Computational Physics - M Jensen Episode 1 Part 7 docx
Computational Physics - M. Jensen Episode 1 Part 7 docx
... interval [0 ,10 0] with using the
Gauss-Legendre method.
1 1.305 3.334
2 6 .74 7 7. 473
3 16 .030 10 .954
4 28.330 13 .463
5 42.556 14 .77 6
6 57. 444 14 .77 6
7 71 . 670 13 .463
8 83. 970 10 .954
9 93.253 7. 473
10 98.695 ... different methods as functions of the num-
ber of mesh points
.
Trapez Simpson Gauss-Legendre
10 1. 8 210 20 1. 214 025 0 .14 60448
20 0. 912 678 0.60...
Computational Physics - M. Jensen Episode 1 Part 1 ppsx
... . 319
17 .1. 1 The histogram method . . . . . . . . . . . . . . . . . . . . . . . . . . . 319
17 .1. 2 Multi-histogram method . . . . . . . . . . . . . . . . . . . . . . . . . . 319
17 .2 Renormalization ... several good
1
With Fortran we will consistently mean Fortran 90/95. There are no programming examples in Fortran 77 in
this text.
COMPUTATIONAL PHYSICS
M. Hjorth -Jensen
D...
Computational Physics - M. Jensen Episode 1 Part 2 pot
... 0.93 576 230E -1 3 -0 .3066 811 1E-04 10 0
40.000000 0.42483543E - 17 -0 . 316 57 319 E+ 01 1 27
50.000000 0 .19 2 874 98E- 21 0 .11 072 933E+05 15 5
60.000000 0. 875 6 510 8E-26 -0 .33 516 811 E+09 18 2
70 .000000 0.3 975 4497E-30 -0 .32 979 605E +14 ... 0.4 874 60E-08 72
30.0 0.93 576 2E -1 3 -0 .34 213 4E-04 10 0
40.0 0.424835E - 17 -0 .2 210 33E+ 01 1 27
5...
Computational Physics - M. Jensen Episode 1 Part 3 doc
... mechanical prob-
lems from both atomic physics and nuclear physics. In atomic and nuclear physics the single-
particle degrees are represented by quantum numbers such orbital angular momentum, total
angular ... 12 7 .
sigma1 =SQRT( ( sumsq2 sum xbar ) / 1 26.)
! second method to ev aluat e the st andard d e vi a tio n
sumsq2 =0.
DO i =1 , 12 7
sumsq2=sumsq2 +(x ( i ) xbar ) 2
EN...
Computational Physics - M. Jensen Episode 1 Part 4 pdf
... 1. 000834 1. 000008 1. 000000 1. 000000 1. 010 303 1. 000000
1. 0 2 .72 0548 2. 71 8 304 2. 71 8 282 2. 71 8 282 2 .75 3353 2. 71 8 282
2.0 7. 395 216 7. 38 911 8 7. 3890 57 7.389056 7. 283063 7. 389056
3.0 20 .10 2280 20.08 570 4 ... 20.0855 37 20.2504 67 20.0855 37
4.0 54.643664 54.598605 54.59 815 5 54.59 815 1 54. 71 1 78 9 54.59 815 0
5.0 14 8.536 878 14 8. 414 396 14...
Computational Physics - M. Jensen Episode 1 Part 5 pptx
... pointers this means
that matr is
pointer-to-a-pointer-to-an-integer
which we can write matr. Furthermore matr is
a-pointer-to-a-pointer
of five integers. This interpretation is important when ... Programming details
In the following discussion, matrices are always two-dimensional arrays while vectors are one-
dimensional arrays. Many programming problems arise from improper treatment of ... so...
Computational Physics - M. Jensen Episode 1 Part 6 doc
... divided
difference of order as
(7 .15 )
meaning that the corresponding coefficient is given by
(7 .16 )
With these definitions we see that Eq. (7. 7) can be rewritten as
(7 . 17 )
If we replace
in Eq. (7 .15 ) with , that ... slight modifications) steps
and the other on more adaptive steps, namely so-called Gaussian quadrature methods. Both main
methods encompass a plethora of approximati...
Computational Physics - M. Jensen Episode 1 Part 8 pdf
... 999 10 30 993
0. 3-0 .4 939 960 10 23 9 37
0. 4-0 .5 10 38 10 01 1002 992
0. 5-0 .6 10 37 10 47 10 09 10 09
0. 6-0 .7 10 05 989 10 03 989
0. 7- 0 .8 986 962 985 954
0. 8-0 .9 10 00 10 27 10 09 10 23
0. 9 -1 .0 9 91 1 015 9 61 1026
0.49 97 ... 1. 59064E-02
10 00 7. 83486E- 01 5 .14 102E-03
10 000 7. 85488E- 01 1.60 311 E-03
10 0000 7. 85009E- 01 5.0...
Computational Physics - M. Jensen Episode 1 Part 9 pptx
... rewriting
(9 .10 9)
since
(9 .11 0)
Perform then a Monte Carlo sampling for
(9 .11 1)
with ,
9.5. IMPROVED MONTE CARLO INTEGRATION 15 3
where is a random number in the interval [0 ,1] .
The algorithm for the ... (&idum ) sq rt2 ;
}
fx=gaussian_MC ( x ) ;
int_mc += fx ;
sum_sigma += fx fx ;
}
16 4 CHAPTER 10 . RANDOM WALKS AND THE METROPOLIS ALGORITHM
This mimicks the way a real system...
Computational Physics - M. Jensen Episode 2 Part 7 pot
... eigenvalues until Eq. (15 .23) is satisfied.
14 .9. PHYSICS PROJECT: STUDIES OF NEUTRON STARS 2 91
Quantity Units
MeVfm
MeVfm
fm
MeVc
Kg= MeVc
1 Kg = MeVc
m
MeV c
19 7. 3 27 MeVfm
list here the units ... matrix
(16 .42)
we can reformulate again the problem as a matrix-vector multiplication
(16 .43)
meaning that we can rewrite the problem as
(16 .44)
If
does not depend on time , w...
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