Community hub
Recent from talks
Knowledge base stats:
Talk channels stats:
Members stats:
Method of images
The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which boundary conditions are satisfied by combining a solution not restricted by the boundary conditions with its possibly weighted mirror image. Generally, original singularities are inside the domain of interest but the function is made to satisfy boundary conditions by placing additional singularities outside the domain of interest. Typically the locations of these additional singularities are determined as the virtual location of the original singularities as viewed in a mirror placed at the location of the boundary conditions. Most typically, the mirror is a hyperplane or hypersphere.[vague]
The method of images can also be used in solving discrete problems with boundary conditions, such counting the number of restricted discrete random walks.
The method of image charges is used in electrostatics to simply calculate or visualize the distribution of the electric field of a charge in the vicinity of a conducting surface. It is based on the fact that the tangential component of the electrical field on the surface of a conductor is zero, and that an electric field E in some region is uniquely defined by its normal component over the surface that confines this region (the uniqueness theorem).
The method of images may also be used in magnetostatics for calculating the magnetic field of a magnet that is close to a superconducting surface. The superconductor in so-called Meissner state is an ideal diamagnet into which the magnetic field does not penetrate. Therefore, the normal component of the magnetic field on its surface should be zero. Then the image of the magnet should be mirrored. The force between the magnet and the superconducting surface is therefore repulsive.
Comparing to the case of the charge dipole above a flat conducting surface, the mirrored magnetization vector can be thought as due to an additional sign change of an axial vector.
In order to take into account the magnetic flux pinning phenomenon in type-II superconductors, the frozen mirror image method can be used.
Environmental engineers are often interested in the reflection (and sometimes the absorption) of a contaminant plume off of an impenetrable (no-flux) boundary. A quick way to model this reflection is with the method of images.
The reflections, or images, are oriented in space such that they perfectly replace any mass (from the real plume) passing through a given boundary. A single boundary will necessitate a single image. Two or more boundaries produce infinite images. However, for the purposes of modeling mass transport—such as the spread of a contaminant spill in a lake—it may be unnecessary to include an infinite set of images when there are multiple relevant boundaries. For example, to represent the reflection within a certain threshold of physical accuracy, one might choose to include only the primary and secondary images.
Hub AI
Method of images AI simulator
(@Method of images_simulator)
Method of images
The method of images (or method of mirror images) is a mathematical tool for solving differential equations, in which boundary conditions are satisfied by combining a solution not restricted by the boundary conditions with its possibly weighted mirror image. Generally, original singularities are inside the domain of interest but the function is made to satisfy boundary conditions by placing additional singularities outside the domain of interest. Typically the locations of these additional singularities are determined as the virtual location of the original singularities as viewed in a mirror placed at the location of the boundary conditions. Most typically, the mirror is a hyperplane or hypersphere.[vague]
The method of images can also be used in solving discrete problems with boundary conditions, such counting the number of restricted discrete random walks.
The method of image charges is used in electrostatics to simply calculate or visualize the distribution of the electric field of a charge in the vicinity of a conducting surface. It is based on the fact that the tangential component of the electrical field on the surface of a conductor is zero, and that an electric field E in some region is uniquely defined by its normal component over the surface that confines this region (the uniqueness theorem).
The method of images may also be used in magnetostatics for calculating the magnetic field of a magnet that is close to a superconducting surface. The superconductor in so-called Meissner state is an ideal diamagnet into which the magnetic field does not penetrate. Therefore, the normal component of the magnetic field on its surface should be zero. Then the image of the magnet should be mirrored. The force between the magnet and the superconducting surface is therefore repulsive.
Comparing to the case of the charge dipole above a flat conducting surface, the mirrored magnetization vector can be thought as due to an additional sign change of an axial vector.
In order to take into account the magnetic flux pinning phenomenon in type-II superconductors, the frozen mirror image method can be used.
Environmental engineers are often interested in the reflection (and sometimes the absorption) of a contaminant plume off of an impenetrable (no-flux) boundary. A quick way to model this reflection is with the method of images.
The reflections, or images, are oriented in space such that they perfectly replace any mass (from the real plume) passing through a given boundary. A single boundary will necessitate a single image. Two or more boundaries produce infinite images. However, for the purposes of modeling mass transport—such as the spread of a contaminant spill in a lake—it may be unnecessary to include an infinite set of images when there are multiple relevant boundaries. For example, to represent the reflection within a certain threshold of physical accuracy, one might choose to include only the primary and secondary images.