Editing Psionics (section)

== [[Psi Energy]] Density [[Scalar Field]] ==

* '''Psi Energy Density Equation''':
** The psi energy density scalar field, denoted as <math>\Psi</math>, represents the concentration of psi energy at each point in space and time. Mathematically, it can be defined as:
<math>\Psi(x, y, z, t)</math>
*** In this equation:
**** <math>\Psi</math> is the psi energy density scalar field.
**** <math>x, y, z</math> are the spatial coordinates.
**** <math>t</math> is time.
** This scalar field assigns a numerical value to each point in space-time, representing the amount of psi energy present at that location and time.

* '''Psi Energy Flux Equation''':
** The flux of psi energy through a surface can be calculated using the psi energy density scalar field and the velocity vector field representing the flow of psi energy. Mathematically, it can be expressed as:
<math>\Phi = \int_S \Psi \vec{v} \cdot d\vec{S}</math>
*** In this equation:
**** <math>\Phi</math> is the psi energy flux through the surface <math>S</math>.
**** <math>\Psi</math> is the psi energy density scalar field.
**** <math>\vec{v}</math> is the velocity vector field of psi energy flow.
**** <math>d\vec{S}</math> is the differential surface area vector.
** Integrating the product of the psi energy density and velocity over the surface yields the total psi energy flux passing through that surface.

* '''Psi Energy Conservation Equation''':
** The rate of change of psi energy density within a volume can be described by an equation analogous to the conservation of energy principle. Mathematically, it can be written as:
<math>\frac{\partial \Psi}{\partial t} + \nabla \cdot (\Psi \vec{v}) = - \nabla \cdot \vec{J}</math>
*** In this equation:
**** <math>\frac{\partial \Psi}{\partial t}</math> is the time rate of change of psi energy density.
**** <math>\nabla \cdot (\Psi \vec{v})</math> represents the divergence of the psi energy flux.
**** <math>\vec{J}</math> represents a source or sink term for psi energy.
** This equation states that changes in psi energy density within a volume are due to the divergence of the psi energy flux and any external sources or sinks of psi energy.

* '''Psi Energy Laplace Equation''':
** The Laplace equation for the psi energy density scalar field describes how psi energy distributes itself in space in the absence of sources or sinks. Mathematically, it can be written as:
<math>\nabla^2 \Psi = 0</math>
*** In this equation:
**** <math>\nabla^2 \Psi</math> represents the Laplacian of the psi energy density scalar field.
** Solutions to this equation yield the spatial distribution of psi energy density under conditions of equilibrium or absence of external influences.

* '''Psi Energy Potential Equation''':
** Analogous to the electrostatic potential in electromagnetism, the psi energy potential <math>V_\Psi</math> can be defined in terms of the psi energy density scalar field. Mathematically, it can be expressed as:
<math>V_\Psi = -\int \Psi \, dV</math>
*** In this equation:
**** <math>V_\Psi</math> is the psi energy potential.
**** <math>\Psi</math> is the psi energy density scalar field.
**** <math>dV</math> is the differential volume element.
** This equation defines the potential energy associated with psi energy density, with negative values indicating regions of higher psi energy density.