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Biomimetic scale-covered substrates are architected meta-structures exhibiting fascinating emergent nonlinearities via the geometry of collective scales contacts. Despite much progress in understanding their elastic nonlinearity, their dissipative behavior arising from scales sliding is relatively uninvestigated in the dynamic regime. Recently discovered is the phenomena of viscous emergence, where dry Coulomb friction between scales can lead to apparent viscous damping behavior of the overall multi-material substrate. In contrast to this structural dissipation, material dissipation common in many polymers has never been considered, especially synergistically with geometrical factors. This aspect is addressed here, where material viscoelasticity is introduced via a simple Kelvin–Voigt model for brevity and clarity. The results contrast the two damping sources in these architectured systems: material viscoelasticity and geometrical frictional scales contact. It is discovered that although topically similar in effective damping, viscoelastic damping follows a different damping envelope than dry friction, including starkly different effects on damping symmetry and specific damping capacity.

Abstract We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in general noncommutativity yields a canonical time evolution, while at the same time allowing for the coexistence of discrete and continuous variables. The spectral approach to geometry is then explained to encompass two natural ingredients: the line element and the algebra. The relation between these two is dictated by so-called higher Heisenberg relations, from which both spin geometry and non-abelian gauge theory emerges. Our exposition indicates some of the applications in physics, including Pati–Salam unification beyond the Standard Model, the criticality of dimension 4, second quantization and entropy.

Many real-world applications require real-time and robust positioning of Internet of Things (IoT) devices. In this context, visible light communication (VLC) is a promising approach due to its advantages in terms of high accuracy, low cost, ubiquitous infrastructure, and freedom from RF interference. Nevertheless, there is a growing need to improve positioning speed and accuracy. In this paper, we propose and prototype a VLC-based positioning solution using retroreflectors attached to the IoT device of interest. The proposed algorithm uses the retroreflected power received by multiple photodiodes to estimate the euclidean and directional coordinates of the underlying IoT device. In particular, the relative relationship between reflected light magnitude and reflected power is used as input to trainable machine learning regression models. Such models are trained to estimate the coordinates. The proposed algorithm excels in its simplicity and fast computation. It also reduces the need for sensory devices and active operation. Additionally, after regression, Kalman filtering is applied as a post-processing operation to further stabilize the obtained estimates. The proposed algorithm is shown to provide stable, accurate, and fast. This has been verified by extensive experiments performed on a prototype in real-world environments. Experiments confirm a high level of positioning accuracy andmore »the added benefit of Kalman filtering stabilization.« less

We focus on studying, numerically, the scalar curvature tensor in a two-dimensional discrete space. The continuous metric of a two-sphere is transformed into that of a lattice using two possible slicings. In the first, we use two integers, while in the second we consider the case where one of the coordinates is ignorable. The numerical results of both cases are then compared with the expected values in the continuous limit as the number of cells of the lattice becomes very large.

The 1.5 formalism played a key role in the discovery of supergravity and it has been used to prove the invariance of essentially all supergravity theories under local supersymmetry. It emerged from the gauging of the super Poincaré group to find supergravity. We review both of these developments as well as the auxiliary fields for simple supergravity and its most general coupling to matter using the tensor calculus.

Abstract We formulate a supersymmetric version of gravity with mimetic dark matter. The coupling of a constrained chiral multiplet to $$N = 1$$ N = 1 supergravity is made locally supersymmetric using the rules of tensor calculus. The chiral multiplet is constrained with a Lagrange multiplier multiplet that could be either a chiral multiplet or a linear multiplet. We obtain the fully supersymmetric Lagrangians in both cases. It is then shown that the system consisting of the supergravity multiplet, the chiral multiplet and the Lagrange multiplier multiplet can break supersymmetry spontaneously leading to a model of a graviton, massive gravitino and two scalar fields representing mimetic dark matter. The combination of the chiral multiplet and Lagrange multiplier multiplet can act as the hidden sector breaking local $$N = 1$$ N = 1 supersymmetry.

A bstract We assume that the points in volumes smaller than an elementary volume (which may have a Planck size) are indistinguishable in any physical experiment. This naturally leads to a picture of a discrete space with a finite number of degrees of freedom per elementary volume. In such discrete spaces, each elementary cell is completely characterized by displacement operators connecting a cell to the neighboring cells and by the spin connection. We define the torsion and curvature of the discrete spaces and show that in the limiting case of vanishing elementary volume the standard results for the continuous curved differentiable manifolds are completely reproduced.