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A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was proposed by Lev Landau in 1933 [1] and Solomon Pekar in 1946 [2] to describe an electron moving in a dielectric crystal where the atoms displace from their equilibrium positions to effectively screen the charge of an electron ...
Controlled burn of oil creating a smoke plume. In hydrodynamics, a plume or a column is a vertical body of one fluid moving through another. Several effects control the motion of the fluid, including momentum (inertia), diffusion and buoyancy (density differences).
Using this plane-wave displacement, the equation of motion becomes the eigenvalue equation [15] [16] (,) = (), where M is the diagonal mass matrix and D is the harmonic dynamical matrix. Solving this eigenvalue equation gives the relation between the angular frequency ω p and the wave vector κ p , and this relation is called the phonon ...
In chemical engineering, transport phenomena are studied in reactor design, analysis of molecular or diffusive transport mechanisms, and metallurgy. The transport of mass, energy, and momentum can be affected by the presence of external sources: An odor dissipates more slowly (and may intensify) when the source of the odor remains present.
Characterization of transport properties requires fabricating a device and measuring its current-voltage characteristics. Devices for transport studies are typically fabricated by thin film deposition or break junctions. The dominant transport mechanism in a measured device can be determined by differential conductance analysis.
R describes sources or sinks of the quantity c, i.e. the creation or destruction of the quantity. For example, for a chemical species, R > 0 means that a chemical reaction is creating more of the species, and R < 0 means that a chemical reaction is destroying the species. For heat transport, R > 0 might occur if thermal energy is being ...
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space.
The general equation can then be written as [6] = + + (),. where the "force" term corresponds to the forces exerted on the particles by an external influence (not by the particles themselves), the "diff" term represents the diffusion of particles, and "coll" is the collision term – accounting for the forces acting between particles in collisions.