Nonlinear Regime Research Articles

Identifying regime shifts, transients and late warning signals for proactive ecosystem management

Conservation Biology fosters the study of Earth's ecosystems and biodiversity aiming at protecting species and their habitats from menaces causing the erosion of biotic interactions and extinctions. Its ultimate goal is to preserve biodiversity and promote sustainable ecological management maintaining both ecosystem's resilience and services. Ecosystems display complex patterns in time and space due to the intrinsic nonlinear nature of their interactions and can suffer regime shifts driven by the agents of global change. During the last decades, Ecology has turned from the equilibrium metaphor to the paradigm of non-equilibrium dynamics. This involves putting into the scene multiple stable states, nonlinear regime shifts, stochasticity, and ecological transients. These aspects are also crucial for biological conservation since they play a fundamental role in species' persistence, ecosystems' resilience, and in detecting warning signals prior to either the collapse or the recovery of the ecosystem. In this contribution, we discuss ecological regime shifts caused by tipping points in real ecosystems. Then, we provide information on some known dynamical features from theoretical ecology and dynamical systems theory associated to tipping points, mainly given by transient phenomena and the characteristic statistical patterns tied to early warning signals. These features are illustrated with a single-species mathematical model including facilitation and immigration. We also introduce and provide evidence of late warning signals as a way to identify when a tipping point has been surpassed but the system still remains in a transient state and recovery may be still possible. Our main goal is to near non-equilibrium concepts in Ecology to the conservationist community and promote bridges between such concepts and the management and conservation of ecosystems.

Sinusoidally Pitching Foils in Transonic Flow: Insights into Flutter from Time Accurate Simulations

The impact of shock formation and vortex dynamics on airfoil flutter in the transonic regime is investigated through a series of two-dimensional time-accurate simulations of a sinusoidally pitching airfoil at a Reynolds number of 10,000. To gain insight into transonic flutter in the fully nonlinear regime, an energy-based approach that employs prescribed kinematics is utilized. Flutter stability boundaries are identified as a function of the Mach number and the reduced velocity, the latter of which is a surrogate for structural stiffness or flight speed. The results show a subcritical instability near Mach numbers of M∞=0.7 for a range of oscillation frequencies. Additionally, three shock-induced mechanisms are identified that influence the transfer of energy from the flow to the airfoil. The primary mechanism is flow separation triggered by the generation of a lambda shock. The influence of the lambda-shock dynamics on airfoil flow separation is determined for different Mach numbers, providing insight into the well-known “transonic dip” observed in flutter boundaries.

Trapping and guiding soliton through Airy pulse

We show that Airy soliton interaction in anomalous dispersion and focussing nonlinear regime provides an effective control on the co-propagating sech soliton dynamics. Cross phase modulation (XPM) induced nonlinear phase results varying group velocity of the sech soliton which leads to its temporal shift towards leading edge. The soliton could be made either advanced or delayed by choosing an appropriate initial time delay between the two co-propagating pulses. The effect of the initial time delay on trapping efficiency is also disclosed. Additionally, we have studied the effect of temporal chirp in Airy pulse on sech soliton dynamics. It is found that introduction of positive chirp inhibits the XPM-induced temporal shift of the soliton, while negative chirp boosts the XPM-induced acceleration. Further, the effect of group delay on the trapping and guiding of the soliton has been investigated. Moreover, the role of relative dispersion and nonlinear length on the soliton pulse acceleration are investigated. These results are expected to provide a better understanding on manipulation of light by light that could be useful in all-optical switching and signal control.

Electromagnetic TE- and TM-waves propagation in a plane waveguide covered with graphene characterized by nonlinear conductivity

Background. Guiding properties of waveguiding structures with graphene are of great importance for various applications and have been studied in many papers. In all such studies, graphene was characterized, as a rule, by linear surface conductivity. However, if the intensity of an electromagnetic wave is large enough, the interaction of graphene with the electromagnetic wave becomes nonlinear; in this case, it is more correct to describe graphene by nonlinear conductivity.
 Aim. This work is aimed at studying the influence of cubic nonlinearity of graphene, corresponding to the so-called self-action effects (not affecting the frequency of the incident wave), on the propagation of TE- and TM-polarized waves in the structure, which is a plain dielectric layer covered on one side by graphene.
 Methods. In this study, the guiding properties of the waveguide are studied using primarily an analytical approach. Thus, from Maxwell's equations, material equations and boundary conditions, a couple of dispersion equations for TE-and TM-polarized waves is derived and then its solvability is studied. In addition, some numerical experiments are carried out in the study.
 Results. The dispersion equations of the studied waveguiding structure for TE- and TM-polarized waves are derived in explicit form. Studying analytically obtained equations, conditions for waveguide parameters are found, providing the existence of a given number of waveguide modes. In addition, some numerical results are obtained in the paper, which give an idea of the influence of nonlinear effects on the electromagnetic waves propagating in the structure.
 Conclusion. The results obtained in this paper reveal two effects related to the cubic nonlinearity of graphene. Firstly, in a plain dielectric layer with graphene coating in the strong nonlinear regime TE-waves with longer wavelength and TM-waves with shorter wavelength propagate compared to electromagnetic waves that propagate in the same structure in the linear regime. Secondly, the strong cubic nonlinearity leads to a greater localization of the electromagnetic wave within the waveguiding structure.

Understanding the rheological properties from linear to nonlinear regimes and spatiotemporal structure of mixed kappa and reduced molecular weight lambda carrageenan gels

Blends of different carrageenan types have proven to be useful in tuning carrageenan gels' rheological properties. However, understanding the influence of a reduced molecular weight on the gelation of mixed carrageenan gels is still limited. Here, the gelation of mixed kappa-(KC) and reduced molecular weight lambda-(LC) carrageenan systems at different mixing ratios was evaluated using rheology from linear to nonlinear regimes via large amplitude oscillatory shear (LAOS), small-angle X-ray scattering (SAXS), pulsed nuclear magnetic resonance (NMR) and particle tracking. A single-step increase in moduli was seen for mixed kappa-lambda carrageenan (KCLC) gels with decreasing temperature while LC demonstrated nongelling behavior. The LAOS response of KCLC mixed gels showed the characteristic signature of strain-stiffening corresponding to the difference in the size and dynamics of the aggregates. The cross-sectional size revealed by SAXS and dynamics of the aggregates revealed by pulsed-NMR demonstrate that KCLC gels has higher segmental mobility and formed small aggregates that reduce with decreasing the KC fraction whereas pure KC gels formed large and rigid aggregates. Thus, the spatiotemporal features of the aggregates are considered to be the origin of the strain-stiffening in mixed gels under large deformation. Moreover, the microscopic properties of the KCLC gels evaluated using particle tracking revealed a homogenous network suggesting the formation of a swollen KC network in the LC solution. Hence, our findings provide insights into the rheological behavior and network structure design of KC and reduced molecular weight LC mixed gels.

Chaos control and exceptional point engineering via dissipative optomechanical coupling

Abstract We study a dissipative mechanically coupled optomechanical system that hosts gain and loss. The gain (loss) is engineered by driving a purely dispersive optomechanical cavity with a blue-detuned (red-detuned) electromagnetic field. By taking into account the dissipative coupling, the Exceptional Point (EP), which is a non-Hermitain degeneracy, occurs at low threshold driving strength compared to what happens in a solely dispersive system. In the linear regime, the dissipative term induces strong coupling between the mechanical resonators, leading to an increase of energy exchange. For strong enough driving, the system enters into a nonlinear regime where a weak coupling regime takes place. In this regime, the mechanical resonators exhibit chaotic beats like-behaviour in the purely dispersive system. By switching on the dissipative coupling, the complex dynamics is switched off, and this restores regular dynamics into the system. This work suggests a way to probe quantum phenomena in dissipative systems at low-threshold driving strength. It also provides a new control scheme of complex dynamics in optomechanics and related fields.

Nonlinear compression of few-cycle multi-mJ 5 µm pulses in ZnSe around zero-dispersion.

We present a compact nonlinear compression scheme for the generation of millijoule few-cycle pulses beyond 4 µm wavelength. For this purpose 95 fs pulses at 5 µm from a 1 kHz midwave-IR optical parametric chirped pulse amplifier (OPCPA) are spectrally broadened due to a self-phase modulation in ZnSe. The subsequent compression in a bulk material yields 53 fs pulses with 1.9 mJ energy. The compression succeeds efficiently with only slight beam distortions and an energy throughput of 85%, which results in a peak power of 34 GW. The nonlinear refractive index of ZnSe was derived from the nonlinear compression and self-focusing measurements. Furthermore, we explore to which extent multiphoton absorption affects the nonlinear compression regime.

Mapping GENERIC Hydrodynamics into Carter’s Multifluid Theory

We show that the GENERIC model for relativistic heat conduction is a multifluid of Carter; this allows one to compute the multifluid constitutive relations directly from the GENERIC formalism. As a quick application, we prove that in the limit of infinite heat conductivity, GENERIC heat conduction reduces to the relativistic two-fluid model for superfluidity. This surprising “crossover” is a consequence of relativistic causality: if diffusion happens too fast, all the diffusing charge cumulates on the surface of the light cone, and it eventually travels at the speed of light like a wave. Our analysis is non-perturbative and carried out in a fully non-linear regime.

Analysis of the microstructural connectivity and compressive behavior of particle aggregated silica aerogels

AbstractPorous media such as aerogels can exhibit unique properties including low thermal conductivity, low bulk density, and low sound velocity. However, the limited mechanical properties of aerogels restrict their widespread application. This study focuses on understanding the mechanical behavior of aggregated silica aerogels by investigating their microstructural connectivity and densification mechanisms under uniaxial compression. The interparticle connectivity is generated using the diffusion‐limited cluster–cluster aggregation (DLCA) algorithm, and the particle connections are modeled by beam elements that account for contact interaction. The mechanical response of representative volume elements (RVEs) is analyzed in both linear and nonlinear regimes while applying periodic boundary conditions. The model is correlated with experimental compression test data to validate the simulation results. With increasing compressive strain, load transitions between multiple backbone paths appear in the network structure. Thus, the simulation model provides insight into the compression process. Moreover, the simulation model enables the examination of the influence of various model parameters and facilitates the evaluation of the power–law relationship between the elasticity modulus and porosity of aerogels.

Properties of Intense H‐Band Electromagnetic Ion Cyclotron Waves: Implications for Quasi‐Linear, Nonlinear, and Nonresonant Wave‐Particle Interactions

AbstractResonant interactions between relativistic electrons and electromagnetic ion cyclotron (EMIC) waves provide an effective loss mechanism for this important electron population in the outer radiation belt. The diffusive regime of electron scattering and loss has been well incorporated into radiation belt models within the framework of the quasi‐linear diffusion theory, whereas the nonlinear regime has been mostly studied with test particle simulations. There is also a less investigated, nonresonant regime of electron scattering by EMIC waves. All three regimes should be present, depending on the EMIC waves and ambient plasma properties, but the occurrence rates of these regimes have not been previously quantified. This study provides a statistical investigation of the most important EMIC wave‐packet characteristics for the diffusive, nonlinear, and nonresonant regimes of electron scattering. We utilize 3 years of observations to derive distributions of wave amplitudes, wave‐packet sizes, and rates of frequency variations within individual wave‐packets. We demonstrate that EMIC waves typically propagate as wave‐packets with ∼10 wave periods each, and that ∼3–10% of such wave‐packets can reach the regime of nonlinear resonant interaction with 2–6 MeV electrons. We show that EMIC frequency variations within wave‐packets reach 50–100% of the center frequency, corresponding to a significant high‐frequency tail in their wave power spectrum. We explore the consequences of these wave‐packet characteristics for high and low energy electron precipitation by H‐band EMIC waves and for the relative importance of quasi‐linear and nonlinear regimes of wave‐particle interactions.

A new causal and stable theory of viscous chiral hydrodynamics

We construct the general theory of first-order relativistic hydrodynamics for a fluid exhibiting a chiral anomaly, including all possible viscous terms allowed by symmetry. Using standard techniques, we compute the necessary and sufficient conditions for this theory to be relativistically causal in the nonlinear regime and for thermal equilibria to be linearly stable. This is the first theory of first-order chiral hydrodynamics suitable for numerical simulations.

Kerr frequency comb generation in fiber Fabry-Pérot resonator: Technological locks and leveraging fiber properties

We explore fiber Fabry-Pérot (FFP) resonators, a new platform for frequency comb generation We experimentally identified mirror diffraction losses dependent on the effective area of the fiber and simulated them via Fourier optics. In the nonlinear regime, a linear stability analysis of a generalized Lugiato-Lefever equation revealed optimization of reflectivity and detuning, leading to a significant reduction in the required power threshold for comb generation compared to linear regime, and to improved energy frugality. Furthermore, controlled or exploited birefringence in various experimental settings enabled the generation of Kerr frequency combs and stimulated Brillouin lasers. In this communication we propose an overview of the practical characteristics related to the fabrication and use of these resonators.

Scale-dependent interactions enable emergent microrheological stress response of actin-vimentin composites.

The mechanical properties of the mammalian cell regulate many cellular functions and are largely dictated by the cytoskeleton, a composite network of protein filaments, including actin, microtubules, and intermediate filaments. Interactions between these distinct filaments give rise to emergent mechanical properties that are difficult to generate synthetically, and recent studies have made great strides in advancing our understanding of the mechanical interplay between actin and microtubule filaments. While intermediate filaments play critical roles in the stress response of cells, their effect on the rheological properties of the composite cytoskeleton remains poorly understood. Here, we use optical tweezers microrheology to measure the linear viscoelastic properties and nonlinear stress response of composites of actin and vimentin with varying molar ratios of actin to vimentin. We reveal a surprising, nearly opposite effect of actin-vimentin network mechanics compared to single-component networks in the linear versus nonlinear regimes. Namely, the linear elastic plateau modulus and zero-shear viscosity are markedly reduced in composites compared to single-component networks of actin or vimentin, whereas the initial response force and stiffness are maximized in composites versus single-component networks in the nonlinear regime. While these emergent trends are indicative of distinct interactions between actin and vimentin, nonlinear stiffening and long-time stress response appear to both be dictated primarily by actin, at odds with previous bulk rheology studies. We demonstrate that these complex, scale-dependent effects arise from the varied contributions of network density, filament stiffness, non-specific interactions, and poroelasticity to the mechanical response at different spatiotemporal scales. Cells may harness this complex behavior to facilitate distinct stress responses at different scales and in response to different stimuli to allow for their hallmark multifunctionality.

Three-dimensional diffusive-thermal instability of flames propagating in a plane Poiseuille flow

The three-dimensional diffusive-thermal stability of a two-dimensional flame propagating in a Poiseuille flow is examined. The study explores the effect of three non-dimensional parameters, namely the Lewis number Le, the Damköhler number Da, and the flow Peclet number Pe. Wide ranges of the Lewis number and the flow amplitude are covered, as well as conditions corresponding to small-scale narrow (Da≪1) to large-scale wide (Da≫1) channels. The instability experienced by the flame appears as a combination of the traditional diffusive-thermal instability of planar flames and the recently identified instability corresponding to a transition from symmetric to asymmetric flame. The instability regions are identified in the Le-Pe plane for selected values of Da by computing the eigenvalues of a linear stability problem. These are complemented by two- and three-dimensional time-dependent simulations describing the full evolution of unstable flames into the non-linear regime. In narrow channels, flames are found to be always symmetric about the mid-plane of the channel. Additionally, in these situations, shear flow-induced Taylor dispersion enhances the cellular instability in Le<1 mixtures and suppresses the oscillatory instability in Le>1 mixtures. In large-scale channels, however, both the cellular and the oscillatory instabilities are expected to persist. Here, the flame has a stronger propensity to become asymmetric when the mean flow opposes its propagation and when Le<1; if the mean flow facilitates the flame propagation, then the flame is likely to remain symmetric about the channel mid-plane. For Le>1, both symmetric and asymmetric flames are encountered and are accompanied by temporal oscillations.

Beam-profile compensation for quantum yield characterisation of Yb-Tm codoped upconverting nanoparticles emitting at 474 nm, 650 nm and 804 nm.

Upconverting nanoparticles (UCNPs) have found widespread applications in biophotonics and energy harvesting due to their unique non-linear optical properties arising from energy transfer upconversion (ETU) mechanisms. However, accurately characterising the power density-dependent efficiency of UCNPs using the internal quantum yield (iQY) is challenging due to the lack of methods that account for excitation beam-profile distortions. This limitation hinders the engineering of optimal UCNPs for diverse applications. To address this, this work present a novel beam profile compensation strategy based on a general analytical rate-equations model, enabling the evaluation of iQY for ETU processes of arbitrary order, such as ETU2, ETU3, and beyond. The method was applied to characterise the ETU2 and ETU3 processes corresponding to the main emission peaks (474 nm, 650 nm, and 804 nm) of a Yb-Tm codoped core-shell β-UCNP. Through this approach, the transition power density points (which delimit the distinct non-linear regimes of the upconversion luminescence (UCL)), and the saturation iQY values (which are reached at high excitation power densities above the transition points) were determined. The ETU2 process exhibits a single transition power density point, denoted as ρ2, while the ETU3 processes involve two transition points, ρ2 and ρ3. By compensating for the beam profile, we evaluate the iQY of individual lines across a wide dynamic range of excitation power densities (up to 105 W cm-2), encompassing both non-linear and linear regimes of UCL. This study introduces a valuable approach for accurately characterising the iQY of UCNPs, facilitating a deeper understanding of the upconversion and its performance. By addressing excitation beam-profile distortions, this method provides a comprehensive and reliable assessment of the power density-dependent iQY. The results highlight the applicability and effectiveness of this beam profile compensation strategy, which can be employed for a wide range of UCNPs. This advancement opens new avenues for the tailored design and application of UCNPs in various fields, especially for biophotonics.

Theory for nonlinear conductivity switching in semiconducting organic ferroelectrics.

In this work, the ferroelectric and semiconducting properties of the organic semiconducting ferroelectric benzotrithiophene tricarboxamide (BTTTA), and especially their nonlinear coupling, are theoretically investigated. BTTTA is an exponent of a small class of semiconducting organic ferroelectrics for which experiments have established a surprising polarization direction dependence of the bulk conductivity at finite fields. First, molecular dynamics (MD) simulations are used to investigate the occurrence and, under the influence of an external electric field, the inversion of the macroscopic electric dipole that forms along the axis of supramolecular columns of BTTTA. The MD results are consistent with the experimentally observed ferroelectric behavior of the material. Building on the MD results, a QM/MM scheme is used to investigate the charge carrier mobility in the quasi-1D BTTTA stacks in the linear and non-linear regimes. Indeed, at finite electric fields, a clear resistance switching effect was observed in the form of a hole mobility that is a factor ∼2 larger for antiparallel orientations of the polarization and field than for a parallel orientation. This phenomenon can be understood as a microscopic ratchet that is based on the non-equilibrium interaction between the (oriented) dipoles and the (direction of the) charge transport.

Field-dependent THz transport nonlinearities in semiconductor nano structures.

Charge transport nonlinearities in semiconductor quantum dots and nanorods are studied. Using a density matrix formalism, we retrieve the field-dependent nonlinear mobility and show the possibility of intra-pulse gain. We further demonstrate that the dynamics of master equations can be captured in an analytical formula for the field-dependent charge carrier mobility, e.g. for two-level systems. This equation extends the linear response theory based Kubo-Greenwood result to nonlinear processes at elevated field strength, easily reached in THz transport spectroscopy. With these tools we analyze the field strength, chirp, temperature and dephasing dependence of the charge carrier mobility in the model system of CdSe quantum dots and wires. Stark broadening and Rabi splitting result in strong alterations of the mobility spectra, pronounced at low temperatures. The mobility spectra are strongly temperature and pulse shape dependent in the nonlinear regime. The findings are of immediate interest e.g. for nonlinear THz generation, conversion and amplification in 6G technology and nano electronics. Our results further enable experimentalists to fit and understand measured charge transport nonlinearities with analytical expressions and to design nanosystems with engineered material properties.

The fluid dynamics of a viscoelastic fluid dripping onto a substrate.

Extensional flows of complex fluids play an important role in many industrial applications, such as spraying and atomisation, as well as microfluidic-based drop deposition. The dripping-on-substrate (DoS) technique is a conceptually-simple, but dynamically-complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. It incorporates the capillary-driven thinning of a liquid bridge, produced by a single drop as it is slowly dispensed from a syringe pump onto a solid partially-wetting substrate. By following the filament thinning and pinch-off process the extensional viscosity and relaxation time of the sample can be determined. Importantly, DoS allows experimentalists to measure the extensional properties of lower viscosity solutions than is possible with commercially available capillary break-up extensional rheometers. Understanding the fluid mechanics behind the operation of DoS will enable users to optimise and extend the performance of this protocol. To achieve this understanding, we employ a computational rheology approach, using adaptively-refined time-dependent axisymmetric numerical simulations with the open-source Eulerian code, Basilisk. The volume-of-fluid technique is used to capture the moving interface, and the log-conformation transformation enables a stable and accurate solution of the viscoelastic constitutive equation. Here, we focus on understanding the roles of surface tension, elasticity and finite chain extensibility in controlling the elasto-capillary (EC) regime, as well as the perturbative effects that gravity and substrate wettability play in setting the evolution of the self-similar thinning and pinch-off dynamics. To illustrate the interplay of these different forces, we construct a simple one-dimensional model that captures the initial rate of thinning when the dynamics are dominated by a balance between inertia and capillarity. This model also captures the structure of the transition region to the nonlinear EC regime in which the rapidly growing elastic stresses in the thread balance the capillary pressure as the filament thins towards breakup. Finally, we propose a fitting methodology based on the analytical solution for FENE-P fluids to improve the accuracy in determining the effective relaxation time of an unknown fluid.

Instabilities in Models of Supergiants MWC 137 and MWC 314

In several B-type supergiants, photometric and spectroscopic variabilities together with episodes of enhanced mass-loss have been observed. Here we present the preliminary results of a linear stability analysis followed by nonlinear numerical simulations in two B-type supergiants MWC 137 and MWC 314. All the considered models of MWC 137 having mass in the range of 30M⊙ to 70M⊙ are unstable while for the case of MWC 314 models with mass below 31M⊙ are unstable. The instabilities have been followed into the nonlinear regime for selected models of these two supergiants. During the nonlinear numerical simulations, instabilities lead to a finite pulsation amplitude with a well defined saturation level in the considered models of MWC 137 with mass greater than 42M⊙. The model of MWC 314 with mass of 40M⊙ - the suggested mass for the primary star - does not show any instabilities both in linear stability analysis and nonlinear numerical simulations. The velocity amplitude reaches to 107 cm s−1 in the nonlinear regime for the model of MWC 314 with mass of 30M⊙. Further extensive numerical simulations and observations are required to understand the origin of the observed variabilities in these stars.

Nonlinear regimes of spin wave propagation in a waveguide with a one-dimensional hole array

Purpose. Investigation of spin-wave signal passage in a system of magnetic microwaves separated from each other by a one-dimensional array of holes. Using numerical and experimental methods to show controlled spatial-frequency selection of the signal in linear and nonlinear modes of operation. Methods. Micromagnetic modeling of the spatial intensity distributions of spin waves. Obtaining S-parameters of spin waves propagating in a tangentially magnetized structure using a vector circuit analyzer. Results. The spatially selective properties of the structure in linear and nonlinear modes are demonstrated using micromagnetic modeling. A mechanism for controlling the frequency range of the Bragg zone is revealed using a vector analyzer. Conclusion. The proposed structure can be used as a functional element in planar topologies of magnon networks and parallel signal processing devices based on them.