“Ion-conducting pathways are quasi one-dimensional at short times and evolve into larger, branched structures characterized by a robust fractal dimension $d_f\simeq1.7$.”

“Classical approaches retain high-order accuracy and strong computational efficiency for single-instance problems... Physics-informed neural networks (PINNs) are also able to reproduce qualitative solutions but are generally less accurate and less efficient in low dimensions than classical solvers.”

“The paper finds that for bulk superconductors, the states of the chain are stable for energies lying inside the superconducting gap while in lower-dimensional superconductors phase fluctuations yield finite temperature-dependent lifetimes even inside the gap.”

“The paper constructs standing waves of the NLS equation whose leading-order profile is a modulation of Bloch waves by means of the components of a spinor solving an appropriate cubic nonlinear Dirac (NLD) equation.”

“The paper demonstrates how the Geometric View organizes quantum-mechanical representations and dualities in geometric terms.”

“”

“The article likely discusses the experimental methods used to observe these channels, the materials used, and the properties of the observed channels, such as their conductance and stability.”

“Uniqueness of the solution is established in two cases - the one-dimensional setting and the Gaussian case.”

“Singlet state populations of geminal protons propagate along (CH_2)_n segments forming magnetically silent spin waves.”

“The study likely contributes to the understanding of wave propagation in complex media.”

“The study likely aims to understand how the interplay between trions and excitons affects the optical and electronic properties of the material.”

“The excitation velocities can be calculated from the knowledge of the matrices of compressibility and the Drude weights, as their squares are the eigenvalues of the product of the two matrices.”

“”

“The research focuses on using AI to push the limits of 1D NMR spectroscopy.”