Tootfinder

Sub-supersolutions method for singular quasilinear systems involving gradient terms
Abdelkrim Moussaoui
https://arxiv.org/abs/2508.06359 https://arxiv.org/…

Sub-supersolutions method for singular quasilinear systems involving gradient terms
Existence, regularity and location of solutions to quasilinear singular elliptic systems with general gradient dependence are established developing a method of sub-supersolution. The abstract theorems involving sub-supersolutions are applied to prove the existence of positive solutions for convective and absorption singular systems.

Adaptive control mechanisms in gradient descent algorithms
Andrea Iannelli
https://arxiv.org/abs/2508.19100 https://arxiv.org/pdf/2508.19100

Adaptive control mechanisms in gradient descent algorithms
The problem of designing adaptive stepsize sequences for the gradient descent method applied to convex and locally smooth functions is studied. We take an adaptive control perspective and design update rules for the stepsize that make use of both past (measured) and future (predicted) information. We show that Lyapunov analysis can guide in the systematic design of adaptive parameters striking a balance between convergence rates and robustness to computational errors or inexact gradient informa…

Delayed transitions, promoted states and multistability in a pressure-driven nematic under an electric field
G. McKay, N. J. Mottram
https://arxiv.org/abs/2508.14826 https://

Delayed transitions, promoted states and multistability in a pressure-driven nematic under an electric field
We consider the effects of an applied pressure gradient on the classical Freedericksz transition, finding a delayed transition, the promotion of particular director configurations and even pressure-induced multistability. Using the theoretical framework developed by Ericksen and Leslie, we find that the applied pressure gradient adapts the normal pitchfork bifurcation at critical applied voltage, leading to both a delayed bifurcation to higher voltages and a transformation from a supercritical …

The Trinity-One PeV-Neutrino Telescope
David A. Raudales O., A. Nepomuk Otte, D. R. Bergman, J. Bogdan, A. M. Brown, M. Doro, M. Fedkevych, F. Giordano, C. Hao, D. Kieda, M. Mariotti, Y. Onel, E. Schapera, D. Soldin, W. Springer, S. Stepanoff, I. Taboada, K. Tran
https://arxiv.org/abs/2509.18237

Near-resonant nuclear spin detection with megahertz mechanical resonators
Diego A. Visani, Letizia Catalini, Christian L. Degen, Alexander Eichler, Javier del Pino
https://arxiv.org/abs/2508.14754

Near-resonant nuclear spin detection with megahertz mechanical resonators
Mechanical resonators operating in the megahertz range have become a versatile platform for fundamental and applied quantum research. Their exceptional properties, such as low mass and high quality factor, make them also appealing for force sensing experiments. In this work, we propose a method for detecting, and ultimately controlling, nuclear spins by coupling them to megahertz resonators via a magnetic field gradient. Dynamical backaction between the sensor and an ensemble of $N$ nuclear spi…