Related papers: Higher Order Rigidity and Energy
We give a combinatorial characterization of generic frameworks that are minimally rigid under the additional constraint of maintaining symmetry with respect to a finite order rotation or a reflection. To establish these results we develop a…
Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although…
High-energy factorization in QCD is investigated beyond leading order and its relationship to the factorization theorem of mass singularities is established to any collinear accuracy. Flavour non-singlet observables are shown to be regular…
In "Universal rigidity on the line, point orde" it is shown, answering a question of Jord\'an and Nguyen, that universal rigidity of a generic bar-joint framework in R^1 depends on more than the ordering of the vertices. The graph G that…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
Discrete element (DEM) simulations demonstrate that granular materials are non-simple, meaning that the incremental stiffness of a granular assembly depends on the gradients of the strain increment as well as on the strain increment itself.…
We study the canonical structure of the real first order formulation of general relativity on a null foliation. We use a tetrad decomposition which allows to elegantly encode the nature of the foliation in the norm of a vector in the fibre…
Based on the generalized Routh-Hurwitz criterion, we propose a sufficient and necessary criterion for testing the stability of fractional-order linear systems with order {\alpha}{\in}[1,2), called the fractional-order Routh-Hurwitz…
Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite…
If general relativity is the correct theory of physics on large scales, then there is a differential equation that relates the Hubble expansion function, inferred from measurements of angular diameter distance and luminosity distance, to…
Robustness of neural networks has recently attracted a great amount of interest. The many investigations in this area lack a precise common foundation of robustness concepts. Therefore, in this paper, we propose a rigorous and flexible…
In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. In this paper, we will…
Despite of some progresses in investigating the roles of the higher-order strain gradients on elastic stabilities of solids, the physical nature on the higher-order elastic instabilities of crystals, especially under extreme strain rates,…
In many scenarios, a state-space model depends on a parameter which needs to be inferred from data. Using stochastic gradient search and the optimal filter (first-order) derivative, the parameter can be estimated online. To analyze the…
We investigate the existence and non-existence of a function-valued strain solution in various models of elastoplasticity from the perspective of the constraint-based ``dual'' formulations. We describe abstract frameworks for linear…
We consider the global rigidity problem for bar-joint frameworks where each vertex is constrained to lie on a particular line in $\mathbb R^d$. In our setting we allow multiple vertices to be constrained to the same line. Under a mild…
A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the…
This work focuses on the bearing rigidity theory, namely the branch of knowledge investigating the structural properties necessary for multi-element systems to preserve the inter-units bearings when exposed to deformations. The original…
In this work, we develop and analyse a novel Hybrid High-Order discretisation of the Brinkman problem. The method hinges on hybrid discrete velocity unknowns at faces and elements and on discontinuous pressures. Based on the discrete…
We extend the mathematical theory of rigidity of frameworks (graphs embedded in $d$-dimensional space) to consider nonlocal rigidity and flexibility properties. We provide conditions on a framework under which (I) as the framework flexes…