arXiv subjects

Kjell S. Heinrich

Publications and source records attributed to Kjell S. Heinrich.

3 recordsLinked to original sources

arXiv2026

Exact dispersion relation for linear surface waves on arbitrary vertical shear

We derive the formal solution to the dispersion relation for linear surface waves on a horizontal mean current with arbitrary vertical dependence. The problem is cast in a Green's function framework for the Rayleigh equation, neglecting viscosity but making no further approximations about the mean velocity profile. The solution is the dispersion relation in the form of a single, implicit equation relating -- and containing only -- the velocity profile, wave frequency, and wavenumber. By isolating curvature effects in a path-ordered exponential, we obtain a solution that serves as a natural starting point for systematic approximations. We demonstrate that our solution reduces to the expression found by Shrira (1993, J. Fluid Mech. 252, 565--584) in the deep-water limit, yields known asymptotic approximations, and recovers known analytical solutions in special cases.

physics.flu-dyn↗

arXiv2025

Rediscovering shallow water equations from experimental data

New data-driven methods have advanced the discovery of governing equations from observations, enabling parsimonious models for complex systems. Here, we 'rediscover' a shallow-water equation closely related to Korteweg--de Vries (KdV) using only video recordings of solitons in a simple flume. Two fundamentally different approaches -- weak-form sparse identification of nonlinear dynamics (WSINDy) and a novel Fourier-multiplier method -- recover the same PDE, demonstrating that the equation is inherent in the data and robust to the choice of method. Both identify the same terms with comparable magnitudes and errors. To validate the models, we solve the discovered equations forward in time and compare them with additional experimental cases that were not used in the discovery. Based on the results, we discuss absolute and cumulative errors, as well as the strengths and limitations of the two discovery approaches. Together, these results demonstrate the potential of equation discovery from everyday experiments ('GoPro physics') and highlight shallow-water waves as an ideal test bed for developing and benchmarking new methods.

physics.flu-dyn↗

arXiv2025

Bending-strain effects in conventional superconductors and superconducting junctions

We consider the effect of bending-strain in thin films of clean, conventional superconductors (S), and the proximity-induced effect of this strain in SN bilayers with a normal metal (N), and SNS junctions with equal curvatures in each superconductor. We find that the effective spin-orbit coupling due to strain in the superconductor induces both spin-polarized and unequal-spin even-frequency p-wave triplet pairings throughout the superconductor. When interfaced with a normal metal, additional odd-frequency pairings are induced, and their magnitudes can be tuned with the strain. In SNS junctions, the strain alone can induce a superconducting spin current in the junction. The spin-polarized current can undergo a $0-π$-transition, resulting in an in-plane, strain-induced magnetization that switches sign as a function of the strain. We discuss the underlying physics and its implications for superconducting spintronics.

cond-mat.supr-con↗