Theory of Curves and Knots with Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".
Deadline for manuscript submissions: 31 August 2024 | Viewed by 541
Special Issue Editors
Interests: differential geometry of curves and surfaces; geometric knot theory; infinitesimal bending; generalized Riemannian spaces; applications of geometry to natural processes
Interests: infinitesimal deformations; knots; generalized Riemannian spaces; applied geometry at civil engineering and architecture; computer graphics
Special Issue Information
Dear Colleagues,
We are pleased to announce the Special Issue entitled “Theory of Curves and Knots with Applications” to be published in the journal Axioms.
Curves are the fundamental geometric elements that have a deep history and still represent an area of intense research activity. Theory of curves can be studied from various aspects and serves as a bridge between different mathematical disciplines. Knot theory is concerned with the study of mathematical knots that represent closed curves without self-intersections. The beauty and depth of curves and knots extend beyond pure mathematics, finding applications in areas such as molecular biology and quantum physics.
This Special Issue is devoted to both the foundational concepts of curves and knots as well as its newer, multidisciplinary applications in various fields of study.
The topics covered in this Special Issue include, but are not limited to the following:
- Various aspects of the theory of curves: differential geometry of curves, topological aspects, algebraic curves, analytic curves, curves on the surfaces, curve deformation, curves in Minkowski space, curves on manifolds, magnetic curves, geodesics, dual curves in dual spaces, fractal curves, etc;
- Traditional aspects of knot theory: knot invariants, knot polynomials, and braids. Connections with low-dimensional topology, 3-manifolds and higher dimension spaces, algebraic structures, geometry, and combinatorics;
- Interdisciplinary applications of curves and knots in fields outside of pure mathematics like molecular biology (e.g., DNA knotting and unknotting), physics (e.g., quantum mechanics, statistical mechanics, kinematics), computer science (e.g., algorithms for knot recognition and classification, computer graphics and design), architecture (curved structures and their stability), engineering, etc.
The purpose of this Special Issue is to present the latest research findings in curves and knots, to highlight the diverse applications and to provide a platform for researchers to share knowledge, collaborate, and advance the study and applications of curve and knot theory.
This Special Issue will serve as a contribution to existing literature by bringing together interdisciplinary research that showcases the breadth of applications of curves and knots.
Dr. Marija S. Najdanović
Prof. Dr. Ljubica Velimirovic
Guest Editors
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- geometry of curves
- curvature
- curve deformation
- variational principles
- dual curves
- magnetic curves
- algebraic curves
- analytic curves
- geodesics
- fractal curves
- curves in Minkowski space
- curves on manifolds
- knots
- knot invariants
- knot polynomials
- braid theory
- topological transformations
- knot energies
- link theory
- DNA knotting
- knot recognition algorithms
- quantum knot invariants
- geometric knot theory
- virtual knots
- statistical mechanics
- kinematics
- biophysics
- computer graphics
