Forces

Forces are one of the fundamental processes in Mechanica that cause objects to move. We provide a suite of pre-built forces, and users can create their own.

some stuff here

The forces module collects all of the built-in forces that Mechanica provides. This module contains a variety of functions that all generate a force object.

mechanica.forces.berendsen_thermostat(tau)

Creates a Berendsen thermostat

Param:tau: time constant that determines how rapidly the thermostat effects the system.

The thermostat picks up the target temperature \(T_0\) from the object that it gets bound to. For example, if we bind a temperature to a particle type, then it uses the

The Berendsen thermostat effectively re-scales the velocities of an object in order to make the temperature of that family of objects match a specified temperature.

The Berendsen thermostat force \(\mathbf{F}_{temp}\) has a function form of:

\[\mathbf{F}_{temp} = \frac{\mathbf{p}_i}{\tau_T} \left(\frac{T_0}{T} - 1 \right),\]

where \(T\) is the measured temperature of a family of particles, \(T_0\) is the control temperature, and \(\tau_T\) is the coupling constant. The coupling constant is a measure of the time scale on which the thermostat operates, and has units of time. Smaller values of \(\tau_T\) result in a faster acting thermostat, and larger values result in a slower acting thermostat.

mechanica.forces.dpd_conservative(a, min = 0.1, cutoff=1)

Parameters:

• a – interaction strength constant
• min – The smallest radius for which the potential will be constructed.
• cutoff – The largest radius for which the potential will be constructed.
• tol – The tolerance to which the interpolation should match the exact

\[\mathbf{F}^C_{ij} = a \left(1 - \frac{r_{ij}}{r_{cutoff}}\right) \mathbf{e}_{ij}\]

mechanica.forces.dpd_dissipative(gamma, min = 0.1, cutoff=1)

Parameters:

• gamma – interaction strength constant
• min – The smallest radius for which the potential will be constructed.
• cutoff – The largest radius for which the potential will be constructed.
• tol – The tolerance to which the interpolation should match the exact

\[\mathbf{F}^D_{ij} = -\gamma_{ij}\left(1 - \frac{r_{ij}}{r_c}\right)^{0.41}(\mathbf{e}_{ij} \cdot \mathbf{v}_{ij}) \mathbf{e}_{ij}\]

mechanica.forces.dpd_random(gamma, sigma, min, cutoff, tol)

Parameters:

• gamma – interaction strength constant
• sigma – standard deviation of the gaussian random noise
• min – The smallest radius for which the potential will be constructed.
• cutoff – The largest radius for which the potential will be constructed.
• tol – The tolerance to which the interpolation should match the exact

\[\mathbf{F}^R_{ij} = \sigma_{ij}\left(1 - \frac{r_{ij}}{r_c}\right)^{0.2} \xi_{ij}\Delta t^{-1/2}\mathbf{e}_{ij}\]