β

v n ( t , 0 )

v n t ( t , 0 )

< β < 0

v n ( t , 0 ) < 0

v n ( t , 0 ) 0

t

v n t ( t , 0 ) > 0

β = 0

v n ( t , 0 ) = 0

v n t ( t , 0 ) = 0

0 < β < 3 2

v n ( t , 0 ) > 0

v n ( t , 0 ) 0

t

v n t ( t , 0 ) < 0

β = 3 2

v n ( t , 0 ) > 0

v n ( t , 0 ) = constant

v n t ( t , 0 ) = 0

3 2 < β < 5 3

v n ( t , 0 ) > 0

v n ( t , 0 )

t

v n t ( t , 0 ) > 0

β = 5 3

v n ( t , 0 ) = 0

v n ( t , 0 )

t

Exponentially

v n t ( t , 0 ) > 0

5 3 < β 2

v n ( t , 0 ) = 0

v n ( t , 0 )

t t 1

v n t ( t , 0 ) > 0