Language as the Working Model of Human Mind

The Human Mind, functional aspect of Human Brain, has been envisaged to be working on the tenets of Chaos, a seeming order within a disorder, the premise of Universe. The armamentarium of Human Mind makes use of distributed neuronal networks sub-serving Sensorial Mechanisms, Mirror Neurone System (MNS) and Motor Mechanisms etching a stochastic trajectory on the virtual phase-space of Human Mind, obeying the ethos of Chaos. The informational sensorial mechanisms recruit attentional mechanisms channelising through the window of chaotic neural dynamics onto MNS that providing algorithmic image information flow along virtual phase- space coordinates concluding onto motor mechanisms that generates and mirrors a stimulus- specific and stimulus-adequate response. The singularity of self-iterating fractal architectonics of Event-Related Synchrony (ERS), a Power Spectral Density (PSD) precept of electroencephalographic (EEG) time-series denotes preferential and categorical inhibition gateway and an Event-Related Desynchrony (ERD) represents event related and locked gateway to stimulatory/excitatory neuronal architectonics leading to stimulus-locked and adequate neural response. The contextual inference in relation to stochastic phase-space trajectory of self- iterating fractal of Off-Center α ERS (Central)-On-Surround α ERD-On Surround θ ERS document efficient neural dynamics of working memory., across patterned modulation and flow of the neurally coded information.

Nonlinear Dynamic Analysis of Shale Gas Engine Combustion Stability

The traditional analysis method of engine combustion cycle variation is a statistical method based on a small amount of data. In essence, the obtained cycle variation is random data. In order to reveal the dynamic nature of the cyclical changes during the combustion of a shale gas engine, a nonlinear dynamics method was used to study the stability of the combustion process. The motion law of the phase space trajectory is analyzed, the influence of the shale gas composition on the trajectory distribution is analyzed, the return mapping point of the average indicated pressure in the cylinder is discussed. The relationship between adjacent combustion characteristic parameters is studied; the chaotic characteristics of the shale gas engine combustion process are discussed. The results show that during the working process of the shale gas engine, the in-cylinder pressure shows a similar quasi-periodic state in the entire phase space, and the working process has a certain chaotic law; with the increase of the CH4, N2 and CO2 content in the shale gas, the combustion cycle variation increases, and the randomness of the engine working process increases. The phase space trajectory shows a monotonously increasing distribution of Poincaré mapping points on the ∑XY+ section. With the increase of the combustion cycle, the linear relationship of the scattered points gradually increases, and the randomness of the combustion process increases. The return map points of the engine combustion characteristic parameters are distributed in a cluster. When the CH4 content increases, the distribution range of the average indicated pressure return map points increases. With the increase of N2 and CO2 content, abnormal combustion phenomena such as partial combustion or misfire occur during the engine combustion process, the uncertainty of the combustion process increases, and the combustion stability decreases. With the increase of engine speed, the correlation dimension and the maximum Lyapunov exponent increase, the randomness of the combustion process increases, and the chaotic characteristics of the engine working process are obvious; the time series of the cylinder pressure is more sensitive to the content of inert gas. With the increase of N2 and CO2 content in the gas, the correlation dimension and the maximum Lyapunov exponent increase significantly, the complexity of the phase space trajectory increases, and the chaotic characteristics become more obvious.

An experimental test of the geodesic rule proposition for the noncyclic geometric phase

The geometric phase due to the evolution of the Hamiltonian is a central concept in quantum physics and may become advantageous for quantum technology. In noncyclic evolutions, a proposition relates the geometric phase to the area bounded by the phase-space trajectory and the shortest geodesic connecting its end points. The experimental demonstration of this geodesic rule proposition in different systems is of great interest, especially due to the potential use in quantum technology. Here, we report a previously unshown experimental confirmation of the geodesic rule for a noncyclic geometric phase by means of a spatial SU(2) matter-wave interferometer, demonstrating, with high precision, the predicted phase sign change and π jumps. We show the connection between our results and the Pancharatnam phase. Last, we point out that the geodesic rule may be applied to obtain the red shift in general relativity, enabling a new quantum tool to measure gravity.

Dynamical Temperature from the Phase Space Trajectory

In classical statistical mechanics the trajectory in phase space represents the propagation of a classical Hamiltonian system. While trajectories play a key role in chaotic system theory, exploitation of a single trajectory has yet to be considered. This work shows that for ergodic dynamical systems the dynamical temperature can be derived using phase space trajectories.

DETECTING THE STATE OF THE DUFFING OSCILLATOR BY PHASE SPACE TRAJECTORY AUTOCORRELATION

Detecting the state of the Duffing oscillator, a type of well-known chaotic oscillator, deeply affects the accuracy of its application. Considering this, the present paper introduced a novel method for detecting the state of the Duffing oscillator. Binary outputs, simple calculation, high precision and fast response time were the main advantages of the phase space trajectory autocorrelation. Also, this study explained the largest Lyapunov exponent as well as a number of other methods commonly employed in detecting the state of the Duffing oscillator. The precision and effectiveness of the method introduced was compared with other well-known state detection methods such as the 0-1 test and the largest Lyapunov exponent.