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Non-self-adjoint sixth-order eigenvalue problems arising from clamped elastic thin films on closed domains
N C Papanicolaou, I C Christov
https://arxiv.org/abs/2508.01952 https:…

Non-self-adjoint sixth-order eigenvalue problems arising from clamped elastic thin films on closed domains
Sixth-order boundary value problems (BVPs) arise in thin-film flows with a surface that has elastic bending resistance. We consider the case in which the elastic interface is clamped at the lateral walls of a closed trough and thus encloses a finite amount of fluid. For a slender film undergoing infinitesimal deformations, the displacement of the elastic surface from its initial equilibrium position obeys a sixth-order (in space) initial boundary value problem (IBVP). To solve this IBVP, we con…

Data-Driven Transient Growth Analysis
Zhicheng Kai, Peter Frame, Aaron Towne
https://arxiv.org/abs/2507.02525 https://arxiv.org/pdf/2…

Data-Driven Transient Growth Analysis
The transient growth of disturbances made possible by the non-normality of the linearized Navier-Stokes equations plays an important role in bypass transition for many shear flows. Transient growth is typically quantified by the maximum energy growth among all possible initial disturbances, which is given by the largest squared singular value of the matrix exponential of the linearized Navier-Stokes operator. In this paper, we propose a data-driven approach to studying transient growth wherein …

Generalized Schur partition functions and RG flows
Anirudh Deb, Shlomo S. Razamat
https://arxiv.org/abs/2506.13764 https://arxiv.org/…

Generalized Schur partition functions and RG flows
We revisit a double-scaled limit of the superconformal index of ${\cal N}=2$ superconformal field theories (SCFTs) which generalizes the Schur index. The resulting partition function, $\hat {\cal Z}(q,α)$, has a standard $q$-expansion with coefficients depending on a continuous parameter $α$. The Schur index is a special case with $α=1$. Through explicit computations we argue that this partition function is an invariant of certain mass deformations and vacuum expectation value (vev) deformat…

Operator Splitting Methods: Numerical Solutions of Ordinary Differential Equations via Separation of Variables
A. Banjara, I. AlJabea, T. Papamarkou, F. Neubrander
https://arxiv.org/abs/2506.17524

Operator Splitting Methods: Numerical Solutions of Ordinary Differential Equations via Separation of Variables
This paper applies the concept of linear semigroups induced by nonlinear flows, originally developed by Dorroh and Neuberger in the 1990s, to the approximation of uniquely solvable initial value problems for nonlinear ordinary differential equations. Building on a framework rooted in the earlier works of Lie, Kowalewski, and Groebner, we analyze nonlinear systems through the lens of the Koopman-Lie semigroup exp(tK), where K is the linear Lie generator associated with the flow induced by the no…