulse, with more uniform cloud expansion and collapse observed for early (-100 ns) arrival. Finally, RBC phantom experiments showed that dual-frequency exposures were capable of generating precise lesions with smaller areas and higher ablation efficiencies than previously published results for 500 kHz or 3 MHz. Overall, results demonstrate dual-frequency histotripsy's ability to modulate bubble cloud size and dynamics can be leveraged to produce precise lesions at higher ablation efficiencies than previously observed for single-frequency pulsing.

physics.med-ph↗