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Table 4

Glossary of symbols.

aT, bT, AT, BT,
αT, βT Parameters for Tillotson EoS
α,β Parameters for artificial viscosity
cg Crack growth speed
cs Sound speed
C αβ Correction tensor
d Dimension
d t Depth of tree node
D Dimension
E 0 Parameter for Tillotson EoS
E cv Energy of complete vaporization
E iv Energy of incipient vaporization
ϵ Scalar strain
ϵ s Parameter for artificial stress
ϵ v Parameter for artificial viscosity
Strain rate tensor
ζ αβ Artificial stress
η ϱ/ϱ0
G Gravitational constant
h Smoothing length
J 2 Second invariant of Sαβ
k Parameter for Weibull distribution
K 0 Bulk modulus at zero pressure
m Parameter for Weibull distribution
m a Mass of particle a
μ Shear modulus
M Solar mass
n(ε) Weibull distribution
n Parameter for artificial stress
n act Number of activated flaws
n M Parameter for Murnaghan EoS
n tot Number of total flaws of a particle
N children Number of children of a tree node, 2D
N flaws Number of total flaws
N threads Number of threads on GPU
N p Number of SPH particles
p Pressure
Πab Artificial pressure for particle a and b
r ab Distance between particle a and b
R 0 Initial radius of cloud sphere
R αβ Rotation rate tensor
ϱ Density
ϱ 0 Initial density
s Parameter for kernel function
s 0 Edge length of root node
s d t Edge length of node of depth dt
S αβ Deviatoric stress tensor
σ αβ Stress tensor
t Time
t f Free-fall time
T Temperature
ϑ Parameter for Barnes-Hut tree
u Internal Energy
χ η−1
v esc Escape velocity
W(rab;h) Kernel function
x a Coordinates of particle a
x sph Factor for XSPH algorithm
v a Velocity of particle a
Y 0 Von Mises yield stress
Ω Angular velocity

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