scholarly journals S5-3: Dynamic Invariants in Walking through an Aperture While Holding a Tray with Two Hands

i-Perception ◽  
10.1068/if598 ◽  
2012 ◽  
Vol 3 (9) ◽  
pp. 598-598 ◽  
Author(s):  
Endre Kadar ◽  
Georgina Török
Keyword(s):  
Dynamic Invariants

scholarly journals Neural Networks for Prediction and Control of Chaotic Fluidized Bed Hydrodynamics

Fractals ◽  
1997 ◽  
Vol 05 (03) ◽  
pp. 523-530 ◽  
Author(s):  
R. Bakker ◽  
R. J. de Korte ◽  
J. C. Schouten ◽  
C. M. Van Den Bleek ◽  
F. Takens
Keyword(s):  
Fluidized Bed ◽  
Prediction Error ◽  
Control Of Chaos ◽  
Short Term ◽  
Prediction And Control ◽  
Short Term Prediction ◽  
Capacitance Tomography ◽  
And Control ◽  
Dynamic Invariants ◽  
Tomography Data

A neural-network-based model that has learnt the chaotic hydrodynamics of a fluidized bed reactor is presented. The network is trained on measured electrical capacitance tomography data. A training algorithm is used that does not only minimize the short-term prediction error but also the information needed to synchronize the model with the real system. This forces the model to focus more on learning the longer term dynamics of the system, expressed in the average multi-step-ahead prediction error and dynamic invariants such as correlation entropy and dimension. The availability of the model is an important step towards control of chaos in gas-solid fluidized beds.

Invariants in dissipationless hydrodynamic media

1993 ◽  
Vol 248 ◽  
pp. 67-106 ◽  
Author(s):  
A. V. Tur ◽  
V. V. Yanovsky
Keyword(s):  
Lie Algebra ◽  
Vector Fields ◽  
Infinite Family ◽  
Type Systems ◽  
Topological Invariant ◽  
Systems Of Equations ◽  
Integral Invariants ◽  
New Type ◽  
General Relations ◽  
Dynamic Invariants

We propose a general geometric method of derivation of invariant relations for hydrodynamic dissipationless media. New dynamic invariants are obtained. General relations between the following three types of invariants are established, valid in all models: Lagrangian invariants, frozen-in vector fields and frozen-in co-vector fields. It is shown that frozen-in integrals form a Lie algebra with respect to the commutator of the frozen fields. The relation between frozen-in integrals derived here can be considered as the Backlund transformation for hydrodynamic-type systems of equations. We derive an infinite family of integral invariants which have either dynamic or topological nature. In particular, we obtain a new type of topological invariant which arises in all hydrodynamic dissipationless models when the well-known Moffatt invariant vanishes.

Program analysis with risk-based classification of dynamic invariants for logical error detection

2017 ◽  
Vol 71 ◽  
pp. 36-50
Author(s):  
George Stergiopoulos ◽  
Panayiotis Katsaros ◽  
Dimitris Gritzalis
Keyword(s):  
Error Detection ◽  
Program Analysis ◽  
Logical Error ◽  
Dynamic Invariants

MODELING OF CHAOTIC SYSTEMS WITH MULTIWAVELET TRANSFORM COMBINED WITH RECURRENT LEAST SQUARES SUPPORT VECTOR MACHINES

2007 ◽  
Vol 05 (01) ◽  
pp. 1-13
Author(s):  
ZHENG XIANG ◽  
TAIYI ZHANG ◽  
JIANCHENG SUN
Keyword(s):  
Time Series ◽  
Support Vector Machines ◽  
Least Squares ◽  
Chaotic Systems ◽  
Support Vector ◽  
Vector Machines ◽  
Temporal Structures ◽  
Multiwavelet Transform ◽  
Original Time ◽  
Dynamic Invariants

A new algorithm for modeling of chaotic systems is presented in this paper. First, more information is acquired utilizing the reconstructed embedding phase space, and the multiwavelets transform provides a sensible decomposition of the data so that the underlying temporal structures of the original time series become more tractable. Second, based on the Recurrent Least Squares Support Vector Machines (RLS-SVM), modeling of the chaotic system is realized. To demonstrate the effectiveness of our algorithm, we use the power spectrum and dynamic invariants involving the Lyapunov exponents and the correlation dimension as criterions, and then apply our method to Chua's circuit time series. The similarity of dynamic invariants between the original and generated time series shows that the proposed method can capture the dynamics of the chaotic time series more effectively.

scholarly journals AN EXACT SOLUTION TO THE QUANTIZED ELECTROMAGNETIC FIELD IN D-DIMENSIONAL DE SITTER SPACE–TIMES

2012 ◽  
Vol 27 (30) ◽  
pp. 1250177 ◽  
Author(s):  
G. ALENCAR ◽  
I. GUEDES ◽  
R. R. LANDIM ◽  
R. N. COSTA FILHO
Keyword(s):  
Electromagnetic Field ◽  
Extra Dimensions ◽  
Particle Production ◽  
De Sitter Space ◽  
Thermal Bath ◽  
De Sitter ◽  
Microwave Background ◽  
Quantum Behavior ◽  
Dynamic Invariants ◽  
Do So

In this work, we investigate the quantum theory of light propagating in D-dimensional de Sitter space–times. To do so, we use the method of dynamic invariants to obtain the solution of the time-dependent Schrödinger equation. The quantum behavior of the electromagnetic field in this background is analyzed. As the electromagnetism loses its conformality in D≠4, we point out that there will be particle production and comoving objects will feel a Bunch–Davies thermal bath. This may become important in extra dimension physics and raises the intriguing possibility that precise measurements of the Cosmic Microwave Background could verify the existence of extra dimensions.

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