Chaotic Defects Research Articles

Machine learning applied to pattern characterization in spatially extended dynamical systems

This new tool, in the form of Machine Learning (ML), has proven to be very useful in several areas of physics, due to its strong versatility, its ability to obtain patterns in very complex systems. In this work we explore techniques from Machine Learning (ML) to characterize spatio-temporal patterns in complex dynamical systems. These techniques are applied in coupled map lattices, for which the relevant parameters are the nonlinearity and coupling strength. As a training phase of our ML, we show several samples with the dynamic characteristics of each known space–time profile, such as frozen random pattern, pattern selection, chaotic defects, intermittency and fully developed space–time chaos, for example. After the training phase, we apply our algorithm to different values of non-linearity and coupling, where given the dynamic characteristics, for each pair of parameters, we can accurately identify the regions where each of these profiles is formed.

Applications of a neural network to detect the percolating transitions in a system with variable radius of defects.

We systematically study the percolation phase transition at the change of concentration of the chaotic defects (pores) in an extended system where the disordered defects additionally have a variable random radius, using the methods of a neural network (NN). Two important parameters appear in such a material: the average value and the variance of the random pore radius, which leads to significant change in the properties of the phase transition compared with conventional percolation. To train a network, we use the spatial structure of a disordered environment (feature class), and the output (label class) indicates the state of the percolation transition. We found high accuracy of the transition prediction (except the narrow threshold area) by the trained network already in the two-dimensional case. We have also employed such a technique for the extended three-dimensional (3D) percolation system. Our simulations showed the high accuracy of prediction in the percolation transition in 3D case too. The considered approach opens up interesting perspectives for using NN to identify the phase transitions in real percolating nanomaterials with a complex cluster structure.

Correlated Brownian motion and diffusion of defects in spatially extended chaotic systems.

One of the spatiotemporal patterns exhibited by coupled map lattices with nearest-neighbor coupling is the appearance of chaotic defects, which are spatially localized regions of chaotic dynamics with a particlelike behavior. Chaotic defects display random behavior and diffuse along the lattice with a Gaussian signature. In this note, we investigate some dynamical properties of chaotic defects in a lattice of coupled chaotic quadratic maps. Using a recurrence-based diagnostic, we found that the motion of chaotic defects is well-represented by a stochastic time series with a power-law spectrum 1/fσ with 2.3≤σ≤2.4, i.e., a correlated Brownian motion. The correlation exponent corresponds to a memory effect in the Brownian motion and increases with a system parameter as the diffusion coefficient of chaotic defects.

Fracture features of granite under various deformation conditions

Fracture mechanisms of dry and water-saturated granite samples and slip (displacement) along a ready fault have been studied by measuring acoustic emission signals. It has been found that disperse defect formation is observed in dry samples under mechanical load, then localization occurs, and a fracture source is formed, whose development results in macrofault formation. In water saturated samples, chaotic defect formation occurs in the entire volume, which leads to a high degree of material damage. At the closing deformation stage, several fault source zones are formed in which main cracks develop. In the case of slip along a ready fault, stoppers at crack edges are broken.

Polymer rheology at high shear rate for microinjection moulding

In this paper, we present the rheology of a high-density polyethylene for microinjection moulding. At high flow rate, pressure becomes high enough so that shear heating and pressure-dependence of the viscosity cannot be neglected. Moreover, spurt and chaotic defects related to wall slip were encountered. Nevertheless, we used classical data processing. We obtained viscosity at high shear rate which is lower than the viscosity obtained with the Carreau-Yasuda extrapolation of the moderate shear rate data. In order to discuss the origin of this difference, we developed a flow numerical simulation in the capillary where we take into account pressure and temperature dependent viscosity. The relative importance of these phenomena and their coupling is presented. Then, injection moulding experiments were carried out in a plaque mould. Different moulding parameters were tested. A three dimensional injection moulding numerical simulation, using Rem3D software, was carried out. The quality of the different sets of rheological data is assessed by comparing computed and measured pressure.

Dynamics of elastic waves in two-dimensional phononic crystals with chaotic defect

The authors study dynamics of wave function in two-dimensional phononic crystals with different billiard defects. It is found that the elastic wave is localized in the defect region with soft material. The spatial statistical properties of wave function are studied. More strikingly, they find that given the same area, the chaotic billiard contains more energy than the integrable billiards such as rectangular and circular billiards. The dependence of this “chaotic effect” on wave number k is also studied.

Volume defects during extrusion of polystyrene investigated by flow induced birefringence and laser-Doppler velocimetry

The flow of a polystyrene in an abrupt slit contraction with transparent side walls has been characterized using both flow induced birefringence (FIB) and laser-Doppler velocimetry (LDV), under stable and unstable flow conditions. Under steady-state flow conditions, at the contraction entry recirculating vortices are observed, with velocities depending on flow conditions. When the flow rate is increased, periodic oscillations with the same frequency are observed for FIB patterns and the velocity field, independent of the flow rate. The oscillations correspond to periodic volume instabilities of the extruded strands. For higher flow rates, entry vortices destabilization leads to a sudden discharging of these vortices into the main flow, inducing chaotic defects in the extrudate.

Controlling localized spatiotemporal chaos in a one-dimensional coupled map lattice

Suppression of the localized spatiotemporal chaos observed in the one-dimensional coupled map lattice system of Kaneko [Physica D 37 (1989) 60] is achieved using feedback control. The control is successful both for the frozen random patterns (the chaotic domains are fixed in space) and for the chaotic defect moving around in space. The control algorithm is completely automated and is only implemented on lattice sites where the local dynamics is determined to be chaotic via evaluation of the local Lyapunov exponent. This could have possible relevance to situations where localized turbulence results in degradation of the system performance.

Spatiotemporal periodic and chaotic patterns in a two-dimensional coupled map lattice system

The pattern dynamics of a two-dimensional coupled map lattice system is studied using both analytical and numerical calculations. Two interesting spatiotemporal periodic patterns are solved analytically. Their stability boundaries for small system size are obtained by linear stability analysis. As the system sizes mismatch the spatial periodicity of the patterns, a frozen random chaotic defect cluster and a slow random propagated chaotic defect string appear.

Pattern dynamics of a coupled map lattice for open flow

The pattern dynamics of the one-way coupled logistic lattice which can serve as a phenomenological model for open flow is investigated and shown to be extremely rich. For medium and large coupling strengths, we find spatially periodic, quasiperiodic and chaotic patterns with temporal periodicity and analyze their stability with the help of a newly introduced spatial map. Criteria are established for predicting the down-flow bifurcation behavior of the coupled map lattice, and for selecting attractors through modulation of the boundary. For smaller coupling strengths we find a novel regime in which chaotic defects form a periodic lattice that is shown to be the result of a boundary crisis.

Periodic lattices of chaotic defects.

A type of lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic state, when suddenly another defect appears. The distance between successive defects is found to be generally predetermined and diverging logarithmically when approaching a certain critical point. The phenomena are analyzed and shown to be explicable as the results of a boundary crisis for the spatially extended system.

Critical phenomena in delayed maps

A phase transition mediated by chaotic defect dynamics is observed in a simple discrete-time model of a delayed dynamical system. A numerical estimate of critical exponents permits one to insert the transition in a proper universality class, within percolation phenomena.