Chapter 6 Scaling Laws in Miniaturization

a nucleus and organelles.Lipids - 脂 質 , 脂6.3 Scaling in Rigid-Body Dynamics6.3.1 Scaling in Dynamic Forces1 s + at2= v20 t(6.3)By letting = 0 0,v22sa = (6.4)t2 sM3 2∝ ( l)(l )−2F = Ma =t(6.5)t6.3.2 The Trimmer Force Scaling Vector• Trimmer (1989) proposed a unique matrix to represent force scaling with relativeparameters of acceleration a, time t, and power density P/V 0 .• Force scaling factor:F= [ lF⎡l⎢⎢l] =⎢l⎢⎣l1234⎤⎥⎥⎥⎥⎦(6.6)• Acceleration a: from Eq. (6.5),a = [ lF][ l]3 −1⎡l⎢⎢l=⎢l⎢⎣l1234⎤⎥⎥[l⎥⎥⎦−3⎡l⎢⎢l] =⎢ l⎢⎣ l−2−101⎤⎥⎥⎥⎥⎦(6.7)• Time t: from Eq. (6.5),t =2sMF1∝ ([ l ][ l3][ l−F])0.5⎡l⎢⎢ l=⎢l⎢⎣ l1.510.50⎤⎥⎥⎥⎥⎦(6.8)4