Süper Elipsler için bir Çevre Formülü Önerisi ve Fizikte Dikdörtgensel Sınır Değer Problemlerinde Kullanımı

Gabriel Lame tarafından tanıtılan süper elipsler veya Lame eğrileri, son yıllarda fizik ve mühendislikte sıkça çalışılan konular olmuştur. Süper elips alanlarının hesaplanması analitik olarak mümkün olsa da, çevre hesaplamaları için formüllerin eksikliği dikkat çekicidir. Bu eksikliği gidermek için bu çalışma, süper elipslerin çevrelerini sayısal olarak hesaplayan bir kod yazmayı ve sayısal sonuçlarla uyumlu yaklaşık bir çevre formülasyonu bulmayı amaçlamıştır. Ek olarak, elde edilen çevre formülasyonu, bir dikdörtgen sınır koşulunda, Laplace denkleminin süper elipslerle yaklaşık bir boyuta indirgenebileceğini ve zor bir fiziksel probleme pratik bir yaklaşık çözüm bulunabileceğini göstermektedir.

Anahtar Kelimeler:

Süper elips, çevre, Laplace denklemi, dikdörtgensel sınırlar

Suggestion of a Perimeter Formula for Super Ellipses and their Use in Rectangular Boundary Value Problems in Physics

Super ellipses or Lame curves introduced by Gabriel Lame have been frequently studied subjects in physics and engineering in recent years. While the calculation of the area of super-ellipses is analytically possible, the lack of formulations for circumference calculations is noteworthy. To overcome this deficiency, this study aimed to write a code that computes the circumferences of super ellipses numerically and to find an approximate circumference formulation compatible with the numerical results. Additionally, the perimeter formulation obtained shows that in a rectangular boundary condition, Laplace's equation can be reduced to approximately one dimension with super ellipses and a practical approximate solution to a difficult physical problem can be found.

Keywords:

Super ellipse perimeter, circumference, Laplace equation, rectangular boundary,

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