▁for ▁techniques ▁involving ▁the ▁modification ▁of ▁time - ste pping ▁computer ▁codes ▁to ▁perform ▁the ▁tasks ▁of ▁b if ur cation ▁analysis . ▁He ▁has ▁applied ▁this ▁approach ▁in ▁several ▁areas ▁of ▁fluid ▁dynamics , ▁in ▁particular ▁to ▁stability ▁analysis ▁of ▁the ▁cyl inder ▁w ake ▁and ▁back ward - f acing ▁step . ▁ ▁B ark ley ▁works ▁on ▁the ▁transition ▁to ▁tur bul ence ▁in ▁she ar ▁flows , ▁including ▁the ▁formation ▁of ▁tur bul ent - lam inar ▁bands ▁and ▁the ▁critical ▁point ▁for ▁pipe ▁flow . ▁ ▁He ▁is ▁also ▁known ▁for ▁der iving ▁an ▁equation ▁to ▁estimate ▁how ▁long ▁it ▁will ▁be ▁until ▁a ▁child ▁in ▁a ▁car ▁asks ▁the ▁question ▁" are ▁we ▁there ▁yet ?" ▁ ▁Awards ▁ ▁In ▁ 2 0 0 5 ▁he ▁was ▁awarded ▁the ▁J . ▁D . ▁C raw ford ▁Prize ▁for ▁out standing ▁research ▁in ▁non linear ▁science , ▁" for ▁his ▁development ▁of ▁high ▁quality , ▁robust ▁and ▁efficient ▁numerical ▁algorithms ▁for ▁pattern ▁formation ▁phen omena ▁in ▁spatial ly ▁extended ▁dynam ical ▁systems ". ▁ ▁In ▁ 2 0 0 8 ▁he ▁was ▁elected ▁Fellow ▁of ▁the ▁American ▁Phys ical ▁Society ▁" for ▁combining ▁computation ▁and ▁dynam ical ▁systems ▁anal ys es ▁to ▁obtain ▁remarkable ▁ins ights ▁into ▁hyd rod ynamic ▁inst abilities ▁and ▁patterns ▁in ▁diverse ▁systems , ▁including ▁flow ▁past ▁a ▁cyl inder , ▁channel ▁flow , ▁l amin ar - t ur bul ent ▁bands , ▁and ▁thermal ▁con ve ction ." ▁That ▁same ▁year ▁he