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Register a new userExcitations of oscillations in loaded systems with internal degrees of freedom
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Michael Gedalin
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We show that oscillations are excited in a complex system under the influence of the external force, if the parameters of the system experience rapid change due to the changes in its internal structure. This excitation is collision-like and does not require any phase coherence or periodicity. The change of the internal structure may be achieved by other means which may require much lower energy expenses. The mechanism suggests control over switching oscillations on and off and may be of practical use.
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We answered the old question: does there exist a mechanical system with 3 degrees of freedom, except for the Coulomb system, which has 6 first integrals generating the Lie algebra o(4) by means of the Poisson brackets? We presented a system which is not centrally symmetric, but has such 6 first integrals. We showed also that not every mechanical system with 3 degrees of freedom possesses such Lie algebra o(4).
One of the main objectives of equilibrium state statistical physics is to analyze which symmetries of an interacting particle system in equilibrium are broken or conserved. Here we present a general result on the conservation of translational symmetry for two-dimensional Gibbsian particle systems. The result applies to particles with internal degrees of freedom and fairly arbitrary interaction, including the interesting cases of discontinuous, singular, and hard core interaction. In particular we thus show the conservation of translational symmetry for the continuum Widom Rowlinson model and a class of continuum Potts type models.
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Old and recent theoretical works by Andrzej Pekalski (APE) are recalled as possible sources of interest for describing network formation and clustering in complex (scientific) communities, through self-organisation and percolation processes. Emphasis is placed on APE self-citation network over four decades. The method is that used for detecting scientists field mobility by focusing on authors self-citation, co-authorships and article topics networks as in [1,2]. It is shown that APEs self-citation patterns reveal important information on APE interest for research topics over time as well as APE engagement on different scientific topics and in different networks of collaboration. Its interesting complexity results from degrees of freedom and external fields leading to so called internal shock resistance. It is found that APE network of scientific interests belongs to independent clusters and occurs through rare or drastic events as in irreversible preferential attachment processes, similar to those found in usual mechanics and thermodynamics phase transitions.
By adding a large inductance in a dc-SQUID phase qubit loop, one decouples the junctions dynamics and creates a superconducting artificial atom with two internal degrees of freedom. In addition to the usual symmetric plasma mode ({it s}-mode) which gives rise to the phase qubit, an anti-symmetric mode ({it a}-mode) appears. These two modes can be described by two anharmonic oscillators with eigenstates $ket{n_{s}}$ and $ket{n_{a}}$ for the {it s} and {it a}-mode, respectively. We show that a strong nonlinear coupling between the modes leads to a large energy splitting between states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$. Finally, coherent frequency conversion is observed via free oscillations between the states $ket{0_{s},1_{a}}$ and $ket{2_{s},0_{a}}$.
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