Coexistence of conservative and dissipative behavior in reversible dynamical systems

Politi, Antonio; Oppo, Gian-Luca; Badii, R.

doi:10.1103/physreva.33.4055

Cited by 115 publications

(68 citation statements)

References 11 publications

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“…The local velocity of a surface point of an extended particle need not coincide with the fluid velocity that one would observe at this point in the absence of the particle. As a consequence, the volume of the state space spanned by the particle's degrees of freedom is no longer conserved by the dynamics, which, as a result may display attractors for stationary flow fields, in spite of the fact that the dynamics is reversible [12]. In general, several attractors will coexist.…”

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confidence: 99%

Chiral Separation in Microflows

et al. 2006

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Molecules that only differ by their chirality, so called enantiomers, often possess different properties with respect to their biological function. Therefore, the separation of enantiomers presents a prominent challenge in molecular biology and belongs to the "Holy Grail" of organic chemistry. We suggest a new separation technique for chiral molecules that is based on the transport properties in a microfluidic flow with spatially variable vorticity. Because of their size the thermal fluctuating motion of the molecules must be taken into account. These fluctuations play a decisive role in the proposed separation mechanism.

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confidence: 99%

Chiral Separation in Microflows

et al. 2006

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“…The Rimmer bifurcations have been observed earlier in conservative systems, e.g. in the appearance of two period-6 orbits in the H6non map [11], and in period-2 orbits in a Poincar6 section associated with a set of reversible non-Hamiltonian differential equations arising from laser physics [4,5]. In the second case dissipative features including the appearance of an attractor and a repeller have been observed.…”

Section: G(x)mentioning

confidence: 81%

Bifurcations in two-dimensional reversible maps

Post

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Quispel

et al. 1990

Physica A: Statistical Mechanics and its Applications

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We give a treatment of the non-resonant bifurcations involving asymmetric fixed points with Jacobian J ~ 1 in reversible mappings of the plane. These bifurcations include the saddlenode bifurcation not in the neighbourhood of a fixed point with J = 1, as well as the so-called transcritical bifurcations and generalized Rimmer bifurcations taking place at a fixed point with Jacobian J = 1. The bifurcations are illustrated by some simple examples of model maps. The Rimmer type of bifurcation, with e.g. a center point with J = 1 changing into a saddle with Jacobian ~,~ = 1, an attractor and a repeller, occurs under more general conditions, i.e. also in non-reversible mappings if only a certain order of local reversibility is satisfied. These Rimmer bifurcations are important in connection with the emergence of dissipative features in non-measure-preserving reversible dynamical systems.

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“…For x-independent solutions system (14) reduces to that explored in [18]. In general, in the basis of new functions u ± (x, t) = u(x, t) ± v(x, t) system (14) decouples into two nonlinear Schrödinger equations [21,22] …”

Section: On the Physical Modelmentioning

confidence: 99%

Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler

Zezyulin¹

2017

J. Phys. A: Math. Theor.

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Abstract. We introduce a nonlinear parity-time-symmetric dispersive coupler which admits Hamiltonian and Lagrangian formulations. We show that, in spite of the gain and dissipation, the model has several conservation laws. The system also supports a variety of exact solutions. We focus on exact bright solitons and demonstrate numerically that they are dynamically stable in a wide parameter range and undergo elastic interactions, thus manifesting nearly-integrable dynamics. Physical applications of the introduced model in the theory of Bose-Einstein condensates in nonlinear lattices are discussed.

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Coexistence of conservative and dissipative behavior in reversible dynamical systems

Cited by 115 publications

References 11 publications

Chiral Separation in Microflows

Chiral Separation in Microflows

Bifurcations in two-dimensional reversible maps

Solitons in a Hamiltonian $\newcommand{\PT}{\mathcal{ PT}}{\boldsymbol \PT}$ -symmetric coupler

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