Simulation Ions in water (abstract model)

Ions in water may show strange behavior due to their hydration shell. This is a early draft using current web technologies with a python back end to calculate the first mineral nucleus. The scientific side is described in my blog post water-proteins-ions. I welcome any ideas to this project, please post them in my blog.

Simulation Parameter

Choose Parameter and click calculate. The effects are obvious in the threshold graph:

Plot Calculated Data

X = loops (=time) ;
Here: Loops (or time) Y = Number of ions Here: number of ions in the cluster

1.0 ; 1
2.0 ; 1
3.0 ; 2
4.0 ; 1
5.0 ; 2
6.0 ; 3
7.0 ; 4
8.0 ; 5
9.0 ; 4
10.0 ; 3
11.0 ; 2
12.0 ; 1
13.0 ; 2
14.0 ; 3
15.0 ; 2
16.0 ; 1
17.0 ; 1
18.0 ; 2
19.0 ; 3
20.0 ; 4
21.0 ; 5
22.0 ; 4
23.0 ; 5
24.0 ; 6
25.0 ; 5
26.0 ; 4
27.0 ; 3
28.0 ; 2
29.0 ; 1
30.0 ; 1
31.0 ; 1
32.0 ; 1
33.0 ; 1
34.0 ; 1
35.0 ; 1
36.0 ; 2
37.0 ; 1
38.0 ; 1
39.0 ; 1
40.0 ; 2
41.0 ; 1
42.0 ; 1
43.0 ; 1
44.0 ; 1
45.0 ; 1
46.0 ; 1
47.0 ; 2
48.0 ; 1
49.0 ; 1
50.0 ; 2
51.0 ; 1
52.0 ; 1
53.0 ; 2
54.0 ; 1
55.0 ; 2
56.0 ; 1
57.0 ; 1
58.0 ; 1
59.0 ; 1
60.0 ; 1
61.0 ; 1
62.0 ; 1
63.0 ; 1
64.0 ; 1
65.0 ; 1
66.0 ; 1
67.0 ; 1
68.0 ; 2
69.0 ; 1
70.0 ; 1
71.0 ; 1
72.0 ; 2
73.0 ; 3
74.0 ; 2
75.0 ; 1
76.0 ; 2
77.0 ; 1
78.0 ; 1
79.0 ; 1
80.0 ; 1
81.0 ; 2
82.0 ; 1
83.0 ; 2
84.0 ; 3
85.0 ; 2
86.0 ; 3
87.0 ; 2
88.0 ; 1
89.0 ; 1
90.0 ; 2
91.0 ; 1
92.0 ; 1
93.0 ; 1
94.0 ; 1
95.0 ; 1
96.0 ; 2
97.0 ; 1
98.0 ; 1
99.0 ; 1
100.0 ; 1
101.0 ; 2
102.0 ; 1
103.0 ; 1
104.0 ; 1
105.0 ; 1
106.0 ; 1
107.0 ; 1
108.0 ; 1
109.0 ; 1
110.0 ; 2
111.0 ; 1
112.0 ; 2
113.0 ; 3
114.0 ; 2
115.0 ; 1
116.0 ; 1
117.0 ; 2
118.0 ; 3
119.0 ; 4
120.0 ; 5
121.0 ; 4
122.0 ; 5
123.0 ; 6
124.0 ; 5
125.0 ; 6
126.0 ; 5
127.0 ; 4
128.0 ; 3
129.0 ; 2
130.0 ; 1
131.0 ; 2
132.0 ; 1
133.0 ; 2
134.0 ; 1
135.0 ; 1
136.0 ; 1
137.0 ; 1
138.0 ; 2
139.0 ; 1
140.0 ; 2
141.0 ; 3
142.0 ; 4
143.0 ; 5
144.0 ; 6
145.0 ; 7
146.0 ; 6
147.0 ; 5
148.0 ; 6
149.0 ; 5
150.0 ; 4
151.0 ; 5
152.0 ; 4
153.0 ; 3
154.0 ; 4
155.0 ; 5
156.0 ; 4
157.0 ; 3
158.0 ; 4
159.0 ; 5
160.0 ; 6
161.0 ; 5
162.0 ; 4
163.0 ; 3
164.0 ; 2
165.0 ; 3
166.0 ; 4
167.0 ; 5
168.0 ; 4
169.0 ; 5
170.0 ; 6
171.0 ; 5
172.0 ; 4
173.0 ; 3
174.0 ; 4
175.0 ; 3
176.0 ; 4
177.0 ; 3
178.0 ; 4
179.0 ; 3
180.0 ; 4
181.0 ; 3
182.0 ; 4
183.0 ; 3
184.0 ; 2
185.0 ; 3
186.0 ; 4
187.0 ; 3
188.0 ; 4
189.0 ; 5
190.0 ; 6
191.0 ; 7
192.0 ; 6
193.0 ; 7
194.0 ; 8
195.0 ; 9
196.0 ; 10
197.0 ; 11
198.0 ; 12
199.0 ; 13
200.0 ; 14
201.0 ; 15
202.0 ; 14
203.0 ; 15
204.0 ; 16
205.0 ; 17
206.0 ; 18
207.0 ; 19
208.0 ; 20
209.0 ; 21
210.0 ; 22
211.0 ; 21
212.0 ; 22
213.0 ; 23
214.0 ; 24
215.0 ; 25
216.0 ; 24
217.0 ; 23
218.0 ; 24
219.0 ; 25
220.0 ; 26
221.0 ; 25
222.0 ; 26
223.0 ; 25
224.0 ; 26
225.0 ; 27
226.0 ; 26
227.0 ; 27
228.0 ; 26
229.0 ; 27
230.0 ; 28
231.0 ; 27
232.0 ; 26
233.0 ; 25
234.0 ; 24
235.0 ; 25
236.0 ; 24
237.0 ; 23
238.0 ; 24
239.0 ; 23
240.0 ; 24
241.0 ; 25
242.0 ; 24
243.0 ; 25
244.0 ; 24
245.0 ; 23
246.0 ; 22
247.0 ; 23
248.0 ; 22
249.0 ; 21
250.0 ; 22
251.0 ; 23
252.0 ; 24
253.0 ; 25
254.0 ; 24
255.0 ; 25
256.0 ; 24
257.0 ; 23
258.0 ; 24
259.0 ; 23
260.0 ; 22
261.0 ; 21
262.0 ; 20
263.0 ; 19
264.0 ; 20
265.0 ; 19
266.0 ; 20
267.0 ; 19
268.0 ; 20
269.0 ; 21
270.0 ; 20
271.0 ; 19
272.0 ; 18
273.0 ; 17
274.0 ; 16
275.0 ; 15
276.0 ; 16
277.0 ; 15
278.0 ; 14
279.0 ; 13
280.0 ; 12
281.0 ; 11
282.0 ; 12
283.0 ; 11
284.0 ; 10
285.0 ; 11
286.0 ; 10
287.0 ; 9
288.0 ; 8
289.0 ; 7
290.0 ; 6
291.0 ; 5
292.0 ; 6
293.0 ; 5
294.0 ; 4
295.0 ; 3
296.0 ; 2
297.0 ; 1
298.0 ; 1
299.0 ; 2
300.0 ; 1
301.0 ; 1
302.0 ; 1
303.0 ; 2
304.0 ; 1
305.0 ; 1
306.0 ; 2
307.0 ; 1
308.0 ; 1
309.0 ; 1
310.0 ; 1
311.0 ; 2
312.0 ; 1
313.0 ; 2
314.0 ; 1
315.0 ; 1
316.0 ; 1
317.0 ; 1
318.0 ; 1
319.0 ; 1
320.0 ; 1
321.0 ; 2
322.0 ; 1
323.0 ; 2
324.0 ; 1
325.0 ; 1
326.0 ; 2
327.0 ; 3
328.0 ; 4
329.0 ; 3
330.0 ; 4
331.0 ; 3
332.0 ; 2
333.0 ; 1
334.0 ; 2
335.0 ; 3
336.0 ; 2
337.0 ; 1
338.0 ; 2
339.0 ; 1
340.0 ; 1
341.0 ; 2
342.0 ; 1
343.0 ; 1
344.0 ; 2
345.0 ; 1
346.0 ; 2
347.0 ; 3
348.0 ; 2
349.0 ; 1
350.0 ; 1
351.0 ; 1
352.0 ; 2
353.0 ; 1
354.0 ; 2
355.0 ; 3
356.0 ; 2
357.0 ; 1
358.0 ; 1
359.0 ; 2
360.0 ; 1
361.0 ; 2
362.0 ; 3
363.0 ; 2
364.0 ; 3
365.0 ; 4
366.0 ; 5
367.0 ; 4
368.0 ; 3
369.0 ; 2
370.0 ; 1
371.0 ; 1
372.0 ; 2
373.0 ; 1
374.0 ; 2
375.0 ; 3
376.0 ; 2
377.0 ; 3
378.0 ; 2
379.0 ; 3
380.0 ; 2
381.0 ; 3
382.0 ; 2
383.0 ; 1
384.0 ; 2
385.0 ; 1
386.0 ; 2
387.0 ; 1
388.0 ; 2
389.0 ; 3
390.0 ; 2
391.0 ; 3
392.0 ; 2
393.0 ; 3
394.0 ; 4
395.0 ; 3
396.0 ; 2
397.0 ; 3
398.0 ; 2
399.0 ; 3
400.0 ; 4
401.0 ; 3
402.0 ; 4
403.0 ; 3
404.0 ; 4
405.0 ; 3
406.0 ; 4
407.0 ; 5
408.0 ; 6
409.0 ; 5
410.0 ; 4
411.0 ; 5
412.0 ; 6
413.0 ; 7
414.0 ; 8
415.0 ; 7
416.0 ; 8
417.0 ; 7
418.0 ; 8
419.0 ; 7
420.0 ; 6
421.0 ; 7
422.0 ; 8
423.0 ; 9
424.0 ; 8
425.0 ; 9
426.0 ; 8
427.0 ; 7
428.0 ; 8
429.0 ; 7
430.0 ; 6
431.0 ; 7
432.0 ; 6
433.0 ; 7
434.0 ; 8
435.0 ; 9
436.0 ; 10
437.0 ; 11
438.0 ; 10
439.0 ; 11
440.0 ; 12
441.0 ; 13
442.0 ; 12
443.0 ; 11
444.0 ; 10
445.0 ; 11
446.0 ; 12
447.0 ; 13
448.0 ; 14
449.0 ; 15
450.0 ; 14
451.0 ; 13
452.0 ; 14
453.0 ; 15
454.0 ; 16
455.0 ; 17
456.0 ; 18
457.0 ; 17
458.0 ; 18
459.0 ; 17
460.0 ; 18
461.0 ; 19
462.0 ; 18
463.0 ; 19
464.0 ; 20
465.0 ; 19
466.0 ; 18
467.0 ; 19
468.0 ; 20
469.0 ; 21
470.0 ; 20
471.0 ; 19
472.0 ; 18
473.0 ; 19
474.0 ; 20
475.0 ; 21
476.0 ; 20
477.0 ; 19
478.0 ; 20
479.0 ; 21
480.0 ; 22
481.0 ; 21
482.0 ; 20
483.0 ; 21
484.0 ; 20
485.0 ; 21
486.0 ; 22
487.0 ; 21
488.0 ; 20
489.0 ; 21
490.0 ; 22
491.0 ; 21
492.0 ; 20
493.0 ; 21
494.0 ; 22
495.0 ; 23
496.0 ; 24
497.0 ; 25
498.0 ; 26
499.0 ; 27

To get the data, click in the text field and copy the values (Crtl + a)

In this little simulation a random number is generated and compared to a threshold. Ions are added or removed from the cluster, depending whether the random number is above or below the threshold. The threshold changes with the time (=loops).

Threshold Graph

X = loops ;
Here: Loops (or time) Y = threshold functions Here: strength of the damping function

1.0;4e-06;0;0.00251500954433
2.0;1.6e-05;0.0652439160544;0.0376543898452
3.0;3.6e-05;0.15782650632;0.0864639337126
4.0;6.4e-05;0.212685445292;0.116410894131
5.0;0.0001;0.252408020378;0.138787333545
6.0;0.000144;0.283781326104;0.156985221964
7.0;0.000196;0.309801047881;0.172500829838
8.0;0.000256;0.33207154503;0.186134770567
9.0;0.000324;0.351559330689;0.19836874144
10.0;0.0004;0.368894739043;0.209516358238
11.0;0.000484;0.384513065055;0.219793726079
12.0;0.000576;0.398728212004;0.22935626416
13.0;0.000676;0.411774359463;0.238319540712
14.0;0.000784;0.423831057818;0.246771821226
15.0;0.0009;0.435039112378;0.254782011457
16.0;0.001024;0.445511054135;0.262404893751
17.0;0.001156;0.4553382792;0.269684697699
18.0;0.001296;0.464596057867;0.276657605599
19.0;0.001444;0.473347136149;0.283353554137
20.0;0.0016;0.48164438087;0.289797557845
21.0;0.001764;0.489532758807;0.296010699567
22.0;0.001936;0.497050842077;0.302010884035
23.0;0.002116;0.504231970075;0.307813419711
24.0;0.002304;0.511105158132;0.313431473979
25.0;0.0025;0.517695816588;0.318876433523
26.0;0.002704;0.524026325938;0.324158192738
27.0;0.002916;0.530116501393;0.329285386825
28.0;0.003136;0.535983971475;0.334265581895
29.0;0.003364;0.541644489101;0.339105431294
30.0;0.0036;0.547112189122;0.343810805154
31.0;0.003844;0.552399803047;0.348386898503
32.0;0.004096;0.557518839219;0.352838322098
33.0;0.004356;0.562479734927;0.357169179199
34.0;0.004624;0.567291985541;0.361383130844
35.0;0.0049;0.571964254729;0.365483451642
36.0;0.005184;0.57650446898;0.369473077704
37.0;0.005476;0.580919899058;0.373354648016
38.0;0.005776;0.585217230487;0.377130540315
39.0;0.006084;0.589402624802;0.380802902321
40.0;0.0064;0.593481772984;0.384373679042
41.0;0.006724;0.597459942242;0.38784463674
42.0;0.007056;0.601342017115;0.391217384025
43.0;0.007396;0.60513253571;0.394493390499
44.0;0.007744;0.608835721733;0.397674003282
45.0;0.0081;0.612455512912;0.400760461702
46.0;0.008464;0.615995586262;0.403753910393
47.0;0.008836;0.619459380634;0.406655411
48.0;0.009216;0.622850116856;0.409465952674
49.0;0.009604;0.626170815808;0.412186461493
50.0;0.01;0.629424314641;0.41481780895
51.0;0.010404;0.632613281398;0.417360819601
52.0;0.010816;0.635740228199;0.419816277983
53.0;0.011236;0.638807523171;0.422184934877
54.0;0.011664;0.641817401247;0.42446751298
55.0;0.0121;0.644771973985;0.426664712065
56.0;0.012544;0.647673238487;0.428777213664
57.0;0.012996;0.65052308553;0.430805685335
58.0;0.013456;0.653323306987;0.432750784546
59.0;0.013924;0.656075602612;0.43461316222
60.0;0.0144;0.658781586248;0.436393465967
61.0;0.014884;0.661442791528;0.438092343028
62.0;0.015376;0.664060677103;0.439710442972
63.0;0.015876;0.666636631458;0.441248420149
64.0;0.016384;0.669171977341;0.442706935935
65.0;0.0169;0.67166797585;0.444086660768
66.0;0.017424;0.674125830208;0.445388276019
67.0;0.017956;0.676546689255;0.446612475679
68.0;0.018496;0.678931650672;0.447759967906
69.0;0.019044;0.681281763984;0.448831476413
70.0;0.0196;0.683598033328;0.449827741737
71.0;0.020164;0.685881420043;0.450749522378
72.0;0.020736;0.688132845062;0.451597595822
73.0;0.021316;0.69035319115;0.452372759458
74.0;0.021904;0.692543304984;0.453075831394
75.0;0.0225;0.694703999094;0.453707651177
76.0;0.023104;0.696836053677;0.454269080428
77.0;0.023716;0.698940218289;0.45476100339
78.0;0.024336;0.701017213428;0.455184327398
79.0;0.024964;0.703067732024;0.455539983274
80.0;0.0256;0.705092440818;0.455828925655
81.0;0.026244;0.707091981674;0.456052133252
82.0;0.026896;0.709066972799;0.456210609043
83.0;0.027556;0.71101800989;0.456305380412
84.0;0.028224;0.712945667219;0.456337499229
85.0;0.0289;0.714850498641;0.456308041871
86.0;0.029584;0.716733038558;0.456218109199
87.0;0.030276;0.718593802816;0.45606882648
88.0;0.030976;0.720433289556;0.455861343265
89.0;0.031684;0.722251980013;0.45559683322
90.0;0.0324;0.724050339275;0.455276493915
91.0;0.033124;0.725828816998;0.454901546573
92.0;0.033856;0.727587848078;0.454473235775
93.0;0.034596;0.729327853294;0.453992829136
94.0;0.035344;0.731049239909;0.453461616935
95.0;0.0361;0.732752402249;0.452880911717
96.0;0.036864;0.734437722236;0.452252047861
97.0;0.037636;0.736105569911;0.451576381112
98.0;0.038416;0.737756303919;0.450855288089
99.0;0.039204;0.739390271972;0.450090165755
100.0;0.04;0.741007811288;0.449282430873
101.0;0.040804;0.742609249012;0.448433519419
102.0;0.041616;0.744194902611;0.447544885979
103.0;0.042436;0.745765080253;0.446618003123
104.0;0.043264;0.747320081167;0.445654360747
105.0;0.0441;0.748860195983;0.444655465402
106.0;0.044944;0.750385707063;0.443622839594
107.0;0.045796;0.751896888809;0.442558021069
108.0;0.046656;0.753394007956;0.441462562078
109.0;0.047524;0.754877323864;0.440338028616
110.0;0.0484;0.756347088779;0.439185999658
111.0;0.049284;0.757803548094;0.438008066364
112.0;0.050176;0.759246940595;0.436805831278
113.0;0.051076;0.760677498698;0.435580907506
114.0;0.051984;0.762095448669;0.434334917886
115.0;0.0529;0.763501010845;0.433069494139
116.0;0.053824;0.764894399833;0.431786276011
117.0;0.054756;0.766275824713;0.430486910408
118.0;0.055696;0.767645489221;0.429173050508
119.0;0.056644;0.769003591935;0.42784635488
120.0;0.0576;0.770350326443;0.426508486578
121.0;0.058564;0.77168588151;0.42516111224
122.0;0.059536;0.773010441238;0.423805901172
123.0;0.060516;0.774324185219;0.422444524428
124.0;0.061504;0.77562728868;0.421078653884
125.0;0.0625;0.77691992262;0.41970996131
126.0;0.063504;0.778202253953;0.418340117432
127.0;0.064516;0.779474445629;0.416970790996
128.0;0.065536;0.780736656763;0.415603647829
129.0;0.066564;0.781989042754;0.414240349892
130.0;0.0676;0.783231755398;0.412882554343
131.0;0.068644;0.784464943002;0.411531912589
132.0;0.069696;0.785688750484;0.410190069345
133.0;0.070756;0.786903319483;0.40885866169
134.0;0.071824;0.788108788452;0.407539318131
135.0;0.0729;0.789305292754;0.40623365766
136.0;0.073984;0.790492964754;0.404943288825
137.0;0.075076;0.791671933908;0.403669808796
138.0;0.076176;0.792842326844;0.402414802441
139.0;0.077284;0.794004267447;0.401179841406
140.0;0.0784;0.795157876937;0.3999664832
141.0;0.079524;0.796303273944;0.398776270288
142.0;0.080656;0.797440574582;0.397610729191
143.0;0.081796;0.798569892519;0.396471369594
144.0;0.082944;0.799691339046;0.395359683461
145.0;0.0841;0.800805023144;0.394277144162
146.0;0.085264;0.801911051544;0.393225205609
147.0;0.086436;0.803009528792;0.3922053014
148.0;0.087616;0.804100557304;0.391218843979
149.0;0.088804;0.805184237431;0.390267223803
150.0;0.09;0.806260667505;0.389351808523
151.0;0.091204;0.807329943899;0.38847394218
152.0;0.092416;0.808392161078;0.38763494441
153.0;0.093636;0.809447411646;0.386836109666
154.0;0.094864;0.810495786398;0.386078706456
155.0;0.0961;0.811537374365;0.38536397659
156.0;0.097344;0.812572262858;0.384693134449
157.0;0.098596;0.813600537517;0.38406736627
158.0;0.099856;0.814622282348;0.383487829438
159.0;0.101124;0.815637579767;0.38295565181
160.0;0.1024;0.816646510639;0.382471931042
161.0;0.103684;0.817649154317;0.382037733945
162.0;0.104976;0.81864558868;0.381654095853
163.0;0.106276;0.819635890169;0.381322020013
164.0;0.107584;0.820620133821;0.381042476991
165.0;0.1089;0.821598393304;0.380816404102
166.0;0.110224;0.822570740953;0.380644704857
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470.0;0.8836;0.990043463803;0.868367021309
471.0;0.887364;0.990385467651;0.872273547082
472.0;0.891136;0.990726746132;0.876225776909
473.0;0.894916;0.991067302318;0.88022251503
474.0;0.898704;0.991407139258;0.88426253986
475.0;0.9025;0.991746259985;0.888344604763
476.0;0.906304;0.992084667512;0.892467438843
477.0;0.910116;0.992422364831;0.896629747742
478.0;0.913936;0.992759354917;0.900830214462
479.0;0.917764;0.993095640728;0.9050675002
480.0;0.9216;0.993431225199;0.909340245189
481.0;0.925444;0.993766111251;0.913647069563
482.0;0.929296;0.994100301785;0.917986574227
483.0;0.933156;0.994433799683;0.922357341742
484.0;0.937024;0.994766607812;0.926757937222
485.0;0.9409;0.995098729018;0.93118690924
486.0;0.944784;0.99543016613;0.935642790748
487.0;0.948676;0.995760921963;0.940124100001
488.0;0.952576;0.99609099931;0.944629341497
489.0;0.956484;0.996420400949;0.949157006923
490.0;0.9604;0.996749129642;0.953705576105
491.0;0.964324;0.997077188132;0.958273517971
492.0;0.968256;0.997404579147;0.962859291522
493.0;0.972196;0.997731305397;0.967461346801
494.0;0.976144;0.998057369577;0.972078125876
495.0;0.9801;0.998382774363;0.976708063825
496.0;0.984064;0.998707522419;0.981349589724
497.0;0.988036;0.999031616388;0.986001127641
498.0;0.992016;0.999355058902;0.990661097633
499.0;0.996004;0.999677852573;0.995327916742

Try plotting a second time if it doesn't work the first time (press "clear all", then "plot data")

The tool plotting the data is called JSXGraph and was developed by the Universty of Bayreuth.

The threshold function is a sum of three functions:
x² *w + + ln x *(2-w) + + sin x *u
These functions are summed up and normalized to 1. The dominance of each function can be adjusted with the simulation parameters, e. g.: w is the damping weight, u is the sinus amplitude.

Further reading: water-proteins-ions. Cheer, Ralf.

Damping Weight Relative weight between log and square function. Small value (0.01): log function; big value (1.8): square function value: 0 to 2	Sinus Frequency Threshold cycles during reaction value: 0 to 100	Sinus Amplitude Increases or decreases the sinus amplitude. Fractions like 0.01 are possible. Greater 1 = boost, smaller 1 = damping, 1 means plain sinus. value: 0 to 10	Loops Representing time (more or less) value: 0 to 20000	Ions Start number of Ions in the cluster value: 0 to 10 000