Simulations pour Cours de Physique

Simulations of this site are principally related to physics taught in universities for under-graduate students; but some of them can also interest curious peoples with some background. They can be be shown, during lectures,  by the professor, to support demonstrations or illustrateused, and also  by students. Executables , programs which start with a  double click,  are to be downloaded (it’s free) from this site; they  are .jar, that is they are written in Java and require a download into your computer of this language (free from the site of the Oracle Corporation) . It is probably better to have a modern version of Java (Java 7 is the version used here). Quantum mechanics is not used here, except for the tunnel effect and stationary states in potential wells.
Here are simulated the following physical phenomena:

– Optical devices : Michelson- Morley interferometer , Fabry-Perot devices, Young-slits, and also devices of geometrical optics: diopters , lenses, microscope, Galileo telescope, or the eye.

Link to a more precise description and also downloading of executables: 

                                  optics

-gas in two dimensions , in order to illustrate the kinetic theory of gases ,

Link: Two dimension gas

– chain of atoms and propagation phenomena in one dimension decomposition into stationary waves, etc …

Link:   chain of atomes or springs

– electrical balance of parallel cylindrical conductors ,

Link: Electric equilibrium of conductors

– wire chambers (Charpak chambers), charged particles  detectors .

Link:  Wire chambers of Charpak.

– electric and magnetic dipoles, and dielectrics and ferromagnetic materials in an external field.

Link: Dipoles, susceptibility

– physics of particles: quarks , described in a naive model, only to show what it consists of.

Link:   A naive quark model

Studies of wave packets, of tunnel effect and of stationary states of  potential wells (quantum mechanics):

Lien:                   wave packet, tunnel effect, potential wells

To have access to a simulation, you may also  click on its title in the left column.

An electric dipole  est composed of two electric charges  -q et -+q set at a distance  λ: d=qλ . A magnetic dipole  est composed  of a small  loop of current I and of surface s: d=Isn, where n est la positive normal . The fields  of the two kinds of  dipoles are closely  similar.

The program, which  you may download, in its first  part, allows to compare  field lines from  differents dipoles et quadripoles (two identical neighbour dipôles) and  to vary their parameters.

In its second part, you may see and compare volumes, made of dielectric and ferromagnetic material, put inside an external  uniform field , so that they  are ensembles of dipoles. Charges and currents  neutralize themselves inside the volume, but not at its surface. . Resulting  fields are shown, with  their field lines,  together with surface densities of charge and current. Shown  volumes are: a sphere, an ellipsoid of revolution (rugby ball ) and a cylindric bar  of  finite length.

To get the executable, please click below:
https://github.com/LAL/dipoles-susceptibilite/releases/

Un dipôle électrique est composé de deux charges électriques -q et -+q distantes d’une longueur λ: d=qλ . Un dipole magnétique est composé d’une petite spire de courant I et de surface s: d=Isn, où n est la normale positive. Les champs des deux sortes de dipôles sont très similaires.

Le programme, que vous pouvez télécharger, vous permet, dans une première partie,  et de varier les paramètres des dipôles et d’en visualiser les lignes de champs. Des quadripôles (deux dipôles identiques voisins) sont également montrés.

Dans une seconde partie, vous pourrez voir et comparer  des volumes diélectriques et ferromagnétiques placés dans un champ extérieur uniforme;  ce sont alors des ensembles de dipôles orientés par le champ. Dans ces deux cas, les charges et courants se retrouvent en surface.  Les champs résultants sont montrés, avec les lignes de champ. Les volumes sont: une boule, un ellipsoïde de révolution (ballon de rugby) et un barreau cylindrique de longueur finie.

• Pour atteindre le programme exécutable, cliquez sur le lien ci-dessous:
• lancement du programme

 Wire chambers can locate,   in a gas,  high energy charged elementary particles such as electrons or protons,  and  follow their path, which can for example be deflected by a magnetic field.
     Very thin metallic wires are stretched between two parallel metal plates connected to ground, and charged at high voltages (some thousands volts). The chamber contains a gas whose small electric discharges at the crossing of high-energy charged particles are analysed.
     In all cases , the electric characteristics  are shown (fields at different points and equipotentials ) , which is an excellent example of electric equilibrium of conductors.

To get the executable, please click below:
https://github.com/LAL/chambres-de-Charpak/releases/

A two-dimensional gas with a maximum of 2000 circular molecules is proposed , in order to illustrate the kinetic theory of gases . The physical properties are the same as for three-dimensional: laws of Mariotte , entropy, Maxwell distribution , local particle densities from Poisson law, law of Dulong and Petit , etc. …. A « spin » can be attributed to the particles. The interaction between particles is the default billiard balls , but you can choose to have no interaction at all, or to have a harmonic interaction of limited range. Thus we can verify the importance of the nature of interactions such as the particle diameter or density , on the properties of gas , pressure, entropy …. Two neighboring gas may be selected for comparison . The envelop of the gas can be either inert (reflection without energy loss) or not , which allows you to check the laws of entropy change . Composite particles can be generated from elementary particles. A piston may also be moved between two gases .

• To get the executable, please click below:
• https://github.com/LAL/gaz-a-deux-dimensions/releases/

This module about optics includes simulations about:
– Michelson-Morley and Fabry-Perot  interferometers. In the latter case, we added simulations of parallel  face slide in transmission and reflection (in this case it is a metallic mirror on one side).

-Slits of young.

– geometrical optics devices: diopters, lenses, eye, microscope, binoculars and telescope of Galileo.

We deal here with the equilibrium of  parallel metallic conductors .

The axis of conductors are perpendicular to the screen . The electric field is zero inside the conductor and there are charges only at their outer surface.
The electric field is , just outside of these, on the one hand perpendicular to the surface and on the other hand proportional to the charge density at  local surface. The surface charge density can therefore be indicated by the fields at the exit of conductoers, and this is what is done here. The charges are positive for emerging fields from the conductor, negative for entering those .
These properties are enough to determine the electrical fields throughout the space , once known total charge per unit length of each cylindrical conductor.
We consider the case of N conductors ( N < = 4) , whether or not located inside a « wrapping » hollow conductor and whose charge is opposite to the sum of the charges of then N conductors ( to satisfy the Gauss theorem ); this « wrapping » conductor is actually always present, but situated at infinity , which allows the total nullity charges . The radii of the conductors , their positions and their charges can be varied at will .

To get the  executable, please click below:

https://github.com/LAL/Equilibre-electrique-des-conducteurs/releases

In the case also of a chain of masses linked by springs,  masses are attracted by their neighbors by harmonic forces (of the type -kx, k being the constant of the springs, and x its strain) . This is the classic model of a chain of atoms in a solid, and this is similar to what happens in a transmission electronic line ( the equations are of the same type ) . The number of atoms may vary here between two (which by the way is the cas of the  hydrogen molecule ) and 400 . The waves can be longitudinal or transverse . In the program are introduced only the laws of mechanics, applied to harmonic forces , and the found wave properties are only a consequence of these laws. We can thus observe the behavior of sinusoidal waves :
the positive or negative reflections , lack of reflection when the terminal mass  is submitted to a viscous force properly choosen ( characteristic impedance in case of electronic line),
the partial reflections in the case of a chain of atoms having different masses ( sonards case or echography ) ,
transmission attenuated for frequencies above the cutoff frequency ,
damping,
eigenmodes or stationary waves,
the decompositions of forced oscillation, which can be accurately observed by the graph of the total energy of the system as a function of time: there are flutterings between adjacent frequencies of the frequency imposed ; by adjusting the driving frequency and observing the graph , it is then possible to find the resonance frequencies of the chain.
the change over time of a system initially quiet but out of equilibrium, consisting of two, three or N springs and masses.

To get the exacutable, please click below:

https://github.com/LAL/chaine-d-atomes/releases

You can view simple planar models for proton and meson formed of quarks ( 3 quarks to the proton, a quark and an antiquark in the meson ) . These models are far from reality , but they have the merit of giving an image , which is required to consider this reality. The next step is, for research workers , to introduce quantum mechanics, relativity, etc. ….
The attraction force between quarks is  » harmonic  » attractive and proportional to their distance. It is necessary to limit the range of these harmonic forces , so that they are not infinite at infinity : beyond a certain distance, the force is switched to zero . In two models « classic » distance limiting the range is the distance between quarks for the first, the distance of the quark to the center of gravity of the proton or meson. In a quantum model , the position of quarks changes any time depending on the probability wave function, which we assume uniform here; we’re not going very far in this model.
In all cases , the orbital angular momentum is assumed to be zero . Quarks are  » colored  » , and forces are symbolized by elastic with two colors. The proton and meson , which are  » hadrons  » ( particles formed of quarks and detectable by our apparatus) must be of « neutral color »: three different colors for the proton, color and anti- color for the meson .
We propose a very simple model of scattering of two particles (proton on proton, meson on proton ); there, quarks of two different hadrons (proton or meson ) attract when the particles are closer than a distance equal to the range of potential described above. You can follow the reaction both in the frames of center-of- mass and  « laboratory » where the target is fixed, and see statistics on the scattering angle of the projectile particle; and one is then in conditions of an experiment.
Finally, we can look at the generation of hadrons from a quark-antiquark pair , the particles belonging initially to two hadrons which collide at very high energy.