Related papers: Chersiphron & Son Engineers
7-dimensional closed and simply-connected manifolds have been attractive as central and explicit objects in algebraic topology and differential topology of higher dimensional closed and simply-connected manifolds, which were studied…
We construct embeddings of simplicial complexes into a (surface of a) simplicial ball whose triangulation has bounded degrees and low volume. This construction can be used either to efficiently "simplify a complicated space" by realizing it…
Excellent computer simulations are done for a purpose. The most valid purposes are to explore uncharted territory, to resolve a well-posed scientific or technical question, or to make a design choice. Stand-alone modeling can serve the…
A problem that is simple to state in the context of spherical geometry, and that seems rather interesting, appears to have been unexamined to date in the mathematical literature. The problem can also be recast as a problem in the real…
In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with…
The beam-beam effects have been the dominating sources of beam loss and lifetime limitations in the Tevatron proton-antiproton collider [1]. Electron lenses were originally proposed for compensation of electromagnetic long-range and head-on…
Convolutional Neural Networks (CNNs) are extremely efficient, since they exploit the inherent translation-invariance of natural images. However, translation is just one of a myriad of useful spatial transformations. Can the same efficiency…
Bayesian mechanics is a new approach to studying the mathematics and physics of interacting stochastic processes. Here, we provide a worked example of a physical mechanics for classical objects, which derives from a simple application…
The experimental observations that led to the quark structure of matter and the development of hadron physics are reviewed with emphasis on the discoveries of mesons and baryons, starting in the 1940s with the pion and kaon which mediate…
A web application prototype is described, aimed at the generation of synthetic seismograms for user-defined earthquake models. The web application graphical user interface hides the complexity of the underlying computational engine, which…
Dynamics is a core discipline in Mechanical and Aerospace Engineering programs and with the ubiquitous nature of control in modern day applications, the field of mechatronics has gained popularity. Mechatronics refers to the field of…
There is this old, eternal question: Why don't animals have wheels? In this perspective we show that they actually do. And they do so in a physically extraordinary way -- by combining incompatible elasticity, differential geometry and…
Szil\'ard's information engine is a canonical example in the field of thermodynamics of information. We realize experimentally a macroscopic many-particle Szil\'ard engine that consists of active particles and use it to lift a mass against…
The problem of a conducting checkerboard has recently been solved via an elliptic function whose argument is another elliptic function. The behavior of the fields and currents near a vertex of the checkerboard pattern can be discussed by…
Magic squares have been an enthralling topic in mathematics for centuries. They are formed by filling in all the cells of a square matrix with the numbers starting from one so that the sum of all rows, columns, and diagonals is the same.…
The flight characteristics of bats remarkably have been overlooked in aerial drone designs. Unlike other animals, bats leverage the manipulation of inertial dynamics to exhibit aerial flip turns when they perch. Inspired by this unique…
We construct a quartic threefold with L-rational singularities which has torsion in its middle homology group. This answers a question of Brown and Schnetz for all fields of characteristic zero.
We use principal angles between two subspaces to define Jordan planes. Jordan planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given two subspaces. We apply Jordan planes to show that two pairs of of subspaces…
The Dirac belt trick is often employed in physics classrooms to show that a $2\pi$ rotation is not topologically equivalent to the absence of rotation whereas a $4\pi$ rotation is, mirroring a key property of quaternions and their…
Before we dive into the accessibility stream of nowadays indicatory applications of octonions to computer and other sciences and to quantum physics let us focus for a while on the crucially relevant events for todays revival on interest to…