Weak Perturbation Research Articles

Fluorinated graphene nanomaterial causes potential mechanical perturbations to a biomembrane.

Fluorinated graphene (F-GRA) has attracted great interest in biomedical applications. In this context, the direct interaction between F-GRA and various biomolecules is a vital process guiding the bio-function of this nanomaterial. Nevertheless, information regarding the interaction of F-GRA with biomolecules is scarce, particularly at the molecular level. In this study, using an in silico approach, we investigate the adsorption of F-GRA to a phospholipid bilayer to evaluate the potential effect of the nanomaterial to a biomembrane and its mechanism. Our results indicate that F-GRA can either slightly insert into the membrane or parallelly adhere on the membrane surface, different from the complete insertion of graphene. Detailed analysis confirms that the electrostatic forces dominantly mediate the adsorption process. F-GRA in its parallel binding pattern causes a partial enlargement in the membrane thickness via the disruption of the lipids' order parameters, indicating a mild mechanical influence to the membrane structure. Although the potential mechanical perturbation of F-GRA to membrane is detected, this impact is much weaker than graphene. These findings suggest the potentially weak physical perturbations of F-GRA to the cellular membrane, which may establish the basis for the future biomedical applications of this material after proper surface coating.

Enhanced on-chip frequency measurement using weak value amplification.

We present an integrated design to sensitively measure changes in optical frequency using weak value amplification with a multi-mode interferometer. The technique involves introducing a weak perturbation to the system and then post-selecting the data in such a way that the signal is amplified without amplifying the technical noise, as has previously been demonstrated in a free-space setup. We demonstrate the advantages of a Bragg grating with two band gaps for obtaining simultaneous, stable high transmission and high dispersion. The device is more robust and easily scalable than the free-space implementation, and provides amplified sensitivity compared to other methods of measuring changes in optical frequency on a chip, such as an integrated Mach-Zehnder interferometer.

Intrinsic instabilities in premixed hydrogen flames: parametric variation of pressure, equivalence ratio, and temperature. Part 2 – Non‐linear regime and flame speed enhancement

The propensity of lean premixed hydrogen flames to develop intrinsic instabilities is studied by means of a series of simulations at different equivalence ratios [0.4–1.0], unburned temperatures [298 K–700 K], and pressures [1 bar–20 bar]. In addition to the Darrieus-Landau or hydrodynamic instability, lean premixed hydrogen flames are prone to thermodiffusive instabilities, which lead to significant flame front wrinkling and a chaotic process of formation and destruction of cellular structures along the flame front. In part 1 of this work (L.Berger et al., Combust. Flame, 2022), the stability of planar flames that are exposed to weak harmonic perturbations has been studied. In this part, the long-term dynamics of these flames, which become strongly corrugated and show strong flame speed enhancements and variations of the local reaction rates, are studied. In particular, local extinction events and strong peaks of the reaction rates, sub- and super-adiabatic temperatures in the burned gas, and variations of the local flame thickness are observed such that the flame reactivity significantly deviates from an unstretched laminar flamelet. Consistent with the stability analysis in part 1, the impact of instabilities increases if the equivalence ratio or unburned temperature are decreased or the pressure is increased. In particular, the propensity of intrinsic instabilities to increase at high pressure is relevant to several combustion applications operating at elevated pressures. Further, the effect of the global flame parameters such as the expansion ratio, Zeldovich number, and Lewis number on the flame speed enhancement is quantitatively assessed. Finally, the flame speed enhancement due to instabilities is found to correlate well with the maximum growth rates of the perturbed flames that have been measured in part 1 indicating a strong link between the two different flame regimes.

Intrinsic instabilities in premixed hydrogen flames: Parametric variation of pressure, equivalence ratio, and temperature. Part 1 - Dispersion relations in the linear regime

The impact of intrinsic combustion instabilities is studied for lean premixed hydrogen flames by means of a series of simulations at different equivalence ratios [0.4-1.0], unburned temperatures [298K-700K], and pressures [1bar-20bar]. In addition to the Darrieus-Landau, or hydrodynamic, instability, lean premixed hydrogen flames are prone to thermodiffusive instabilities, which lead to significant flame front wrinkling and a chaotic process of formation and destruction of cellular structures along the flame front. Theoretical models are not yet capable of accurately describing the evolution of such flames, so the propensity of lean hydrogen flames to develop instabilities is studied numerically in a parametric variation in this work. A stability analysis is conducted, in which planar flames are initially exposed to weak harmonic perturbations and the response of the flame is studied. In the initial phase referred to as linear phase, a growth or decrease of the initially imposed perturbation amplitude is observed, while for long times, chaotic cellular structures are formed along the flame front, which are studied in part 2 of this work (L.Berger et al., Combust. Flame, 2022). The growth rates of the perturbation amplitude that are obtained from the initial phase are a measure of the strength of the intrinsic instability mechanisms and vary with respect to the wave number of the harmonic perturbation yielding characteristic dispersion relations. A decrease of equivalence ratio and unburned temperature and an increase of pressure are found to enhance the growth rates and hence intrinsic instabilities. The variation of dispersion relations is analyzed with respect to variations of the expansion ratio, the effective Lewis number of the mixture, and the Zeldovich number. For the lean hydrogen flames, with increasing pressure a decrease of the cut-off wave number, which represents the change of the sign of the dispersion relation at high wave numbers, is observed. This is the opposite trend compared to flames that are not affected by thermodiffusive instabilities. Further, numerical growth rates are compared to theoretical models. The results show that lean hydrogen flames are prone to develop instabilities at conditions that are relevant to several combustion devices such as gas turbines that operate at lean equivalence ratios, elevated pressures and temperatures or domestic and industrial heaters that operate at low temperatures and ambient pressure.

Robust separation of topological in-plane and out-of-plane waves in a phononic crystal

Valley degree of freedom, associated with the valley topological phase, has propelled the advancement of the elastic waveguide by offering immunity to backscattering against bending and weak perturbations. Despite many attempts to manipulate the wave path and working frequency of the waveguide, internal characteristic of an elastic wave such as rich polarization has not yet been utilized with valley topological phases. Here, we introduce the rich polarization into the valley degree of freedom, to achieve topologically protected in-plane and out-of-plane mode separation of an elastic wave. Accidental degeneracy proves its real worth of decoupling the in-plane and out-of-plane polarized valley Hall phases. We further demonstrate independent and simultaneous control of in-plane and out-of-plane waves, with intact topological protection. The presenting procedure for designing the topologically protected wave separation based on accidental degeneracy will widen the valley topological physics in view of both generation mechanism and application areas.

Advances in phase-sensitive optical time-domain reflectometry

Phase-sensitive optical time-domain reflectometry (Φ-OTDR) has attracted numerous attention due to its superior performance in detecting the weak perturbations along the fiber. Relying on the ultra-sensitivity of light phase to the tiny deformation of optical fiber, Φ-OTDR has been treated as a powerful technique with a wide range of applications. It is fundamental to extract the phase of scattering light wave accurately and the methods include coherent detection, I/Q demodulation, 3 by 3 coupler, dual probe pulses, and so on. Meanwhile, researchers have also made great efforts to improve the performance of Φ-OTDR. The frequency response range, the measurement accuracy, the sensing distance, the spatial resolution, and the accuracy of event discrimination, all have been enhanced by various techniques. Furthermore, lots of researches on the applications in various kinds of fields have been carried out, where certain modifications and techniques have been developed. Therefore, Φ-OTDR remains as a booming technique in both researches and applications.

Dispersed Pixel Perturbation-Based Imperceptible Backdoor Trigger for Image Classifier Models

Typical deep neural network (DNN) backdoor attacks are based on triggers embedded in inputs. Existing imperceptible triggers are computationally expensive or low in attack success. In this paper, we propose a new backdoor trigger, which is easy to generate, imperceptible, and highly effective. The new trigger is a uniformly randomly generated three-dimensional (3D) binary pattern that can be horizontally and/or vertically repeated and mirrored and superposed onto three-channel images for training a backdoored DNN model. Dispersed throughout an image, the new trigger produces weak perturbation to individual pixels, but collectively holds a strong recognizable pattern to train and activate the backdoor of the DNN. We also analytically reveal that the trigger is increasingly effective with the improving resolution of the images. Experiments are conducted using the ResNet-18 and MLP models on the MNIST, CIFAR-10, and BTSR datasets. In terms of imperceptibility, the new trigger outperforms existing triggers, such as BadNets, Trojaned NN, and Hidden Backdoor, by over an order of magnitude. The new trigger achieves an almost 100% attack success rate, only reduces the classification accuracy by less than 0.7%–2.4%, and invalidates the state-of-the-art defense techniques.

CONTROLLABILITY OF FREDHOLM’S INTEGRO-DIFFERENTIAL EQUATIONS WITH BY A DEGENERATE KERNEL IN HILBERT SPACES

The work examines integro-differential equations Fredholm with a degenerate kernel with Hilbert control spaces. The need to study these equations is related to numerous ones applications of integro- differential equations in mathematics, physics, technology, economy and other fields. Complexity the study of integro-differential equations is connected with the fact that the integral-differential operator is not solvable everywhere. There are different approaches to the solution of not everywhere solvable linear operator equations: weak perturbation of the right-hand side of this equation with further application of the Vishyk-Lyusternyk method, introduction to system of impulse action, control, etc. The problem of obtaining coefficient conditions of solvability and analytical presentation of general solutions of integro-differential equations is a rather difficult problem, so frequent solutions will suffice are obtained by numerical methods. In this connection, Fredholm’s integro-differential equations with degenerate kernel and control in Hilbert spaces no were investigated. Therefore, the task of establishing conditions is urgent controllability, construction of general solutions in an analytical form and corresponding general controls of integro-differential equations with a degenerate kernel in abstract Hilbert spaces. As an intermediate result in the work using the results of pseudoinversion of integral operators in Hilbert spaces the solvability criterion and the form of general solutions are established integro-differential equations without control in the abstract Hilbert spaces. To establish the controllability criterion is not solvable everywhere integro-differential equations with Hilbert control spaces, the general theory of research is not applied everywhere solvable operator equations. At the same time, they are used significantly orthoprojectors, pseudo-inverse operators to normally solvable ones operators in Hilbert spaces. With the use of orthoprojectors, pseudo-inverse operators and pseudoinversion of integraloperators, a criterion is obtained solutions and the general form of solutions of integro-differential equations with a degenerate kernel with control y Hilbert spaces. An image of the general appearance is obtained control under which these solutions exist.

Phase discontinuities induced scintillation enhancement: coherent vortex beams propagating through weak oceanic turbulence

Under the impact of an infinitely extended edge phase dislocation, optical vortices (screw phase dislocations) with tight spacing induce scintillation enhancement. As the simplest case, the scintillation index of an interfering beam consisting of two Gaussian vortex beams with topological charges through weak oceanic turbulence is researched via derivation and phase screen simulation to present this phenomenon. Different combinations of two types of phase discontinuities can be obtained by changing the overlapping degree and the phase difference of two coherent Gaussian vortex beams. The scintillation indexes for them verify that the formation condition of the phenomenon is the coexistence of two types of phase discontinuities. And the enhanced scintillation index can be several orders of magnitude larger than that of a plane wave under weak perturbation (Rytov variance). This phenomenon could be useful for both optical vortex detection and perturbation measurement.

STRANGE NONCHAOTIC ATTRACTORS IN A PERIODICALLY FORCED PIECEWISE LINEAR SYSTEM WITH NOISE

The study of strange nonchaotic attractors (SNAs) has been mainly restricted to quasiperiodically forced systems. At present, SNAs have also been uncovered in several periodically forced smooth systems with noise. In this work, we consider a periodically forced nonsmooth system and find that SNAs are created by a small amount of noise. SNAs can be generated in different periodic windows with weak noise perturbation. If the parameter is varied further from the chaotic range, a larger noise intensity is required to induce SNAs. Besides, noise-induced SNAs can be generated by the periodic attractors near the boundary crisis. In addition, with the increasing noise intensity, the intermittency between SNAs and periodic attractors can be induced by transient chaos. The characteristics of SNAs are analyzed by the Lyapunov exponent, power spectrum, singular continuous spectrum, spectral distribution functions, and finite time Lyapunov exponent.

Single-shot measurement of few-cycle optical waveforms on a chip

The measurement of transient optical fields has proven critical to understanding the dynamical mechanisms underlying ultrafast physical and chemical phenomena, and is key to realizing higher speeds in electronics and telecommunications. Complete characterization of optical waveforms, however, requires an optical oscilloscope capable of resolving the electric field oscillations with sub-femtosecond resolution and with single-shot operation. Here, we show that strong-field nonlinear excitation of photocurrents in a silicon-based image sensor chip can provide the sub-cycle optical gate necessary to characterize carrier-envelope phase-stable optical waveforms in the mid-infrared. By mapping the temporal delay between an intense excitation and weak perturbing pulse onto a transverse spatial coordinate of the image sensor, we show that the technique allows single-shot measurement of few-cycle waveforms.

Controlling Infectious Diseases: The Decisive Phase Effect on a Seasonal Vaccination Strategy

The study of epidemiological systems has generated deep interest in exploring the dynamical complexity of common infectious diseases driven by seasonally varying contact rates. Mathematical modeling and field observations have shown that, under seasonal variation, the incidence rates of some endemic infectious diseases fluctuate dramatically and the dynamics is often characterized by chaotic oscillations in the absence of specific vaccination programs. In fact, the existence of chaotic behavior has been precisely stated in the literature as a noticeable feature in the dynamics of the classical Susceptible-Infected-Recovered (SIR) seasonally forced epidemic model. However, in the context of epidemiology, chaos is often regarded as an undesirable phenomenon associated with the unpredictability of infectious diseases. As a consequence, the problem of converting chaotic motions into regular motions becomes particularly relevant. In this article, we consider the so-called phase control method applied to the seasonally forced SIR epidemic model to suppress chaos. Interestingly, this method of controlling chaos has a clear meaning as a weak perturbation on a seasonal vaccination strategy. Numerical simulations show that the phase difference between the two periodic forces — contact rate and vaccination — plays a very important role in controlling chaos.

Confinement and renormalization group equations in string-inspired nonlocal gauge theories

As an extension of weak perturbation theory obtained in a recent analysis of infinite-derivative nonlocal non-Abelian gauge theories motivated from $p$-adic string field theory, and postulated as a direction of UV completion in four-dimensional quantum field theory, here we investigate the confinement conditions and $\ensuremath{\beta}$ function in the strong coupling regime. We extend the confinement criterion, previously obtained by Kugo and Ojima for the local theory based on the Becchi-Rouet-Stora-Tyutin invariance, to the nonlocal theory by using a set of exact solutions of the corresponding local theory. We show that the infinite derivatives which are active in the UV provide finite contributions also in the infrared limit and provide a proof of confinement, granted by the absence of the Landau pole. We also show that in the limit of the energy scale of nonlocality $M\ensuremath{\rightarrow}\ensuremath{\infty}$ we reproduce the local theory results and see how asymptotic freedom is properly recovered.

Compact Thermal Imager (CTI) for Atmospheric Remote Sensing

The demonstration of a newly developed compact thermal imager (CTI) on the International Space Station (ISS) has provided not only a technology advancement but a rich high-resolution dataset on global clouds, atmospheric and land emissions. This study showed that the free-running CTI instrument could be calibrated to produce scientifically useful radiance imagery of the atmosphere, clouds, and surfaces with a vertical resolution of ~460 m at limb and a horizontal resolution of ~80 m at nadir. The new detector demonstrated an excellent sensitivity to detect the weak limb radiance perturbations modulated by small-scale atmospheric gravity waves. The CTI’s high-resolution imaging was used to infer vertical cloud temperature profiles from a side-viewing geometry. For nadir imaging, the combined high-resolution and high-sensitivity capabilities allowed the CTI to better separate cloud and surface emissions, including those in the planetary boundary layer (PBL) that had small contrast against the background surface. Finally, based on the ISS’s orbit, the stable detector performance and robust calibration algorithm produced valuable diurnal observations of cloud and surface emissions with respect to solar local time during May–October 2019, when the CTI had nearly continuous operation.

Generic mechanism for remote triggering of earthquakes.

"Remote triggering" refers to the inducement of earthquakes by weak perturbations that emanate from faraway sources, typically intense earthquakes that happen at much larger distances than their nearby aftershocks, sometimes even around the globe. Here, we propose a mechanism for this phenomenon; the proposed mechanism is generic, resulting from the breaking of Hamiltonian symmetry due to the existence of friction. We allow a transition from static to dynamic friction. Linearly stable stressed systems display giant sensitivity to small perturbations of arbitrary frequency (without a need for resonance), which trigger an instability with exponential oscillatory growth. Once nonlinear effects kick in, the blow up in mean-square displacements can reach 15-20 orders of magnitude. Analytic and numerical results of the proposed model are presented and discussed.

Waves in a coherent two-dimensional flow

A condensate in two-dimensional turbulence confined to a finite domain was predicted by Kraichnan. The most common spatial form of the condensate is a coherent vortex of radius comparable with the domain size, which is statistically steady over times much longer than its turnover time. The vortices were successively studied during the last four decades, and their time-averaged properties were recently and extensively considered in theory and measured in experiments. Here, we consider weak perturbations of the coherent flow in the vortices. Our interest lies in slow perturbations, which implies that they are homogeneous along the streamlines of the coherent flow. We show that such kind of perturbations can be considered as waves of condensate propagating in the radial direction with some dispersion law. In the present work, the dispersion law and the propagation length of the waves are found as a function of the radial position inside a vortex flow. Cases of condensate saturated due to bottom friction and of viscous condensate are different. In the first case, there are waves with low damping. In the second case, all waves are of a similar kind as the shear waves in an unsteady laminar boundary layer.

Light-ray moments as endpoint contributions to modular Hamiltonians

We consider excited states in a CFT, obtained by applying a weak unitary perturbation to the vacuum. The perturbation is generated by the integral of a local operator J(n) of modular weight n over a spacelike surface passing through x = 0. For |n| ≥ 2 the modular Hamiltonian associated with a division of space at x = 0 picks up an endpoint contribution, sensitive to the details of the perturbation (including the shape of the spacelike surface) at x = 0. The endpoint contribution is a sum of light-ray moments of the perturbing operator J(n) and its descendants. For perturbations on null planes only moments of J(n) itself contribute.

Final state sensitivity in noisy chaotic scattering

The unpredictability in chaotic scattering problems is a fundamental topic in physics that has been studied either in purely conservative systems or in the presence of weak perturbations. In many systems noise plays an important role in the dynamical behavior and it models their internal irregularities or their coupling with the environment. In these situations the unpredictability is affected by both the chaotic dynamics and the stochastic fluctuations. In the presence of noise two trajectories with the same initial condition can evolve in different ways and converge to a different asymptotic behavior. For this reason, even the exact knowledge of the initial conditions does not necessarily lead to the predictability of the final state of the system. Hence, the noise can be considered as an important source of unpredictability that cannot be fully understood using the conventional methods of nonlinear dynamics, such as the exit basins and the uncertainty exponent. By adopting a probabilistic point of view, we develop the concepts of probability basin, uncertainty basin and noise-sensitivity exponent, that allow us to carry out both a quantitative and qualitative analysis of the unpredictability on noisy chaotic scattering problems.

Multiple quantum scar states and emergent slow thermalization in a flat-band system

Quantum many-body scars (QMBS) appear in a flat-band model with interactions on the saw-tooth lattice. The flat-band model includes a compact support localized eigenstates, called compact localized state (CLS). Some characteristic many-body states can be constructed from the CLSs at a low-filling on the flat-band. These many-body states are degenerate. Starting with such degenerate states we concretely show how to construct multiple QMBSs with different eigenenergies embedded in the entire spectrum. If the degeneracy is lifted by introducing hopping modulation or weak perturbations, these states lifted by these ways can be viewed as multiple QMBSs. In this work, we focus on the study of the perturbation-induced QMBS. Perturbed states, which are connected to the exact QMBSs in the unperturbed limit, indicate common properties of conventional QMBS systems, that is, a subspace with sub-volume or area law scaling entanglement entropy, which indicates the violation of the strong eigenstate thermalization hypothesis (ETH). Also for a specific initial state, slow-thermalization dynamics appears. We numerically demonstrate these subjects. The flat-band model with interactions is a characteristic example in non-integrable systems with the violation of the strong ETH and the QMBS.

Effect of chaos on the simulation of quantum critical phenomena in analog quantum simulators

We study how chaos, introduced by a weak perturbation, affects the reliability of the output of analog quantum simulation. As a toy model, we consider the Lipkin-Meshkov-Glick model. Inspired by the semiclassical behavior of the order parameter in the thermodynamic limit, we propose a protocol to measure the quantum phase transition in the ground state and the dynamical quantum phase transition associated with quench dynamics. We show that the presence of a small time-dependent perturbation can render the dynamics of the system chaotic. We then show that the estimates of the critical points of these quantum phase transitions, obtained from the quantum simulation of its dynamics, are robust to the presence of this chaotic perturbation, while other aspects of the system, such as the mean magnetization, are fragile and therefore cannot be reliably extracted from this simulator. This can be understood in terms of the simulated quantities that depend on the global structure of phase space vs those that depend on local trajectories.