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Motivated by the increased interest in modeling nondissipative materials by constitutive relations more general than those from Cauchy elasticity, we initiate the study of a class of stretch-limited elastic strings: the string cannot be…
Alignment, the tendency of adjacent weight matrices in deep networks to develop compatible subspace orientations, underlies gradient flow, Neural Collapse, and representation similarity across architectures. Despite extensive empirical…
An elastic double pendulum subject to a force acting along a fixed straight line, the so-called "Reut's column problem", is a structure exhibiting flutter and divergence instability, which was never realized in practice and thus debated…
Non-conservative loads of the follower type are usually believed to be the source of dynamic instabilities such as flutter and divergence. It is shown that these instabilities (including Hopf bifurcation, flutter, divergence, and…
We address the mechanics of an elastic ribbon subjected to twist and tensile load. Motivated by the classical work of Green and a recent experiment that discovered a plethora of morphological instabilities, we introduce a comprehensive…
A general class of nonconvex optimization problems is considered, where the penalty is the composition of a linear operator with a nonsmooth nonconvex mapping, which is concave on the positive real line. The necessary optimality condition…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
Quasi-static strain-controlled measurements of stress vs strain curves in macroscopic amorphous solids result in a nonlinear looking curve that ends up either in mechanical collapse or in a steady-state with fluctuations around a mean…
The effective elasticity of highly charged stiff polyelectrolytes is studied in the presence of counterions, with and without added salt. The rigid polymer conformations may become unstable due to an effective attraction induced by…
Over the past three decades, considerable effort has been devoted to studying the rich and diverse phenomenologies of heterotic strings exhibiting spacetime supersymmetry. Unfortunately, during this same period, there has been relatively…
In this work we analyze the stability and convergence properties of a loosely-coupled scheme, called the kinematically coupled scheme, and its extensions for the interaction between an incompressible, viscous fluid and a thin, elastic…
This paper investigates the effects of geometric nonlinearity and structural flexibility on the flight dynamics of high-aspect-ratio wings representative of high-altitude long endurance aircraft configurations. A coupled aeroelastic flight…
There has been a surge of interest in effective non-Lorentzian theories of excitations with restricted mobility, known as fractons. Examples include defects in elastic materials, vortex lattices or spin liquids. In the effective theory…
We present a concise overview of the physical and mathematical structures underpinning the appearence of nonassociative deformations of geometry in non-geometric string theory. Starting from a quick recap of the appearence of noncommutative…
A general nonlinear theory for the elasticity of pre-stressed single crystals is presented. Various types of elastic moduli are defined, their importance is determined, and relationships between them are presented. In particular, B moduli…
This perspective will overview an emerging paradigm for self-organized soft materials, {\it geometrically-frustrated assemblies}, where interactions between self-assembling elements (e.g. particles, macromolecules, proteins) favor local…
The stability analysis of self-similar solutions is an important approach to confirm whether they act as an attractor in general non-self-similar gravitational collapse. Assuming that the collapsing matter is a perfect fluid with the…
We study geometrical clues of a rigidity transition due to the emergence of a system-spanning state of self stress in under-constrained systems of individual polygons and spring networks constructed from such polygons. When a polygon with…
Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the…
The transformation theory of optics and acoustics is developed for the equations of linear anisotropic elasticity. The transformed equations correspond to non-unique material properties that can be varied for a given transformation by…