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(the apparent motion of the wave due to the successive oscillations of particles or fields about their equilibrium positions) propagates at the phase and group velocities parallel or antiparallel to the propagation direction, which is common to longitudinal and transverse waves.
When talking about solid materials, the discussion is mainly around crystals – periodic lattices. Here we will discuss a 1D lattice of positive ions. Assuming the spacing between two ions is a, the potential in the lattice will look something like this: The mathematical representation of the potential is a periodic function with a period a.
The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and eigenstates ) can be expressed ...
The standard interpretation of this is as a stream of particles being fired at the step from the left (the direction of negative x): setting A r = 1 corresponds to firing particles singly; the terms containing A r and C r signify motion to the right, while A l and C l – to the left.
In physics, a pulse is a generic term describing a single disturbance that moves through a transmission medium. This medium may be vacuum (in the case of electromagnetic radiation ) or matter , and may be indefinitely large or finite.
A moving line of cars, a situation susceptible to the accordion effect.. In physics, the accordion effect (also known as the slinky effect, concertina effect, elastic band effect, and string instability) occurs when fluctuations in the motion of a traveling body cause disruptions in the flow of elements following it.
A two-dimensional Poincaré section of the forced Duffing equation. In mathematics, particularly in dynamical systems, a first recurrence map or Poincaré map, named after Henri Poincaré, is the intersection of a periodic orbit in the state space of a continuous dynamical system with a certain lower-dimensional subspace, called the Poincaré section, transversal to the flow of the system.
While periodic travelling waves have been known as solutions of the wave equation since the 18th century, their study in nonlinear systems began in the 1970s. A key early research paper was that of Nancy Kopell and Lou Howard [1] which proved several fundamental results on periodic travelling waves in reaction–diffusion equations.