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261.
The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox(1952),has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given(much earlier)by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed. 相似文献
262.
M. A. Jafarizadeh M. Mahdian A. Heshmati K. Aghayar 《The European Physical Journal D - Atomic, Molecular, Optical and Plasma Physics》2008,50(1):107-121
The three qubits mutually unbiased bases (MUB) diagonal density matrices with maximally entanglement in Greenberger-Horne-Zeilinger
(GHZ) basis are studied. These are a natural generalization of Bell-state diagonal density matrices. The linearity of positive
partial transpose (PPT) conditions allows one to specify completely PPT states or feasible region (FR) which form a polygon,
where the projection of the feasible region to some two dimensional planes has lead to better visualization. To reveal the
PPT entangled regions of these density matrices, we manipulate some appropriate optimal non-decomposable linear entanglement
witnesses (EWs) as the envelope of family of linear optimal non-decomposable EWs. These nonlinear EWs are nonlinear functional
of MUB diagonal states, so that they are nonnegative valued over all separable, but they are negative valued over some PPT
entangled MUB diagonal states. Even though, these nonlinear EWs can not separate completely, the PPT entanglement region from
separable one, but however in special cases they lead to necessary and sufficient condition for separability. To support the
evidence, we study three categories for special choices of parameters in density matrices, and using the nonlinear EWs we
can distinguish the region of PPT entangled states and separable states, completely. At the end some numerical simulations
are provided to show the practical applicability of these nonlinear EWs in detecting some PPT entangled MUB diagonal states. 相似文献