Biomedical Engineering Reference
In-Depth Information
∇×
H
−
ε
n
∂
E
s
q
q
q
v
d
t
=
(2.5e)
+
ν
n
∂
E
∇×
N
d
t
=
0
(2.5f)
where the modified Lorentz equation for the forces acting on the
quarks is
×
M (2.5g)
and constitutive equations B
=
μ
n
H, D
=
ε
n
Eand M
=
ν
n
N
where
ε
n
μ
n
and
ε
n
are invariant scalars, the nuclear constitutive
parameters similar to those of free space,
ε
0
and
μ
0
,exceptthe
energy density within the nucleus now depends upon the three
gluon fields
F
q
q
E
×
B
q
q
q
q
=
+
v
+
v
1
2
(
ε
0
E
·
E
+
μ
0
H
·
H
+
ν
0
N
·
N
)
d
V
d
U
N
=
ρ
N
d
V
=
(2.5h)
where
N
istermedthenuclearfieldand
˜
M
isthenuclearfluxdensity.
As with
c
ε
0
μ
0
)
−
1
/
2
there are corresponding relationships
between the gluon speed and the ratios of the three fields. These
modified equations provide three orthogonal motions per quark.
There are 6 unknowns per particle, 18 in the nuclear system. The
curl equations, Eqs. (2.5d-f), provide four scalar equations, and
therearetwovirialequationstogivesixequationsinsixunknowns.
Like the photon, the resulting analytic parametric solutions may be
compared to the experimental results given by particle physics.
In the strong nuclear case there are 3
×
4 scalar curl equations
plus 3
×
2 force balance equations, making 18 equations in 3
particles altogether that can be solved to yield 6 quantum numbers
per particle in nuclear structures. This compares with the 2
×
3
scalar equations from Maxwell's curl equations plus 2 force balance
equations, totalling 8 equations per 2 particles, giving 4 quantum
numbers per particle for atomic structures. The two extra quantum
numbers agree with the experimental observations of high-energy
physics. The three quarks have three-way streams so that each
particle performs spinor motions in three planes and not two as in
the case of EM-related particles such as the proton and the electron.
=
(
