forces Package¶

`forces` Package¶

`force` Module¶

class pyparticles.forces.force.Force(size, dim, m=None, Conts=1.0)¶

Bases: object

The main abstract class used as interface for the forces classes

Constructor

Parameters:	size – the number of particles in the system dim – the dimension of the system (3D, 2D..) m – a vector containig the masses Const – the force constants (Like G, K ...)

A¶: (property) return the array of the acclerations

F¶: (property) returns the array of the forces

const¶: (property) returns the force contants

getA()¶: return the array of the acclerations

getF()¶: returns the array of the forces

get_const()¶: returns the force contants

set_masses(m)¶

Set the masses used for computing the forces.

Parameters:	m – An array containig the masses

update_force(p_set)¶

Computes the forces of the current status ad return the accelerations of the particles

Parameters:	p_set – Particles set obj.

`force_constrained` Module¶

class pyparticles.forces.force_constrained.ForceConstrained(size, dim, m=None, Conts=1.0, f_inter=None)¶

Bases: pyparticles.forces.force.Force

force_interactions¶

get_force_interactions()¶

set_force_interactions(fi)¶

`gravity` Module¶

class pyparticles.forces.gravity.Gravity(size, dim=3, m=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Compute the gravitational force between the particles

The gravity between two particles is defined as follow:

$\mathbf{F}_{12}=-G \frac{m_1 m_2 }{r^2}\hat{r}_{12}$

Constructor

Parameters:	size – the number of particles in the system dim – the dimension of the system m – a vector containig the masses Const – the gravitational constant

A¶: Return the currents accelerations of the particles (getter only)

F¶: Return the currents forces on the particles (getter only)

getA()¶: Return the currents accelerations of the particles

getF()¶: Return the currents forces on the particles

set_masses(m)¶: Set the masses used for computing the forces.

update_force(p_set)¶: Compute the force of the current status of the system and return the accelerations of every particle in a size by dim array

`const_force` Module¶

class pyparticles.forces.const_force.ConstForce(size, dim=3, m=None, u_force=[0, 0, 0], Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Constant force field.

Constructor

Parameters:	size – the number of particles in the system dim – the dimension of the system m – a vector containig the masses u_force – The force vector (Force per unit of mass)

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(p_set)¶

`drag` Module¶

class pyparticles.forces.drag.Drag(size, dim=3, m=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Calculate the forces of resistance. Drag is a force that reacts to the movement with respect to a square law speed. It’s commonly used for describing the resistance of a fluid

The force is given the equation:

$F_i=-\frac{1}{2}K\dot{X}^2$

Constructor:

Parameters:	size – the number of particles in the system dim – the dimension of the system m – a vector containig the masses Const – the drag factor K

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(pset)¶

`damping` Module¶

class pyparticles.forces.damping.Damping(size, dim=3, m=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Compute the damping forces, the damping is a force that react proportionally to the velocity

The force is given the equation:

$F_i = -C\dot{X}$

Constructor

Parameters:	size – the number of particles in the system dim – the dimension of the system m – a vector containig the masses Const – the damping factor

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(pset)¶

`electrostatic` Module¶

class pyparticles.forces.electrostatic.Electrostatic(size, dim=3, m=None, q=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Compute the electrostatic force using the Culomb law.

..note:

The real forces of an electrodynamic system is given by the **Maxwell equations**! and not from the Culomb law.

The Culomb law is adapt for computing forces in a static system of particles and not for moving particles.

But for a very slow movement it should be a good approximation.

$\vec F = k \, q_1 \, q_2 \, \frac {\vec r_1 - \vec r_2}{\left \| \vec r_1 - \vec r_2 \right \|^3}$

A¶

F¶

getA()¶

getF()¶

set_charges(q)¶

set_masses(m)¶

update_force(p_set)¶

`electromagnetic_field` Module¶

class pyparticles.forces.electromagnetic_field.ElectromagneticField(size, dim=3, m=None, q=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Compute the electromagnetic force of a system of charged and non-selfinteracting particles system immersed in an electromagnetic filed according to the Lorenz formulation.

$\mathbf{F} = q(\mathbf{E} + \mathbf{v} \times \mathbf{B})$

A¶

F¶

append_electric_field(ef, key=None)¶

Append a vector field funcion to the list of electric field funtions.

append_magnetic_field(bf, key=None)¶

Append a vector field funcion to the list of megnetic field funtions.

It return the key used to identify the funtion, if key == None it uses a random number.

getA()¶

getF()¶

set_charges(q)¶

set_masses(m)¶

update_force(pset)¶

`lennard_jones` Module¶

class pyparticles.forces.lennard_jones.LenardJones(size, dim=3, m=None, Consts=(1.0, 1.0))¶

Bases: pyparticles.forces.force.Force

Compute the lenard jones force between the particles

The L. J. force between two particles is defined as follow:

$\mathbf{F}(r) = 4 \epsilon \left(12\,{\frac{{\sigma}^{12}}{{r}^{13}}}-6\,{\frac{{\sigma}^{6}}{{r}^{7}}}\right)\hat{\mathbf{r}}$

Constructor:

Parameters:	size – the number of particles in the system dim – the dimension of the system m – a vector containig the masses Const – An indexable object[*] with the two contants

[*] Const[0] = $\epsilon$: Const[1] = $\sigma$

A¶: Return the currents accelerations of the particles (getter only)

F¶: Return the currents forces on the particles (getter only)

getA()¶: Return the currents accelerations of the particles

getF()¶: Return the currents forces on the particles

set_masses(m)¶: Set the masses used for computing the forces.

update_force(p_set)¶

Compute the force of the current status of the system and return the accelerations of every particle in a size by dim array

Parameters:	p_set – Particles set obj.

`linear_spring` Module¶

class pyparticles.forces.linear_spring.LinearSpring(size, dim=3, m=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

Compute the forces according to the Hooke’s law.

$F_i = -k X$

Parameters:	size – size of the particles system dim – dimension of the system m – an array containing the masses const – spring constant ( K )

A¶

F¶

const¶

getA()¶

getF()¶

get_const()¶

set_masses(m)¶: set the masses of the particles

update_force(p_set)¶

`linear_spring_constrained` Module¶

class pyparticles.forces.linear_spring_constrained.LinearSpringConstrained(size, dim, m=None, Consts=1.0, f_inter=None)¶

Bases: pyparticles.forces.force_constrained.ForceConstrained

A¶

F¶

const¶

getA()¶

getF()¶

get_const()¶

set_masses(m)¶: set the masses of the particles

update_force(pset)¶

`multiple_force` Module¶

class pyparticles.forces.multiple_force.MultipleForce(size, dim=3, m=None, Conts=None)¶

Bases: object

Combine the effect of some forces, for example constant force and springs. It behaves like any other force, and can be used with all methods of numerical integration.

A¶

F¶

append_force(force)¶: Append a new force to the forces list

getA()¶

getF()¶

set_masses(m)¶: Set the masses in the forces system

update_force(p_set)¶

`pseudo_bubble` Module¶

class pyparticles.forces.pseudo_bubble.PseudoBubble(size, dim=3, m=None, Consts=(0.3, 2.0))¶

Bases: pyparticles.forces.force.Force

Pseudo Bubble is a fake force that produce the effect of the bubbles in a fluid.

$\begin{cases} & \text{ if } d_{i,j} < R \,\,\, \text{then} \,\,\,F_{i,j}= -\frac{B}{R}d_{i,j}+\frac{B}{d_{i,j}} \\ & \text{ if } d_{i,j} \geqslant R \,\,\, \text{then} \,\,\,F_{i,j}= 0 \end{cases}$

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(pset)¶

`van_der_waals_force` Module¶

class pyparticles.forces.van_der_waals_force.VanDerWaals(size, dim=3, m=None, Consts=1.0)¶

Bases: pyparticles.forces.force.Force

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(p_set)¶

`vector_field_force` Module¶

class pyparticles.forces.vector_field_force.VectorFieldForce(size, dim=3, m=None)¶

Bases: pyparticles.forces.force.Force

A¶

F¶

getA()¶

getF()¶

set_masses(m)¶

update_force(p_set)¶

vect_fun(X)¶

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forces Package¶

`forces` Package¶

`force` Module¶

`force_constrained` Module¶

`gravity` Module¶

`const_force` Module¶

`drag` Module¶

`damping` Module¶

`electrostatic` Module¶

`electromagnetic_field` Module¶

`lennard_jones` Module¶

`linear_spring` Module¶

`linear_spring_constrained` Module¶

`multiple_force` Module¶

`pseudo_bubble` Module¶

`van_der_waals_force` Module¶

`vector_field_force` Module¶

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forces Package¶

forces Package¶

force Module¶

force_constrained Module¶

gravity Module¶

const_force Module¶

drag Module¶

damping Module¶

electrostatic Module¶

electromagnetic_field Module¶

lennard_jones Module¶

linear_spring Module¶

linear_spring_constrained Module¶

multiple_force Module¶

pseudo_bubble Module¶

van_der_waals_force Module¶

vector_field_force Module¶

Navigation

`forces` Package¶

`force` Module¶

`force_constrained` Module¶

`gravity` Module¶

`const_force` Module¶

`drag` Module¶

`damping` Module¶

`electrostatic` Module¶

`electromagnetic_field` Module¶

`lennard_jones` Module¶

`linear_spring` Module¶

`linear_spring_constrained` Module¶

`multiple_force` Module¶

`pseudo_bubble` Module¶

`van_der_waals_force` Module¶

`vector_field_force` Module¶