Analyzer
An analyzer includes a magnetic moment application unit configured to apply a magnetic moment to a particle system defined in a virtual space, a magnetic field calculation unit configured to calculate a magnetic physical quantity related to the particle system including particles, to which the magnetic moment is applied by the magnetic moment application unit, and a particle state calculation unit configured to numerically calculate a governing equation, which governs the movement of each particle, using the calculation result in the magnetic field calculation unit. The magnetic field calculation unit numerically calculates an induction magnetic field using induced magnetization induced in each particle due to a time variation in an external magnetic field and a magnetic field obtained by interaction between magnetic moments based on the induced magnetization.
1. An analyzer comprising:
a processor; and
a memory coupled to the processor, the memory including a plurality of program modules executable by the processor, the plurality of program modules including:
a magnetic moment application module configured to cause the processor to apply a magnetic moment to a particle system defined in a virtual space,
a magnetic field calculation module configured to cause the processor to calculate a magnetic physical quantity related to the particle system including particles, to which the magnetic moment is applied by the processor as a result of executing the magnetic moment application module, and
a particle state calculation module configured to cause the processor to numerically calculate a governing equation, which governs a movement of each particle, using the calculation result in the magnetic field calculation module,
wherein the magnetic field calculation module causes the processor to numerically calculate an induction magnetic field in a particle group using an expression for an induction magnetic field derived by gauge transformation using a local gravity center vector representing a gravity center position of the particle group to be analyzed, in which particles within the particle group are not electrically insulated from one another,
wherein the expression for the induction magnetic field is:
H
(
r
i
)
=
-
a
3
6
∑
j
⋐
i
N
i
σ
j
[
B
.
j
-
(
n
ij
·
B
.
j
)
n
ij
r
ij
-
(
r
ij
·
d
ii
)
B
.
j
-
(
r
ij
·
B
.
j
)
d
ii
r
ij
3
]
-
1
6
σ
i
a
2
B
.
i
-
1
30
∑
j
⋐
i
N
i
σ
j
a
5
3
(
n
ij
·
B
.
j
)
n
ij
-
B
.
j
r
ij
3
wherein a is a particle size, N is a number of particles, σ is an electrical conductivity, n is an expansion order of spherical harmonics, r is vector based on a radial position, B is a magnetic flux density, d is a vector based on the local gravity center vector, and i and j are integer indices.
2. The analyzer according to claim 1 ,
wherein the magnetic field calculation module causes the processor to numerically calculate an induction magnetic field in the particle group using the expression for an induction magnetic field derived by transforming a vector potential of the particle system to a gauge described using a vector product of the local gravity center vector and the magnetic flux density of the particle system.
3. The analyzer according to claim 1 ,
wherein a plurality of particle groups including a first particle group and a second particle group electrically insulated from each other are arrangeable in the particle system, and
the magnetic field calculation module causes the processor to calculate an induction magnetic field in the first particle group using an expression for a first induction magnetic field derived by the gauge transformation using a first local gravity center vector representing the gravity center position of the first particle group and to calculate an induction magnetic field in the second particle group using an expression for a second induction magnetic field derived by the gauge transformation using a second local gravity center vector representing the gravity center position of the second particle group.
4. A non-transitory computer-readable medium storing thereon a computer program which, when executed by a processor of a computer, causes the computer to perform operations comprising:
applying a magnetic moment to each of particles of a particle system defined in a virtual space;
calculating a magnetic physical quantity related to the particle system including the particles, to which the magnetic moment is applied; and
numerically calculating a governing equation, which governs a movement of each particle, using the calculation result of the magnetic physical quantity,
wherein the calculating the magnetic physical quantity includes numerically calculating an induction magnetic field in a particle group using an expression for an induction magnetic field derived by gauge transformation using a local gravity center vector representing a gravity center position of the particle group to be analyzed, in which particles within the particle group are not electrically insulated from one another,
wherein the expression for the induction magnetic field is:
H
(
r
i
)
=
-
a
3
6
∑
j
⋐
i
N
i
σ
j
[
B
.
j
-
(
n
ij
·
B
.
j
)
n
ij
r
ij
-
(
r
ij
·
d
ii
)
B
.
j
-
(
r
ij
·
B
.
j
)
d
ii
r
ij
3
]
-
1
6
σ
i
a
2
B
.
i
-
1
30
∑
j
⋐
i
N
i
σ
j
a
5
3
(
n
ij
·
B
.
j
)
n
ij
-
B
.
j
r
ij
3
wherein a is a particle size, N is a number of particles, σ is an electrical conductivity, n is an expansion order of spherical harmonics, r is vector based on a radial position, B is a magnetic flux density, d is a vector based on the local gravity center vector, and i and j are integer indices.
5. An analyzer comprising:
a magnetic moment application hardware component configured to apply a magnetic moment to a particle system defined in a virtual space;
a magnetic field calculation hardware component configured to calculate a magnetic physical quantity related to the particle system including particles, to which the magnetic moment is applied by the magnetic moment application hardware component; and
a particle state calculation hardware component configured to numerically calculate a governing equation, which governs a movement of each particle, using the calculation result in the magnetic field calculation hardware component;
wherein the magnetic field calculation hardware component numerically calculates an induction magnetic field in a particle group using an expression for an induction magnetic field derived by gauge transformation using a local gravity center vector representing a gravity center position of the particle group to be analyzed, in which particles within the particle group are not electrically insulated from one another,
wherein the expression for the induction magnetic field is:
H
(
r
i
)
=
-
a
3
6
∑
j
⋐
i
N
i
σ
j
[
B
.
j
-
(
n
ij
·
B
.
j
)
n
ij
r
ij
-
(
r
ij
·
d
ii
)
B
.
j
-
(
r
ij
·
B
.
j
)
d
ii
r
ij
3
]
-
1
6
σ
i
a
2
B
.
i
-
1
30
∑
j
⋐
i
N
i
σ
j
a
5
3
(
n
ij
·
B
.
j
)
n
ij
-
B
.
j
r
ij
3
wherein a is a particle size, N is a number of particles, σ is an electrical conductivity, n is an expansion order of spherical harmonics, r is vector based on a radial position, B is a magnetic flux density, d is a vector based on the local gravity center vector, and i and j are integer indices.
6. The analyzer according to claim 5 ,
wherein the magnetic field calculation hardware component numerically calculates an induction magnetic field in the particle group using the expression for an induction magnetic field derived by transforming a vector potential of the particle system to a gauge described using a vector product of the local gravity center vector and the magnetic flux density of the particle system.
7. The analyzer according to claim 5 ,
wherein a plurality of particle groups including a first particle group and a second particle group electrically insulated from each other are arrangeable in the particle system, and
the magnetic field calculation hardware component calculates an induction magnetic field in the first particle group using an expression for a first induction magnetic field derived by the gauge transformation using a first local gravity center vector representing the gravity center position of the first particle group and calculates an induction magnetic field in the second particle group using an expression for a second induction magnetic field derived by the gauge transformation using a second local gravity center vector representing the gravity center position of the second particle group.