Experiment 1:Leave all adjustments as given and click at the button "Start".
Comment:When clicking at the "Start" button, the program starts calculating the torque operating on the single magnets. The used computing model is highly simplified. Magnetic monopoles are sitting at the tip of the magnets and the action of forces is similar to those of Coulomb's law. Nevertheless some processes occurring inside para and ferromagnetic materials can be visualized with the help of the Java application.
The forces of all magnets, acting on the calculated magnet, are added up and according to the resulting torque, the magnets rotate clockwise or anticlockwise. After some time has passed away, you will recognize areas with magnets pointing to the same direction. The preferred direction at the screen is vertical or horizontal. That's because the gap between the tips of the magnets is as small as possible in horizontal and vertical direction. A small distance between the tips means there are strong forces acting. The magnet needles are arranged on a quadratic grid. The neighboring needles at the diagonal points are more distant than the magnets at the horizontal or vertical positions leading to a stronger interaction.
After approximately one minute has passed away, a balance of forces is reached and the magnets don't turn around any longer. According to the initial state, some magnets may still move after those time and the equilibrium is reached some later. Click at the Button "Arrange new" to create a new initial state leading to a different final state.
Experiment 2:Adjust "Fixed magnet" to a value of 53 and click at "Arrange new".
Comment:The fixed magnet doesn't turn according to the forces acting. Therefore the magnets next to the fixed one will point favored into the same direction when the final state is reached. If the fixed magnet is oriented horizontally with the north pole pointing to the right, the magnets next to the fixed one will be arranged favored (not necessarily) in the same way. Click at the button "Arrange new" and observe the neighboring magnets for several times. Alter the orientation of the fixed magnet by adjusting the values of "Angle" to 90, 180, 270 or 45. The influence is minimal while the angle is adjusted to 45 degrees, because the distance between the needle tips is maximal.
Experiment 3:Click at the button "Arrange new" and wait until the final state is reached. Afterwards increase the value for "External field" slowly.
Comment:The value "External field" adjusts the strength of a homogeneous, external magnetic field acting on the magnets. The stronger the value of this external field becomes, the stronger a torque acts on the magnets trying to turn the needles into the direction of the field. By increasing the strength of the field slowly, you can see groups of magnets starting to point into the direction of the field. Often one magnet starts turning carrying his neighbors with him. Like in a chain reaction multiple magnets alter their arrangement.
Alter the angle of the external field and observe the magnets. You will see that you need a lower field strength to make the magnets follow the field at values of 0, 90, 180 and 270 degrees.
Experiment 4:Adjust the value for the external field to 100%. Wait until all magnets point to the direction of the field and suspend the calculation by clicking the "Stop" button. Adjust the value of the external field to 0% and resume the calculation by clicking at "Start".
Comment:Like expected, the magnets are arranged in parallel to the external field as soon as the final state is reached. After reducing the external field to 0% and resuming the computation, the magnets remain in their positions. In horizontal direction, the south pole of one magnet points to the north pole of it's neighbor magnet and vice versa. The magnets are in a stable state.
Rerun the experiment with a value of 45 degrees for the angle of the external field. Like before, the magnets start pointing into the direction of the external field. Have a closer look and you will see that not all magnets point exactly into the direction of the external field. The divergence is highest at the border area. When reducing the field strength to zero and resuming the computation, the magnets don't remain in their positions. They start turning to a horizontal or vertical position, arranged in groups.
Adjust the fixed Magnet to 53 and it's angle to 0, 90, 180 and 270 degrees. Rerun the experiment and observe the neighbor magnets. They will try to point into the same direction.
Experiment 5:Click at the button "Triangle" and rerun the experiments 1 - 4.
Comment:Now the magnets are arranged in equilateral triangles instead of squares. Therefore the magnets don't try to arrange in horizontal or vertical position but in an angle of 60 respectively 120 degrees. The angle between the two preferred orientations is no longer 90 degrees.
Experiment 6:Click on the Button Triangle and increase the value for "Strength" to 100%. Set the temperature to 0!
Comment:When starting the computation, some of the magnets start flickering around their position. That is because of the simplified computing model used. The forces acting between all magnets are calculated each 25 milliseconds. If the force acting between the magnets becomes too strong, the resulting rotation becomes too large and the needles start vibrating around their rest position. By reducing the computing interval, the flickering stops, but a faster computer is needed to calculate all forces in a smaller period of time. For the calculation of many strong, small magnets, a supercomputer is needed. Reduce the strength of the magnets until the flickering stops.
Experiment 7:Adjust the following values:
Size=35%, Strength=50%, Distance=20%, Number of magnets=135, External field=0%, Angle=0%, Fixed magnet=0, Angle=0, Temperature=0%, click at "Triangle".
Wait until the final state is reached and increase the value of the temperature slowly.
Comment:To simulate the influence of temperature, the magnets get a little kick from time to time. The elongation of each kick is higher, the higher the temperature gets. While the temperature is set to small values, the magnets vibrate around their resting position. At a special value for the temperature all needles are arranged randomly and no grouped areas exist. The magnet needles are turning too fast to influence their neighbors any longer.
The grouped areas of magnets disappear at lower temperatures, the smaller the value for the magnet strength or the greater the distance between the magnets becomes.
Experiment 8:Choose a value of 2 for the number of magnets and 100% for their size. Set the temperature to 0.
Comment:You can observe the number of stable positions between two magnets. Set the fixed magnet to 1 and it's angle to 90, 0 180 and 270 degrees. There are two metastable states at 90 and 270 degrees while both north or south poles are at the top or at the bottom.