Accretive growth kinematics in Minkowski 3-space

Self Cite

It is known that the kinematics on the Lorentzian surfaces changes according to the casual characters of the vector fields. Suspicions, the character of the generator curve affects the surface growth. Therefore, we determine the model of the growth function in the three-dimensional Minkowski spacetime with a null generating curve. Moreover, the proposed method is illustrated with various examples.

Section: Introductionmentioning

confidence: 79%

Accretive growth kinematics via null evolution curve

Özdemi̇r

Tuğ

2020

Self Cite

“…Quaternions were used to create a fresh viewpoint. The surface formulation was obtained in this manner, and visualization was made simpler [18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Multiplicative generalized tube surfaces with multiplicative quaternions algebra

Ceyhan,

Özdemir,

Gök

2024

Along with other types of calculus, multiplicative calculus brings an entirely new perspective. Geometry now has a new field as a result of this new understanding. In this study, multiplicative differential geometry was used to explore peculiar surfaces. Multiplicative quaternions are also used to depict surfaces. Additionally, multiplicative differential geometry was used to generate the accretive surface subject, which is a developing subject. The derived surfaces' perspective silhouette curve equation is provided. The Bishop multiplicative frame was also established and applied when expressing surfaces along with these. Finally, the surfaces and perspective silhouette curves were visualized using Maple, and the equations were obtained.

Accretive Darboux growth in Lorentz–Minkowski spacetime

Tuğ

Özdemi̇r

Gök

2021

Self Cite

It is known that the geometric methods are used in most fields in natural sciences. Kinematics on curves and surfaces as one of these methods is an essential tool for investigating the growth of some biological objects. In this study, the time-dependent and quaternionic models of accretive growth are considered. For this, first, it is defined as a growth velocity in the direction of the Darboux vector at every point on a spatial non-null curve in three-dimensional Lorentz-Minkowski spacetime. Second, accretive surface growth is presented through quaternions. With the help of the quaternionic form of the growth model, we reach that a point (cell tract) on the accretive surface makes a homothetic motion. Also, several examples and visualizations are given to support the theory.