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Dieter Joensson
Freeware software jMD
for molecular dynamics simulation of ideal gases in three-dimensional real-time motion

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jMD Argon 512 Atome

For the inert gases helium, neon, argon, krypton and xenon as well as for dry air (idealised as a monatomic gas), a maximum of 4096 particles are shown in motion at different temperatures and gas densities or particle distances.

Typical particle characteristics such as mutual atomic distances, velocities and free path lengths are illustrated in relation to the thermodynamic parameters of temperature, pressure and entropy.

The present software programme is only designed for demonstration within the framework of ideal gas theory.

The atoms simulated in jMD are only idealised as hard, elastic spheres with smooth surfaces, i.e. they do not interact with each other except for the mechanical transfer of impact momentum. This is in contrast to real gases.

At low pressures up to about 10 bar and temperatures between -100°C and + 1000°C, the above-mentioned gases behave largely like ideal gases in reality.

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Detailed description of the jMD programme

Joensson, D.: Molekulardynamische Simulation idealer Gase mit Delphi.
In: Technische Mechanik, Magdeburg 29 (2009) Heft 1, S. 13 - 26

Joensson, D.: Erläuterungen zur Entropie und zur Maxwellverteilung in jMD.
In: Technische Mechanik, Magdeburg 29 (2009) Heft 1, S. 27 - 37

Joensson, D.: Numerische  Echtzeitsimulation molekulardynamischer Bewegungsvorgänge. Forschungsbericht FHTW Berlin 2007

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    ( 1165 KByte )

The folder contains two executable programmes for Microsoft Windows:

          jMD_2 for three-dimensional molecular dynamics (version 2.0 from 2017)

          jMD_1e for planar motions of elastic spheres

The zip folder only needs to be unzipped, then both programmes are ready to use without further installations.

Version 2.0 allows the simulation of a maximum of 4096 particles (16 to the power of 3) as opposed to a maximum of 1000 in version 1.0 from 2007.

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Maxwell distribution

With the button [ Maxwell ] the Maxwell velocity distribution of the particles is shown in comparison to the current distribution:

Maxwell's distribution shows how frequently certain velocity amounts occur in the steady state equilibrium.

The velocity components in the x, y and z directions each have normally distributed frequencies over negative and positive velocities.
In contrast, the amounts (the resultants) of the velocities are only positive and NOT normally distributed. Maxwell was the first to derive and describe exactly how they are distributed.

The actual velocity amounts can be made visible in jMD with the button [ Vectors ].

Here, for example, for 216 particles and, of course, in the programme in motion:

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In jMD, in addition to pressure and temperature, the entropy S is calculated and displayed in joules per kelvin and mole.

Why entropy?
While pressure and volume together characterise the state of compression of a body, entropy and temperature together determine the state of heating.

What is entropy?
Similar to the electrical charge of a body, entropy as "thermal charge" is an extensive (quantity-like) state variable.

This parameter is described very well didactically, for example, in the "Handreichung zur Energie und Entropie" (Handbook on Energy and Entropy) for physics lessons by Josef Leisen, on his homepage in the folder "Downloads zur Physikdidaktik" > Energie und Entropie.

The fact that entropy is absorbed or squeezed out of a body (which can of course also be gaseous) in a similar way to water being absorbed or squeezed out of a sponge can be demonstrated in jMD with isothermal volume change. With this type of volume change, the container walls are idealised to be heat-permeable and thus also entropy-permeable.

With isothermal volume enlargement, there is an increase in entropy and thus a positive entropy difference Delta-S compared to the initial state.

With volume reduction, entropy is "squeezed out" and Delta-S is consequently negative.

Example argon in jMD
with initial state T = 25°C , pressure p = 1 bar and entropy S = 155 J/K per mole in a cube-shaped initial volume Vo
yields the following values when the volume is reduced by half:

Entropie isentrop

If the walls are perfectly heat-insulated, the entropy remains unchanged for ideal gases (isentropic change of state).

If the volume in the example shown is reduced from Vo to 0.50 Vo isentropically, the temperature rises to 200°C and the pressure also becomes greater than with isothermal volume change.

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Two-dimensional simulation

After downloading, the zip folder contains two executable programmes: jMD_2 and jMD_1e.

With jMD_1e, plane impact calculations for a maximum of 300 balls can be simulated.

This clearly shows how the movements change in elastic collisions.

The red sphere can also be enlarged and reduced.
When starting, you can choose whether all balls should move first except the red ball or only one ball.

jMD_1e Bild


From the first draft to the current state with three-dimensional shock pulse analysis and interactive 3D graphics, all algorithms were written by me.

When programming with Delphi, two books helped me the most to realise my goals in detail. These were the basics and the cookbook on Borland Delphi 6 by W. Doberenz and Th. Kowalski.

Dieter Joensson in Sept. 2007

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