Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2609.28701

Equivalence Groups of Inhomogeneous Hyperelasticity

Saadet S. Özer
View original source ↗Read source document ↗Export metadata ↓

Abstract

Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.

Explore related subjects

math-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Saadet S. Özer. 2026-09-23. Equivalence Groups of Inhomogeneous Hyperelasticity. https://doi.org/10.1007/s10659-026-10231-2

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Superized Leznov-Saveliev equations as the zero-curvature condition on a reduced connection

The equations of open 2-dimensional Toda lattice (TL) correspond to Leznov-Saveliev equations (LSE) interpreted as zero-curvature Yang-Mills equations on the variety of $O(3)$-orbits on the Minkowski space when the gauge algebra is the image of $\mathfrak{sl}(2)$ under a principal embedding into a simple finite-dimensional Lie algebra $\mathfrak{g}(A)$ with Cartan matrix $A$. The known integrable super versions of TL equations correspond to matrices $A$ of two different types. I interpret the super LSE of one type 1 as zero-curvature equations for the \textit{reduced} connection on the non-integrable distribution on the supervariety of $OSp(1|2)$-orbits on the $N=1$-extended Minkowski superspace; the Leznov-Saveliev method of solution is applicable only to $\mathfrak{g}(A)$ finite-dimensional and admitting a superprincipal embedding $\mathfrak{osp}(1|2)\to\mathfrak{g}(A)$. The simplest LSE1 is the super Liouville equation; it can be also interpreted in terms of the superstring action. Olshanetsky introduced LSE2 -- another type of equations of super TL. Olshanetsky's equations, as well as LSE1 with infinite-dimensional $\mathfrak{g}(A)$, can be solved by the Inverse Scattering Method. To interpret these equations remains an open problem, except for the super Liouville equation -- the only case where these two types of LSE coincide. I consider also the ($N>1$)-extended versions of super Liouville equations, why $N\leq 4$, related superprincipal embeddings $\mathfrak{osp}(N|2)\to\mathfrak{g}(A)$ and the interpretation of LSE as a condition on a reduced connection applies, same as for $N=1$. I also review related less known and less popular mathematical constructions involved.

math-ph↗
arXiv2026

Uniform Hyperbolicity, Bandgaps and Edge Modes in Aperiodic Systems of Subwavelength Resonators

We aim to characterise the spectral distributions of bi-infinite, semi-infinite, and finite aperiodic one-dimensional arrays of subwavelength resonators, constructed by sampling from a finite library of building blocks. By adopting the modern formalism of uniform hyperbolicity, we are able to strengthen and rigorously prove a Saxon-Hutner-type result, characterising the spectral gaps of the composite bi-infinite aperiodic system in terms of its constituent blocks through a strict multicone criterion. Crucial to this approach is a change of basis from transfer matrices to propagation matrices, allowing for a block-level characterisation. This approach also enables an explicit characterisation of edge-induced eigenmodes in the semi-infinite setting. Finally, we leverage finite section methods for Jacobi operators to extend our results to finite systems -- providing strict bounds for their spectra in terms of their constituent blocks.

math-ph↗
arXiv2026

From entropic constraints to reinforced processes: a probabilistic origin of multiscale measures

We study multiscale measures, defined by a hierarchy of partial Gibbs equilibria, from variational and probabilistic perspectives. We first show that they are the unique solutions of a generalized maximum-entropy principle in which conditional entropies at different levels carry different weights. We then construct a hierarchical reinforced multinomial process proving a large-deviation principle for its empirical measure. The stochastic process leaves the typical empirical distribution unchanged but modifies the exponential cost of its fluctuations. The resulting rate function is a weighted sum of conditional Kullback-Leibler divergences, establishing a direct link with the entropic principle above. The relation between the reinforcement and Poisson-Dirichlet processes is discussed.

math-ph↗