#!python
from __future__ import division,print_function
from pyPRISM.potential.Potential import Potential
import numpy as np
[docs]class HardSphere(Potential):
r'''Simple hard sphere potential
**Mathematical Definition**
.. math::
U_{\alpha,\beta}(r>\sigma_{\alpha,\beta}) = 0.0
.. math::
U_{\alpha,\beta}(r\leq\sigma_{\alpha,\beta}) = C^{high}
**Variable Definitions**
:math:`\sigma_{\alpha,\beta}`
Length scale of interaction between sites
:math:`\alpha` and :math:`\beta`.
:math:`r`
Distance between sites.
:math:`C^{high}`
High value used to approximate an infinite potential due to overlap
**Description**
This potential models the simiple hard-sphere fluid, in which sites
have hard-core repulsion and no interactions outside their contact
distance.
Example
-------
.. code-block:: python
import pyPRISM
#Define a PRISM system and set the A-B interaction potential
sys = pyPRISM.System(['A','B'],kT=1.0)
sys.domain = pyPRISM.Domain(dr=0.1,length=1024)
sys.potential['A','B'] = pyPRISM.potential.HardSphere(sigma=1.0,high_value=10**6)
.. warning::
If sigma is specified such that it does not fall on the solution grid
of the :class:`~pyPRISM.core.Domain.Domain` object specified in
:class:`~pyPRISM.core.System.System`, then the sigma will effectively
be rounded. A warning should be emitted during the construction of a
:class:`~pyPRISM.core.PRISM.PRISM` object if this occurs.
'''
[docs] def __init__(self,sigma=None,high_value=1e6):
r''' Constructor
Arguments
---------
sigma: float, *optional*
Contact distance. If not specified, sigma will be calculated from
the diameters specified in the :class:`~pyPRISM.core.System.System`
object.
high_value: float, *optional*
High value used to approximate an infinite potential due to overlap
'''
self.sigma = sigma
self.high_value = high_value
self.funk = lambda r,sigma: np.where(r>sigma,0.0,high_value)
def __repr__(self):
return '<Potential: HardSphere>'
[docs] def calculate(self,r):
r'''Calculate value of potential
Attributes
----------
r: float np.ndarray
Array of pair distances at which to calculate potential values
'''
assert (self.sigma is not None), 'Sigma must be set before evaluating potential!'
magnitude = self.funk(r,self.sigma)
return magnitude