Boundary value problemIn the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics as any physical differential equation will have them. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems.
Electric dipole momentThe electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The debye (D) is another unit of measurement used in atomic physics and chemistry. Theoretically, an electric dipole is defined by the first-order term of the multipole expansion; it consists of two equal and opposite charges that are infinitesimally close together, although real dipoles have separated charge.
Neumann boundary conditionIn mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. When imposed on an ordinary or a partial differential equation, the condition specifies the values of the derivative applied at the boundary of the domain. It is possible to describe the problem using other boundary conditions: a Dirichlet boundary condition specifies the values of the solution itself (as opposed to its derivative) on the boundary, whereas the Cauchy boundary condition, mixed boundary condition and Robin boundary condition are all different types of combinations of the Neumann and Dirichlet boundary conditions.
Transcranial magnetic stimulationTranscranial magnetic stimulation (TMS) is a noninvasive form of brain stimulation in which a changing magnetic field is used to induce an electric current at a specific area of the brain through electromagnetic induction. An electric pulse generator, or stimulator, is connected to a magnetic coil connected to the scalp. The stimulator generates a changing electric current within the coil which creates a varying magnetic field, inducing a current within a region in the brain itself.
Cerebral atrophyCerebral atrophy is a common feature of many of the diseases that affect the brain. Atrophy of any tissue means a decrement in the size of the cell, which can be due to progressive loss of cytoplasmic proteins. In brain tissue, atrophy describes a loss of neurons and the connections between them. Brain atrophy can be classified into two main categories: generalized and focal atrophy. Generalized atrophy occurs across the entire brain whereas focal atrophy affects cells in a specific location.
Electric fieldAn electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges and time-varying electric currents. Electric fields and magnetic fields are both manifestations of the electromagnetic field, one of the four fundamental interactions (also called forces) of nature.
Cerebral hypoxiaCerebral hypoxia is a form of hypoxia (reduced supply of oxygen), specifically involving the brain; when the brain is completely deprived of oxygen, it is called cerebral anoxia. There are four categories of cerebral hypoxia; they are, in order of increasing severity: diffuse cerebral hypoxia (DCH), focal cerebral ischemia, cerebral infarction, and global cerebral ischemia. Prolonged hypoxia induces neuronal cell death via apoptosis, resulting in a hypoxic brain injury.
Cauchy boundary conditionIn mathematics, a Cauchy (koʃi) boundary condition augments an ordinary differential equation or a partial differential equation with conditions that the solution must satisfy on the boundary; ideally so as to ensure that a unique solution exists. A Cauchy boundary condition specifies both the function value and normal derivative on the boundary of the domain. This corresponds to imposing both a Dirichlet and a Neumann boundary condition. It is named after the prolific 19th-century French mathematical analyst Augustin-Louis Cauchy.
Electromagnetic radiationIn physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. Types of EMR include radio waves, microwaves, infrared, (visible) light, ultraviolet, X-rays, and gamma rays, all of which are part of the electromagnetic spectrum. Classically, electromagnetic radiation consists of electromagnetic waves, which are synchronized oscillations of electric and magnetic fields.
Mixed boundary conditionIn mathematics, a mixed boundary condition for a partial differential equation defines a boundary value problem in which the solution of the given equation is required to satisfy different boundary conditions on disjoint parts of the boundary of the domain where the condition is stated. Precisely, in a mixed boundary value problem, the solution is required to satisfy a Dirichlet or a Neumann boundary condition in a mutually exclusive way on disjoint parts of the boundary.
Cerebral edemaCerebral edema is excess accumulation of fluid (edema) in the intracellular or extracellular spaces of the brain. This typically causes impaired nerve function, increased pressure within the skull, and can eventually lead to direct compression of brain tissue and blood vessels. Symptoms vary based on the location and extent of edema and generally include headaches, nausea, vomiting, seizures, drowsiness, visual disturbances, dizziness, and in severe cases, coma and death.
Nuclear electromagnetic pulseA nuclear electromagnetic pulse (nuclear EMP or NEMP) is a burst of electromagnetic radiation created by a nuclear explosion. The resulting rapidly varying electric and magnetic fields may couple with electrical and electronic systems to produce damaging current and voltage surges. The specific characteristics of a particular nuclear EMP event vary according to a number of factors, the most important of which is the altitude of the detonation.
