By Pierre Pelce, A. Libchaber
In recent times, a lot development has been made within the realizing of interface dynamics of assorted structures: hydrodynamics, crystal progress, chemical reactions, and combustion. Dynamics of Curved Fronts is a vital contribution to this box and may be an integral reference paintings for researchers and graduate scholars in physics, utilized arithmetic, and chemical engineering. The publication include a a hundred page advent by way of the editor and 33 seminal articles from quite a few disciplines. Read more...
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Additional resources for Dynamics of Curved Fronts
Le t u s begi n wit h a simpl e example , a plana r fron t movin g wit h constan t velocit y V. A n elemen t of th e kerne l of L is a perturbatio n of th e interfac e whic h is margina l (it doe s not evolve with time) . In thi s case, th e margina l mode s ar e of th e for m exp(ikl), wher e k is a zer o of th e dispersio n relatio n ω = = Ι*ΐ(^- % k 2 ( 2 - 3 2 a) \ wit h ø = 0. Ther e ar e thre e solutions . On e is a constan t (k = 0) which correspond s t o a simpl e translatio n of th e fron t in th e directio n of propa › wher e gation .
Th e solid) an d • is th e norma l velocit y of th e interface . Since th e laten t hea t per uni t volum e of solid is Q = (hx - hs)ps an d th e diffusio n constan t is D = X/cp, wher e cp is th e specific hea t per uni t volume , on e can expres s th e conservatio n of energ y as Qv • = (Ac (vr) , - DxcpX(vT\) • n. 5. The Free Boundary Problem I n th e mode l explore d in th e following, we will assum e tha t diffusio n coeffi› cient s an d specific hea t per uni t volum e ar e equa l in bot h phase s (th e symmetri c model) .
Th e relatio n θ (I) for th e Ivantso v parabol a is easily obtaine d fro m STATIONAR Y S H A P E S O F A NEEDL E CRYSTA L 49 Pierr e PelcØ wher e æ is th e radiu s of curvatur e at th e tip . 48) as [ + 0 G ( T ? ) e x p ( / C ^ ( r ? ) ) di\ = 0. 51) ar e th e sam e as thos e obtaine d b y Barbier i et al. . 50) is evaluate d b y steepes t descen t method s (see Bende r an d Orzsa g ). Th e functio n ( ) ha s tw o stationar y phas e point s at η = ±i. 50) dominates . T o evaluat e thi s contributio n on e deform s th e origina l contou r (th e rea l axis) to a contou r of steepes t descen t whic h goes close t o th e poin t η = i an d turn s aroun d th e branc h cut whic h begin s at η = z’(l ^2β ) (see Fig .
Dynamics of Curved Fronts by Pierre Pelce, A. Libchaber