Chaotic Instability Research Articles

Emerging Design Tools for Functional Architectures in Monofilament Fibers

The structural control of the monofilament fiber cross‐sectional architecture is a well‐established method for imparting its active functionality. Resulting from a thermal draw, the fiber device, until recently, is expected to be a cross‐sectionally scaled‐down and axially scaled‐up replica of its preform. However, thermal draw is a melt‐shaping process in which the preform is heated to a viscous liquid to be scaled into a fiber. Thus, it is prone to capillary instabilities on the interfaces between preform cladding and materials it encapsulates, distorting the fiber‐embedded architecture and complicating preform‐to‐fiber geometry translation. Traditionally, capillary instabilities are suppressed by performing the draw at a high‐viscosity, large‐feature‐size regime, such that the scaling of the preform into the fiber happens faster than a pronounced instability can develop. It is discovered recently that highly nonlinear, at times even chaotic capillary instabilities, in some fluid dynamic regimes, become predictable and thus engineerable. Driven by ever‐growing demand for enhancing the fiber‐device functionality, piggybacking on a capillary instability, instead of suppressing it, establishes itself as a new material processing strategy to achieve fiber‐embedded systems with user‐engineered architecture in all 3D, including the axial. Considering this development, the notable emerging methodologies are cross‐compared for designing 3D fiber‐embedded architectures.

Wave energy converter with multiple degrees of freedom for sustainable repurposing of decommissioned offshore platforms: An experimental study

Targeting at the sustainable repurposing of decommissioned offshore platforms, a novel wave energy converter with a distinct mechanical-motion-rectifier power take-off system is developed to provide renewable energy. A scaled prototype is constructed and experimentally investigated in a large wave tank, as an essential step before sea trials. A new phenomenon of parametric oscillation is observed and explored, as physical evidence of chaotic instabilities of wave energy devices. Several advantages of the multi-degree-of-freedom device over its single-degree-of-freedom counterpart are disclosed physically for the first time. Releasing the pitch and roll degrees of freedom helps enlarge the heave amplitude of the energy-absorbing buoy, receive a larger hydrodynamic force from water waves to the power take-off system, reduce structural deflection and friction of the transmission machinery, and eliminate spiky and noisy vibrations of the internal force. Accordingly, the maximum efficiencies in the energy absorption and transmission stages increase from 45% and 11% to 90% and 30%, respectively; the overall efficiency of energy conversion is increased by up to three times in a broad spectrum of wave conditions.

Classical chaos in quantum computers

The development of quantum computing hardware is facing the challenge that current-day quantum processors, comprising 50–100 qubits, already operate outside the range of quantum simulation on classical computers. In this paper we demonstrate that the simulation of limits can be a potent diagnostic tool for the resilience of quantum information hardware against chaotic instabilities potentially mitigating this problem. As a testbed for our approach we consider the transmon qubit processor, a computing platform in which the coupling of large numbers of nonlinear quantum oscillators may trigger destabilizing chaotic resonances. We find that classical and quantum simulations lead to similar stability metrics (classical Lyapunov exponents vs quantum wave function participation ratios) in systems with O(10) transmons. However, the big advantage of classical simulation is that it can be pushed to large systems comprising up to thousands of qubits. We exhibit the utility of this classical toolbox by simulating all current IBM transmon chips, including the 433-qubit processor of the Osprey generation, as well as devices with 1121 qubits (Condor generation). For realistic system parameters, we find a systematic increase of Lyapunov exponents with system size, suggesting that larger layouts require added efforts in information protection. Published by the American Physical Society 2024

Abundant Closed-Form Soliton Solutions to the Fractional Stochastic Kraenkel–Manna–Merle System with Bifurcation, Chaotic, Sensitivity, and Modulation Instability Analysis

An essential mathematical structure that demonstrates the nonlinear short-wave movement across the ferromagnetic materials having zero conductivity in an exterior region is known as the fractional stochastic Kraenkel–Manna–Merle system. In this article, we extract abundant wave structure closed-form soliton solutions to the fractional stochastic Kraenkel–Manna–Merle system with some important analyses, such as bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability. This fractional system renders a substantial impact on signal transmission, information systems, control theory, condensed matter physics, dynamics of chemical reactions, optical fiber communication, electromagnetism, image analysis, species coexistence, speech recognition, financial market behavior, etc. The Sardar sub-equation approach was implemented to generate several genuine innovative closed-form soliton solutions. Additionally, phase portraiture of bifurcation analysis, chaotic behaviors, sensitivity, and modulation instability were employed to monitor the qualitative characteristics of the dynamical system. A certain number of the accumulated outcomes were graphed, including singular shape, kink-shaped, soliton-shaped, and dark kink-shaped soliton in terms of 3D and contour plots to better understand the physical mechanisms of fractional system. The results show that the proposed methodology with analysis in comparison with the other methods is very structured, simple, and extremely successful in analyzing the behavior of nonlinear evolution equations in the field of fractional PDEs. Assessments from this study can be utilized to provide theoretical advice for improving the fidelity and efficiency of soliton dissemination.

Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

The fully nonlinear notion of resonance−geometrical resonance−in the general context of dissipative systems subjected to spatially periodic phase-modulated potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system’s energy when the potential is stationary. The geometrical resonance solutions represent a local symmetry whose critical breaking leads to a new analytical criterion for the onset of chaotic instabilities. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new physical criterion for the onset of chaotic instabilities is shown to be valid over large regions of parameter space, thus being useful beyond the scope of current mathematical techniques. More importantly, the present theory helps to understand the unreasonable effectiveness of the Melnikov’s method beyond the perturbative regime.

Observation of sarcomere chaos induced by changes in calcium concentration in cardiomyocytes.

Heating cardiomyocytes to 38-42°C induces hyperthermal sarcomeric oscillations (HSOs), which combine chaotic instability and homeostatic stability. These properties are likely important for achieving periodic and rapid ventricular expansion during the diastole phase of the heartbeat. Compared with spontaneous oscillatory contractions in cardiomyocytes, which are sarcomeric oscillations induced in the presence of a constant calcium concentration, we found that calcium concentration fluctuations cause chaotic instability during HSOs. We believe that the experimental fact that sarcomeres, autonomously oscillating, exhibit such instability due to the action of calcium concentration changes is important for understanding the physiological function of sarcomeres. Therefore, we have named this chaotic sarcomere instability that appears under conditions involving changes in calcium concentration as Sarcomere Chaos with Changes in Calcium Concentration (S4C). Interestingly, sarcomere instability that could be considered S4C has also been observed in the relaxation dynamics of EC coupling. Unlike ADP-SPOCs and Cell-SPOCs under constant calcium concentration conditions, fluctuations in oscillation amplitude indistinguishable from HSOs were observed. Additionally, like HSO, a positive Lyapunov exponent was measured. S4C is likely a crucial sarcomeric property supporting the rapid and flexible ventricular diastole with each heartbeat of the heart.

On the degree of dynamical packing in the Kepler multiplanet systems

ABSTRACT Current planet formation theories rely on initially compact orbital configurations undergoing a (possibly extended) phase of giant impacts following the dispersal of the dissipative protoplanetary disc. The orbital architectures of observed mature exoplanet systems have likely been strongly sculpted by chaotic dynamics, instabilities, and giant impacts. One possible signature of systems continually reshaped by instabilities and mergers is their dynamical packing. Early Kepler data showed that many multiplanet systems are maximally packed – placing an additional planet between an observed pair would make the system unstable. However, this result relied on placing the inserted planet in the most optimistic configuration for stability (e.g. circular orbits). While this would be appropriate in an ordered and dissipative picture of planet formation (i.e. planets dampen into their most stable configurations), we argue that this best-case scenario for stability is rarely realized due to the strongly chaotic nature of planet formation. Consequently, the degree of dynamical packing in multiplanet systems under a realistic formation model is likely significantly higher than previously realized. We examine the full Kepler multiplanet sample through this new lens, showing that $\sim 60{{-}}95~{{\ \rm per\ cent}}$ of Kepler multiplanet systems are strongly packed and that dynamical packing increases with multiplicity. This may be a signature of dynamical sculpting or of undetected planets, showing that dynamical packing is an important metric that can be incorporated into planet formation modelling or when searching for unseen planets.

Neural network analysis of unstable temporal intensity peaks in continuous wave modulation instability

We report the application of a neural network to correlate spectral and temporal properties for modulation instability excited by a continuous wave field with random quantum noise. Using numerical simulations to generate large ensembles of chaotic modulation instability data, a trained neural network is shown to be able to correlate unstable intensity spectra and associated temporal intensity peaks with correlation coefficients exceeding ρ=0.90 for dynamic ranges exceeding 40 dB. Such excellent correlation is obtained both in the initial evolving phase of modulation instability where spectra typically possess significant sideband structure, as well as in the stationary phase of the instability when distinct sideband structure is not apparent. For both cases, we also test the degree to which a neural network may be able to “forecast” temporal instability peaks based on analyzing spectral intensity at an earlier spatial reference position, but conclude that such forecasting is successful over only within a very localized distance range much less than the characteristic nonlinear length.

Effects of inlet total pressure on the formation and propagation characteristics of n-decane two-phase rotating detonation waves

In this paper, three-dimensional numerical simulations are carried out to study the influence of inlet total pressure (such as 1 MPa, 1.5 MPa and 2 MPa) on the two-phase rotating detonation wave behavior. The flow field characteristics, the formation mechanism and propagation parameters of two-phase rotating detonation wave are discussed in detail. The simulation results show that the inlet total pressure has a significant impact on the two-phase rotating detonation wave in the scope of our study. Specifically, it is found that n-decane droplets are not completely consumed around the detonation wave, the escaping droplets are still evaporated and deflagrated behind the detonation wave. The increasing total pressure contributes to droplets evaporation. In addition, the generation of hot spots is a crucial factor in the detonation formation process. The shock wave induction and pressure wave accumulation are two mechanisms for it. As the total pressure increases, chaotic instability is observed before the stable stage, including the quenching, re-ignition and re-orientation, which is responsible for the variation of the propagation mode and direction of the rotating detonation waves. Moreover, in our study, with the increasing of total pressure, the intensity and stability of the detonation waves both increase, while the variation of detonation velocity is not sensitive. Our results can provide useful guidance for the research of two-phase rotating detonation engines.

Chaotic instability in the BFSS matrix model

Chaotic scattering is a manifestation of transient chaos realized by the scattering with non-integrable potential. When the initial position is taken in the potential, a particle initially exhibits chaotic motion, but escapes outside after a certain period of time. The time to stay inside the potential can be seen as lifetime and this escape process may be regarded as a kind of instability. The process of this type exists in the Banks-Fischler-Shenker-Susskind (BFSS) matrix model in which the potential has flat directions. We discuss this chaotic instability by reducing the system with an ansatz to a simple dynamical system and present the associated fractal structure. We also show the singular behavior of the time delay function and compute the fractal dimension. This chaotic instability is the basic mechanism by which membranes are unstable, which is also common to supermembranes at quantum level.

Nonlinear and chaotic vibrations of FG double curved sandwich shallow shells resting on visco-elastic nonlinear Hetenyi foundation under combined resonances

In this study, the nonlinear and chaotic instability of functionally graded (FG) double curved shallow sandwich shells resting on a viscoelastic Hetenyi foundation, under simultaneous effect of in-plane and transverse excitations is studied. Employing the third-order Reddy theory and von-Karman relations and the Hamilton principle, the partial differential equations of motion under movable SS boundary conditions are derived. Introducing the trigonometric Airy stress function and applying the Galerkin’s method, the equations are reduced to a set of nonlinear ODEs with time. Then, under forcing resonance conditions and using the perturbation method, the modulation equations at the stationary conditions are derived and solved numerically. Then stability of non-trivial solutions for the resonance amplitude corresponding to the presence of limit cycle oscillation is investigated. Then by extracting the characteristic resonance amplitude curves, the effect of various parameters, including: frequency detuning parameter, in-plane excitation amplitude, linear, shear and nonlinear stiffness and damping parameters of the foundation on nonlinear response are analyzed. Finally, by extracting two degrees of freedom system time response, bifurcation and chaotic characteristic curves of the problem, the conditions for occurrence the periodic, double periodic, multi-periodic and chaotic behaviors under the simultaneous effect of parametric and internal resonances are studied comprehensively.

A hybrid lattice Boltzmann model for simulating viscoelastic instabilities

Low-Reynolds-number viscoelastic fluids exhibit a chaotic behaviour linked to the growth of elastic instabilities when the polymer molecules are stretched excessively. Despite offering various exciting benefits, the numerical difficulties associated with simulating this complex regime have left a lot still unexplored regarding the transition and onset of these low-Reynolds number viscoelastic instabilities. Recently, methods based on the lattice Boltzmann method (LBM) have emerged as a viable numerical tool for studying the behaviour of viscoelastic fluids largely due to the simplicity, adaptability, and intrinsic parallel features of LBM. However, extensive memory requirements and the inability to preserve numerical stability have restricted previous attempts from simulating viscoelastic instabilities. In this work, a hybrid lattice Boltzmann model is applied to simulate low-Reynolds number viscoelastic instabilities. In this approach, the hydrodynamic field is solved using a lattice Boltzmann model, whereas the polymer field is solved separately using a high-resolution finite difference scheme with the logarithmic Cholesky decomposition. The model is first validated for steady viscoelastic flows using the four-roll mill case, where the results are compared against the analytical solution and previous numerical studies. The model is then applied to simulate a chaotic low-Reynolds number viscoelastic instability by initialising a small perturbation to the isotropic polymer stress. The results at different Weissenberg numbers experience complex flow dynamics at sufficiently long time durations, which transition from quasi-periodic to periodic to aperiodic states with increasing elastic effects. The quasi-periodic regime was found to experience the fastest transition into the transient regime, with the transitioning time being delayed as the Weissenberg number increased. This work proves the capability of applying a coupled lattice Boltzmann method for exploring the complex flow behaviour of elastic instabilities, allowing the potential to explore more challenging and practical viscoelastic instability cases.

UNIQUE AND NATURALLY DETERMINED ATTRIBUTES OF THE MODERN UNDERSTANDING OF A STATE

The article analyzes the issues of the modern understanding of a state, as well as the factors and determinants that define its essence. The idea is put forward that the most important factor determining the necessity to rethink the essence of the state is the modern global crisis and chaotic instability. A methodology for research of the state is proposed that meets post-non-classical scientific and managerial rationality. The article substantiates a new European nature and attributes of modern statehood, which is also influenced by the three-level structure of statehood in the world system, as well as the peculiarities of the historical genesis of specific countries. The author proposes researching of the state through the correlation of the triad of parameters «power – population – territory», the interaction of which generates various types of power organization. Purpose: to propose new methods suitable for studying the state in the context of the current global crisis, accompanied by a decrease in the heuristic and cognitive potential of the methodology formed within the framework of liberal geoculture; to analyze the essence and nature of modern statehood on the basis of the proposed methods. The author uses the following methods: post-non-classical scientific paradigm, the principle of the observer's involvement in the cognizable reality, world-system analysis, subjective approach, spatial dimension, historical approach. Results: the research reveals a new European nature of modern statehood, which is declining as a result of the global crisis, and historical features of the formation of this type of statehood, in relation to the Republic of Belarus in particular.

Prediction and suppression of chaotic instability in brake squeal

Chaotic instability in a vibration phenomenon, known as brake squeal, is investigated including the combined effects of falling friction, sprag-slip and mode coupling. Brake squeal is a high-pitched noise that occurs sometimes when a vehicle is decelerated using disc brakes. The equations of motion for the two dominant coupled modes of the brake system reduce to two autonomous coupled nonlinear second-order systems. The mode coupling instability via friction causes limit cycle behaviour via a supercritical Hopf bifurcation. This limit cycle is shown to break up into chaotic motion characterised by a Poincare map with a less than one-dimensional attractor, similar to that found in a forced dry friction oscillator. For the first time, conservative analytical conditions for brake squeal chaos are developed and verified numerically over a range of sprag angles and brake pressures for fundamental and real brake systems. The predictive model is then used to identify and quantify means to suppress brake squeal chaos to unlikely, excessive friction levels. The results provide predictive insight into conditions under which brake squeal chaos occurs and its suppression.

Controlling the lasing modes in random lasers operating in the Anderson localization regime.

Random lasers, which rely on random scattering events unlike traditional Fabry-Pérot cavities, are much simpler and cost-effective to fabricate. However, because of the chaotic fluctuations and instability of the lasing modes, controlling the lasing properties is challenging. In this study, we use random InP nanowire (NW) arrays that operate in the Anderson localization regime with stable modes as the random lasers. We show that by changing the design parameters of the NW arrays, such as filling factor, dimensions of the NWs, degree of randomness, and the size of the array, the properties of the lasing modes including the number of modes, lasing wavelengths, and lasing threshold can be controlled.

Stable, multi-mode lasing in the strong localization regime from InP random nanowire arrays at low temperature

Disorder is generally considered an undesired element in lasing action. However, in random lasers whose feedback mechanism is based on random scattering events, disorder plays a very important and critical role. Even though some unique properties in random lasers such as large-angle emission, lasing from different surfaces, large-area manufacturability, and wavelength tunability can be advantageous in certain applications, the applicability of random lasers has been limited due to the chaotic fluctuations and instability of the lasing modes because of weak confinement. To solve this, mode localization could reduce the spatial overlap between lasing modes, thus preventing mode competition and improving stability, leading to laser sources with high quality factors and very low thresholds. Here, by using a random array of III-V nanowires, high-quality-factor localized modes are demonstrated. We present the experimental evidence of strong light localization in multi-mode random nanowire lasers which are temporally stable at low temperatures.

Effect of Changing Crude Oil Grade on Slug Characteristics and Flow Induced Mechanical Stresses in Pipes

Slug multiphase flow is known to be the most prevalent regime because of its extensive encounters associated with chaotic behaviour, complexity and instability that cause significant fluctuations in operating conditions and thus lead to undesirable effects. In this study, the effect of varying crude oil grades on slug characteristics is numerically investigated. A partitioned one-way coupling framework of fluid–structure interaction (FSI) one-way coupling framework is adopted to investigate the influence of changing oil grades and slug characteristics on the maximum induced stresses in horizontal carbon steel pipe. It was found that increasing crude oil density causes frequent slugging and promotes the formation of liquid slugs further upstream near the inlet with high translational velocity and short wavelength. Therefore, the maximum induced stresses resulting from the interaction between slugs and the inner surface of pipes are strongly dependent on crude oil grade. In modelling extra heavy crude oil, a 40% increase in maximum induced stresses is recorded when the liquid superficial velocity decreases from 1 to 0.86 m/s at a constant natural gas superficial velocity.

Nonlinear states and dynamics in a synthetic frequency dimension

Recent advances in the study of synthetic dimensions revealed a possibility to employ the frequency space as an additional degree of freedom which allows for investigating and exploiting higher-dimensional phenomena in a priori low-dimensional systems. However, the influence of nonlinear effects on the synthetic frequency dimensions was studied only under significant restrictions. In the present paper, we develop a generalized mean-field model for the optical field envelope inside a single driven-dissipative resonator with quadratic and cubic nonlinearities, whose frequencies are coupled via an electro-optical resonant temporal modulation. The leading-order equation takes the form of a driven Gross-Pitaevskii equation with a cosine potential. We numerically investigate the nonlinear dynamics in such a microring resonator with a synthetic frequency dimension in the regime where parametric frequency conversion occurs. We observe that the modulation brings additional control to the system, enabling one to readily create and manipulate bright and dark dissipative solitons inside the cavity. In the case of anomalous dispersion, we find that the presence of electro-optical mode coupling confines and stabilizes the chaotic modulation instability region. This leads to the appearance of an unconventional type of stable coherent structure which emerges in the synthetic space with restored translational symmetry, in a region of parameters where conventionally only chaotic modulation instability states exist. This structure appears in the center of the synthetic band and, therefore, is referred to as the band soliton. Finally, we extend our results to the case of multiple modulation frequencies with controllable relative phases creating synthetic lattices with nontrivial geometry. We show that an asymmetric synthetic band leads to the coexistence of chaotic and coherent states of the electromagnetic field inside the cavity, i.e., dynamics that can be interpreted as chimeralike states. Recently developed ${\ensuremath{\chi}}^{(2)}$ microresonators can open the way to experimentally exploring our findings.

Imperfect Bifurcation and Chaos of Slightly Curved Carbon Nanotube Conveying Hot Pressurized Fluid Resting on Foundations

AbstractUnintended slight curvature of a straight pipe and temperature variation in a pipe has been found to create uncertainties in tubes and pipes. Fluttering, divergence, and chaotic instabilities of slightly curved carbon nanotubes (SCCNT) conveying hot pressurized fluid are investigated in this paper. The SCCNT is modeled on the basis of large deformation strains. Their gradients are included in the strain energy expression and the velocity and its gradients in the kinetic energy derivation. In modeling the size effects, both the static and kinetic length scales in the energy equations were considered. Governing equation is derived using Lagrangian approach. The effects of geometric imperfection (which leads to cusp bifurcation), small length scale, and kinetic material length parameter on the static and dynamic instability characteristics of the pipes are studied. Analysis is performed using the eigenfunction expansion method. It is found that the material length scale parameter increase tends to shift instability to the lower fluid velocity while the kinematic material length parameter increase does not change the buckling point but lowers the frequency. In the nonlinear dynamic case, both the parameters lead to chaos of the nanotube beyond the critical fluid velocity. The thermal loading changes the sudden supercritical pitchfork bifurcation to cusp bifurcation. The increasing linear and nonlinear foundation stiffness leads the system to chaotic features after the critical point.

Origin and chaotic propagation of multiple rotating detonation waves in hydrogen/air mixtures

The origin and chaotic propagation of multiple detonative waves in the two-dimensional modelled rotating detonation combustor fueled by premixed hydrogen/air mixtures are numerically investigated with detailed chemical mechanism. The discrete reactants inlets are adopted, to mimic the spatial non-uniformity of the propellant in the practical Rotating Detonation Engine (RDE) combustor. The emphasis is laid on the mechanism to induce the new detonation waves in the RDE and the influence of the reactant non-uniformity in RDE on the critical detonation combustion dynamics. The numerical experiments show that the stability and number of the rotating detonation wave are affected by the inlet total pressures and reactant equivalence ratios. The RDE with high inlet total pressure would experience chaotic instability before reaching stable propagation of detonation waves in near-stoichiometric mixtures, while for the RDE with low inlet total pressure, no chaotic propagation transient after the detonation initiation is observed. It is found that the chaotic propagation stage is responsible for the variation of the rotating detonative wave number and propagation direction. Frequent detonation extinction, re-ignition and re-orientation, irregular reactants refill zones, co-rotating and counter-rotating detonation waves are observed during chaotic stage. The explosive spots arising during this stage, which may initiate new detonation waves, result from the mutual enhancement between the travelling shock waves and the deflagrative fronts. Furthermore, the predictability of the chaotic detonation wave propagation is further confirmed in terms of the initial and boundary conditions, mesh and chemical mechanism. It is also found that the fuel equivalence ratio has a considerable impact on the number of the stabilized detonation wave and velocity deficit.