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
,φ
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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