potentials_util
Short description
@author: Moritz F P Becker
- pyrid.system.potentials_util.CSW(r, args)[source]
Calculates potential energy and force for a Continuous Square-Well (CSW) potential.
- Parameters
- rwfloat
Radius of the attractive well
- eps_cwfloat
Interaction energy constant (units of kJ).
- alphafloat
Steepness of the attractive well (the larger alpha, the better the approximation to a square well).
- Returns
- (float64, float64)
returns the potential energy and force of the interaction
Notes
The CSW potential has been introduced in Espinosa et al. [29] and is a continuous approximation of the square-well potential and thereby suited for moelcular dynamics simulations Espinosa et al. [30].
\[U_{CSW}(r) = - \frac{\epsilon_{CSW}}{2} \Big[1 - \tanh\Big(\frac{r-r_w}{\alpha}\Big)\Big]\]
- pyrid.system.potentials_util.FENE(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.Lennard_Jones(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.PHS(r, args)[source]
Calculates potential energy and force for a Pseudo Hard Sphere (PHS) potential.
- Parameters
- EpsRfloat
Interaction energy constant (units of kJ).
- lrfloat
Exponent of the repulsive term.
- lafloat
Exponent of the attractive term.
- Returns
- (float64, float64)
returns the potential energy and force of the interaction
Notes
The Pseudo Hard Sphere interaction potential is a continuous approximation of the hard sphere and thereby suited for molecular dynamics simulations Jover et al. [31], Espinosa et al. [30].
\[U_{HS} = \Biggl \lbrace { \lambda_r (\frac{\lambda_r}{\lambda_a})^{\lambda_a} \epsilon_R [(\frac{\sigma}{r})^{\lambda_r}-(\frac{\sigma}{r})^{\lambda_a}]+\epsilon_R,\text{ if } { r < (\frac{\lambda_r}{\lambda_a}) \sigma } \atop 0, \text{ if } { r < (\frac{\lambda_r}{\lambda_a}) \sigma } }\]
- pyrid.system.potentials_util.WLC_force(z, Lp, L0)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.Weeks_Chandler_Anderson(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.execute_force(ID, r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.harmonic_repulsion(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.piecewise_harmonic(r, args)[source]
Calculates potential energy and force for a weak piecewise harmonic potential.
- Parameters
- rcfloat
cutoff radius
- kfloat
force constant (units of kJ/length_unit^2).
- hfloat
depth of potential well (units of kJ).
- dfloat
radius of the repulsive part!
- Returns
- (float64, float64)
returns the potential energy and force of the interaction
Notes
The weak piecewise harmonic interaction potential is also used in the particle-based reaction-diffusion simulator ReaDDy Hoffmann et al. [23] as it is well suited for brownian dynamics simulations, which allow larger time steps than conventional molecular dynamics simualtions, however forces acting on the particles must not change too much in bewteen two integration step. Therefore, soft potentials are used. Hard potentials like the PHS may also be used. In this case, however, the integration time step needs to be chosen much smaller, reducing the benefit of simulating overdamped langevin dynamics to a degree!
\[\begin{split}U_{ha}(r) = \begin{cases} \frac{1}{2}k(r-(d_1+d_2))^2-h,& \text{if } r<(d_1+d_2), \\ \frac{h}{2}(\frac{r_c-(d_1+d_2)}{2})^{-2}(r-(d_1+d_2))^2-h,& \text{if } d \le r < d + \frac{r_c-(d_1+d_2)}{2}, \\ -\frac{h}{2}(\frac{r_c-(d_1+d_2)}{2})^{-2}(r-r_c)^2,& \text{if } d + \frac{r_c-(d_1+d_2)}{2} \le r < r_c, \\ 0, & \text{otherwise} \end{cases}\end{split}\]
- pyrid.system.potentials_util.repulsive_membrane(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.screened_electrostatics(r, args)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised
- pyrid.system.potentials_util.wall(r, d, k)[source]
A brief description of what the function (method in case of classes) is and what it’s used for
- Parameters
- parameter_1dtype
Some Information
- parameter_2dtype
Some Information
- Returns
- dtype
Some information
- Raises
- NotImplementedError (just an example)
Brief explanation of why/when this exception is raised