The Application Gallery features COMSOL Multiphysics^{®} tutorial and demo app files pertinent to the electrical, structural, acoustics, fluid, heat, and chemical disciplines. You can use these examples as a starting point for your own simulation work by downloading the tutorial model or demo app file and its accompanying instructions.

Search for tutorials and apps relevant to your area of expertise via the Quick Search feature. To download the MPH-files, log in or create a COMSOL Access account that is associated with a valid COMSOL license. Note that many of the examples featured here can also be accessed via the Application Libraries that are built into the COMSOL Multiphysics^{®} software and available from the *File* menu.

### Rotating Galaxy

This tutorial model shows how to add customized particle-particle interaction forces. In this example the gravitational force between 2500 stars in a galaxy is modeled. The galaxy initially rotates as a rigid body, then begins to change shape due to gravitational forces.

### Molecular Flow Through an S-Bend

This model computes the transmission probability through an s-bend geometry using both the angular coefficient method available in the Free Molecular Flow interface and a Monte Carlo method using the Mathematical Particle Tracing interface. The computed transmission probability by the two methods is in excellent agreement with less than a 1% difference. This model requires the Particle Tracing ...

### Ion Drift Velocity Benchmark

The drift velocity of Ar+ is calculated using a Monte Carlo simulation in which the elastic collisions of Argon ions with ambient neutrals are explicitly modeled. The model uses energy-dependent collision cross-section data from experiment. The average ion velocity values are consistent with experimental data over a wide range of reduced electric field magnitudes. This agreement suggests that ...

### Motion of Trapped Protons in Earth's Magnetic Field

This model demonstrates the path of non-relativistic protons within Earth's magnetic field. Due to the dipole nature of Earth's magnetic field, charged particles, such as electrons and protons, can get trapped in stable configurations within it for long periods of time. These configurations involve the particles rapidly bouncing from magnetic pole to magnetic pole, and drifting around the ...

### Ion Cyclotron Motion

This model computes the trajectory of an ion in a uniform magnetic field using the Newtonian, Lagrangian and Hamiltonian formulations available in the Mathematical Particle Tracing interface.

### Ion Range Benchmark

The Ion Range Benchmark model simulates the passage of energetic protons through silicon with both ionization losses and nuclear scattering. The initial energy of the protons is varied using a parametric sweep from 1 keV to 100 MeV. The average path length of the protons is compared to published values of the ion range under the continuous slowing down approximation (CSDA) as well as the ...

### Child's Law Benchmark

Space charge limited emission is a phenomenon that restricts the current of charged particles that can be released from a surface. As the electron current released by a cathode increases, so does the magnitude of the charge density in the immediate vicinity of the cathode. This distribution of charge density exerts an electric force on the emitted electrons, directed toward the cathode. The ...

### Molecular Flow Through an RF Coupler

This model computes the transmission probability through an RF coupler using both the angular coefficient method available in the Free Molecular Flow interface and a Monte Carlo method using the Mathematical Particle Tracing interface. The computed transmission probability determined by the two methods is in excellent agreement with less than a 1% difference. This model requires the Particle ...

### Sensitive High-Resolution Ion Microprobe

This tutorial utilizes the Particle Beam feature to examine the performance of a high-precision spectrometer. An ion beam is subjected to electric and magnetic forces, and only a fraction of the incoming beam is transmitted to the detector. The Particle Counter feature is used to compute the transmission probability, and to visualize the nominal trajectory of the transmitted beam.

### Rössler Attractor

A Rossler attractor is a system of three non-linear, ordinary differential equations. The Rossler attractor is similar in nature to the Lorenz attractor. The non-linear equations can be solved in COMSOL by conveniently using the Massless formulation available in the Mathematical Particle Tracing interface.