External noise and its interaction with spatial degrees of freedom in nonlinear dissipative systems

1989 ◽  
Vol 54 (5-6) ◽  
pp. 1111-1119 ◽  
Author(s):  
Helmut R. Brand ◽  
Charles R. Doering ◽  
Robert E. Ecke
Keyword(s):  
Degrees Of Freedom ◽  
External Noise ◽  
Dissipative Systems ◽  
Spatial Degrees Of Freedom

scholarly journals Spherical harmonic based noise rejection and neuronal sampling with multi-axis OPMs

2021 ◽  
Author(s):  
Tim M Tierney ◽  
Stephanie Mellor ◽  
George C O'Neill ◽  
Ryan C Timms ◽  
Gareth R Barnes
Keyword(s):  
Degrees Of Freedom ◽  
External Noise ◽  
Interference Rejection ◽  
Optically Pumped ◽  
Vector Spherical Harmonics ◽  
Noise Rejection ◽  
Neuronal Signal ◽  
Very High ◽  
Spatial Degrees Of Freedom ◽  
Irregular Solid Harmonics

In this study we explore the interference rejection and spatial sampling properties of multi-axis Optically Pumped Magnetometer (OPM) data. We use both vector spherical harmonics and eigenspectra to quantify how well an array can separate neuronal signal from environmental interference while adequately sampling the entire cortex. We found that triaxial OPMs have superb noise rejection properties allowing for very high orders of interference (L=6) to be accounted for while minimally affecting the neural space (2dB attenuation for a 60-sensor triaxial system). To adequately model the signals arising from the cortex, we show that at least 11th order (143 spatial degrees of freedom) irregular solid harmonics or 95 eigenvectors of the lead field are needed to model the neural space for OPM data (regardless of number of axes measured). This can be adequately sampled with 75-100 equidistant triaxial sensors (225-300 channels) or 200 equidistant radial channels. In other words, ordering the same number of channels in triaxial (rather than purely radial) configuration gives significant advantages not only in terms of external noise rejection but also minimizes cost, weight and cross-talk.

scholarly journals The Doubling of the Degrees of Freedom in Quantum Dissipative Systems, and the Semantic Information Notion and Measure in Biosemiotics

Proceedings ◽  
2020 ◽  
Vol 47 (1) ◽  
pp. 60
Author(s):  
Gianfranco Basti ◽  
Antonio Capolupo ◽  
GiuseppeVitiello
Keyword(s):  
Degrees Of Freedom ◽  
Semantic Information ◽  
Quantum Dissipative Systems ◽  
Dissipative Systems ◽  
Recent History ◽  
History Of

In the recent history of the effort for defining a suitable. [...]

The Motion of the Human Center of Mass and its Relationship to Mechanical Impedance

1966 ◽  
Vol 8 (5) ◽  
pp. 399-405 ◽  
Author(s):  
Edmund B. Weis ◽  
Frank P. Primiano
Keyword(s):  
Transfer Function ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Center Of Mass ◽  
Mechanical Impedance ◽  
Second Order ◽  
Analysis Tool ◽  
Isotropic Theory ◽  
Spatial Degrees Of Freedom

This report concerns the development of a relationship between the human mechanical impedance and the coupling of the human center of mass to the environment. The mechanical impedance is a common analysis tool in biomechanics while the analysis of the coupling of the center of mass to the environment is technically more difficult, if not impossible. The development is based on linear, passive, isotropic theory and shows that the transfer function which expresses the relation between the motion of the center of mass and the motion of the source is similar to a linear second order mechanical system in each of the translational spatial degrees of freedom.

Dynamics of bell-nonlocality for two atoms interacting with a vacuum multi-mode noise field

2016 ◽  
Vol 14 (03) ◽  
pp. 1650011 ◽  
Author(s):  
Yu-Jie Liu ◽  
Li Zheng ◽  
Dong-Mei Han ◽  
Huan-Lin Lü ◽  
Tai-Yu Zheng
Keyword(s):  
Degrees Of Freedom ◽  
Internal State ◽  
Bell Inequality ◽  
Entanglement Dynamics ◽  
Noise Field ◽  
Chsh Inequality ◽  
Internal States ◽  
Bell Nonlocality ◽  
Multi Mode ◽  
Spatial Degrees Of Freedom

We investigate the internal-state Bell nonlocal entanglement dynamics, as measured by CHSH inequality of two atoms interacting with a vacuum multi-mode noise field by taking into account the spatial degrees of freedom of the two atoms. The dynamics of Bell nonlocality of the atoms with the atomic internal states being initially in a Werner-type state is studied, by deriving the analytical solutions of the Schrödinger equation, and tracing over the degrees of freedom of the field and the external motion of the two atoms. In addition, through comparison with entanglement as measured by concurrence, we find that the survival time of entanglement is much longer than that of the Bell-inequality violation. And the comparison of the quantum correlation time between two Werner-type states is discussed.

Wigner Distribution Function for Open Quantum Systems

1997 ◽  
Vol 11 (09n10) ◽  
pp. 391-397 ◽  
Author(s):  
S. Baskoutas
Keyword(s):  
Distribution Function ◽  
Degrees Of Freedom ◽  
Wigner Distribution ◽  
Open Quantum Systems ◽  
Equations Of Motion ◽  
Analytical Form ◽  
Dissipative Systems ◽  
Wigner Distribution Function ◽  
Dissipative Tunneling ◽  
Lie Algebraic Structure

Using the modified biorthonormal Heisenberg equations of motion for non-Hermitian (NH) Hamilton operators, in order to imply a consistent Lie-algebraic structure and also the equivalence between the Heisenberg and Schrödinger pictures, we have obtained the analytical form of the Wigner distribution function which is unavoidable complex. Its imaginary part accounts for the influence of additional degrees of freedom, which are always present in the phenomenological representation of dissipative systems through (NH) Hamiltonians. Applications of the above formalism can be found, for instance, in dissipative macroscopic quantum tunneling (MQT) effect for Josephson junctions, and in the dissipative tunneling of trapped atoms in optical crystals.

scholarly journals Energy coupling among the degrees of freedom in an electron–positron plasma

2010 ◽  
Vol 76 (3-4) ◽  
pp. 329-335 ◽  
Author(s):  
WENMIN ZHANG ◽  
M. Y. YU ◽  
A. R. KARIMOV ◽  
L. STENFLO
Keyword(s):  
Exact Solutions ◽  
Degrees Of Freedom ◽  
Energy Coupling ◽  
Nonlinear Coupling ◽  
Irrotational Flow ◽  
Flow Component ◽  
Electron Positron ◽  
Rotational Components ◽  
Flow Components ◽  
Spatial Degrees Of Freedom

AbstractNonlinear coupling of the motion in the three spatial degrees of freedom of a cold fluid electron–positron plasma is investigated. Exact solutions describing expanding flows with oscillations are obtained. It is found that the energy in the irrotational flow component is in general transferred to the rotational components, but not in the reversed direction. Furthermore, since the density evolution need not be related to all the three flow components, oscillations in one or two of the flow fields can be purely electromagnetic and are not accompanied by density oscillations.

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