Results 61 to 70 of about 65,019 (298)

On the motion of billiards in ellipses [PDF]

European Journal of Mathematics, 2022
AbstractFor billiards in an ellipse e with an ellipse as caustic, there exist canonical coordinates on e such that the billiard transformation from vertex to vertex is equivalent to a shift of coordinates. A kinematic analysis of billiard motions offers a new approach to canonical parametrizations of billiards and associated Poncelet grids.
openaire   +3 more sources

Phase Field Failure Modeling: Brittle‐Ductile Dual‐Phase Microstructures under Compressive Loading

Advanced Engineering Materials, EarlyView.
The approach by Amor and the approach by Miehe and Zhang for asymmetric damage behavior in the phase field method for fracture are compared regarding their fitness for microcrack‐based failure modeling. The comparison is performed for the case of a dual‐phase microstructure with a brittle and a ductile constituent.
Jakob Huber, Jan Torgersen, Ewald Werner
wiley   +1 more source

Fostering Innovation: Streamlining Magnetocaloric Materials Research by Digitalization

Advanced Engineering Materials, EarlyView.
Magnetocaloric cooling (MCE) is an environmentally friendly refrigeration method with great potential. Optimizing MCE materials involves the preparation and screening of large quantities of samples, which in turn generates a large amount of data. A digitalization approach is presented that uses ontologies, knowledge graphs, and digital workflows to ...
Simon Bekemeier, Moritz Blum, Luana Caron, Alisa Chirkova, Philipp Cimiano, Basil Ell, Inga Ennen, Michael Feige, Maik Gaerner, Thomas Hilbig, Andreas Hütten, Günter Reiss, Tapas Samanta, Sonja Schöning, Christian Schröder, Lennart Schwan, Chris Taake, Martin Wortmann   +17 more
wiley   +1 more source

DERIVING THE EXACT FORMULA FOR PERIMETER OF AN ELLIPSE USING COORDINATE TRANSFORMATION

Alifmatika, 2022
The ellipse can be transformed into a circle by dilating the coordinates of the ellipse relative to the x-axis and y-axis. Therefore, this study aimed to derive the formula for the equation of the perimeter of an ellipse by using the transformation of an
Harun Abdul Rohman
doaj   +1 more source

Microstructure‐Controlled Crack Propagation and Fracture Resistance in MoSiBTiC Alloy Revealed by Multiscale Extended Finite Element Method Modeling

Advanced Engineering Materials, EarlyView.
A two‐dimensional multiscale finite element analysis framework was established for the first‐generation MoSiBTiC alloy, and the mechanical and fracture‐related parameters of the constituent phases were calibrated through experiments and simulations. The framework provides a basis for analyzing crack propagation behavior in its complex microstructure ...
Junfeng Du, Takahiro Kaneko, Xinyu Yan, Takahito Ohmura, Kyosuke Yoshimi   +4 more
wiley   +1 more source

Polarization singularities in paraxial vector fields: morphology and statistics

, 2002
Polarization patterns in the transverse plane generically contain singularities: points of circular polarization (C points), lines of linear polarization (L lines), instantaneous zeros (disclinations) and component zeros.
Dennis, MR, Dennis, M.R., M. R. Dennis, Dennis, Mark; id_orcid   +3 more
core   +1 more source

Numerical Calculation of Area of Elliptical Segments

Mathematics, 2020
In this paper, we introduce the notion of an elliptical segment as some analogy of the circular segment and we focus on the problem of calculation of its area.
Dusan Vallo, Jozef Fulier, Lucia Rumanova   +2 more
doaj   +1 more source

Creep‐Induced Microstructural Evolution in an A2‐B2 Superalloy

Advanced Engineering Materials, EarlyView.
A 27.3Ta‐27.3Mo‐27.3Ti‐8Cr‐10Al (at.%) refractory high‐entropy alloy with precipitation‐strengthened A2‐B2 microstructure was studied by creep tests at 1030°C, which demonstrate a transition in deformation mechanisms in the range of 100–150 MPa applied stress. This is associated with changes in dislocation–precipitate interactions. Relevant deformation
Liu Yang, Aparajita Pramanik, Sandipan Sen, Shubhashis Dixit, Marcel Muench, R. J. Vikram, Daniel Schliephake, Yolita M. Eggeler, Ankur Chauhan, Martin Heilmaier, Alexander Kauffmann   +10 more
wiley   +1 more source

Calculating Ellipse Overlap Areas

, 2014
We present an approach for finding the overlap area between two ellipses that does not rely on proxy curves. The Gauss-Green formula is used to determine a segment area between two points on an ellipse.
Hughes, Gary B., Chraibi, Mohcine
core   +2 more sources

Electrified Damage in Motion Systems

Advanced Engineering Materials, EarlyView.
The electrified damage in motion systems is a fundamental framework presenting the degradation pathway arising from the coupling of electrical energy transport with mechanical contact and interfacial chemistry. The framework positions electrified damage as a distinct degradation regime with unique characteristic surface morphologies and failures of ...
M. Humaun Kabir, Angelina Nguyen, Hong Liang   +2 more
wiley   +1 more source