A Potential object is a compiled interpolation of a given function. The Universe applies potentials to particles to calculate the net force on them. More...

#include <tfPotential.h>

Inheritance diagram for TissueForge::Potential:

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Collaboration diagram for TissueForge::Potential:

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Public Member Functions
FPTYPE	operator() (const FPTYPE &r, const FPTYPE &r0=-1.0)

FPTYPE	operator() (const std::vector< FPTYPE > &r)

FPTYPE	operator() (struct ParticleHandle *pi, const FVector3 &pt)

FPTYPE	operator() (struct ParticleHandle pi, struct ParticleHandle pj)

FPTYPE	operator() (struct ParticleHandle pi, struct ParticleHandle pj, struct ParticleHandle *pk)

FPTYPE	operator() (struct ParticleHandle pi, struct ParticleHandle pj, struct ParticleHandle pk, struct ParticleHandle pl)

FPTYPE	force (FPTYPE r, FPTYPE ri=-1.0, FPTYPE rj=-1.0)

std::vector< FPTYPE >	force (const std::vector< FPTYPE > &r)

std::vector< FPTYPE >	force (struct ParticleHandle *pi, const FVector3 &pt)

std::vector< FPTYPE >	force (struct ParticleHandle pi, struct ParticleHandle pj)

std::pair< std::vector< FPTYPE >, std::vector< FPTYPE > >	force (struct ParticleHandle pi, struct ParticleHandle pj, struct ParticleHandle *pk)

std::pair< std::vector< FPTYPE >, std::vector< FPTYPE > >	force (struct ParticleHandle pi, struct ParticleHandle pj, struct ParticleHandle pk, struct ParticleHandle pl)

std::vector< Potential * >	constituents ()

Potential &	operator+ (const Potential &rhs)

virtual std::string	toString ()
	Get a JSON string representation.

FPTYPE	getMin ()

FPTYPE	getMax ()

FPTYPE	getCutoff ()

std::pair< FPTYPE, FPTYPE >	getDomain ()

int	getIntervals ()

bool	getBound ()

void	setBound (const bool &_bound)

FPTYPE	getR0 ()

void	setR0 (const FPTYPE &_r0)

bool	getShifted ()

bool	getPeriodic ()

bool	getRSquare ()

Static Public Member Functions
static Potential *	fromString (const std::string &str)
	Create from a JSON string representation.

static Potential *	lennard_jones_12_6 (FPTYPE min, FPTYPE max, FPTYPE A, FPTYPE B, FPTYPE *tol=NULL)
	Creates a 12-6 Lennard-Jones potential.

static Potential *	lennard_jones_12_6_coulomb (FPTYPE min, FPTYPE max, FPTYPE A, FPTYPE B, FPTYPE q, FPTYPE *tol=NULL)
	Creates a potential of the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.

static Potential *	ewald (FPTYPE min, FPTYPE max, FPTYPE q, FPTYPE kappa, FPTYPE tol=NULL, unsigned int periodicOrder=NULL)
	Creates a real-space Ewald potential.

static Potential *	coulomb (FPTYPE q, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE tol=NULL, unsigned int periodicOrder=NULL)
	Creates a Coulomb potential.

static Potential *	coulombR (FPTYPE q, FPTYPE kappa, FPTYPE min, FPTYPE max, unsigned int *modes=NULL)
	Creates a Coulomb reciprocal potential.

static Potential *	harmonic (FPTYPE k, FPTYPE r0, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates a harmonic bond potential.

static Potential *	linear (FPTYPE k, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates a linear potential.

static Potential *	harmonic_angle (FPTYPE k, FPTYPE theta0, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates a harmonic angle potential.

static Potential *	harmonic_dihedral (FPTYPE k, FPTYPE delta, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates a harmonic dihedral potential.

static Potential *	cosine_dihedral (FPTYPE k, int n, FPTYPE delta, FPTYPE *tol=NULL)
	Creates a cosine dihedral potential.

static Potential *	well (FPTYPE k, FPTYPE n, FPTYPE r0, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates a well potential.

static Potential *	glj (FPTYPE e, FPTYPE m=NULL, FPTYPE n=NULL, FPTYPE k=NULL, FPTYPE r0=NULL, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE tol=NULL, bool shifted=NULL)
	Creates a generalized Lennard-Jones potential.

static Potential *	morse (FPTYPE d=NULL, FPTYPE a=NULL, FPTYPE r0=NULL, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE tol=NULL, bool *shifted=NULL)
	Creates a Morse potential.

static Potential *	overlapping_sphere (FPTYPE mu=NULL, FPTYPE kc=NULL, FPTYPE kh=NULL, FPTYPE r0=NULL, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE *tol=NULL)
	Creates an overlapping-sphere potential from :cite:`Osborne:2017hk`.

static Potential *	power (FPTYPE k=NULL, FPTYPE r0=NULL, FPTYPE alpha=NULL, FPTYPE min=NULL, FPTYPE max=NULL, FPTYPE tol=NULL)
	Creates a power potential.

static Potential *	dpd (FPTYPE alpha=NULL, FPTYPE gamma=NULL, FPTYPE sigma=NULL, FPTYPE cutoff=NULL, bool *shifted=NULL)
	Creates a Dissipative Particle Dynamics potential.

static Potential *	custom (FPTYPE min, FPTYPE max, FPTYPE(f)(FPTYPE), FPTYPE(fp)(FPTYPE), FPTYPE(f6p)(FPTYPE), FPTYPE tol=NULL, uint32_t *flags=NULL)
	Creates a custom potential.

Public Attributes
uint32_t	kind

uint32_t	flags

FPTYPE	alpha [4]

FPTYPE *	c

FPTYPE	r0_plusone

FPTYPE	a

FPTYPE	b

FPTYPE	mu

FPTYPE	offset [3]

int	n

PotentialCreate	create_func

PotentialClear	clear_func

PotentialEval_ByParticle	eval_bypart

PotentialEval_ByParticles	eval_byparts

PotentialEval_ByParticles3	eval_byparts3

PotentialEval_ByParticles4	eval_byparts4

Potential *	pca

Potential *	pcb

const char *	name

Detailed Description

A Potential object is a compiled interpolation of a given function. The Universe applies potentials to particles to calculate the net force on them.

For performance reasons, Tissue Forge implements potentials as interpolations, which can be much faster than evaluating the function directly.

A potential can be treated just like any callable object.

Member Function Documentation

◆ cosine_dihedral()

static Potential * TissueForge::Potential::cosine_dihedral	(	FPTYPE	k,
		int	n,
		FPTYPE	delta,
		FPTYPE *	tol = NULL )

static

Creates a cosine dihedral potential.

The cosine dihedral potential has the form:

$k \left( 1 + \cos( n \theta-\delta ) \right)$

Parameters

k	energy of the dihedral.
n	multiplicity of the dihedral.
delta	minimum energy dihedral.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.01.

Returns: Potential*

◆ coulomb()

static Potential * TissueForge::Potential::coulomb	(	FPTYPE	q,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL,
		unsigned int *	periodicOrder = NULL )

static

Creates a Coulomb potential.

The Coulomb potential has the form:

$\frac{q}{r}$

Parameters

q	The charge scaling of the potential.
min	The smallest radius for which the potential will be constructed. Default is 0.01.
max	The largest radius for which the potential will be constructed. Default is 2.0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001 * (max - min).
periodicOrder	Order of lattice periodicity along all periodic dimensions. Defaults to 0.

Returns: Potential*

◆ coulombR()

static Potential * TissueForge::Potential::coulombR	(	FPTYPE	q,
		FPTYPE	kappa,
		FPTYPE	min,
		FPTYPE	max,
		unsigned int *	modes = NULL )

static

Creates a Coulomb reciprocal potential.

The Coulomb reciprocal potential has the form:

$\frac{\pi q}{V} \sum_{||\mathbf{m}|| \neq 0} \frac{1}{||\mathbf{m}||^2} \exp \left( \left( i \mathbf{r}_{jk} - \left( \frac{\pi}{\kappa} \right)^{2} \mathbf{m} \right) \cdot \mathbf{m} \right)$

Here $ V $ is the volume of the domain and $\mathbf{m}$ is a reciprocal vector of the domain.

Parameters

q	Charge scaling of the potential.
kappa	Screening distance.
min	Smallest radius for which the potential will be constructed.
max	Largest radius for which the potential will be constructed.
modes	Number of Fourier modes along each periodic dimension. Default is 1.

Returns: Potential*

◆ custom()

static Potential * TissueForge::Potential::custom	(	FPTYPE	min,
		FPTYPE	max,
		FPTYPE(*)(FPTYPE)	f,
		FPTYPE(*)(FPTYPE)	fp,
		FPTYPE(*)(FPTYPE)	f6p,
		FPTYPE *	tol = NULL,
		uint32_t *	flags = NULL )

static

Creates a custom potential.

Parameters

min	The smallest radius for which the potential will be constructed.
max	The largest radius for which the potential will be constructed.
f	function returning the value of the potential
fp	function returning the value of first derivative of the potential
f6p	function returning the value of sixth derivative of the potential
tol	Tolerance, defaults to 0.001.

Returns: Potential*

◆ dpd()

static Potential * TissueForge::Potential::dpd	(	FPTYPE *	alpha = NULL,
		FPTYPE *	gamma = NULL,
		FPTYPE *	sigma = NULL,
		FPTYPE *	cutoff = NULL,
		bool *	shifted = NULL )

static

Creates a Dissipative Particle Dynamics potential.

The Dissipative Particle Dynamics force has the form:

$\mathbf{F}_{ij} = \mathbf{F}^C_{ij} + \mathbf{F}^D_{ij} + \mathbf{F}^R_{ij}$

The conservative force is:

$\mathbf{F}^C_{ij} = \alpha \left(1 - \frac{r_{ij}}{r_c}\right) \mathbf{e}_{ij}$

The dissapative force is:

$\mathbf{F}^D_{ij} = -\gamma \left(1 - \frac{r_{ij}}{r_c}\right)^{2}(\mathbf{e}_{ij} \cdot \mathbf{v}_{ij}) \mathbf{e}_{ij}$

The random force is:

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

Parameters

alpha	interaction strength of the conservative force. Defaults to 1.0.
gamma	interaction strength of dissapative force. Defaults to 1.0.
sigma	strength of random force. Defaults to 1.0.
cutoff	cutoff distance. Defaults to 1.0.
shifted	Flag for whether using a shifted potential. Defaults to false.

Returns: Potential*

◆ ewald()

static Potential * TissueForge::Potential::ewald	(	FPTYPE	min,
		FPTYPE	max,
		FPTYPE	q,
		FPTYPE	kappa,
		FPTYPE *	tol = NULL,
		unsigned int *	periodicOrder = NULL )

static

Creates a real-space Ewald potential.

The Ewald potential has the form:

$q \frac{\mathrm{erfc}\, ( \kappa r)}{r}$

Parameters

min	The smallest radius for which the potential will be constructed.
max	The largest radius for which the potential will be constructed.
q	The charge scaling of the potential.
kappa	The screening distance of the Ewald potential.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001 * (max - min).
periodicOrder	Order of lattice periodicity along all periodic dimensions. Defaults to 0.

Returns: Potential*

◆ fromString()

static Potential * TissueForge::Potential::fromString ( const std::string & str )

static

Create from a JSON string representation.

Parameters

str

Returns: Potential*

◆ glj()

static Potential * TissueForge::Potential::glj	(	FPTYPE	e,
		FPTYPE *	m = NULL,
		FPTYPE *	n = NULL,
		FPTYPE *	k = NULL,
		FPTYPE *	r0 = NULL,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL,
		bool *	shifted = NULL )

static

Creates a generalized Lennard-Jones potential.

The generalized Lennard-Jones potential has the form:

$\frac{\epsilon}{n-m} \left[ m \left( \frac{r_0}{r} \right)^n - n \left( \frac{r_0}{r} \right)^m \right]$

Parameters

e	effective energy of the potential.
m	order of potential. Defaults to 3
n	order of potential. Defaults to 2*m.
k	mimumum of the potential. Defaults to 1.
r0	mimumum of the potential. Defaults to 1.
min	The smallest radius for which the potential will be constructed. Defaults to 0.05 * r0.
max	The largest radius for which the potential will be constructed. Defaults to 5 * r0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.01.
shifted	Flag for whether using a shifted potential. Defaults to true.

Returns: Potential*

◆ harmonic()

static Potential * TissueForge::Potential::harmonic	(	FPTYPE	k,
		FPTYPE	r0,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a harmonic bond potential.

The harmonic potential has the form:

$k \left( r-r_0 \right)^2$

Parameters

k	The energy of the bond.
r0	The bond rest length.
min	The smallest radius for which the potential will be constructed. Defaults to .
max	The largest radius for which the potential will be constructed. Defaults to .
tol	The tolerance to which the interpolation should match the exact potential. Defaults to $0.01 \abs(max-min)$ .

Returns: Potential*

◆ harmonic_angle()

static Potential * TissueForge::Potential::harmonic_angle	(	FPTYPE	k,
		FPTYPE	theta0,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a harmonic angle potential.

The harmonic angle potential has the form:

$k \left(\theta-\theta_{0} \right)^2$

Parameters

k	The energy of the angle.
theta0	The minimum energy angle.
min	The smallest angle for which the potential will be constructed. Defaults to zero.
max	The largest angle for which the potential will be constructed. Defaults to PI.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.005 * (max - min).

Returns: Potential*

◆ harmonic_dihedral()

static Potential * TissueForge::Potential::harmonic_dihedral	(	FPTYPE	k,
		FPTYPE	delta,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a harmonic dihedral potential.

The harmonic dihedral potential has the form:

$k \left( \theta - \delta \right) ^2$

Parameters

k	energy of the dihedral.
delta	minimum energy dihedral.
min	The smallest angle for which the potential will be constructed. Defaults to zero.
max	The largest angle for which the potential will be constructed. Defaults to PI.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.005 * (max - min).

Returns: Potential*

◆ lennard_jones_12_6()

static Potential * TissueForge::Potential::lennard_jones_12_6	(	FPTYPE	min,
		FPTYPE	max,
		FPTYPE	A,
		FPTYPE	B,
		FPTYPE *	tol = NULL )

static

Creates a 12-6 Lennard-Jones potential.

The Lennard Jones potential has the form:

$\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right)$

Parameters

min	The smallest radius for which the potential will be constructed.
max	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001 * (max - min).

Returns: Potential*

◆ lennard_jones_12_6_coulomb()

static Potential * TissueForge::Potential::lennard_jones_12_6_coulomb	(	FPTYPE	min,
		FPTYPE	max,
		FPTYPE	A,
		FPTYPE	B,
		FPTYPE	q,
		FPTYPE *	tol = NULL )

static

Creates a potential of the sum of a 12-6 Lennard-Jones potential and a shifted Coulomb potential.

The 12-6 Lennard Jones - Coulomb potential has the form:

$\left( \frac{A}{r^{12}} - \frac{B}{r^6} \right) + q \left( \frac{1}{r} - \frac{1}{max} \right)$

Parameters

min	The smallest radius for which the potential will be constructed.
max	The largest radius for which the potential will be constructed.
A	The first parameter of the Lennard-Jones potential.
B	The second parameter of the Lennard-Jones potential.
q	The charge scaling of the potential.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001 * (max - min).

Returns: Potential*

◆ linear()

static Potential * TissueForge::Potential::linear	(	FPTYPE	k,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a linear potential.

The linear potential has the form:

$k r$

Parameters

k	interaction strength; represents the potential energy peak value.
min	The smallest radius for which the potential will be constructed. Defaults to 0.0.
max	The largest radius for which the potential will be constructed. Defaults to 10.0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001.

Returns: Potential*

◆ morse()

static Potential * TissueForge::Potential::morse	(	FPTYPE *	d = NULL,
		FPTYPE *	a = NULL,
		FPTYPE *	r0 = NULL,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL,
		bool *	shifted = NULL )

static

Creates a Morse potential.

The Morse potential has the form:

$d \left(1 - e^{ -a \left(r - r_0 \right) } \right)^2$

Parameters

d	well depth. Defaults to 1.0.
a	potential width. Defaults to 6.0.
r0	equilibrium distance. Defaults to 0.0.
min	The smallest radius for which the potential will be constructed. Defaults to 0.0001.
max	The largest radius for which the potential will be constructed. Defaults to 3.0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001.
shifted	Flag for whether using a shifted potential. Defaults to true.

Returns: Potential*

◆ overlapping_sphere()

static Potential * TissueForge::Potential::overlapping_sphere	(	FPTYPE *	mu = NULL,
		FPTYPE *	kc = NULL,
		FPTYPE *	kh = NULL,
		FPTYPE *	r0 = NULL,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates an overlapping-sphere potential from :cite:Osborne:2017hk.

The overlapping-sphere potential has the form:

$\mu_{ij} s_{ij}(t) \hat{\mathbf{r}}_{ij} \log \left( 1 + \frac{||\mathbf{r}_{ij}|| - s_{ij}(t)}{s_{ij}(t)} \right) \text{ if } ||\mathbf{r}_{ij}|| < s_{ij}(t) ,$

$\mu_{ij}\left(||\mathbf{r}_{ij}|| - s_{ij}(t)\right) \hat{\mathbf{r}}_{ij} \exp \left( -k_c \frac{||\mathbf{r}_{ij}|| - s_{ij}(t)}{s_{ij}(t)} \right) \text{ if } s_{ij}(t) \leq ||\mathbf{r}_{ij}|| \leq r_{max} ,$

$0 \text{ otherwise} .$

Osborne refers to $\mu_{ij}$ as a "spring constant", this controls the size of the force, and is the potential energy peak value. $\hat{\mathbf{r}}_{ij}$ is the unit vector from particle $ i $ center to particle $ j $ center, $ k_C $ is a parameter that defines decay of the attractive force. Larger values of $ k_C $ result in a shaper peaked attraction, and thus a shorter ranged force. $s_{ij}(t)$ is the is the sum of the radii of the two particles.

Parameters

mu	interaction strength, represents the potential energy peak value. Defaults to 1.0.
kc	decay strength of long range attraction. Larger values make a shorter ranged function. Defaults to 1.0.
kh	Optionally add a harmonic long-range attraction, same as :meth:`glj` function. Defaults to 0.0.
r0	Optional harmonic rest length, only used if `kh` is non-zero. Defaults to 0.0.
min	The smallest radius for which the potential will be constructed. Defaults to 0.001.
max	The largest radius for which the potential will be constructed. Defaults to 10.0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.001.

Returns: Potential*

◆ power()

static Potential * TissueForge::Potential::power	(	FPTYPE *	k = NULL,
		FPTYPE *	r0 = NULL,
		FPTYPE *	alpha = NULL,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a power potential.

The power potential the general form of many of the potential functions, such as :meth:linear, etc. power has the form:

$k \lvert r-r_0 \rvert ^{\alpha}$

Parameters

k	interaction strength, represents the potential energy peak value. Defaults to 1
r0	potential rest length, zero of the potential, defaults to 0.
alpha	Exponent, defaults to 1.
min	minimal value potential is computed for, defaults to r0 / 2.
max	cutoff distance, defaults to 3 * r0.
tol	Tolerance, defaults to 0.01.

Returns: Potential*

◆ toString()

virtual std::string TissueForge::Potential::toString ( )

virtual

Get a JSON string representation.

Returns: std::string

Reimplemented in TissueForge::DPDPotential.

◆ well()

static Potential * TissueForge::Potential::well	(	FPTYPE	k,
		FPTYPE	n,
		FPTYPE	r0,
		FPTYPE *	min = NULL,
		FPTYPE *	max = NULL,
		FPTYPE *	tol = NULL )

static

Creates a well potential.

Useful for binding a particle to a region.

The well potential has the form:

$\frac{k}{\left(r_0 - r\right)^{n}}$

Parameters

k	potential prefactor constant, should be decreased for larger n.
n	exponent of the potential, larger n makes a sharper potential.
r0	The extents of the potential, length units. Represents the maximum extents that a two objects connected with this potential should come apart.
min	The smallest radius for which the potential will be constructed. Defaults to zero.
max	The largest radius for which the potential will be constructed. Defaults to r0.
tol	The tolerance to which the interpolation should match the exact potential. Defaults to 0.01 * abs(min-max).

Returns: Potential*

Member Data Documentation

◆ a

FPTYPE TissueForge::Potential::a

Interval edges.

◆ alpha

FPTYPE TissueForge::Potential::alpha[4]

Coefficients for the interval transform.

◆ c

FPTYPE* TissueForge::Potential::c

The coefficients.

◆ flags

uint32_t TissueForge::Potential::flags

Flags.

◆ mu

FPTYPE TissueForge::Potential::mu

potential scaling constant

◆ n

int TissueForge::Potential::n

Nr of intervals.

◆ name

const char* TissueForge::Potential::name

pointer to what kind of potential this is.

◆ offset

FPTYPE TissueForge::Potential::offset[3]

coordinate offset

The documentation for this struct was generated from the following file:

source/mdcore/include/tfPotential.h

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Member Function Documentation

◆ cosine_dihedral()

◆ coulomb()

◆ coulombR()

◆ custom()

◆ dpd()

◆ ewald()

◆ fromString()

◆ glj()

◆ harmonic()

◆ harmonic_angle()

◆ harmonic_dihedral()

◆ lennard_jones_12_6()

◆ lennard_jones_12_6_coulomb()

◆ linear()

◆ morse()

◆ overlapping_sphere()

◆ power()

◆ toString()

◆ well()

Member Data Documentation

◆ a

◆ alpha

◆ c

◆ flags

◆ mu

◆ n

◆ name

◆ offset