strings with junctions: cuspy events and unzipping mechanisms

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1 strings with junctions: cuspy events and unzipping mechanisms mairi sakellariadou king s college london university of london

2 outline cusps and pseudo-cusps elghozi, nelson, sakellariadou (2014) bursts of GW elghozi, sakellariadou (in progress) zipping and unzipping stability of junctions avgoustidis, pourtsidou, sakellariadou (2014)

3 cusps and pseudo-cusps

4 cusps and pseudo-cusps motivation FD-string junctions generically contain cusps DBI string ending on D1-branes DBI string ending on D2 branes L davis, nelson, rajamanoharan, sakellariadou JCAP 0811 (2008) 022

5 heavy b.c. for light string:

6 heavy b.c. for light string:

7 heavy b.c. for light string: a ( + t), b ( t) periodic for a dense subset of Ψ [ /2, /2] decompose them in fourier series

8 heavy b.c. for light string: a ( + t), b ( t) periodic for a dense subset of Ψ [ /2, /2] decompose them in fourier series symmetries between 2 movers on the string: b a = 0 reflection of through axis // to end of string (z-axis)

9 analytic estimation of cusps/pseudo-cusps: average and standard deviation of a and b in unit sphere cusps when how many times the standard deviation is larger than the average distance in unit sphere between 2 average circles

10 analytic estimation of cusps/pseudo-cusps: average and standard deviation of a and b in unit sphere cusps when more cusps for a long string with large amplitude waves than a short straight string or a small-scale structured string

11 pseudo-cusps l 4-velocity at point of closest approach cusps: null vector pseudo-cusps: theoretical velocity l 0 = 1 l i 1+cos = c c/8 + 4 c/384 softness of relativistic part of string for a cusp: c = 0 and v=c

12 numerical simulation string s ends fixed on heavy strings position/velocity at t=0 defined by fourier series

13 numerical simulation string s ends fixed on heavy strings position/velocity at t=0 defined by fourier series inputs: -- string s length -- interstring distance -- parameters to fix oscillatory behavior of string n h m : # harmonics m / m : highest value (amplitudes in [ hm, hm] )

14 numerical simulation string s ends fixed on heavy strings position/velocity at t=0 defined by fourier series inputs: -- string s length -- interstring distance -- parameters to fix oscillatory behavior of string n h m : # harmonics how wavy is the string; m / m : highest value (amplitudes in [ hm, hm] ) a xa x a x 2 and b xb x b x 2

15 numerical simulation string s ends fixed on heavy strings position/velocity at t=0 defined by fourier series inputs: -- string s length -- interstring distance -- parameters to fix oscillatory behavior of string n h m : # harmonics how wavy is the string; m / m : highest value (amplitudes in [ hm, hm] ) a xa x a x 2 and b xb x b x 2 decompose strings in large # pieces travelling at velocity of their geometric center and compute their evolution over a period

16 numerical simulation 237 strings 8719 cusps and 4659 pseudo-cusps string s ends fixed on heavy strings position/velocity at t=0 defined by fourier series inputs: -- string s length -- interstring distance -- parameters to fix oscillatory behavior of string n h m : # harmonics how wavy is the string; m / m : highest value (amplitudes in [ hm, hm] ) a xa x a x 2 and b xb x b x 2 decompose strings in large # pieces travelling at velocity of their geometric center and compute their evolution over a period

17 about 4300 pseudo-cusps equality case 80 % of pseudo-cusps with a difference between two velocities below 10 4 cusps: pseudo-cusps v > ( )c v [( )c, ( )c]

18 to check criterion: a xa x 1+ 2 a cuspy phenomena R( = 4.1) 1 a xa x a

19 number of cusps and pseudo-cusps / m and a x a x, b x b x / m 21 (ripple s size) 41 (smallest ) m 2n eff

20 number of cusps and pseudo-cusps / m and a x a x, b x b x / m 21 (ripple s size) 41 (smallest ) m 2n eff

21 number of cusps and pseudo-cusps / m and a x a x, b x b x the more energy is on the string, the more cusps appear

22 8% without cuspy events (80-90)%with >50 cuspy events

23 deviation from average over a period in time almost linear smaller radius of curvature for strings with many cusps time-average of space-averaged radius of curvature of each string a smaller radius of curvature means more waves, hence more cusps

24 unzipping mechanisms

25 unzipping mechanisms motivation rajantie, sakellariadou, stoica, JCAP 0711 (2007) 021 sakellariadou, stoica, JCAP 0808 (2008) 022

26 zipping/unzipping in NG approximation t = 0 evolution of local angle at a massive junction t= t

27 s 3 s 3 = const. crit equilibrium value: vector sum of 3 tensions vanishes

28 2 cos w 3 = 0 even though the constant zipper growth prediction is based on special configurations: 2 cos w 3 = 0 these configurations are stable Unzipping cannot happen by simply perturbing crit s 3 s 3 = const. crit equilibrium value: vector sum of 3 tensions vanishes

29 unequal tensions s 3 equal tensions 2 cos w 3 = 0 s 3 = const. crit equilibrium value: vector sum of 3 tensions vanishes

30 possible unzipping mechanisms: velocity damping in expanding background monopole/string forces string curvature (loops with junctions)

31 monopole force Unperturbed case reduce monopole mass unzipping happens faster results depend on monopole mass and magnitude of force increase monopole mass unzipping is delayed

32 string force close to junction: linear force away from junction: force exponentially damped attractive force < crit junction accelerates repulsive force > crit junction decelerates

33 string curvature (loops with junctions)

34 heavier bound states can actually unzip, leading to a lower abundance of heavy strings in the network in agreement with numerical simulations

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