Environmental Engineering Reference
In-Depth Information
φ st
stationary point of the
φ
dynamics
φ
lower boundary of the
φ
dynamics
φ +
upper boundary of the
φ
dynamics
ω
(r)
kernel function in the integral operator
C.2 Latin symbols
B 1 [
·
]
first-order modified Bessel function
C
integration constant
D
coefficient expressing the strength of the spatial coupling
f (
φ
)
deterministic function (drift term)
f 1 (
φ
), f 2 (
φ
)
drift term in states 1 and 2
F ( t )
time-dependent forcing
g (
φ
)
deterministic function (multiplicative term)
g S (
φ
)
deterministic function arising from the relation
g (
φ
)
ξ
( t )
=
s
g S (
φ
)
G ( r )
correlation function
h
random height of a jump in the compound Poisson process
h L
Fourier transform of the spatial operator
L
(
φ
)
I
integral scale
i p
intensity of the peak in the structure function S ( k )
=
,
k
wave-number vector, k
( k x
k y )
k 1 , k 2
transition rates of dichotomous noise
K dn
cumulant generating function of dichotomous noise
L
[
φ
]
operator expressing the spatial coupling of the
φ
dynamics
l (
φ i j )
finite-difference equivalent of
L
[
φ
]
M dn
moment-generating function of dichotomous noise
n 1 , n 2
residence time in the above- (below-) threshold state
P 1 ( t ), P 2 ( t )
state probability of dichotomous noise
p (
φ
)or p (
φ
)
probability density function (pdf ) of the variable
φ
P (
φ
)or P (
φ
)
cumulative distribution function of the variable
φ
q ( t )
external random driver
r
coordinate vector, r
=
( x
,
y )
s dn
intensity of dichotomous noise
s gn
intensity of Gaussian white noise
s sn
intensity of shot noise
S ( k )
structure function
t
time
V (
φ
)
deterministic potential of the state variable
V
(
φ
)
probabilistic potential of the state variable
φ
φ
V 1 (
), V 2 (
)
potential of the state variable in states 1 and 2
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