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In nuclear physics, the Bateman equation is a mathematical model describing abundances and activities in a decay chain as a function of time, based on the decay rates and initial abundances. The model was formulated by Ernest Rutherford in 1905 [1] and the analytical solution was provided by Harry Bateman in 1910. [2]
A quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation , where N is the quantity and λ ( lambda ) is a positive rate called the exponential decay constant , disintegration constant , [ 1 ] rate constant , [ 2 ] or ...
Time taken for half the number of atoms present to decay + / / s [T] Number of half-lives n (no standard symbol) = / / dimensionless dimensionless Radioisotope time constant, mean lifetime of an atom before decay
Moreover, if the system is given a fixed, finite input (i.e., a step), then any resulting oscillations in the output will decay at an exponential rate, and the output will tend asymptotically to a new final, steady-state value.
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance between events in a Poisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any meaningful mono-dimensional measure of the process, such as time ...
In order to derive the dephasing rate formula from first principles, a purity-based definition of the dephasing factor can be adopted. [ 10 ] [ 11 ] The purity P ( t ) = e − F ( t ) {\displaystyle P(t)=e^{-F(t)}} describes how a quantum state becomes mixed due to the entanglement of the system with the environment.
In the physics of aerosols, deposition is the process by which aerosol particles collect or deposit themselves on solid surfaces, decreasing the concentration of the particles in the air. It can be divided into two sub-processes: dry and wet deposition. The rate of deposition, or the deposition velocity, is slowest for particles of an ...
Secular equilibrium can occur in a radioactive decay chain only if the half-life of the daughter radionuclide B is much shorter than the half-life of the parent radionuclide A. In such a case, the decay rate of A and hence the production rate of B is approximately constant, because the half-life of A is very long compared to the time scales ...