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We present a formalization of geometric instruments that considers separately geometric and arithmetic aspects of them. We introduce the concept of tool, which formalizes a physical instrument as a set of axioms representing its geometric…
Optimal geometrical arrangements, such as the stacking of atoms, are of relevance in diverse disciplines. A classic problem is the determination of the optimal arrangement of spheres in three dimensions in order to achieve the highest…
Softer than soft, squishy granular matter is composed of grains capable of significantly changing their shape (typically larger than 10% of deformation) without tearing or breaking. Because of the difficulty to test these materials…
This paper explores the topologies of caustics observed in instruments that employ charged particles, such as electron and ion microscopes. These geometrical figures are studied here using catastrophe theory. The application of this…
A piecewise flat manifold is a triangulated manifold given a geometry by specifying edge lengths (lengths of 1-simplices) and specifying that all simplices are Euclidean. We consider the variation of angles of piecewise flat manifolds as…
Gauge symmetries are often highlighted as a fundamental cornerstone of modern physics. But at the same time, it is commonly emphasized that gauge symmetries are not a fundamental feature of nature but merely redundancies in our description.…
We extend the construction of so-called encapsulated global summation-by-parts operators to the general case of a mesh which is not boundary conforming. Owing to this development, energy stable discretizations of nonlinear and variable…
Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with a…
One of the challenges in computational acoustics is the identification of models that can simulate and predict the physical behavior of a system generating an acoustic signal. Whenever such models are used for commercial applications an…
The special interest is devoted to such situations when the material space of our object with affine degrees of freedom has generally lower dimension than the one of the physical space. In other words when we have the $m$-dimensional…
Characteristic modes of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise…
We introduce the natural lift of spacetime diffeomorphisms for conformal gravity and discuss the physical equivalence between the natural and gauge natural structure of the theory. Accordingly, we argue that conformal transformations must…
Growth-elasticity is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to…
The regular-geometric-figure solution to the $N$-body problem is presented in a very simple way. The Newtonian formalism is used without resorting to a more involved rotating coordinate system. Those configurations occur for other kinds of…
Neural network models for guitar amplifier emulation, while being effective, often demand high computational cost and lack interpretability. Drawing ideas from physical amplifier design, this paper aims to address these issues with a new…
Listening habits are strongly influenced by two opposing aspects, the desire for variety and the demand for uniformity in music. In this work we quantify these two notions in terms of musical instrumentation and production technologies that…
Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for…
In [J14], a conjecture was proposed on a relation between the global Arthur parameters and the structure of Fourier coefficients of the automorphic representations in the corresponding global Arthur packets. In this paper, we discuss the…
Shape inference is classically ill-posed, because it involves a map from the (2D) image domain to the (3D) world. Standard approaches regularize this problem by either assuming a prior on lighting and rendering or restricting the domain,…
Unlike many other works, where authors are usually focused on one or two quality criteria, the current manuscript, which is a generalization of the article [35] published in Russian, offers a multi-criteria approach to the assessment of the…