Related papers: Geometric auxetics
In this work, we propose a geometric framework for analyzing mechanical manipulation, for instance, by a robotic agent. Under the assumption of conservative forces and quasi-static manipulation, we use energy methods to derive a metric. In…
We show that the path of any accelerated body in an arbitrary space-time geometry $g_{\mu\nu}$ can be described as geodesics in a dragged metric $\hat{q}_{\mu\nu}$ that depends only on the background metric and on the motion of the body.…
Natural objects can be subject to various transformations yet still preserve properties that we refer to as invariants. Here, we use definitions of affine invariant arclength for surfaces in R^3 in order to extend the set of existing…
We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the…
Geometric representations provide a principled framework for structuring the description of latent constructs and clarifying sources of uncertainty in their dimensional characterisation. We introduce a novel geometric representation of…
Time-varying non-Euclidean random objects are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of time-varying data. However, quantifying periodicity in general non-Euclidean random objects…
Some remarkable generic properties, related to isostaticity and potential energy minimization, of equilibrium configurations of assemblies of rigid, frictionless grains are studied. Isostaticity -the uniqueness of the forces, once the list…
In this paper we will present an ongoing project which aims to use model theory as a suitable mathematical setting for studying the formalism of quantum mechanics. We will argue that this approach provides a geometric semantics for such…
In this thesis we study geometric structures from Poisson and generalized complex geometry with mild singular behavior using Lie algebroids. The process of lifting such structures to their Lie algebroid version makes them less singular, as…
We concentrate on the geometric potential in the invariant perturbation theory of quantum adiabatic process which is presented in our recent papers. It is found out to be related to the geodesic curvature of the spherical curve in…
We study the evolution of coherent structures in arbitrary turbulence phenomena, developing some tools, from non-archimedean analysis and algebraic geometry, in order to model its display. We match the scale-dependent, topological structure…
The proliferation of 3D representations, from explicit meshes to implicit neural fields and more, motivates the need for simulators agnostic to representation. We present a data-, mesh-, and grid-free solution for elastic simulation for any…
We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes…
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
We present an axiomatic modification of quaternionic quantum mechanics with a possible-worlds semantics capable of predicting essential "nonquantum" features of an observable universe model - the dimensionality and topology of spacetime,…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…
Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on…
This study aims to make use of two concepts in the field of aeroacoustics; an analogy with relativity, and Geometric Algebra. The analogy with relativity has been investigated in physics and cosmology, but less has been done to use this…
Symmetry-driven phenomena arising in nonlocal metasurfaces supporting quasi-bound states in the continuum (q-BICs) have been opening new avenues to tailor enhanced light-matter interactions via perturbative design principles. Geometric…