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Keywords = haptic strip

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10 pages, 10394 KiB  
Article
A Haptic Model for the Quantum Phase of Fermions and Bosons in Hilbert Space Based on Knot Theory
by Stefan Heusler and Malte Ubben
Symmetry 2019, 11(3), 426; https://doi.org/10.3390/sym11030426 - 22 Mar 2019
Cited by 4 | Viewed by 4954
Abstract
A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of [...] Read more.
A generalization of the famous Dirac belt trick opens up the way to a haptic model for quantum phases of fermions and bosons in Hilbert space based on knot theory. We introduce a simple paper strip model as an aid for visualization of the quantum phases before and after Hopf-mapping, which can be extended to arbitrary spin states with almost no mathematical formalism. Knot theory arises naturally, leading to the Jones polynomials derived from Artin’s braid group for fermionic knots and for bosonic links. The paper strip model explicitly illuminates the relation between these knots and links within the S U ( 2 ) -representation of spin-jstates in C 2 j + 1 before Hopf-mapping and the number p = 2 j of nodes in the stellar representation in C P 1 after Hopf mapping. Full article
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22 pages, 17302 KiB  
Article
Force Sensitive Handles and Capacitive Touch Sensor for Driving a Flexible Haptic-Based Immersive System
by Mario Covarrubias, Monica Bordegoni and Umberto Cugini
Sensors 2013, 13(10), 13487-13508; https://doi.org/10.3390/s131013487 - 9 Oct 2013
Cited by 7 | Viewed by 8188
Abstract
In this article, we present an approach that uses both two force sensitive handles (FSH) and a flexible capacitive touch sensor (FCTS) to drive a haptic-based immersive system. The immersive system has been developed as part of a multimodal interface for product design. [...] Read more.
In this article, we present an approach that uses both two force sensitive handles (FSH) and a flexible capacitive touch sensor (FCTS) to drive a haptic-based immersive system. The immersive system has been developed as part of a multimodal interface for product design. The haptic interface consists of a strip that can be used by product designers to evaluate the quality of a 3D virtual shape by using touch, vision and hearing and, also, to interactively change the shape of the virtual object. Specifically, the user interacts with the FSH to move the virtual object and to appropriately position the haptic interface for retrieving the six degrees of freedom required for both manipulation and modification modalities. The FCTS allows the system to track the movement and position of the user’s fingers on the strip, which is used for rendering visual and sound feedback. Two evaluation experiments are described, which involve both the evaluation and the modification of a 3D shape. Results show that the use of the haptic strip for the evaluation of aesthetic shapes is effective and supports product designers in the appreciation of the aesthetic qualities of the shape. Full article
(This article belongs to the Special Issue Tactile Sensors and Sensing Systems)
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