Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (4)

Search Parameters:
Keywords = infinitesimal bending

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
18 pages, 5296 KB  
Article
Bending Fields for Dual Curves
by Marija S. Najdanović, Svetozar R. Rančić and Ljubica S. Velimirović
Axioms 2026, 15(2), 112; https://doi.org/10.3390/axioms15020112 - 3 Feb 2026
Abstract
This paper provides several new characterizations of the infinitesimal bending of dual curves, which is defined as an infinitesimal deformation preserving dual arc length (with appropriate precision). The main goal is to consider the infinitesimal deformations of ruled surfaces through the corresponding deformations [...] Read more.
This paper provides several new characterizations of the infinitesimal bending of dual curves, which is defined as an infinitesimal deformation preserving dual arc length (with appropriate precision). The main goal is to consider the infinitesimal deformations of ruled surfaces through the corresponding deformations of dual curves. Some useful properties of the infinitesimal bending of dual curves are obtained, and dual bending fields are determined. The Vekua-type characterization of the infinitesimal bending of dual curves is formulated in terms of the derivative of the dual arc length. Explicit formulas for dual infinitesimal bending fields of dual spherical curves are obtained using the Blaschke frame, considering both an arbitrary real parameter and the dual arc length. A necessary and sufficient condition for the infinitesimal bending of the dual curve to lie on the dual unit sphere is presented in terms of Blaschke and Frenet invariants. Several examples are illustrated graphically using our own software tool. Full article
(This article belongs to the Section Geometry and Topology)
8 pages, 236 KB  
Article
A Note on the Infinitesimal Bending of a Rectifying Curve
by Ştefan-Cezar Broscăţeanu, Adela Mihai and Andreea Olteanu
Symmetry 2024, 16(10), 1361; https://doi.org/10.3390/sym16101361 - 14 Oct 2024
Cited by 2 | Viewed by 1088
Abstract
Both notions, of an infinitesimal bending of a curve and of a rectifying curve, play important roles in the theory of curves. In this short note, we begin the study of the infinitesimal bending of a rectifying curve. Full article
15 pages, 6274 KB  
Article
On the Torsional Energy of Deformed Curves and Knots
by Svetozar R. Rančić, Ljubica S. Velimirović and Marija S. Najdanović
Axioms 2024, 13(10), 661; https://doi.org/10.3390/axioms13100661 - 25 Sep 2024
Viewed by 1258
Abstract
This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on [...] Read more.
This paper deals with the study of torsional energy (total squared torsion) at infinitesimal bending of curves and knots in three dimensional Euclidean space. During bending, the curve is subject to change, and its properties are changed. The effect that deformation has on the curve is measured by variations. Here, we observe the infinitesimal bending of the second order and variations of the first and the second order that occur in this occasion. The subjects of study are curves and knots, in particular torus knots. We analyze various examples both analytically and graphically, using our own calculation and visualization software tool. Full article
(This article belongs to the Special Issue Theory of Curves and Knots with Applications)
Show Figures

Figure 1

16 pages, 3515 KB  
Article
Model-Driven Controlled Alteration of Nanopillar Cap Architecture Reveals its Effects on Bactericidal Activity
by Taiyeb Zahir, Jiri Pesek, Sabine Franke, Jasper Van Pee, Ashish Rathore, Bart Smeets, Herman Ramon, Xiumei Xu, Maarten Fauvart and Jan Michiels
Microorganisms 2020, 8(2), 186; https://doi.org/10.3390/microorganisms8020186 - 28 Jan 2020
Cited by 15 | Viewed by 4657
Abstract
Nanostructured surfaces can be engineered to kill bacteria in a contact-dependent manner. The study of bacterial interactions with a nanoscale topology is thus crucial to developing antibacterial surfaces. Here, a systematic study of the effects of nanoscale topology on bactericidal activity is presented. [...] Read more.
Nanostructured surfaces can be engineered to kill bacteria in a contact-dependent manner. The study of bacterial interactions with a nanoscale topology is thus crucial to developing antibacterial surfaces. Here, a systematic study of the effects of nanoscale topology on bactericidal activity is presented. We describe the antibacterial properties of highly ordered and uniformly arrayed cotton swab-shaped (or mushroom-shaped) nanopillars. These nanostructured surfaces show bactericidal activity against Staphylococcus aureus and Pseudomonas aeruginosa. A biophysical model of the cell envelope in contact with the surface, developed ab initio from the infinitesimal strain theory, suggests that bacterial adhesion and subsequent lysis are highly influenced by the bending rigidity of the cell envelope and the surface topography formed by the nanopillars. We used the biophysical model to analyse the influence of the nanopillar cap geometry on the bactericidal activity and made several geometrical alterations of the nanostructured surface. Measurement of the bactericidal activities of these surfaces confirms model predictions, highlights the non-trivial role of cell envelope bending rigidity, and sheds light on the effects of nanopillar cap architecture on the interactions with the bacterial envelope. More importantly, our results show that the surface nanotopology can be rationally designed to enhance the bactericidal efficiency. Full article
(This article belongs to the Section Medical Microbiology)
Show Figures

Figure 1

Back to TopTop