Related papers: The Stress-Flex Conjecture
The purpose of this paper is to study stable representations of partially ordered sets (posets) and compare it to the well known theory for quivers. In particular, we prove that every indecomposable representation of a poset of finite type…
While it is widely acknowledged that system-spanning particulate structures contribute to the observed yield stress and shear-thinning in attractive colloidal gels, a comprehensive understanding of the underlying microscopic mechanisms…
We characterise finite and infinitesimal rigidity for bar-joint frameworks in R^d with respect to polyhedral norms (i.e. norms with closed unit ball P a convex d-dimensional polytope). Infinitesimal and continuous rigidity are shown to be…
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric…
An inequality on torsional rigidity is established. For tangential polygons this inequality is stronger than an inequality of Polya and Szego for convex domains. (A survey of related work, not in the journal submission, is presented in the…
We show a stability-type theorem for foliations on projective spaces which arise as pullbacks of foliations with a split tangent sheaf on weighted projective spaces. As a consequence, we will be able to construct many irreducible components…
A new type of tensionless superstring theory, called the Inhomogeneous tensionless superstring, has been recently introduced. This is characterised by a residual symmetry algebra on the worldsheet richer in structure than the previously…
The algebraic dichotomy conjecture for Constraint Satisfaction Problems (CSPs) of reducts of (infinite) finitely bounded homogeneous structures states that such CSPs are polynomial-time tractable if the model-complete core of the template…
The purpose of the present paper is to show few examples of nonlinear PDEs (mostly with strong geometric features) for which there is a hidden convex structure. This is not only a matter of curiosity. Once the convex structure is…
We investigate the stress-driven morphological instability of epitaxially growing multilayer films, which are coherent and dislocation-free. We construct a direct elastic analysis, from which we determine the elastic state of the system…
Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars.…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
Here we present a rigidity result in a global (semi-global, homotopy) setting for a restrictive class of polytopes, those that can be inscribed in a unit sphere, with some additional conditions. The proof of the rigidity result for cabled…
We study the flexibility of suspensions (polyhedra having the combinatorial structure of dipyramids) that have an even number of vertexes and provide arguments that there are least five distinct types of flexible suspensions.
This paper presents a comprehensive computational framework for investigating thermo-elastic fracture in transversely isotropic materials, where classical linear elasticity fails to predict physically realistic behavior near stress…
A framework, which is a (possibly infinite) graph with a realization of its vertices in the plane, is called flexible if it can be continuously deformed while preserving the edge lengths. We focus on flexibility of frameworks in which…
A simple graph G=(V,E) is 3-rigid if its generic bar-joint frameworks in R3 are infinitesimally rigid. Block and hole graphs are derived from triangulated spheres by the removal of edges and the addition of minimally rigid subgraphs, known…
Real-stable, Lorentzian, and log-concave polynomials are well-studied classes of polynomials, and have been powerful tools in resolving several conjectures. We show that the problems of deciding whether a polynomial of fixed degree is real…
We investigate the spatial correlations of microscopic stresses in soft particulate gels, using 2D and 3D numerical simulations. We use a recently developed theoretical framework predicting the analytical form of stress-stress correlations…
A $d$-dimensional body-and-hinge framework is a structure consisting of rigid bodies connected by hinges in $d$-dimensional space. The generic infinitesimal rigidity of a body-and-hinge framework has been characterized in terms of the…