Chaotic Field Research Articles

Optimizing chaotic frequency electric fields for deformation analysis of droplets based on numerical modeling

Chaotic pulse group (CPG) electric field has already been proposed to achieve demulsification of water-in-oil (W/O) emulsions; however, the electric field parameters of the CPG electric field for efficient demulsification of emulsions are unknown. Therefore, in this study, the numerical model of droplet deformation under the action of electric field was established by coupling the flow field and electric field, and the effectiveness of the model was verified by comparing with the experimental results. In the numerical model, the electric field parameters are optimized by droplet deformation; moreover, the influence of surface tension and oil viscosity on the optimal electric field parameters is discussed; the deformation of droplets under the optimized CPG electric field was analyzed. The results show that when the droplet radius is 1 mm, the optimal electric field strength is 612 kV/m, the optimal pulse width is 0.023 s, and the optimal pulse rest width is 0.017 s. The increase in interfacial tension leads to the increase in optimal electric field strength, and the decrease in optimal pulse width and pulse rest width. The increase in oil viscosity leads to an increase in the optimal electric field parameters. With the increase in interfacial tension and oil viscosity, their influence on the deformation of droplets gradually decreases. Droplets of different sizes could find their own optimal electric field parameters in the CPG electric field, so as to achieve the maximum deformation. The results provide valuable guidance for the selection of electric field parameters in CPG electric field industrial applications.

Pilot-wave dynamics: Using dynamic mode decomposition to characterize bifurcations, routes to chaos, and emergent statistics.

We develop a data-driven characterization of the pilot-wave hydrodynamic system in which a bouncing droplet self-propels along the surface of a vibrating bath. We consider drop motion in a confined one-dimensional geometry and apply the dynamic mode decomposition (DMD) in order to characterize the evolution of the wave field as the bath's vibrational acceleration is increased progressively. Dynamic mode decomposition provides a regression framework for adaptively learning a best-fit linear dynamics model over snapshots of spatiotemporal data. Thus, DMD reduces the complex nonlinear interactions between pilot waves and droplet to a low-dimensional linear superposition of DMD modes characterizing the wave field. In particular, it provides a low-dimensional characterization of the bifurcation structure of the pilot-wave physics, wherein the excitation and recruitment of additional modes in the linear superposition models the bifurcation sequence. This DMD characterization yields a fresh perspective on the bouncing-droplet problem that forges valuable new links with the mathematical machinery of quantum mechanics. Specifically, the analysis shows that as the vibrational acceleration is increased, the pilot-wave field undergoes a series of Hopf bifurcations that ultimately lead to a chaotic wave field. The established relation between the mean pilot-wave field and the droplet statistics allows us to characterize the evolution of the emergent statistics with increased vibrational forcing from the evolution of the pilot-wave field. We thus develop a numerical framework with the same basic structure as quantum mechanics, specifically a wave theory that predicts particle statistics.

The persistence of magneto-rotational turbulence in gravitationally turbulent accretion disks

Aims. Our main goal is to probe the persistence of turbulence originating from the magneto-rotational instability (MRI) in gravito-turbulent disks. This state is referred to here as GI-MRI coexistence, with GI standing for gravitational instability. We test the influence of GI strength, controlled by the cooling law, and the impact of Ohmic resistivity. Methods. Our starting point was three-dimensional, ideal, magnetohydrodynamic (MHD) simulations of gravitational turbulence in the local shearing-box approximation using the code Athena. We introduced a zero-net-flux magnetic seed field in a GI-turbulent state and investigated the nonlinear evolution. The GI strength was varied by modifying the cooling parameters. We tested the cooling times τcΩ0 = 10, τcΩ0 = 20, and τcΩ0 = 10, with additional background heating. For some resistive cases, ideal-MHD simulations, which had already developed GI-MRI coexistence, were restarted with a finite Ohmic resistivity enabled at the moment of restart. Results. It appears that there are two possible saturated dynamo states in the ideal-MHD regime: a state of GI-MRI coexistence (for low GI activity) and a strong-GI dynamo. The cases with lower GI activity eventually develop a clearly visible butterfly pattern. For the case with the highest GI activity (τcΩ0 = 10, no heating), a clearly visible butterfly pattern is absent, though more chaotic field reversals are observed above (and below) the mid-plane. We were also able to reproduce the results of previous simulations. With Ohmic resistivity, the simulation outcome can be substantially different. There exists a critical magnetic Reynolds number, ⟨Rm⟩ ∼ 500, below which the ideal-MHD outcome is replaced by a new dynamo state. For larger Reynolds numbers, one recovers turbulent states that are more reminiscent of the ideal-MHD states, and especially the strong-GI case. This new state leads to oscillations, which are caused by a significant heat production due to the resistive dissipation of magnetic energy. The additional heat periodically quenches GI, and the quenching events correspond to maxima of the Toomre value, Q.

Symmetries and spectral statistics in chaotic conformal field theories

We discuss spectral correlations in coarse-grained chaotic two-dimensional CFTs with large central charge. We study a partition function describing the dense part of the spectrum of primary states in a way that disentangles the chaotic properties of the spectrum from those which are a consequence of Virasoro symmetry and modular invariance. We argue that random matrix universality in the near-extremal limit is an independent feature of each spin sector separately; this is a non-trivial statement because the exact spectrum is fully determined by only the spectrum of spin zero primaries and those of a single non-zero spin (“spectral determinacy”). We then describe an argument analogous to the one leading to Cardy’s formula for the averaged density of states, but in our case applying it to spectral correlations: assuming statistical universalities in the near-extremal spectrum in all spin sectors, we find similar random matrix universality in a large spin regime far from extremality.

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Comparison of reduced order models based on dynamic mode decomposition and deep learning for predicting chaotic flow in a random arrangement of cylinders

Three reduced order models are evaluated in their capacity to predict the future state of an unsteady chaotic flow field. A spatially fully developed flow generated in a random packing of cylinders at a solid fraction of 0.1 and a nominal Reynolds number of 50 is investigated. For deep learning (DL), convolutional autoencoders are used to reduce the high-dimensional data to lower dimensional latent space representations of size 16, which were then used for training the temporal architectures. To predict the future states, two DL based methods, long short-term memory and temporal convolutional neural networks, are used and compared to the linear dynamic mode decomposition (DMD). The predictions are tested in their capability to predict the spatiotemporal variations of velocity and pressure, flow statistics such as root mean squared values, and the capability to predict fluid forces on the cylinders. Relative errors between 15% and 20% are evident in predicting instantaneous velocities, chiefly resulting from phase differences between predictions and ground truth. The spatial distribution of statistical second moments is predicted to be within a maximum of 5%–10% of the ground truth with mean error in the range of 1%–2%. Using the predicted fields, instantaneous fluid drag force predictions on individual particles exhibit a mean relative error within 20%, time-averaged drag force predictions to within 5%, and total drag force over all particles to within 1% of the ground truth values. It is found that overall, the non-linear DL models are more accurate than the linear DMD algorithm for the prediction of future states.

Fluid Mechanical Effects of Fetal Aortic Valvuloplasty for Cases of Critical Aortic Stenosis with Evolving Hypoplastic Left Heart Syndrome

Fetuses with critical aortic stenosis (FAS) are at high risk of progression to HLHS by the time of birth (and are thus termed “evolving HLHS”). An in-utero catheter-based intervention, fetal aortic valvuloplasty (FAV), has shown promise as an intervention strategy to circumvent the progression, but its impact on the heart’s biomechanics is not well understood. We performed patient-specific computational fluid dynamic (CFD) simulations based on 4D fetal echocardiography to assess the changes in the fluid mechanical environment in the FAS left ventricle (LV) directly before and 2 days after FAV. Echocardiograms of five FAS cases with technically successful FAV were retrospectively analysed. FAS compromised LV stroke volume and ejection fraction, but FAV rescued it significantly. Calculations to match simulations to clinical measurements showed that FAV approximately doubled aortic valve orifice area, but it remained much smaller than in healthy hearts. Diseased LVs had mildly stenotic mitral valves, which generated fast and narrow diastolic mitral inflow jet and vortex rings that remained unresolved directly after FAV. FAV further caused aortic valve damage and high-velocity regurgitation. The high-velocity aortic regurgitation jet and vortex ring caused a chaotic flow field upon impinging the apex, which drastically exacerbated the already high energy losses and poor flow energy efficiency of FAS LVs. Two days after the procedure, FAV did not alter wall shear stress (WSS) spatial patterns of diseased LV but elevated WSS magnitudes, and the poor blood turnover in pre-FAV LVs did not significantly improve directly after FAV. FAV improved FAS LV’s flow function, but it also led to highly chaotic flow patterns and excessively high energy losses due to the introduction of aortic regurgitation directly after the intervention. Further studies analysing the effects several weeks after FAV are needed to understand the effects of such biomechanics on morphological development.

Non-axisymmetric magnetohydrodynamic equilibrium and stability in an axisymmetric toroidal device

This paper is dedicated to studying the radial broadening of helical states embedded in three-dimensional nonlinear magnetohydrodynamic (MHD) equilibria in an axisymmetric toroidal device. The stability of these helical equilibria is estimated by analyzing global MHD stability. An equilibrium bifurcation can develop a non-axisymmetric configuration with a helical core encompassed by an axis-symmetric plasma edge when the amplitude of an innermost magnetic helicity exceeds that of the primary axisymmetric magnetic component. It is found that internal negative magnetic shear drives the increase of the helicity and the decrease of the axisymmetric component via triple-mode nonlinear interactions, which induces the helical core to broaden radially. The helical structure mainly rests within the domain where the helicity is larger than the axisymmetric mode. Meanwhile, chaotic fields are generated outside the region predicted by the multi-region relaxed MHD model. Furthermore, the global stability analysis reveals that the helical equilibria are stabilized with flat or weak negative magnetic shear at the plasma core. As the core negative magnetic shear becomes significant, the helical equilibria become destabilized by kink modes even though the helical structure extends radially further out. This work is of importance and interest for reversed-field pinch plasma to reach steady quasi-single-helicity states.

Imaging of Hydrodynamic Field Around Submerged Objects Regular Wave and Tsunami Conditions

Hydrodynamic particle movement under regular waves and tsunami wave are rarely studied due to its complicated sensors. This research is aimed at investigating flow fields around submerged structures due to regular waves and tsunami wave. A series of experiments were performed at Tsunami Flume Workshop Facility at Tsunami and Disaster Mitigation Research Center (TDMRC) of Universitas Syiah Kuala. The flume has 60 m in length, 2.5 m in width and 1.7 m in height. To model the both waves, a set of electrical paddle and sensors were placed at one end of the flume. This set of equipment is able to mimic any waveform model, in this case a regular wave with three scenarios and the 2004 Indian Ocean Tsunami wave scenario. A submerged structure was placed on the bed of the flume to model underwater structures. To capture the flow fields, we use a Laser Particle Image Velocimetry (PIV) Camera made in Seika. During the experiment, the results showed different vortex field for both simulations, regular wave and tsunami, generated in front of the submerged structure. Regular wave flow has maximum velocities of 0.5 m/s, 0.7 m/s, 0.9 m/s in each paddle amplitude change scenario. The flow field produces an anticlockwise vortex around the pipe with differents pattern. Tsunami wave flow velocity during the maximum amplitude phase is about 0.25 m/s with a complex vortex field around the pipe, a combination of clockwise and anticlockwise. This could be interpreted as more chaotic hydrodynamic fields around the submerged structures under regular wave and tsunami conditions.

Do chaotic field lines cause fast reconnection in coronal loops?

Over the past decade, Boozer has argued that three-dimensional (3D) magnetic reconnection fundamentally differs from two-dimensional reconnection due to the fact that the separation between any pair of neighboring field lines almost always increases exponentially over distance in a 3D magnetic field. According to Boozer, this feature makes 3D field-line mapping chaotic and exponentially sensitive to small non-ideal effects; consequently, 3D reconnection can occur without intense current sheets. We test Boozer's theory via ideal and resistive reduced magnetohydrodynamic simulations of the Boozer–Elder coronal loop model driven by sub-Alfvénic footpoint motions [A. H. Boozer and T. Elder, Phys. Plasmas 28, 062303 (2021)]. Our simulation results significantly differ from their predictions. The ideal simulation shows that Boozer and Elder under-predict the intensity of current density due to missing terms in their reduced model equations. Furthermore, resistive simulations of varying Lundquist numbers show that the maximal current density scales linearly rather than logarithmically with the Lundquist number.

Enhanced heat transfer and symmetry breaking in three-dimensional electro-thermo-hydrodynamic convection

In this work, the electro-thermo-hydrodynamic convection system induced by unipolar charge injection between two parallel electrodes is numerically investigated. A two-relaxation-time lattice Boltzmann method coupled with a fast Poisson solver is implemented to obtain the temporal and spatial distributions of the flow field, temperature field, electric field, and charge density of the system. Due to the electric force and destabilizing buoyancy force, the system exhibits electro-thermo-convective vortices and transitions to a chaotic flow field, where the flow fluctuates irregularly in time. The strong electric driving force is shown to double the heat transfer effects measured by the Nusselt number ( Nu). The size of the computational domain is found to influence the stability and flow analysis. Specifically, the system is chaotic in a large computational domain but the same set of parameters can lead to a steady-state condition in a small domain.

Scattering strings off quantum extremal surfaces

We consider a Hayden & Preskill like setup for both maximally chaotic and sub-maximally chaotic quantum field theories. We act on the vacuum with an operator in a Rindler like wedge R and transfer a small subregion I of R to the other wedge. The chaotic scrambling dynamics of the QFT Rindler time evolution reveals the information in the other wedge. The holographic dual of this process involves a particle excitation falling into the bulk and crossing into the entanglement wedge of the complement to r = R\\I. With the goal of studying the locality of the emergent holographic theory we compute various quantum information measures on the boundary that tell us when the particle has entered this entanglement wedge. In a maximally chaotic theory, these measures indicate a sharp transition where the particle enters the wedge exactly when the insertion is null separated from the quantum extremal surface for r. For sub-maximally chaotic theories, we find a smoothed crossover at a delayed time given in terms of the smaller Lyapunov exponent and dependent on the time-smearing scale of the probe excitation. The information quantities that we consider include the full vacuum modular energy R\\I as well as the fidelity between the state with the particle and the state without. Along the way, we find a new explicit formula for the modular Hamiltonian of two intervals in an arbitrary 1+1 dimensional CFT to leading order in the small cross ratio limit. We also give an explicit calculation of the Regge limit of the modular flowed chaos correlator and find examples which do not saturate the modular chaos bound. Finally, we discuss the extent to which our results reveal properties of the target of the probe excitation as a “stringy quantum extremal surface” or simply quantify the probe itself thus giving a new approach to studying the notion of longitudinal string spreading.

Fluid viscoelasticity suppresses chaotic convection and mixing due to electrokinetic instability

When two fluids of different electrical conductivities are transported side by side in a microfluidic device under the influence of an electric field, an electrokinetic instability (EKI) is often generated after some critical values of the applied electric field strength and conductivity ratio. Many prior experimental and numerical studies show that this phenomenon results in a chaotic flow field inside a microdevice, thereby facilitating the mixing of two fluids if they are Newtonian in behavior. However, the present numerical study shows that this chaotic convection arising due to the electrokinetic instability can be suppressed if the fluids are viscoelastic instead of Newtonian ones. In particular, we observe that as the Weissenberg number (ratio of the elastic to that of the viscous forces) gradually increases and the polymer viscosity ratio (ratio of the solvent viscosity to that of the zero-shear rate viscosity of the polymeric solution) gradually decreases, the chaotic fluctuation inside a T microfluidic junction decreases within the present range of conditions encompassed in this study. We demonstrate that this suppression of the chaotic motion occurs due to the formation of a strand of high elastic stresses at the interface of the two fluids. We further show that this suppression of the chaotic fluctuation (particularly, the span-wise one) inhibits the mixing of two viscoelastic fluids. Therefore, one needs to be cautious when the EKI phenomenon is planned to use for mixing such viscoelastic fluids. Our observations are in line with that seen in limited experimental studies conducted for these kinds of viscoelastic fluids.

Runaway dynamics in tokamak disruptions with current relaxation

The safe operation of tokamak reactors requires a reliable modelling capability of disruptions, and in particular the spatio-temporal dynamics of associated runaway electron currents. In a disruption, instabilities can break up magnetic surfaces into chaotic field line regions, causing current profile relaxation, as well as a rapid radial transport of heat and particles. Using a mean-field helicity transport model implemented in the disruption runaway modelling framework Dream, we calculate the dynamics of runaway electrons in the presence of current relaxation events. In scenarios where flux surfaces remain intact in parts of the plasma, a skin current is induced at the boundary of the intact magnetic field region. This skin current region becomes an important centre concerning the subsequent dynamics: it may turn into a hot ohmic current channel, or a sizeable radially localized runaway beam, depending on the heat transport. If the intact region is in the plasma edge, runaway generation in the countercurrent direction can occur, which may develop into a sizeable reverse runaway beam. Even when the current relaxation extends to the entire plasma, the final runaway current density profile can be significantly affected, as the induced electric field is reduced in the core and increased in the edge, thereby shifting the centre of runaway generation towards the edge.

A chaotic lattice field theory in one dimension* *Dedicated to Fritz Haake 1941–2019 [

Motivated by Gutzwiller’s semiclassical quantization, in which unstable periodic orbits of low-dimensional deterministic dynamics serve as a WKB ‘skeleton’ for chaotic quantum mechanics, we construct the corresponding deterministic skeleton for infinite-dimensional lattice-discretized scalar field theories. In the field-theoretical formulation, there is no evolution in time, and there is no ‘Lyapunov horizon’; there is only an enumeration of lattice states that contribute to the theory’s partition sum, each a global spatiotemporal solution of system’s deterministic Euler–Lagrange equations. The reformulation aligns ‘chaos theory’ with the standard solid state, field theory, and statistical mechanics. In a spatiotemporal, crystallographer formulation, the time-periodic orbits of dynamical systems theory are replaced by periodic d-dimensional Bravais cell tilings of spacetime, each weighted by the inverse of its instability, its Hill determinant. Hyperbolic shadowing of large cells by smaller ones ensures that the predictions of the theory are dominated by the smallest Bravais cells. The form of the partition function of a given field theory is determined by the group of its spatiotemporal symmetries, that is, by the space group of its lattice discretization, best studied on its reciprocal lattice. Already one-dimensional lattice discretization is of sufficient interest to be the focus of this paper. In particular, from a spatiotemporal field theory perspective, ‘time’-reversal is a purely crystallographic notion, a reflection point group, leading to a novel, symmetry quotienting perspective of time-reversible theories and associated topological zeta functions.

New light fields based on integration theory within the Weyl ordering product of operators

The development of quantum optics theory based on the method of integration within an ordered product of operators (IWOP) has greatly stimulated the study of quantum states in the light field, especially non-Gaussian states with various non-classical properties. In this paper, the two-mode squeezing operator is derived with integral theory within the Weyl ordering product of operators using a combinatorial field in which one mode is a chaotic field and the other mode is a vacuum field. The density operator of the new light field, its entanglement property and photon number distribution are analyzed. We also note that tracing a three-mode pure state can yield this new light field. These methods represent a theoretical approach to investigating new density operators of light fields.

Chaotic Mixing Intensification and Flow Field Evolution Mechanism in a Stirred Reactor Using a Dual-Shaft Eccentric Impeller

Chaotic Mixing Intensification and Flow Field Evolution Mechanism in a Stirred Reactor Using a Dual-Shaft Eccentric Impeller

Non-Gaussianities in the statistical distribution of heavy OPE coefficients and wormholes

The Eigenstate Thermalization Hypothesis makes a prediction for the statistical distribution of matrix elements of simple operators in energy eigenstates of chaotic quantum systems. As a leading approximation, off-diagonal matrix elements are described by Gaussian random variables but higher-point correlation functions enforce non-Gaussian corrections which are further exponentially suppressed in the entropy. In this paper, we investigate non- Gaussian corrections to the statistical distribution of heavy-heavy-heavy OPE coefficients in chaotic two-dimensional conformal field theories. Using the Virasoro crossing kernels, we provide asymptotic formulas involving arbitrary numbers of OPE coefficients from modular invariance on genus-g surfaces. We find that the non-Gaussianities are further exponentially suppressed in the entropy, much like the ETH. We discuss the implication of these results for products of CFT partition functions in gravity and Euclidean wormholes. Our results suggest that there are new connected wormhole geometries that dominate over the genus-two wormhole.

The fluid dynamics of propagating fronts with solutal and thermal coupling

We numerically explore the propagation of reacting fronts in a shallow and horizontal layer of fluid. We focus on fronts that couple with the fluid due to density differences between the products and reactants and also due to heat release from the reaction. We explore fronts where this solutal and thermal coupling is cooperative or antagonistic. We quantify the fluid motion induced by the front and investigate the interactions of the front with the fluid as it propagates through quiescent, cellular and chaotic flow fields. The solutal coupling induces an extended convection roll that travels with the front, the thermal coupling due to heat release from the reaction generates a pair of convection rolls that travels with the front, and when both couplings are present there is a complex signature of these contributions. The details of the front dynamics depend significantly upon the interactions of the front-induced flow field with the fluid ahead of the front.

Fractal Structures and Magnetic Footprints in a Divertor Tokamak

Fractal structures appear very often in open Hamiltonian systems, and can be identified in the deposition of chaotic magnetic field line on the plates of a tokamak divertor. Indeed, tokamaks with divertors are used to control the magnetic confinement of plasmas, such that the field lines created by electric currents have escape channels, through which plasma particles can be diverted out of the tokamak wall and redirected to divertor plates. In this work, we use a symplectic map to investigate the deposition patterns on the plates of a divertor. We show that the pattern of magnetic footprints on divertor plates (deposition patterns) underlying the chaotic orbits involves a number of fractal structures related to the existence of a nonattractive invariant chaotic set. In order to investigate the fractal characteristic of magnetic footprints, we analyze quantitatively the degree of stability of the fractal structure by calculating the entropy of the basin. These numerical analyses indicate that the fractal pattern on the divertor plates depends sensibly on the magnetic field structure. We show qualitative evidences of the Wada property.