Influence Of Chaos Research Articles

Turbulence from an Observer Perspective

Turbulence is often studied by tracking its spatiotemporal evolution and analyzing the dynamics of its different scales. The dual to this perspective is that of an observer who starts from measurements, or observations, of turbulence and attempts to identify their back-in-time origin, which is the foundation of data assimilation. This back-in-time search must contend with the action of chaos, which obfuscates the interpretation of the observations. When the available measurements satisfy a critical resolution threshold, the influence of chaos can be entirely mitigated and turbulence can be synchronized to the exact state–space trajectory that generated the observations. The critical threshold offers a new interpretation of the Taylor microscale, one that underscores its causal influence. Below the critical threshold, the origin of measurements becomes less definitive in regions where the flow is inconsequential to the observations. In contrast, flow events that influence the measurements, or are within their domain of dependence, are accurately captured. The implications for our understanding of wall turbulence are explored, starting with the highest density of measurements that entirely tame chaos and proceeding all the way to an isolated measurement of wall stress. The article concludes with a discussion of future opportunities and a call to action.

Household chaos, child temperament, and structure-related feeding practices in toddlerhood: A moderation analysis

Structure-related feeding practices may promote intuitive child eating behaviors and foster responsiveness to internal cues of hunger and satiety. Caregivers' ability to engage in structure-related feeding practices likely depends on a complex ecology of factors, including household- and child-characteristics. This study examined associations between household chaos and structure-related feeding practices, and the moderating effect of child temperament. Data were from 275 caregiver-toddler dyads from central Ohio. Child temperament was reported by caregivers when children were 18 months of age, whereas household chaos and structure-related feeding practices were reported by caregivers when children were 36 months of age. Multivariable linear regression models were constructed to assess the relationship between chaos and structure-related feeding practices. Interaction terms between household chaos and three dimensions of child temperament were tested to determine whether temperament moderated the relationship between chaos and structure-related feeding practices. Household chaos was not independently associated with structure-related feeding practices, but higher levels of child effortful control were associated with greater mealtime structure. There was a statistically significant interaction between household chaos and child temperamental surgency, such that greater levels of chaos were associated with less structured mealtimes, but only when children had low-surgency. Findings suggest household chaos and child temperament inform caregiver feeding practices, but the influence of chaos may depend on more proximal factors, like child temperament. Recommendations to improve caregiver-child feeding interactions should be sensitive to characteristics of the broader family home environment.

The entropy of chaotic transitions of EEG phase growth in bipolar disorder with lithium carbonate

The application of chaos measures the association of EEG signals which allows for differentiating pre and post-medicated epochs for bipolar patients. We propose a new approach on chaos necessary for proof of EEG metastability. Shannon entropies of concealed patterns of Schwarzian derivatives from absolute instantaneous frequency transformations of EEG signals after Hilbert transform are compared and found significantly statistically different between pre and post-medication periods when fitted to von Bertalanffy’s functions. Schwarzian dynamics measures was compared at first baseline and then at the end of the first hour of one dose 300 mg lithium carbonate intake for the same subject in depressive patients. With an application of Schwarzian derivative on the prediction of von Bertalanffy’s models, integration and segregation of phase growth orbits of neural oscillations can be understood as an influence of chaos on the mixing of frequencies. A phase growth constant parameter was performed to determine the bifurcation parameter of von Bertalanffy’s model at each given non-overlapped EEG segment. Schwarzian derivative was sometimes very close positive near the origin but stayed negative for most of the number of segments. Lithium carbonate changed the chaotic invariants of the EEG Schwarzian dynamics and removed sharp boundaries in the bipolar spectrum.

IoT-Based Positive Emotional Contagion for Crowd Evacuation

In emergency evacuations, crowds often become congested and stampeded because of extreme panic, resulting in injuries and fatalities. Safety officers can spread positive emotions and reduce crowd panic by issuing information or appeasement, which is an effective way to ensure evacuation safety. However, how to deploy safety officers appropriately and maximize positive emotional contagion to cover the largest number of chaotic individuals is still a challenging problem. To solve this problem, we propose an IoT-based positive emotional contagion (IoT-PEC) method for crowd evacuation. First, we employ IoT technologies to capture the attributes of crowd movement, such as position and velocity. Based on these attributes, the crowd chaos can be quantified by calculating the macroscopic and microscopic entropies. Second, we propose an entropy-based anisotropic emotional contagion model (E-AECM) to achieve the nonuniform positive emotional contagion considering the influence of chaos on the propagation rate. Third, we formulate the problem of safety officer placement as an optimization problem to maximize the positive emotional contagion on the chaos individuals. Finally, we implement a simulation system for crowd evacuation to visualize the results of positive emotion contagion. The proposed method can provide guidance for emergency response management.

Study and Simulation on Dynamics of a Risk-Averse Supply Chain Pricing Model with Dual-Channel and Incomplete Information

Under the industrial background of dual-channel, volatility in demand of consumers, we use the theory of bifurcations and numerical simulation tools to investigate the dynamic pricing game in a dual-channel supply chain with risk-averse behavior and incomplete information. Due to volatility of demand of consumers, we consider all the players in the supply chain are risk-averse. We assume there exist Bertrand game and Manufacturers’ Stackelberg in the chain which are closer to reality. The main objective of the paper is to investigate the complex influence of the decision parameters such as wholesale price adjustment speed, risk preference and service value on stability of the risk-averse supply chain and average utilities of all the players. We lay emphasis on the influence of chaos on average utilities of all the players which did not appear in previous studies. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed by 2D bifurcation phase portraits, Double Largest Lyapunov exponent, basins of attraction and so on. The study shows that the manufacturers should slow down their wholesale price adjustment speed to get more utilities, if the manufacturers are willing to take on more risk, they will get more profits, but they must keep their wholesale prices in a certain range in order to maintain the market stability.

A bound on chaos

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

A new Monte Carlo method for dynamical evolution of non-spherical stellar systems

We have developed a novel Monte Carlo method for simulating the dynamical evolution of stellar systems in arbitrary geometry. The orbits of stars are followed in a smooth potential represented by a basis-set expansion and perturbed after each timestep using local velocity diffusion coefficients from the standard two-body relaxation theory. The potential and diffusion coefficients are updated after an interval of time that is a small fraction of the relaxation time, but may be longer than the dynamical time. Thus our approach is a bridge between the Spitzer's formulation of the Monte Carlo method and the temporally smoothed self-consistent field method. The primary advantages are the ability to follow the secular evolution of shape of the stellar system, and the possibility of scaling the amount of two-body relaxation to the necessary value, unrelated to the actual number of particles in the simulation. Possible future applications of this approach in galaxy dynamics include the problem of consumption of stars by a massive black hole in a non-spherical galactic nucleus, evolution of binary supermassive black holes, and the influence of chaos on the shape of galaxies, while for globular clusters it may be used for studying the influence of rotation.

The research on price game model and its complex characteristics of triopoly in different decision-making rule

Based on a detailed analysis of the international market, we establish a decentralized dynamics model to describe the situation that a new oligarch wishes to enter into a market which has been occupied by two oligarchs, so they have different decision rules. Then we establish and analyze the corresponding continuity system, and in detail discuss the Lyapunov exponent of this system, studying the influence of the parameter’s change to the Lyapunov exponent in three situations. Proceeding to the next step, we make the analysis of the complex dynamics behavior, such as Hopf bifurcation, chaos attractor and initial sensibility. We make a numerical simulation under different conditions, and the result shows that the process of game will tend to a Nash equilibrium at a lower price adjustment speed, and with the increase of the value, the system will appear to be unstable and go into a chaos state gradually. However, for the new entrant, the influence of chaos is not huge, and the new entrant can be seen as a stable element in the chaotic market. The research leads to a good guidance to the market with a new entrant to do the best decision-making.

Influence of chaos on the fusion enhancement by electron screening

We study the effect of screening by bound electrons in low energy nuclear reactions. We use molecular dynamics to simulate the reactions involving many electrons: D+d, D+D, 3He+d, 3He+D, 6Li+d, 6Li+D, 7Li+p, 7Li+ H. Quantum effects corresponding to the Pauli and Heisenberg principles are enforced by constraints in terms of the phase space occupancy. In addition to the well-known adiabatic and sudden limits, we propose a new “dissipative limit” which is expected to be important not only at high energies but in the extremely low energy region. The dissipative limit is associated with the chaotic behavior of the electronic motion. It affects also the magnitude of the enhancement factor. We discuss also numerical experiments using polarized targets. The derived enhancement factors in our simulation are in agreement with those extracted within the R-matrix approach.

Asymmetric Top Rotors in Electric Fields: Influence of Chaos and Collisions in Molecular Beam Deflection Experiments

We report on electric deflection experiments of structural isomers of aminobenzonitrile. They are used as models to study the influence of the asymmetry of a molecule on the molecule-electric field interaction. Experimental deflection profiles are compared to Stark effect calculations. We found increasing deviations from the calculated Stark effect behavior with increasing asymmetry. This deviation is induced by interactions with other particles and is directly related to the chaotic behavior of the rotational motion of asymmetric rotors in a static electric field.

ADAPTATION BASED ON MEMORY DYNAMICS IN A CHAOTIC NEURAL NETWORK

The complex dynamics that emerge from systems governed by deterministic chaos offer significant advantages to the neuromorphic engineer. Included in these is the potential for a very large memory store and the ease with which chaotic systems can be controlled. By definition, a chaotic system is a periodic. However, during the course of its trajectory through state space, the chaotic system will come infinitely close to points that it has previously visited. These almost repeating trajectories are referred to as Unstable Periodic Orbits (UPOs). Normally, under the influence of chaos, the trajectory would move away exponentially fast from its previous path, thereby describing a new path on the surface of the attractor. It is possible to apply a simple delayed feedback control mechanism to a chaotic system that will constrain it within one of its UPOs. This article presents a neural implementation of this delayed feedback mechanism. The network presented here is able to stabilize different UPOs in response to different input signals, with each UPO corresponding to a dynamic recognition state for that input. We also present two learning rules for this network, which enables it to adapt to novel inputs in a self-organized manner.

Quantum weak chaos in a degenerate system

Quantum weak chaos is studied in a perturbed degenerate system: a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is built and its structure is explored in terms of the quasienergy eigenstates under resonance conditions (when the wave frequency equals the cyclotron frequency) in the regime of weak classical chaos. The new phenomenon of diffusion via the quantum separatrices and the influence of chaos on diffusion are investigated and, in the quasiclassical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion that is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the nonmonotonic dependence of the characteristic localization length of the quasienergy states on the wave amplitude. The width of the quantum separatrices was computed and compared with the width of the classical stochastic web. We give the physical parameters that can be realized experimentally to show the manifestation of quantum chaos in a nonlinear acoustic resonance.

Chaos and avoided level crossings.

The influence of chaos on tunneling in the quantum phase space of the harmonically driven pendulum is studied herein. We analyze the avoided level crossing between a quasienergy state associated with the chaotic part of the phase space and a member of the nearly degenerate doublet localized on the symmetric Kolmogorov-Arnold-Moser (KAM) islands. As a result of the interaction the quasienergy states ``exchange'' their structure. The initially chaotic state evolves into the regular one and vice versa. This interchange significantly affects dynamical tunneling of wave packets centered on the KAM islands.