18 papers · ranked by Valyu relevance
Luca Moroni
We review, from a didactic point of view, the definition of a toric section and the different shapes it can take. We'll then discuss some properties of this curve, investigate its analogies and differences with the most renowned conic section and show how to build its general quartic equation. A curious and unexpected…
Sibaek Yi, G. S. Choe
The representation of magnetic field as a sum of a toroidal field and a poloidal field has not rarely been used in astrophysics, particularly in relation to stellar and planetary magnetism. In this representation, each toroidal field line lies entirely in a surface, which is named a toroidal field surface. The poloidal…
Takashi Sakajo
A steady solution of the incompressible Euler equation on a toroidal surface $T_{R,r}$ of major radius R and minor radius r is provided. Its streamfunction is represented by an exact solution to the modified Liouville equation, $∇_{T_{R,r}}^{2}ψ=c \text{e}dψ+(8(/)d)κ$, where $∇_{T_{R,r}}^{2}$ and κ denote the…
Robert T. Jantzen
In considering the mathematical problem of describing the geodesics on a torus or any other surface of revolution, there is a tremendous advantage in conceptual understanding that derives from taking the point of view of a physicist by interpreting parametrized geodesics as the paths traced out in time by the motion of…
Angana Bhattacharya, Rakesh Sarkar, Gagan Kumar
Title: Summary The vigorous research on low-loss photonic devices has brought significance to a new kind of electromagnetic excitation, known as toroidal resonances. Toroidal excitation, possessing high-quality factor and narrow linewidth of the resonances, has found profound applications in metamaterial (MM) devices.…
Chris L.B. Graham, Matyas Parrag, Phillip J. Stansfeld, Christopher D. A. Rodrigues
The formation of specialised membrane architectures is fundamental to biological processes. Computational modelling of membrane structures offers a means to unravel complex molecular mechanisms that remain inaccessible through in vitro or in vivo approaches. Among these architectures, toroidal membranes, otherwise…
Richard J. Gardner, Erik Hermansen, Marius Pachitariu, Yoram Burak + 4 more
The medial entorhinal cortex (MEC) is part of a neural system for mapping a subject’s position within a physical environment^1,2^. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations^3^, and are organized in modules^4,5^ which collectively form a population code for the…
Jakson M. Fonseca, Vagson L. Carvalho‐Santos, W. A. Moura-Melo, A. R. Pereira
'A. R. Pereira'] An effective Hamiltonian describing the surface states of a toroidal topological insulator is obtained, and it is shown to support both bound-states and charged zero-modes. Actually, the spin connection induced by the toroidal curvature can be viewed as an position-dependent effective vector potential…
Pengfei Qin, Yihao Yang, Muhyiddeen Yahya Musa, Bin Zheng + 5 more
'Zuojia Wang' 'Ran Hao' 'Wenyan Yin' 'Hongsheng Chen' 'Erping Li'] Title: Abstract Localized spoof surface plasmons (LSSPs) have recently emerged as a new research frontier due to their unique properties and increasing applications. Despite the importance, most of the current researches only focus on electric/magnetic…
Natanael Bort-Soldevila, Jaume Cunill-Subiranas, Alvaro Sanchez
The fusion created by magnetically confined plasma is a promising clean and essentially unlimited future energy source. However, there are important problems hindering controlled fusion like the imperfect magnetic confinement and the associated plasma instabilities. We theoretically demonstrate how to create a fully…
J. Richard Gott, Robert J. Vanderbei
Start with Gott (2019)'s envelope polyhedron (Squares—4 around a point): a unit cube missing its top and bottom faces. Stretch by a factor of 2 in the vertical direction so its sides become (2 ×1 unit) rectangles. This has 8 faces (4 exterior, 4 interior), 8 vertices, and 16 edges. F − E + V = 0, implying a (toroidal)…
Yuxing Jared Yao, Iris H.R. Yoon
High-dimensional neural activity often resides in a low-dimensional subspace, referred to as neural manifolds. Grid cells in the medial entorhinal cortex provide a periodic spatial code that is organized near a toroidal manifold, independent of the spatial environment. Due to the periodic nature of this code, it is…
Marcin Płodzień, Łukasz Żyłka, Antun Stoić, Alexander Yu Churyumov
When face milling using a toroidal cutter, with a change in the depth of the cut, the entering angle varies as well. An experimental test of the influence of cutting parameters, such as the depth of the cut and the feed per tooth on the cutting force components and surface roughness parameters, was conducted. The…
Smiet, Christopher Berg
Magnetic confinement fusion devices, such as tokamaks and stellarators, are designed such that magnetic field lines lie in magnetic surfaces that form a foliation of nested genus-1 tori. The Poincaré-Hopf index theorem implies that only surfaces with genus 1 allow for vector fields that lie tangent to the surface and…
Handuo Shi, Jeffrey Nguyen, Zemer Gitai, Joshua Shaevitz + 4 more
Understanding the mechanisms that dictate the localization of cytoskeletal filaments is crucial for elucidating cell shape regulation in prokaryotes. The actin homolog MreB plays a pivotal role in maintaining the shape of many rod-shaped bacteria such as Escherichia coli by directing cell-wall synthesis according to…
Yanjun Bao, Xing Zhu, Zheyu Fang
Plasmonic toroidal resonance has attracted growing interests because of its low loss electromagnetic properties and potential high sensitive nanophotonic applications. However, the realization in a metamaterial requires three-dimensional complicated structural design so far. In this paper, we design a simple…
Siddhartha Sen, Tomas Ryan, David Muldowney, Maurizio Pezzoli
A special charged surface network with surface spin half particles on it, that can be arranged in topologically inequivalent ways, is introduced. It is shown that action potential-like signals can be generated in the network in response to local surface deformations of a particular kind. Signals generated in this way…
Diana K. Davis
This text is aimed at undergraduates, or anyone else who enjoys thinking about shapes and numbers. The goal is to encourage the student to think deeply about seemingly simple things. The main objects of study are lines, squares, and the effects of simple geometric motions on them. Much of the beauty of this subject is…