Article
Mathematics, Applied
Nural Yuksel, Burcin Saltik
Summary: If the arc length and intrinsic curvature of a curve or surface are kept constant, it is considered to be inextensible. Inextensible curve and surface flows are characterized by the absence of motion-induced strain energy. This paper studies inextensible tangential, normal, and binormal ruled surfaces generated by a curve with constant torsion, known as a Salkowski curve. It investigates whether these surfaces are minimal or developable and proves theorems related to inextensible ruled surfaces in three-dimensional Euclidean space.
Article
Multidisciplinary Sciences
Semra Kaya Nurkan, Ibrahim Gurgil
Summary: In this paper, we investigated surfaces with constant negative Gaussian curvature in the simply isotropic 3-Space. We studied the isotropic II-flat, isotropic minimal and isotropic II-minimal, the constant second Gaussian curvature, and the constant mean curvature of surfaces with constant negative curvature (SCNC). Surfaces with symmetry were obtained when the mean curvatures were equal. Furthermore, we investigated the constant Casorati, the tangential and the amalgamatic curvatures of SCNC.
Article
Multidisciplinary Sciences
Melissa R. Requist, Tim Rolvien, Alexej Barg, Amy L. Lenz
Summary: This study used quantitative micro-CT imaging to examine the dimensions, distance maps, and curvature of the four articular surfaces in the first and second tarsometatarsal joints. The results showed that the cuneiforms have larger articular surfaces than the metatarsals, and defined the generally tall and narrow articular surfaces seen in these joints. These findings are valuable for further understanding the surgical anatomy in this poorly understood region of the foot.
SCIENTIFIC REPORTS
(2023)
Article
Mathematics, Applied
Yasemin Yildirim, Erhan Ata
Summary: This study expresses points of a surface in 3-dimensional Euclidean space using dual quaternions and obtains a screw surface through rigid motion, investigating changes in its differential geometric properties. In a special case, the screw surface becomes a parallel surface while maintaining the same properties.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics
Ahmad T. Ali
Summary: In this article, we classify developable surfaces in three-dimensional Euclidean space R-3 that are foliated by general ellipses. We prove that a surface has constant Gaussian curvature (CGC) and is foliated by general ellipses if and only if it is developable, meaning that the Gaussian curvature G vanishes everywhere. We characterize all developable surfaces that are foliated by general ellipses, including conical surfaces and surfaces generated by special base curves.
Article
Mathematics
Dominique Kemp
Summary: We extend the l(2)(L-p) decoupling theorem of Bourgain-Demeter to the full class of developable surfaces in R-3. This completes the l(2) decoupling theory of the zero Gaussian curvature surfaces that lack planar (or umbilic) points. The tangent surface associated to the moment curve is of central interest in our study.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Computer Science, Interdisciplinary Applications
Mihai-Sorin Stupariu
Summary: The study compares methods for computing curvatures of triangle meshes, focusing on terrain data. Through numerical experiments, it is found that the best approximation for Gaussian curvature can be provided by two methods derived from the Gauss-Bonnet theorem and the jet fitting method, while for mean curvatures, one of the Gauss-Bonnet schemes, the method based on Euler's theorem and the tensor approach yield the best matches. The study also demonstrates how curvatures for triangle meshes can highlight specific terrain features.
COMPUTERS & GEOSCIENCES
(2021)
Article
Agronomy
Justin J. Nairn, W. Alison Forster
Summary: The study developed a model that accurately predicted the wetting of adjuvant formulations on different surfaces by combining surface properties measured with the wetting tension dielectric method and formulation properties. The comprehensive wetting model could successfully predict the wetting of adjuvant formulations on synthetic and leaf surfaces, providing a valuable tool for advancing the selection and development of adjuvants for specific surfaces.
PEST MANAGEMENT SCIENCE
(2022)
Article
Mathematics
Sungmin Ryu
Summary: The Gauss-Bonnet formula is widely used in various fundamental fields. Due to its dependence on the choice of a simple region on an orientable smooth surface S, analysis based on this formula can only be done in integral form. This paper aims to establish a differential relation for metric properties at a specific point on S, enabling pointwise analysis and providing new geometric insights for studies utilizing the Gauss-Bonnet formula in integral form.
Article
Chemistry, Physical
Thomas Baaij, Marn Klein Holkenborg, Maximilian Stolzle, Daan van der Tuin, Jonatan Naaktgeboren, Robert Babuska, Cosimo Della Santina
Summary: This letter proposes a method to achieve proprioception in soft robots by using magnetic sensors fully integrated into the robot. A neural architecture is also proposed to understand the nonlinear relationship between the perceived intensity of the magnetic field and the shape of the robot. The effectiveness of this method is demonstrated in simulation and experiments, achieving a mean relative error of 4.5%.
Article
Mathematics, Applied
Ahmet Kazan, Mustafa Altin, Dae Won Yoon
Summary: In this paper, we investigate the weighted mean and weighted Gaussian curvatures of a generalized rotation surface in E4 with specific density functions. We also study the weighted minimal and weighted flat generalized rotation surfaces in E4 and provide results for their minimality and flatness. Furthermore, we obtain the weighted mean and weighted Gaussian curvatures for several examples of generalized rotation surfaces in E4 and discuss their minimality and flatness.
JOURNAL OF GEOMETRY AND PHYSICS
(2023)
Article
Mathematics, Applied
Rachid Regbaoui, Yasmina Reguig
Summary: We propose a flow approach to the prescribed Gaussian curvature problem on compact surfaces with negative Euler characteristic. We establish a new explicit condition on the prescribed function f that guarantees the convergence of the flow to a conformal metric with Gaussian curvature equal to f. The blowing up of the flow at infinity is also investigated.
JOURNAL OF EVOLUTION EQUATIONS
(2023)
Article
Mathematics, Applied
M. Caroccia, S. Ciani
Summary: In this study, the analysis of the contact surface size between a Cheeger set and its ambient space subset is carried out, providing bounds on the Hausdorff dimension of the contact surface. The research demonstrates the interplay between the contact surface size and the regularity of boundaries, eventually obtaining conditions for the contact surface to have positive Hausdorff measure. Explicit examples in two dimensions prove the optimality of the bounds provided.
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES
(2022)
Article
Mathematics, Applied
Guido De Philippis, Antonio De Rosa
Summary: We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature in closed smooth 3-dimensional Riemannian manifolds. These surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to any real number. In particular, we partially solve a conjecture of Allard in dimension 3.
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
(2023)
Article
Engineering, Mechanical
Wei Wang, Yi Sun, Linghui He, Yong Ni
Summary: In this study, the controllable spatially dependent wrinkling pattern of hard films on pre-curved soft substrates was demonstrated through a combination of experiments and numerical simulations by tuning curvature and pre-stretch. Various spatially distributed wrinkling patterns were observed, such as checkerboard, bead-chain, herringbone, radially or circumferentially oriented stripes, providing a new strategy for tunable wrinkling patterns of a film by releasing the pre-bending of its underlying substrate.
EXTREME MECHANICS LETTERS
(2022)
Article
Chemistry, Physical
Lila Bouzar, Martin Michael Muller, Pierre Gosselin, Igor M. Kulic, Herve Mohrbach
EUROPEAN PHYSICAL JOURNAL E
(2016)
Editorial Material
Biology
Martine Ben Amar, Carlo Bianca
PHYSICS OF LIFE REVIEWS
(2016)
Review
Biology
Martine Ben Amar, Carlo Bianca
PHYSICS OF LIFE REVIEWS
(2016)
Article
Chemistry, Physical
Julien Fierling, Albert Johner, Igor M. Kulic, Herve Mohrbach, Martin Michael Mueller
Editorial Material
Physics, Multidisciplinary
Martine Ben Amar
EUROPEAN PHYSICAL JOURNAL PLUS
(2016)
Article
Engineering, Multidisciplinary
Martine Ben Amar, Adrien Bordner
JOURNAL OF ELASTICITY
(2017)
Article
Multidisciplinary Sciences
Fei Jia, Martine Ben Amar, Bernard Billoud, Benedicte Charrier
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2017)
Article
Multidisciplinary Sciences
Martine Ben Amar, Carlo Bianca
SCIENTIFIC REPORTS
(2016)
Article
Physics, Multidisciplinary
Lila Bouzar, Martin Michael Mueller, Rene Messina, Bernd Noeding, Sarah Koester, Herve Mohrbach, Igor M. Kulic
PHYSICAL REVIEW LETTERS
(2019)
Article
Materials Science, Multidisciplinary
Jemal Guven, Martin Michael Mueller, Pablo Vazquez-Montejo
MATHEMATICS AND MECHANICS OF SOLIDS
(2019)
Article
Oncology
Ludovico Mori, Martine Ben Amar
Summary: This study investigates the impact of phenotypical heterogeneity on tumor growth and therapies using the Cancer Stem Model. The results confirm the descriptive power of the model and highlight the importance of considering stochastic factors for a more accurate understanding of tumor evolution and therapy outcomes.
Article
Physics, Multidisciplinary
Niloufar Abtahi, Lila Bouzar, Nadia Saidi-Amroun, Martin Michael Muller
Proceedings Paper
Engineering, Electrical & Electronic
Lila Bouzar, Ferhat Menas, Martin Michael Mueller
XII MAGHREB DAYS OF MATERIAL SCIENCES
(2017)
Article
Biology
Thanh Thi kim Vuong-Brender, Martine Ben Amar, Julien Pontabry, Michel Labouesse
Article
Physics, Fluids & Plasmas
Zakaria Boujja, Chaouqi Misbah, Hamid Ez-Zahraouy, Abdelilah Benyoussef, Thomas John, Christian Wagner, Martin Michael Mueller