By Arioli G.
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Additional resources for Branches of periodic orbits for the planar restricted 3-body problem
For k = 0, it is possible to show that S(k) = H(k), where H(k) is the Fourier transform of H(r). 4 The Broad Categories of Phase Transitions 25 This simple form for S(k) is called the Ornstein–Zernike–Debye approximation for the structure function. Near the critical temperature TC , −1/2 ξ(T ) can be selected in the form ξ(T ) = C st |T − TC | . If k is small, S(k) ≈ ξ 2 → ∞. 26) allows characterizing the way in which the diﬀerent parts of a system are correlated. The correlation length ξ(T ) is a simple spatial translation of this correlation: it expresses the range of ﬂuctuations of a variable characteristic of its state in the material.
The solidiﬁcation of a liquid in the form of a glass, the glass transition, is an exception: if there is no organized or long-range-order structure formation. Glasses are disordered materials beyond equilibrium. ) and are sometimes associated with the appearance of a new property (ferroelectricity, for example). There are essentially two broad categories of structural transitions: • order/disorder transitions; • displacive transitions. Order-disorder transitions are characteristic of binary metal alloys (for example, Cu–Zn alloy, which is β-brass).
The - sign accounts for the fact that the ﬂow and concentration gradient are of opposite signs. If the phase is pure, D is the self–diﬀusion coeﬃcient. 3) is Fick’s second law for diﬀusion. It does not have a simple solution particularly for a three-dimensional system. 4) N is the total number of particles in an inﬁnite volume parallel to the x axis and unit section perpendicular to this axis, where all particles are concentrated in x0 for t = 0. 5) Note that for particles of radius r moving in a ﬂuid of viscosity η, diﬀusion coeﬃcient D is given by the Stokes–Einstein law.
Branches of periodic orbits for the planar restricted 3-body problem by Arioli G.