1. A program for calculating a displacement of a fluid comprising calculating the displacement with the fluid regarded as an elastic structural body for a given period of time.
2. The program according to claim 1, for use in united calculation of compressible fluid, incompressible fluid and elastic structural body, based on a hypothesis that fluid is such a substance that it causes transition from a state (1) at time t1 to a state (2) at time t2 through motion state that can be considered as an elastic body for a short period of time, and after the transition, a memory of elastic deformation is lost to leave only quantity of state.
3. The program according to claim 1, wherein in a complex system composed of a compressible fluid, an incompressible fluid and an elastic structural body, pressures of the compressible fluid and the incompressible fluid at each time are unitedly defined as a function of state quantities of density and temperature at each time, and a viscous stress tensor is defined as a stress concerning motion for a short period of time similarly to elastic body, whereby an overall system unitedly makes Lagrangian movement of physical quantities of fluid and elastic body by directly calculating a displacement up to a next time and employing the displacement.
4. The program according to claim 3, further comprising evaluating effect of pressure gradient \u2207\xb7P at each time as a node force f, and solving a general equation of motion M{u}\u2033+K{u}\u2032+C{u}={f} including a mass matrix M, a stiffness matrix K, a viscosity matrix C, a force vector {f} and a displacement vector {u} to determine the displacement vector {u} at a next time, where \u2032 is a first order differential regarding time and \u2033 is a second order differential regarding time for the compressible fluid, the incompressible fluid and the elastic structural body.
5. The program according to claim 1, wherein material constants of the fluid are transformed into a set of material constants where the fluid is regarded as the elastic structural body for a short period of time, and an entire area to be analyzed is calculated as the elastic structural body using a Navia’s equation that is a fundamental equation for elastic structural body.
6. The program according to claim 1, wherein after performing calculation for one of the given period of time, the displacement of the fluid is reset to zero.
7. The program according to claim 1, wherein a time integration method with respect to a differential equation of second order for the elastic structural body is employed.
8. The program according to claim 1, wherein the time integration method involves applying a Newmark’s \u03b2 method to the entire area to be analyzed.
9. The program according to claim 1, further comprising the steps of dividing space into minute finite elements consisting of elastic structural body elements or fluid elements, calculating a local elasticity matrix employing an appropriate set of elastic structural body material constants for elastic structural body, and calculating for the fluid elements the local elasticity matrix employing a corresponding set of elastic structural body constants that is obtained by multiplying fluid parameters including a time dimension by a short period of time \u0394t or 1\u0394t to offset the time dimension, to determine a overall matrix, thereby solving the same general equation of motion for an overall system composed of the fluid and the elastic structural body.
10. The program according to claim 1, further comprising the calculation procedures of generating a first node position to which the node position has been moved and updated according to the displacement, generating a second node by performing new meshing after updating the node, and interpolating physical quantity of the first node to set and update it as physical quantity of the second node.
11. A program comprising the steps of inputting data of a fluid, transforming material data of the fluid into structural body data with the fluid regarded as an elastic body for a short period of time, feeding the structural body data to an external structure calculation solver to execute structure calculation, and updating variables and resetting displacement of the fluid.
12. The program according to claim 1, wherein for the fluid having a first viscosity \u03bc and a second viscosity \u03bb for a short period of time \u0394t, a Young’s modulus E and a Poisson’s ratio v are determined by
E=\u03bc(3\u03bb+2\u03bc)(\u0394t(\u03bb+\u03bc))
v=0.5\u03bb(\u03bb+\u03bc)
13. The program according to claim 1, wherein the external structure calculation solver has a step of avoiding locking.
14. A calculator for calculating a displacement of a fluid, comprising means for calculating the displacement with the fluid regarded as an elastic structural body for a given period of time.
15. A recording medium storing a program for calculating a displacement of a fluid, comprising a step of calculating the displacement with the fluid regarded as an elastic structural body for a given period of time.
16. A method for acquiring variables concerning at least a state of a fluid, comprising the steps of: acquiring at least information concerning the fluid; and
acquiring the variables concerning at least the state of the fluid by analyzing the acquired information by a Lagrange’s method.
17. The method according to claim 16, wherein the variables are acquired by solving a general equation of motion which are discretized from a governing equations including elasticity terms and viscosity terms to determine an unknown displacement.
18. The method according to claim 17, wherein the variables are acquired by solving simultaneous equations with an unknown displacement as a variable by describing the general equations of motion in terms of known quantities of velocity and acceleration as well as the unknown displacement.
19. The acquisition method according to claim 17, wherein the variables are acquired by solving the general equations of motion in view of a Newmark algorithm or a Wilson algorithm.
20. The acquisition method according to claim 16, further comprising the steps of discretizing a governing equation:
\u03c1
\u2062
\u2003
\u2062
Du
i
Dt
=
{
–
\u2207
P
\u2061
(
\u03c1
,
T
)
+
\u2202
\u03c4
f
,
ij
\u2061
(
u
.
)
\u2202
x
j
+
B
i
\u2062
\u2003
\u2062
\u2026
\u2062
\u2003
\u2062
(
fluid
)
\u2202
\u03c4
e
,
ij
\u2061
(
u
)
\u2202
x
j
+
B
i
\u2062
\u2003
\u2062
\u2026
\u2062
\u2003
\u2062
(
elastics
)
\u2062
\u2062
\u03c4
f
,
,
ij
\u2061
(
u
.
)
=
E
2
\u2062
(
1
+
v
)
\u2062
(
\u2202
u
.
j
\u2202
x
i
+
\u2202
u
.
i
\u2202
x
j
)
+
\u03b4
ij
\u2062
Ev
(
1
+
v
)
\u2062
(
1
–
2
\u2062
v
)
\u2062
\u2202
u
.
k
\u2202
x
k
\u2062
\u2062
\u03c4
e
,
,
ij
\u2062
(
u
)
=
E
2
\u2062
(
1
+
v
)
\u2062
(
\u2202
u
j
\u2202
x
i
+
\u2202
u
i
\u2202
x
j
)
+
\u03b4
ij
\u2062
Ev
(
1
+
v
)
\u2062
(
1
–
2
\u2062
v
)
\u2062
\u2202
u
k
\u2202
x
k
to have the general equations of motion:
M{\xfc}n+1+Kf{{dot over (u)}}n+1+Ke{u}n+1={f}n+1
applying a Newmark algorithm to the general equations of motion, solving simultaneous linear equations regarding an unknown displacement:
(
K
e
+
1
\u03b2\u0394
\u2062
\u2003
\u2062
t
\u2061
K
f
+
1
\u03b2
\u2061
(
\u0394
\u2062
\u2003
\u2062
t
)
2
\u2061
M
)
\u2062
{
u
}
n
+
1
=
{
f
}
n
+
1
+
M
\u2062
(
(
1
2
\u2062
\u03b2
–
1
)
\u2062
{
u
\xa8
}
n
+
1
\u03b2\u0394
\u2062
\u2003
\u2062
t
\u2062
{
u
.
}
n
+
1
\u03b2
\u2061
(
\u0394
\u2062
\u2003
\u2062
t
)
2
\u2062
{
u
}
n
)
+
K
f
\u2062
(
(
\u03b4
2
\u2062
\u03b2
–
1
)
\u2062
\u0394
\u2062
\u2003
\u2062
t
\u2062
{
u
\xa8
}
n
+
(
\u03b4
\u03b2
–
1
)
\u2062
{
u
.
}
n
+
\u03b4
\u03b2\u0394
\u2062
\u2003
\u2062
t
\u2062
{
u
}
n
)
\u2062
K
e
=
\u222b
\u222b
\u222b
B
t
\u2061
D
e
\u2061
B
\u2062
det
\u2062
\u2003
\u2062
J
\u2062
\u2146
\u03c8
\u2062
\u2146
\u03b7
\u2062
\u2146
\u03b6
\u2062
K
f
=
\u222b
\u222b
\u222b
B
t
\u2061
D
f
\u2061
B
\u2062
det
\u2062
\u2003
\u2062
J
\u2062
\u2146
\u03c8
\u2062
\u2146
\u03b7
\u2062
\u2146
\u03b6
\u2062
D
e
=
E
(
1
+
v
)
\u2062
(
1
–
2
\u2062
v
)
\u2061
1
–
v
v
v
0
0
0
v
1
–
v
v
0
0
0
v
v
1
–
v
0
0
0
0
0
0
1
–
2
\u2062
v
2
0
0
0
0
0
0
1
–
2
\u2062
v
2
0
0
0
0
0
0
1
–
2
\u2062
v
2
\u2062
D
f
=
E
f
(
1
+
v
f
)
\u2062
(
1
–
2
\u2062
v
f
)
\u2062
\u2003
1
–
v
f
v
f
v
f
0
0
0
v
f
1
–
v
f
v
f
0
0
0
v
f
v
f
1
–
v
f
0
0
0
0
0
0
1
–
2
\u2062
v
f
2
0
0
0
0
0
0
1
–
2
\u2062
v
f
2
0
0
0
0
0
0
1
–
2
\u2062
v
f
2
\u2062
B
=
\u2202
N
1
\u2202
x
,
\u2026
0
0
0
\u2202
N
1
\u2202
y
,
\u2026
0
0
0
\u2202
N
1
\u2202
z
,
\u2026
\u2202
N
1
\u2202
y
,
\u2026
\u2202
N
1
\u2202
x
,
\u2026
0
0
\u2202
N
1
\u2202
z
,
\u2026
\u2202
N
1
\u2202
y
,
\u2026
\u2202
N
1
\u2202
z
,
\u2026
0
\u2202
N
1
\u2202
x
,
\u2026
and sequentially calculating
B
=
\u2202
N
1
\u2202
x
,
\u2026
0
0
0
\u2202
N
1
\u2202
y
,
\u2026
0
0
0
\u2202
N
1
\u2202
z
,
\u2026
\u2202
N
1
\u2202
y
,
\u2026
\u2202
N
1
\u2202
x
,
\u2026
0
0
\u2202
N
1
\u2202
z
,
\u2026
\u2202
N
1
\u2202
y
,
\u2026
\u2202
N
1
\u2202
z
,
\u2026
0
\u2202
N
1
\u2202
x
,
\u2026
{
u
\xa8
}
n
+
1
=
(
1
–
1
2
\u2062
\u03b2
)
\u2062
{
u
\xa8
}
n
–
1
\u03b2\u0394
\u2062
\u2003
\u2062
t
\u2062
{
u
.
}
n
+
1
\u03b2
\u2061
(
\u0394
\u2062
\u2003
\u2062
t
)
2
\u2062
(
{
u
}
n
+
1
–
{
u
}
n
)
{
u
.
}
n
+
1
=
(
1
–
\u03b4
\u03b2
)
\u2062
{
u
.
}
n
+
(
1
–
\u03b4
2
\u2062
\u03b2
)
\u2062
\u0394
\u2062
\u2003
\u2062
t
\u2062
{
u
\xa8
}
n
+
\u03b4
\u03b2\u0394
\u2062
\u2003
\u2062
t
\u2062
(
{
u
}
n
+
1
–
{
u
}
n
)
for every time, where the acquired information includes a first viscosity coefficient \u03bc, a second viscosity coefficient \u03bb, a Young’s modulus E, and a Poisson’s ratio v, and where Ni is an interpolation function, \u03b2 and \u03b4 are Newmark variables, t is a period of time,
\u0394t is a short period of time, {u}n+1 is node displacement, and {f}n+1 is node load, which may include the node load related to pressure gradient {\u2207P(\u03c1, T)}.
21. The method according to claim 16, further comprising the steps of inputting data necessary for performing at least one of electric field analysis, magnetic field analysis, electrical analysis and optical analysis, solving a fluid-structure analysis concerning fluid, elastic body and visco-elastic body by a Lagrange’s solution, and calculating the electric field analysis, magnetic field analysis, electrical analysis and optical analysis by a meshless calculation method.
22. The acquisition method according to claim 16, further comprising a step of making calculation by a finite element method in performing at least one of electric field analysis, magnetic field analysis, electrical analysis and optical analysis.
23. The acquisition method according to claim 16, wherein the elastic solver has locking avoidance means.
24. The acquisition method according to claim 16, further comprising the steps of setting an objective function, and automatically calculating a maximum or a minimum of the objective function.
25. The acquisition method according to claim 16, wherein a thermodynamic fundamental equation concerning the fluid is made isomorphic to that of the elastic body, whereby a stiffness matrix concerning the fluid is made isomorphic to that of the elastic body.
26. A device for acquiring variables concerning at least a state of a fluid, comprising:
means for acquiring at least information concerning the fluid; and
means for acquiring the variables concerning at least the state of the fluid by analyzing the acquired information by a Lagrange’s method.
27. A recording medium for acquiring variables concerning at least a state of a fluid, comprising:
a step of acquiring at least information concerning the fluid; and
a step of acquiring the variables concerning at least the state of the fluid by analyzing the acquired information by a Lagrange’s method.
The claims below are in addition to those above.
All refrences to claim(s) which appear below refer to the numbering after this setence.
1. A prostacyclin compound of Formula (II), or a pharmaceutically acceptable salt thereof:
wherein R1 is O;
R2 is tetradecyl, pentadecyl, hexadecyl, heptadecyl or octadecyl; and
n is an integer from 0 to 5.
2. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein n is 0 or 1.
3. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein n is 0.
4. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein n is 1.
5. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein R2 is tetradecyl.
6. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein R2 is pentadecyl.
7. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein R2 is hexadecyl.
8. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein R2 is heptadecyl.
9. The prostacyclin compound of claim 1, or a pharmaceutically acceptable salt thereof, wherein R2 is octadecyl.
10. The prostacyclin compound of claim 5, or a pharmaceutically acceptable salt thereof, wherein n is 1.
11. The prostacyclin compound of claim 6, or a pharmaceutically acceptable salt thereof, wherein n is 1.
12. The prostacyclin compound of claim 7, or a pharmaceutically acceptable salt thereof, wherein n is 1.
13. The prostacyclin compound of claim 8, or a pharmaceutically acceptable salt thereof, wherein n is 1.
14. The prostacyclin compound of claim 9, or a pharmaceutically acceptable salt thereof, wherein n is 1.
15. A prostacyclin compound of Formula (II), or a pharmaceutically acceptable salt thereof:
wherein n is 0, R1 is NH or O and R2 is a linear C5-C18 alkyl.
16. The prostacyclin compound of claim 15, or a pharmaceutically acceptable salt thereof, wherein R1 is NH.
17. The prostacyclin compound of claim 15, or a pharmaceutically acceptable salt thereof, wherein R1 is O.
18. The prostacyclin compound of claim 16, or a pharmaceutically acceptable salt thereof, wherein R2 is a heptyl, octyl, nonyl, decyl, undecyl, dodecyl, tridecyl, tetradecyl, pentadecyl, hexadecyl, heptadecyl or octadectyl.
19. The prostacyclin compound of claim 17, or a pharmaceutically acceptable salt thereof, wherein R2 is a heptyl, octyl, nonyl, decyl, undecyl, dodecyl, tridecyl, tetradecyl, pentadecyl, hexadecyl, heptadecyl or octadectyl.