Abstract

Maksims Zigunovs^1,2

1 – Riga Technical University, Institute of Applied Mathematics, Faculty of Computer Science and Information Technology, Riga, Latvia

2 – Liepaja University, Institute of Science and Innovative Technologies, Faculty of Science and Engineering, Liepaja, Latvia

Maksims Zigunovs is going to make a presentation about heat distribution in anisotropic 3D space by using several ways. The aim of the presentation is to show the overview of how it is possible to implement heat transferring process software  and get calculation plots of the heat.

Firstly the heat transferring equation will be described as well as heat source type and energy conversions.

Then the ADI (Alternating direction implicit) method will be described in general and particular ways. The author is going to make an overview of ADI usage for 5 point stencil. As an example it is planned to show full calculation process for parabolic equations. with defined boundary conditions.

The calculation boost is going to be described due to a use of ADI method because in the result there are 3 diagonal matrixes to be calculated in order to get a 3D calculational results.

As the results of the presented works can be used in real life the author is going to make a short overview of parallel calculation approaches in C programming language.

The final stage of the presentation is going to be a short overview of MatLAB software in a field of plot implementations and going through precalculated results in order to make result plots and contour maps.

Heat_Conduction.pptx

Neuron general overview

There are 10^11 neurons in the human brain. Neurons are unique in the sense that only they can transmit electrical signals over long distances.

From the neuronal level we can go down to cell biophysics and to the molecular biology of gene regulation. In addition, from the neuronal level we can go up to neuronal circuits, to cortical structures, to the entire brain, and finally to the behavior of the organism.

A typical neuron receives inputs from more than 10,000 other neurons through the contacts on its dendritic tree called synapses. The inputs produce electrical transmembrane currents that change the membrane potential of the neuron. Synaptic currents produce changes, called postsynaptic potentials (PSPs).

Small currents produce small PSPs; larger currents produce significant PSPs that can be amplified by the voltage-sensitive channels embedded in the neuronal membrane and lead to the generation of an action potential or spike, an abrupt and transient change of membrane voltage that propagates to other neurons via a long protrusion called an axon.

The transition between resting and spiking modes could be triggered by intrinsic slow conductances, resulting in the bursting behavior.

There could be millions of different electrophysiological mechanisms of excitability and spiking.

Ways to simulate the neuron work

There are a lot of ways to simulate the neuron work developed to make adaptive and adaptive response systems.

• Hodgkin-Huxley Model was produced by Hodgkin and Huxley in 1952. The model explains the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon.
• Izhikevich Model is transformed continuous-time Euler’s Discretization.
• 3 Rulkov Models can be used in different chaos prediction.
• Courbage–Nekorkin–Vdovin (CNV) Model is quite similar to chaotic Rulkov Model.
• etc.

The Izhikevich Model was chosen to be used for numerical experiment.

Alzheimer’s Disease Modeling

The Alzheimer’s disease problem for the brain is a fast and tending neuron isolation from the brain neural network. It means that during the Alzheimer’s disease the brain “loose” cells of memory and analytical skills developed in whole live time. Eventually, some part of neural network can loose connections to whole neuron clusters even if they produce signals between themselves.

The Izhikevich Model

The Izhikevich Model is originally continuous-time, but Euler discretization with a time step of 1 ms transforms it into the map.

There are several parameters needed for making Izhikevich neural map-based neural model calculations for calculating the membrane voltage difference between inside and outside) sides and additional variable.

• Calculable equation in Izhikevich Model:

where v [mV] is membrane voltage (potential), u [mV] represents a membrane recovery variable, which accounts for the activation of K+ ionic currents and inactivation of Na+ ionic currents is additional variable depends on membrane voltage, I (synaptic currents or injected dc-currents) is electricity source connected from outside, a, b, c and d are just neuron parameters.

• Another way of these equations:

• The parameter a – describes the time scale of the recovery variable u. Smaller values result in slower recovery. A typical value is a=0,02.
• The parameter b – describes the sensitivity of the recovery variable u to the subthreshold fluctuations of the membrane potential v. Greater values couple v and u more strongly resulting in possible subthreshold oscillations and low-threshold spiking dynamics. A typical value is b=0,2.
• The parameter c – describes the after-spike reset value of the membrane potential v caused by the fast high-threshold K+ conductances. A typical value is c=-65mV.
• The parameter d – describes after-spike reset of the recovery variable u caused by slow high-threshold Na+ and K+ conductances. A typical value is d=2.

The equations for coupled neurons are:

For one of variations of the neuron parameters values the v and u plot would be these:

Time evolution of the Izhikevich Model variables in a bursting orbit. Parameter values are

a = 0.02, b = 0.25, c = −55, d = 0. I = 0.8.

Let’s assume there are 2 neurons without delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 1 time moment delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 2 time moment delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 3 time moment delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 3 time moment delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 10 time moment delay, so the average time distance between spikes for different v values are:

Let’s assume there are 2 neurons with 20 time moment delay, so the average time distance between spikes for different v values are:

For numerical experiments the 6 neuron model was used implementing the connectivity matrix:

The neuron structural model is:

Fast Fourier Transformation allows to find calculate a kind of derivative of the equation or matrixed values approximated equation. That is why it is quite valuable to make Fourier Transformation result overview.

Synchronization degree, Coherence and Phase synchronization degree were analyzed for every calculation was made. And these results prove the Izhikevich Model provides the stable and periodic neuron signal model.

Numerical experiments

I = 0.8, there is no neuron signal delay and the connection is 0.1. FFT for 1:

I = 0.8, there is no neuron signal delay and the connection is 0.1. FFT for 2:

I = 0.8, there is no neuron signal delay and the connection is 0.1. FFT for 3:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 4:

I = 0.8, there is no neuron signal delay and the connection is 0.1. FFT for 5:

I = 0.8, there is no neuron signal delay and the connection is 0.1. FFT for 6:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 1:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 2:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 3:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 4:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 5:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.1. FFT for 6:

The Synchronization degree and all 6 neuron U values plot:

I = 0.8, there is no neuron signal delay and the connection is 0.6. FFT for 1:

I = 0.8, there is no neuron signal delay and the connection is 0.6. FFT for 2:

I = 0.8, there is no neuron signal delay and the connection is 0.6. FFT for 3:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 4:

I = 0.8, there is no neuron signal delay and the connection is 0.6. FFT for 5:

I = 0.8, there is no neuron signal delay and the connection is 0.6. FFT for 6:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 1:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 2:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 3:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 4:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 5:

I = 0.8, the delay for all neurons is 4 time steps and the connection is 0.6. FFT for 6:

The Synchronization degree and all 6 neuron U values plot:

Conclusions

1. There are several useful neuron work simulation models.
2. Several factors such as neuron signal delay and neuron isolation have to present in Alzheimer’s Disease problem analyze solutions.
3. The Izhikevich Model gives stable results during calculations.
4. The neuron signal receiving delay make big impact the overall neuron network system behavior.
5. Neuron synchronization level impacts only the neural network stabilized state process time.

PPT: NeuralNetworkingModel

A simulation algorithm is elaborated for liquid moving into porous media along the predefined directions of velocities.

Aims

• To develop liquid moving model for porous environment.
• To make time-step calculations.

Solution

• To use liquid predefined moving direction and the weight of the each direction.
• To make liquid velocity based on the liquid predefined moving direction.
• To use liquid relaxation time in order to define time the liquid moving part is done in.
• To interpolate the liquid count after moving for the regular grid.

Solution actions

1. Calculate the distribution function for the liquid in each predefined direction value for all the grid points.
2. Sum up the values of distribution functions at each grid point in each direction in order to get the density of the liquid.
3. Compute the velocity of the liquid at each point of the grid.
4. Calculate local equilibrium function for each direction at each point of the grid. By using time step and calculated velocity we get how far the liquid can move in the considered direction.

Liquid predefined moving directions and velocities

The velocity of the liquid in the certain grid point is calculated using:

where p is pressure.
To nd out local distribution of the liquid the equilibrium function should be used in the way of:

where p is the pressure, w is the weighting function, fi is the liquid currently analyzed potential
moving direction and u is the vector of the liquid velocity in a [V x; V y]T form.
The algorithm of the application is:

1. Calculate the liquid each potential directions values for all of the grid points.
2. For each grid point sum the each direction values in order to get the density of the liquid in
   each point of the grid.
3. Compute the velocity of the liquid in each point of the grid.
4. Calculate local equilibrium function for each direction of the each point of the grid. By this
   step we get how far the liquid can move in the potential direction.
5. Compute the time the liquid can move from its position to the new one in the potential
   direction.
6. Calculate the liquid new position after advactive moving step made from the regular grid point
   position for every grid point.
7. By using interpolation nd out the liquid position in the regular grid by using the liquid new
   position after advactive moving step made from the regular grid point position for every grid
   point.

Interpolation

When the liquid moved from the regular grid point to the advective one the value on the liquid in the regular grid point the liquid moved from can be found within the area of 9 point of the analyzed grid.

The central point value is unknown because the liquid moved from it, but the 8 points around the advective point are regular with the previous time step or after interpolation got values.

To solve Ac=B equation, where c – unknown vector the relationship coefficients (size=9).

A – matrix. Each row contains the same set of freely chosen X and/or Y elements of the Taylor series, where x and y component values are the differences between the central advective point and the current point coordinates each row uses coordinates of the only one point of the analyzed grid.

B – vector. Each element is a value at the point in 3×3 matrix used for interpolation.

To calculate the liquid amount in the centre of the regular grid interpolating area it is needed to sum of multiplications of the conforming by index c vector elements and the matrix A Taylor series elements, where x and y are the differences between the central advective point and the coordinates of the point the values should be found for.

Calculation results

PDF document file

The needs for the solution

Nowadays calculation speeds

In the modern technology the large computing power is available.

The current CPU (central processor unit) processor frequency reaches up to 4 GHz. GPU (graphical processor unit) and graphics processor cards have reached up to 1,000 units in a single map, and each processor frequency reaches up to 1GHz.

This means that it is possible to create a computer system that could be designed for solving non-stationary physical phenomena modelling problem of the three-dimensional space.

Heat conduction

The assumed initial boundary condition for the 3D domain G∪Γ is described as follows:

with the corresponding initial and boundary conditions (x1 = x, x2 = y, x3 = z) ∈ Γ, where T = temperature, t = time, x, y and z are coordinate directions, Vx, Vy, Vz = heat transferring velocity in x, y, and z directions, RT – heat retention factor and Λ12 is a heat conduction tensor, where (1) is calculable direction and (2) is a sub direction of direction 1, n = porosity coefficient of material, Q = heat source produced heat in {i,j,k} point.
Robin boundary conditions are used for this calculations.

This 3D temperature distribution equation is implemented as follows:

where T = temperature, t = time, x, y and z are coordinate directions, Vx, Vy, Vz  = heat transferring velocity in x, y, and z directions, RT – heat retention factor and  Λ12 is a heat conduction tensor, where (1) is calculable direction and (2) is a sub direction of direction 1, n = porosity coefficient of material.

5 point stencil for every 2D

Heat conduction

We get the following differential scheme for temperature calculations from the time moment “l” to the time moment “l+1”:

where l = current time step, l+1 next time step, i = discrete position of x, j = discrete position of y, k = discrete position of z, Q = heat source produced heat in point {i,j,k}, Tijk = temperature on the current time step in point {i,j,k}, n = porosity coefficient of material, h*x = (hx+1 + hx) / 2, where hx (step in direction of x) = xi – xi-1.

Averaged flux in x, y and z directions are expressed as follows (equations for x direction are similar to y and z direction equations):

Notice that (Ix)i+1/2jk is calculated similar to other parameters’ calculations:

According to Λ the definition is (same for x, y and z axes directions):

where n = porosity coefficient of material, q = water density, c = specific heat capacity of water (it is assumed that heat source is located inside water because of assumed chemical reactions in water which produces the heat), βc,β_T= longitudinal and transverse thermo-dispersivity, and is V = the absolute velocity, vx, vy, vz = the velocity vectors.

In order to elaborate the parallel calculation method, the difference scheme was decomposed by space and time by applying ADI method:

The ADI technology is used to compute calculations faster and to make implicit difference scheme, the 5 point stencil per 2 axes direction is used. So the ADI technology provides 3 diagonal matrix usage in the Thomas algorithm. Therefore, it makes very fast and efficient calculations.

The other method, for making faster calculations, it is the calculation time step that changes according to the predictions of how the temperature distribution relative to the previous time step calculation results.

Enhancements

In order to make calculation time enhancement the modified time step was created by using absolute and relative errors of calculated temperature for l+1 time moment

Absolute and relative errors calculations for X direction (same for Y and Z)

Finding the maximal error for X direction (same for Y and Z)

In order to make calculation time enhancement the modified time step was created by using absolute and relative errors of calculated temperature for l+1 time moment

Finding the next time step length:

where ErrorXYZ = maximal error between predicted and calculated results, toltol = error threshold, tau1 = temporary variable, tau = time step, taukoef = coefficient of time step changing, taumin = minimal time step, taumax = maximal time step.

New prognoses of next time step temperature matrixes:

The solution data

Porosity: n=0,20

Solid phase density: ρs=2,2 Kg/m3

Water density at Tr: ρf=999,24 kg/m3

Specific heat cap. of water: cf=4186 J/kg.°C

Specific heat cap. of solid phase: cs=837,2 J/kg.°C

Long. Thermodispersivity: βL=10 m

Trans. Thermodispersivity: βT=1 m

Water heat capacity: ρfcf= 4183 kJ/m3.°C

Retardation coefficient: RT=2,32

Water heat conductivity: λf=0,54 J/ms°C

Solid phase heat conductivity: λs=2,09 J/ms°C

Aquifer heat conductivity: λe=1,67 J/ms°C

Calculation results

 

Outside temperature is -20 oC

Outside temperature is -10 oC

Outside temperature is 0 oC

Outside temperature is +10 oC

Outside temperature is +20 oC

Outside temperature is +14.5 oC

Video example of execution (y=5) from 10x10x10 matrix

temp_video1

 

Demonstration files

Just download these files and extract on drive C.

TempCalc.zip

Then run this whole code fragment using MatLAB (need to replace all ‘ sings with non HTML ‘ sings or just download TempCalc.m):

clear
clc
MainDir=’C:\TempCalc’;
colorDepth = 10;
temp_max = +50;
temp_delta = +5;
temp_min = -50;
%cmap = [flipud(gray(colorDepth)); jet(colorDepth)];
cmap = [gray(colorDepth); jet(colorDepth)];
colormap(cmap);
for i=0:5:1000000
if i == 0
continue
end
fprintf(‘%s\n’,strcat(MainDir,’\’,num2str(i),’\ALL_INFO_IS_SAVED’));
while (exist(strcat(MainDir,’\’,num2str(i),’\ALL_INFO_IS_SAVED’)) == 0)
pause(1*1000*0.001)
end;
x     = importdata(strcat(MainDir,’\’,num2str(i),’\DynPointsX_y16zx.txt’));
y     = importdata(strcat(MainDir,’\’,num2str(i),’\DynPointsZ_y16zx.txt’));
data  = importdata(strcat(MainDir,’\’,num2str(i),’\Result_y16.txt’    ));
data2 = importdata(strcat(MainDir,’\’,num2str(i),’\absolutt.txt’       ));
%[C,h] = contourf(x,y,flipud(data),[temp_min:temp_delta:temp_max]);
[C,h] = contourf(x,y,rot90(flipud(data)),10);
clabel(C,h);
hold on;
title(strcat(‘Iteracija ir:’,num2str(i),’. Laiks ir:’,num2str(data2),’sek.’));
caxis([temp_min temp_max]);
[C,h] = contourf(x,y,rot90(flipud(data)),10);
%clabel(C,h,’FontSize’,10,’Color’,’g’,’Rotation’,0);
set(h, ‘LineWidth’,1.0);
shading flat;
mycolorbar = colorbar(‘location’,’EastOutside’);
set(mycolorbar, ‘Ylim’, [temp_min temp_max]);
set(mycolorbar, ‘YTick’, temp_min:temp_delta:temp_max);
hold off;
clear x y data data2 mycolorbar;
pause(0.01*1000*0.001)
end;
clear MainDir colorDepth temp_max temp_delta temp_min cmap;

PDF document file

The final report of the project “Creation of Education module “Climate changes” in Liepaja University” was approved in July 2016.

The Project has been started in April 2015. During the Project were created and approbated 4 study courses – “Climate technologies”, “Use of renewable resources”, “Modelling of environment processes” and “Practical solutions of environmental engineering”. Study courses are oriented on the solution of engineering technologies for reducing of CO2 and contribute to use more renewable energy technologies. There are used modern and innovative computer technologies for developing skills of promoting global data projection, modelling and simulation by creating forecast of environmental factors. Significant role in the project plays the use of modern laboratory equipment such as solar collectors, thin layer evaporation equipment etc.

During the project several seminars and workshops for various target groups were organized and there were designed open-access training materials.

Also after the end of the project development process the study has been continued for professional bachelor study program “Management and Engineering of Environment and Renewable resources”, life-long learning and other programs and also for the research in the Institute of Science and Innovative Technologies and Faculty of Science and Engineering.

Participants of the project took part in the annual national education, innovation and technology conference “LatSTE`2016” – carrier in the digital age” which took place on 25-26 September, 2016 with their report ‘The Use of IT in the Climate Education’.

Ar noslēguma pārskata apstiprināšanu 2016. gada jūlijā ir noslēgusies projekta „Izglītības moduļa „Klimata pārmaiņas” izveide Liepājas Universitātē” īstenošana.

Projekts tika uzsākts 2015. gada aprīlī. Tā īstenošanas laikā ir izstrādāti, aprobēti un pilnveidoti četri studiju kursi- Klimata tehnoloģijas, Atjaunojamo resursu izmantošana, Vides procesu modelēšana un Praktiski risinājumi vides inženierzinātnēs. Studiju kursi ir orientēti uz inženiertehnisko risinājumu apguvi, kas vērsti uz CO2 izmešu samazināšanu un atjaunojamās enerģijas ieguves tehnoloģiju arvien plašāku izmantošanu. Kursu apguvē tiek izmantoti inovatīvi datorprogrammu komplekti, kas veicina globālo datu projektēšanas, modelēšanas un simulācijas prasmju apguvi, veidojot vides faktoru prognozi. Būtiska loma kursu pilnveidē ir arī mūsdienīga laboratorijas aprīkojuma (piemēram, plāno kārtiņu uzputināšanas iekārta, saules kolektori u.c.) izmantošanai.
Projekta īstenošanas laikā notikuši vairāki semināri dažādām mērķauditorijām, izstrādāti brīvpieejas mācību materiāli.

Arī pēc projekta noslēguma turpinās izstrādāto studiju kursu īstenošana un pilnveide profesionālā bakalaura studiju programmā „Vides un atjaunojamo energoresursu pārvaldība un inženierija”, moduļa kursu elementu izmantošana citās studiju programmām un mūžizglītībā, kā arī pētniecības tēmu turpināšana Dabas un inženierzinātņu fakultātē un Dabas zinātņu un inovatīvo tehnoloģiju institūtā.
Projekta dalībnieki ar referātu „Informācijas tehnoloģiju izmantošana klimata izglītībā” piedalījās ikgadējā nacionāla mēroga izglītības, inovāciju un tehnoloģiju konferencē „LatSTE`2016”- karjera digitālā laikmetā”, kas notika 2016. gada 25. un 26. septembrī.

Sestdien, 27. februārī, no 10:00 līdz 16:00, Liepājas Universitātē Kr.Valdemāra ielā 4 notika seminārs “Vides procesu modelēšana un atjaunojamo energoresursu potenciāls, tā apguves iespējas Latvijā”.
Semināru vadīja Liepājas Universitātes projekta „Izglītības moduļa „Klimata pārmaiņas” izveide Liepājas Universitātē” lektori MBA Viesturs Kalniņš un Mg. ing. Maksims Žigunovs.

Seminārs bija sadalīts divās daļās. Pirmajā daļā notika Viestura Kalniņa lekcija par Latvijā pieejamiem atjaunojamo energoresursu veidiem un to ieguves tehniskajiem risinājumiem –termālajiem saules kolektoriem, fotovoltiskiem paneļiem, hidroelektrostacijām, vēja turbīnām, siltumsūkņiem u.c. Otrā daļa bija Maksima Žigunova praktiskā nodarbība / lekcija, kuras laikā apmeklētāji izveidoja globālā klimata simulāciju, ūdenstilpņu 3D modeļus ar piesaistītiem ūdens avotiem un simulēja plūdu modeļus, lai novērotu vai ūdens līmenis pie noteiktiem nosacījumiem pacelsies virs upes krasta līmeņa. Šī praktiskā nodarbība / lekcija bija organizēta līdzīgā veidā kā tā tiek pasniegta Liepājas Universitātes studentiem – pielietojot mūsdienīgu un daudzfunkcionālu vides procesu modelēšanas programmatūru.

Semināra fotogrāfiju galerija:

Projekta Izglītības moduļa “Klimata pārmaiņas” izveide Liepājas Universitātē komanda prezentēja projekta ietvaros izstrādātos studiju kursus. To mērķis ir iemācīt studentus analizēt apkārtējās vides faktorus, veikt prognozes un praktiski darboties ar mūsdienīgām tehnoloģijām.

Projekta ietvaros tika izstrādāti četri studiju kursi. Liepājas Universitātes lektors Viesturs Kalniņš stāstīja par augstākās izglītības lomu atjaunojamo energoresursu apguves veicināšanā, uzsverot inovatīvu un alternatīvu risinājumu nozīmi: “Svarīgi jaunos speciālistus iepazīstināt un informēt par iespējām un attīstības tendencēm atjaunojamo energoresursu izmantošanā, lai studenti, kļūstot par inženierijas jomas speciālistiem, jau zinātu potenciālās nozares iespējas, perspektīvas, izmantojamās tehnoloģijas, materiālus un metodes.”

Pēc rezultātu prezentēšanas notika diskusija par izglītības moduļa “Klimata pārmaiņas” izveidi Liepājas Universitātē. Bioloģijas zinātņu doktore Māra Zeltiņa par diskusijas rezultātu: „Bija svarīgi iepazīstināt prakšu vietu nodrošinātājus un potenciālos darba devējus no uzņēmumiem un pašvaldības ar aspektiem, kam tiek pievērsta uzmanība, gatavojot speciālistus vides jomā, dzirdēt jautājumus un ieteikumus. Ne mazāk svarīgi bija arī tas, ka seminārā tika prezentēti gan Latvijas Universitātes, gan Liepājas Universitātes īstenoto projektu rezultāti. Tas deva iespēju labāk izprast klimata pārmaiņu būtību un vienoties par turpmāk darāmo klimata izglītības nodrošināšanā.”

Abi projekti, par kuru rezultātiem tika diskutēts seminārā, izstrādāti ar Eiropas ekonomiskās zonas finanšu instrumenta atbalstu.

Projektā “Izglītības moduļa “Klimata pārmaiņas” izveide Liepājas Universitātē” uzsākts darbs pie brīvpieejas mācību materiālu izstrādes ar mērķi iepazīstināt plašāku sabiedrību ar lekciju kursā “Vides procesu modelēšana” apskatītajām tēmām.

Izstrādātie materiāli tuvākajā laikā būs pieejami projekta interneta vietnē un dos iespēju ikvienam interesentam iepazīties ar iespējām, izmantojot mūsdienīgu programatūru, veidot globālā klimata modeļus un veikt globālo klimata pārmaiņu simulāciju. Tiks apskatīta arī ūdenstilpnes modelēšana (ūdens tilpnes 3D modeļa sagatavošana, plūdu simulācija, ūdens masu kustības kartes veidošana, u.t.t).