Colloquium 2008

• 題目:
  Amplitude equation for the Rosensweig instability in ferrofluids and ferrogels
  
  
• 講師:
  Prof. H. R. Brand
  ( Universita"t Bayreuth, Germany )
  
• 日時
  2008年9月8日(月曜日)13:00〜14:00
  
• 場所
  理学部2号館2階11号室（2-2-11）
  
• 要旨
  We first present an extensive introduction of the materials investigated on the topic as well as a description of the experimental results modeled. We then derive from the basic hydrodynamic and magnetic equations and boundary conditions an amplitude equation for the Rosensweig instability, which arises when a magnetic field is applied perpendicularly to the free surface of a magnetic liquid or a magnetic gel. Starting from the linear solution, a systematic expansion of those equations and boundary conditions in terms of the distance to the threshold is the standard procedure of the weakly nonlinear analysis. To adapt this method to the Rosensweig instability, the adjoint linear eigenvectors in the presence of a deformable surface are needed to satisfy Fredholm's theorem. This has been achieved recently and is useful for other instability problems involving deformable surfaces, like the Marangoni instability. This enabled us to perform the usual expansion procedure for the full dynamic problem up to third order, which in the limit of vanishing frequency gives the desired amplitude equation for the stationary instability. It contains cubic and quadratic nonlinearities as well as first and second order time derivatives of the pattern amplitudes and will be discussed.
  
  
• 連絡先: 北 孝文 (内線 2687)

物理コロキウム世話人 奥田 浩司 (内線 3442)