15 5 decimal

&[DATE] &[TIME] - &[FILENAME]

Based on Draghilev's method SMath file by Viacheslav N. Mezentsev (uni)

Pod 36.7 - 19.6 - 11.5 - 2.6 - 7.6 15.4 26.1 42.2 60.6 80.1 1510204060100200400760 . . . . . . . . . . 20202020202020202020410 mat transpose :

Vapor pressure = f(Temperature)

points Pod 3 col :

b - unknown parameters T - temperature [K] p - vapor pressure [atm]

size Pod 4 col :

Temperature [C]

Pressure [atm]

t Pod 1 col :

p Pod 2 col :

T t 273 + :

p 10 b 1 el b 2 el T / + b 3 el T 10 log * +^≡

Proposed function for fitting the data:

x φ 11 x / x 10 log 31 mat :

n T length :

n 10

k x φ length :

k 3

T b f b j el T φ j el * (j 1 k sum :

b 78.0124 5018.6253 - 23.9183 - 31 mat :

b S p i el 10 T i el b f^- (2^(i 1 n sum :

b S 1911.24579934548

b S 1 e 719165292610 ln * 80741347236310 / ln * - (* 23630000 /^- (2^5 e 73748584310 ln * 30304486112675 / ln * - 12670000 /^- (2^+ 10 e 74394747810 ln * 178703875232 / ln * - (* 5230000 /^- (2^+ 20 e 6183049110 ln * 2487503213525 / ln * - 1040000 /^- (2^+ 40 e 3667750910 ln * 1459016314035 / ln * - 610000 /^- (2^+ 60 e 87400754310 ln * 34490188614425 / ln * - 14420000 /^- (2^+ 100 e 61049611810 ln * 238465451299110 / ln * - 9970000 /^- (2^+ 200 e 97854415910 ln * 37695240815765 / ln * - 15760000 /^- (2^+ 400 e 75001502710 ln * 1899796416685 / ln * - (* 5560000 /^- (2^+ 760 e 75091843810 ln * 281518391353110 / ln * - 11770000 /^- (2^+

x y z f x y z 31 mat S :

x y z f 1 e 10 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + 2363 /^- (2^5 e 5 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + 1267 /^- (2^+ 10 e 2 y * 523 x * + (10 ln * 523 z * 5232 / ln * + 523 /^- (2^+ 20 e 5 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + 1352 /^- (2^+ 40 e 5 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + 1403 /^- (2^+ 60 e 5 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + 1442 /^- (2^+ 100 e 10 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + 2991 /^- (2^+ 200 e 5 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + 1576 /^- (2^+ 400 e 5 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + 1668 /^- (2^+ 760 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^- (2^+

x y z f1 x y z f x diff :

x y z f1 2 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^* 760 e 11775 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* 55610 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + (* - 1963236 /^400 - e 11775 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* - 111210 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + (* + 1963236 /^1 e 11774175 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* 3945 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* - (* 39411775 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* - 111210 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + (* + (* - 773514984 /^200 - e 4175 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* - 7885 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* + 657192 /^1 e 139157610 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* 29915 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* - (* 9974175 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* - 7885 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* + (* - 655220424 /^100 - e 78810 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* - 29915 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* + 2356908 /^1 e 39429915 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* 144210 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* - (* 72178810 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* - 29915 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* + (* - 1699330668 /^60 - e 29915 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* - 288410 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* + 4313022 /^1 e 299114425 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* 14035 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* - (* 140329915 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* - 288410 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* + (* - 6051169866 /^40 - e 7215 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* - 14035 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* + 1011563 /^1 e 72114035 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* 13525 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* - (* 13527215 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* - 14035 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* + (* - 1367633176 /^20 - e 14035 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* - 27045 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* + 1896856 /^1 e 140313522 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* 5235 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* - (* 52314035 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* - 27045 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* + (* - 992055688 /^10 - e 6762 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* - 5235 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* + 353548 /^1 e 6765235 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* 12672 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* - (* 12676762 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* - 5235 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* + (* - 447945316 /^5 - e 5235 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - 25342 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* + 662641 /^1 e 523126710 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + (* 23635 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - (* 23635235 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - 25342 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* + (* - 1565820683 /^1 - e 126710 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + (* - 47265 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* + 2993921 /^1 e 2126710 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + (* 23635 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - (* 2993921 /^+ (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* + (* - (* 10 ln * -

x y z f2 x y z f y diff :

x y z f2 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^10593 e 11775 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* 55610 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + (* - 1963236 /^* 139 e 4175 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* 3945 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* - 657192 /^* 591 e 157610 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* 29915 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* - 4713816 /^* 997 e 29915 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* 144210 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* - 4313022 /^* 721 e 14425 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* 14035 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* - 2023126 /^* 1403 e 14035 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* 13525 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* - 1896856 /^* 1352 e 13522 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* 5235 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* - 707096 /^* 2615 e 5235 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* 12672 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* - 662641 /^* 2534 e 126710 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + (* 23635 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - 2993921 /^* 1 e 10 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + 2363 /^- (* 23635 e 5 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + 1267 /^- (* + (* 598784210 e 2 y * 523 x * + (10 ln * 523 z * 5232 / ln * + 523 /^- (* + (* 782910341520 e 5 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + 1352 /^- (* + (* 1058494781708040 e 5 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + 1403 /^- (* + (* 742534089368160060 e 5 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + 1442 /^- (* + (* 7138227712459260000100 e 10 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + 2991 /^- (* + (* 4003207328993560000000200 e 5 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + 1576 /^- (* + (* 525754562541153000000000400 e 5 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + 1668 /^- (* + (* 5261751661911850000000000000760 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^- (* + (* 10 ln * 928962255910541000000000000000 / -

x y z f3 x y z f z diff :

x y z f3 2 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^* e 11775 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* 55610 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + (* - 1963236 /^e 4175 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* 3945 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + (* - 657192 /^e 157610 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* 29915 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + (* - 4713816 /^e 29915 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* 144210 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + (* - 4313022 /^e 14425 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* 14035 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + (* - 2023126 /^e 14035 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* 13525 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + (* - 1896856 /^e 13522 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* 5235 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + (* - 707096 /^e 5235 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* 12672 y * 523 x * + (10 ln * 523 z * 5232 / ln * + (* - 662641 /^e 126710 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + (* 23635 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + (* - 2993921 /^1 e 10 y * 2363 x * + (10 ln * 2363 z * 236310 / ln * + 2363 /^- (* 236310 / ln * 5 e 5 y * 1267 x * + (10 ln * 1267 z * 12675 / ln * + 1267 /^- (12675 / ln * + (* 10 e 2 y * 523 x * + (10 ln * 523 z * 5232 / ln * + 523 /^- (5232 / ln * + (* 20 e 5 y * 1352 x * + (10 ln * 1352 z * 13525 / ln * + 1352 /^- (13525 / ln * + (* 40 e 5 y * 1403 x * + (10 ln * 1403 z * 14035 / ln * + 1403 /^- (14035 / ln * + (* 60 e 5 y * 1442 x * + (10 ln * 1442 z * 14425 / ln * + 1442 /^- (14425 / ln * + (* 100 e 10 y * 2991 x * + (10 ln * 2991 z * 299110 / ln * + 2991 /^- (299110 / ln * + (* 200 e 5 y * 1576 x * + (10 ln * 1576 z * 15765 / ln * + 1576 /^- (15765 / ln * + (* 400 e 5 y * 1668 x * + (10 ln * 1668 z * 16685 / ln * + 1668 /^- (16685 / ln * + (* 760 e 10 y * 3531 x * + (10 ln * 3531 z * 353110 / ln * + 3531 /^- (353110 / ln * + (* -

x y z v x0 y0 z0 g1 x y z f1 v x0 y0 z0 f1 * - :

x y z v x0 y0 z0 g2 x y z f2 v x0 y0 z0 f2 * - :

x y z v x0 y0 z0 g3 x y z f3 v x0 y0 z0 f3 * - :

x y z v n1 diff x y z v x0 y0 g1 x y z v 41 mat map2 maple :

x y z v n1 x y z v x0 y0 g1 x diff x y z v x0 y0 g1 y diff x y z v x0 y0 g1 z diff x y z v x0 y0 g1 v diff 41 mat

No solution - or rather time consuming?

x y z f1 (x diff #

x y z v n2 diff x y z v x0 y0 g2 x y z v 41 mat map2 maple :

x y z v n2 x y z v x0 y0 g2 x diff x y z v x0 y0 g2 y diff x y z v x0 y0 g2 z diff x y z v x0 y0 g2 v diff 41 mat

x y z v n3 diff x y z v x0 y0 g3 x y z v 41 mat map2 maple :

x y z v n3 x y z v x0 y0 g3 x diff x y z v x0 y0 g3 y diff x y z v x0 y0 g3 z diff x y z v x0 y0 g3 v diff 41 mat

HOW TO CONTINUE ?????

Vector product:

x y z v dG x y z v n1 vector convert x y v n2 vector convert x y v n2 vector convert crossprod maple :

x y v x0 y0 dG x y v dG 1 el x y v dG 2 el x y v dG 3 el 0051 mat :

x y v x0 y0 dG x y v dG 1 el x y v dG 2 el x y v dG 3 el 0051 mat

t n D n 1 el n 2 el n 3 el n 4 el n 5 el dG :

x0 5.56 - :

y0 4.06 - :

v0 1 :

tmin 0 :

tmax 0.0045 - :

N 100 :

X0 x0 y0 v0 x0 y0 stack :

result X0 tmin tmax N t x D rkfixed :

T result 1 col :

X result 2 col :

Y result 3 col :

V result 4 col :

T X augment T Y augment T V augment 3 1 sys

X - blue Y - red V - green(we have 9 (nine) intersections)

The projection of the curve on the xOy plane

X Y augment

Now we have to find the roots. Each intersection of the parameter V through zero gives us one root.

vector Search N vector length : k 1 : n 1 : k N < vector k el 0 > (vector k 1 + el 0 < (& out n el k : n n 1 + : 21 line vector k el 0 < (vector k 1 + el 0 > (& out n el k : n n 1 + : 21 line vector k el 0 ≡ out n el k : n n 1 + : 21 line n n : if if if k k 1 + : 21 line while out 51 line :

Roots V Search :

Roots rows #

A more accurate value of the roots:

p1 p2 v1 v2 Interpol p1 v1 v2 v1 - / p2 p1 - (* - :

ii 1 : ii Roots length ≤ ii ii 1 + : Rx ii el X Roots ii el el X Roots ii el 1 + el V Roots ii el el V Roots ii el 1 + el Interpol : Ry ii el Y Roots ii el el Y Roots ii el 1 + el V Roots ii el el V Roots ii el 1 + el Interpol : 21 line for

Rx transpose #

Ry transpose #

1 Roots rows / Rx ii el Ry ii el f1 abs ii 1 Roots rows sum * #

ii 1 Roots rows range pp ii el o : for

1 Roots rows / Rx ii el Ry ii el f2 abs ii 1 Roots rows sum * #

X Y augment Rx Ry pp augment 2 1 sys

Values ii 1 Roots rows range out ii el Rx ii el Ry ii el f : for out 21 line :

Rx #

Ry #

Values #

We can use these initial conditions in order to find more accurate values of the roots.