Search results
Results from the WOW.Com Content Network
A large number of fundamental equations in physics involve first or second time derivatives of quantities. Many other fundamental quantities in science are time derivatives of one another: force is the time derivative of momentum; power is the time derivative of energy; electric current is the time derivative of electric charge; and so on.
Snap, [6] or jounce, [2] is the fourth derivative of the position vector with respect to time, or the rate of change of the jerk with respect to time. [4] Equivalently, it is the second derivative of acceleration or the third derivative of velocity, and is defined by any of the following equivalent expressions: = ȷ = = =.
The units of group-delay dispersion are [time] 2, often expressed in fs 2. The group-delay dispersion (GDD) of an optical element is the derivative of the group delay with respect to angular frequency, and also the second derivative of the optical phase:
The equation says the matter wave frequency in vacuum varies with wavenumber (= /) in the non-relativistic approximation. The variation has two parts: a constant part due to the de Broglie frequency of the rest mass ( ℏ ω 0 = m 0 c 2 {\displaystyle \hbar \omega _{0}=m_{0}c^{2}} ) and a quadratic part due to kinetic energy.
The behavior of temperature when the sides of a 1D rod are at fixed temperatures (in this case, 0.8 and 0 with initial Gaussian distribution). The temperature approaches a linear function because that is the stable solution of the equation: wherever temperature has a nonzero second spatial derivative, the time derivative is nonzero as well.
x, y and z are the three spatial coordinates and t being the time coordinate. The equation states that, at any given point, the second derivative of with respect to time is proportional to the sum of the second derivatives of with respect to space, with the constant of proportionality being the square of the speed of the wave.
Group-velocity dispersion is quantified as the derivative of the reciprocal of the group velocity with respect to angular frequency, which results in group-velocity dispersion = d 2 k/dω 2. If a light pulse is propagated through a material with positive group-velocity dispersion, then the shorter-wavelength components travel slower than the ...
in which the last equation is referred to as the Nikolaevsky equation, named after V. N. Nikolaevsky who introduced the equation in 1989, [18] [19] [20] whereas the first two equations has been introduced by P. Rajamanickam and J. Daou in the context of transitions near tricritical points, [17] i.e., change in the sign of the fourth derivative ...