Energy Dissipation in Dynamical Systems Through Sequential Application and Removal of Constraints

A strategy to remove energy from finite-dimensional elastic systems is presented. The strategy is based on the cyclic application and removal of constraints that effectively remove and restore degrees of freedom of the system. In general, application of a constraint removes kinetic energy from the system, while removal of the constraint resets the system for a new cycle of constraint application. Conditions that lead to a net loss in kinetic energy per cycle and bounds on the amount of energy removed are presented. In linear systems, these bounds are related to the modes of the system in its two states, namely, with and without constraints. It is shown that energy removal is always possible, even using a random switching schedule, except in one scenario, when energy is trapped in modes that span an invariant subspace with special orthogonality properties. Applications to nonlinear systems are discussed. Examples illustrate the process of energy removal in both linear and nonlinear systems.

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Quantum optics with one or two photons

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2015.0208 ◽

2015 ◽

Vol 471 (2180) ◽

pp. 20150208 ◽

Cited By ~ 6

Author(s):

G. J. Milburn ◽

S. Basiri-Esfahani

Keyword(s):

Gravitational Field ◽

Nonlinear Systems ◽

Degrees Of Freedom ◽

Single Photon ◽

Optical Cavity ◽

Photon State ◽

Single Photon State ◽

Linear And Nonlinear ◽

Photon States ◽

Linear And Nonlinear Systems

We discuss the concept of a single-photon state together with how they are generated, measured and interact with linear and nonlinear systems. In particular, we consider how a single-photon state interacts with an opto-mechanical system: an optical cavity with a moving mirror and how such states can be used as a measurement probe for the mechanical degrees of freedom. We conclude with a discussion of how single-photon states are modified in a gravitational field due to the red-shift.

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Mathematical modeling of conversion of non-Gaussian random processes, signals and noise in linear and nonlinear systems

Informacionno-technologicheskij vestnik ◽

10.21499/2409-1650-2018-3-66-78 ◽

2018 ◽

pp. 66-78

Author(s):

V. M. Artyushenko ◽

V. I. Volovach

Keyword(s):

Mathematical Modeling ◽

Nonlinear Systems ◽

Random Processes ◽

Mathematical Transformation ◽

Positive And Negative Feedback ◽

Non Linear Systems ◽

Linear And Nonlinear ◽

Non Gaussian ◽

Linear And Nonlinear Systems ◽

Inertial Systems

The questions connected with mathematical modeling of transformation of non-Gaussian random processes, signals and noise in linear and nonlinear systems are considered and analyzed. The mathematical transformation of random processes in linear inertial systems consisting of both series and parallel connected links, as well as positive and negative feedback is analyzed. The mathematical transformation of random processes with polygamous density of probability distribution during their passage through such systems is considered. Nonlinear inertial and non-linear systems are analyzed.

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Correlation between Buoyancy Flux, Dissipation and Potential Vorticity in Rotating Stratified Turbulence

Atmosphere ◽

10.3390/atmos12020157 ◽

2021 ◽

Vol 12 (2) ◽

pp. 157

Author(s):

Duane Rosenberg ◽

Annick Pouquet ◽

Raffaele Marino

Keyword(s):

Energy Dissipation ◽

Kinetic Energy ◽

Potential Vorticity ◽

Isotropic Turbulence ◽

Joint Probability ◽

Buoyancy Flux ◽

Turbulent Regime ◽

Stratified Turbulence ◽

Low Dissipation ◽

Linear And Nonlinear

We study in this paper the correlation between the buoyancy flux, the efficiency of energy dissipation and the linear and nonlinear components of potential vorticity, PV, a point-wise invariant of the Boussinesq equations, contrasting the three identified regimes of rotating stratified turbulence, namely wave-dominated, wave–eddy interactions and eddy-dominated. After recalling some of the main novel features of these flows compared to homogeneous isotropic turbulence, we specifically analyze three direct numerical simulations in the absence of forcing and performed on grids of 10243 points, one in each of these physical regimes. We focus in particular on the link between the point-wise buoyancy flux and the amount of kinetic energy dissipation and of linear and nonlinear PV. For flows dominated by waves, we find that the highest joint probability is for minimal kinetic energy dissipation (compared to the buoyancy flux), low dissipation efficiency and low nonlinear PV, whereas for flows dominated by nonlinear eddies, the highest correlation between dissipation and buoyancy flux occurs for weak flux and high localized nonlinear PV. We also show that the nonlinear potential vorticity is strongly correlated with high dissipation efficiency in the turbulent regime, corresponding to intermittent events, as observed in the atmosphere and oceans.

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