Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT The previously introduced X‐FFT solver permits solving three‐dimensional linear elastic homogenization problems with high accuracy and efficiency. Due to the extended finite element discretization (X‐FEM), matrix‐inclusion problems may be approximated with the error convergence of interface‐conforming finite elements.
Flavia Gehrig, Matti Schneider
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Closed-form spin-relativistic corrections from the Dirac equation enabling a modified Schrödinger solver. [PDF]
Sci RepAmaro MB, Nazeef, Dussech CJ, Qi C.
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Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT We present a numerical study of a weakly symmetric dual‐mixed finite element method for the Stokes source problem, in which the Cauchy stress is the primary unknown and its symmetry is imposed weakly through a vorticity Lagrange multiplier. Viewing the scheme as the incompressible limit of the reduced‐symmetry mixed elasticity framework, we ...
Fleurianne Bertrand, Tugay Dağlı
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Continuation of Periodic Solutions in Conservative Systems Leveraging the First Integral of Motion
Proceedings in Applied Mathematics and Mechanics, Volume 26, Issue 4, December 2026.ABSTRACT Dynamical systems are often analysed with respect to a system parameter, for which numerical continuation methods are typically used. In most cases, dissipative systems are considered. Here, the continuation of periodic solutions requires the existence of an explicit parameter that can be varied during the continuation process.
Julian Vogelei +2 more
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A mathematical analysis of math anxiety dynamics using a classical SAS model: Bridging epidemic theory and pedagogical implications. [PDF]
PLoS OneIslam S, Iqbal D, Saha M, Saha G.
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On the additive image of zeroth persistent homology
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract For a category X$X$ and a finite field F$F$, we study the additive image of the functor H0(−;F)∗:rep(X,Top)→rep(X,VectF)$\operatorname{H}_0(-;F)_* \colon \operatorname{rep}(X, \mathbf {Top}) \rightarrow \operatorname{rep}(X, \mathbf {Vect}_F)$, or equivalently, of the free functor rep(X,Set)→rep(X,VectF)$\operatorname{rep}(X, \mathbf {Set ...
Ulrich Bauer +3 more
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Stability analysis and numerical simulation of nonlocal extended epidemic models using positivity-preserving scheme. [PDF]
Sci RepYousuf M, Alshakhoury N.
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Frequency‐dependent contraction rates for the Bayesian method to the inverse source problem
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This paper addresses an inverse source problem for acoustic waves in a range of frequencies. Our study has two main goals. First, although the problem is severely ill‐posed with a logarithmic stability estimate, we demonstrate, through careful analysis of the forward map's singular values, that increasing the frequency range enhances stability,
Pu‐Zhao Kow, Jenn‐Nan Wang
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Inverse Statistics of Active Matter Trajectories to Distinguish Interaction Kernel Anisotropy from Emergent Correlations. [PDF]
Bull Math BiolMartina-Perez SF.
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Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson +2 more
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