979 research outputs found
Mode competition in a system of two parametrically driven pendulums: the role of symmetry
This paper is the final part in a series of four on the dynamics of two coupled, parametrically driven pendulums. In the previous three parts (Banning and van der Weele, Mode competition in a system of two parametrically driven pendulums; the Hamiltonian case, Physica A 220 (1995) 485¿533; Banning et al., Mode competition in a system of two parametrically driven pendulums; the dissipative case, Physica A 245 (1997) 11¿48; Banning et al., Mode competition in a system of two parametrically driven pendulums with nonlinear coupling, Physica A 245 (1997) 49¿98) we have given a detailed survey of the different oscillations in the system, with particular emphasis on mode interaction. In the present paper we use group theory to highlight the role of symmetry. It is shown how certain symmetries can obstruct period doubling and Hopf bifurcations; the associated routes to chaos cannot proceed until these symmetries have been broken. The symmetry approach also reveals the general mechanism of mode interaction and enables a useful comparison with other systems
A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials
Article / Letter to editorLeids Instituut Onderzoek Natuurkund
A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials
Article / Letter to editorLeids Instituut Onderzoek Natuurkund
Mode competition in a system of two parametrically driven pendulums with nonlinear coupling
This paper is part three in a series on the dynamics of two coupled, parametrically driven pendulums. In the previous parts Banning and van der Weele (1995) and Banning et al. (1997) studied the case of linear coupling; the present paper deals with the changes brought on by the inclusion of a nonlinear (third-order) term in the coupling. Special attention will be given to the phenomenon of mode competition.\ud
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The nonlinear coupling is seen to introduce a new kind of threshold into the system, namely a lower limit to the frequency at which certain motions can exist. Another consequence is that the mode interaction between 1¿ and 2ß (two of the normal motions of the system) is less degenerate, causing the intermediary mixed motion known as MP to manifest itself more strongly
Path-decomposition expansion and edge effects in a confined magnetized free-electron gas
Path-integral methods can be used to derive a `path-decomposition expansion'
for the temperature Green function of a magnetized free-electron gas confined
by a hard wall. With the help of this expansion the asymptotic behaviour of the
profiles for the excess particle density and the electric current density far
from the edge is determined for arbitrary values of the magnetic field
strength. The asymptotics are found to depend sensitively on the degree of
degeneracy. For a non-degenerate electron gas the asymptotic profiles are
essentially Gaussian (albeit modulated by a Bessel function), on a length scale
that is a function of the magnetic field strength and the temperature. For a
completely degenerate electron gas the asymptotic behaviour is again
proportional to a Gaussian, with a scale that is the magnetic length in this
case. The prefactors are polynomial and logarithmic functions of the distance
from the wall, that depend on the number of filled Landau levels . As a
consequence, the Gaussian asymptotic decay sets in at distances that are large
compared to the magnetic length multiplied by .Comment: 16 pages, 2 figures, submitted to J. Phys. A: Math. Gen; corrected
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A characteristic length scale causes anomalous size effects and boundary programmability in mechanical metamaterials
Article / Letter to editorLeids Instituut Onderzoek Natuurkund
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