Amplitude Regime Research Articles

Dilatational rheological studies on the surface micelles of Poly(styrene)-[formula omitted]-Poly(4-vinyl pyridine) block copolymer at the air-water interface

A thin film of an amphiphilic block copolymer, poly(styrene)-b-poly(4-vinyl pyridine), is investigated at the air–water interface. The surface pressure - area per molecule isotherm and the static compressional modulus provide evidence of two phases, assigned as L1 and L2, respectively. The surface topography and the phase images of these phases obtained using atomic force microscope reveal the presence of surface micelles of different sizes and densities. The dilatational rheology of these phases was investigated using the oscillatory barrier method for different strain amplitudes (1−5%) and qualitatively assessed using Lissajous–Bowditch curves. It points out the emergence of nonlinearity (asymmetric shape and distorted ellipse) with an increase in strain amplitude. Using a fast Fourier transform, the amplitudes and the phases of different harmonics of the stress–strain curves were extracted, and the total harmonic distortion was determined. In contrast to L1 phase, the total harmonic distortion for the L2 phase increases monotonically with strain amplitude. Fixing the strain amplitude at 1% (small amplitude regime), the temperature as well as frequency dependence studies of the dilatational moduli were carried out. The dynamic storage moduli of the L1 phase is found to be insensitive to temperature while it decreases for the L2 phase suggesting softening. Further, evidence for solid-like viscoelastic response emerges (explained using the Kelvin–Voigt model) for the L1 phase, whereas the L2 phase show a cross-over behaviour.

Rydberg-atom-based radio-frequency sensors: amplitude-regime sensing.

Rydberg atom-based radio frequency electromagnetic field sensors are drawing wide-spread interest because of their unique properties, such as small size, dielectric construction, and self-calibration. These photonic sensors use lasers to prepare atoms and read out the atomic response to a radio frequency electromagnetic field based on electromagnetically induced transparency, or related phenomena. Much of the theoretical work has focused on the Autler-Townes splitting induced by the radio frequency wave. The amplitude regime, where the change in transmission observed on resonance is measured to determine electric field strength, has received less attention. In this paper, we deliver analytic expressions that are useful for calculating the absorption coefficient in the amplitude regime. Our main goal is to describe the analytic expressions for the absorption coefficient and demonstrate their validity over a large range of the interesting parameter space. The effect of the thermal motion of the atoms is explicitly addressed. The analytic formulas for the absorption coefficient for different types of Doppler broadening are compared to estimate the sensitivity under conditions where it is limited by the laser shot noise. Residual Doppler shifts are shown to limit sensitivity. The expressions, approximations and descriptions presented in the paper are important for understanding the absorption of Rydberg atom-based sensors in the amplitude regime. This provides insight into the physics of multi-level interference phenomena.

Elastic overtaking collisions of large-amplitude ion-acoustic solitons

Overtaking collisions of large-amplitude solitons are investigated via fluid simulations for a plasma consisting of cold ions and Boltzmann-distributed electrons. To achieve this, a new fluid simulation code is presented. In addition, a novel approach to construct soliton initial conditions is developed. Using these ideas, initial conditions are combined that allows the simulation of overtaking collisions. It is shown that, in the small-amplitude regime, simulation results agree well with the two-soliton solution obtained from reductive perturbation theory. Interestingly, in the large amplitude regime, both the slow and fast solitons re-emerge after the collision with no significant change, showing that the collisions remain elastic. A comparison between reductive perturbation analysis and the simulations show that the only significant effect of higher order nonlinearities on overtaking collisions is a reduction in the magnitude of the phase shifts of both solitons.

Comprehensive 7 T CEST: A clinical MRI protocol covering multiple exchange rate regimes.

Chemical exchange saturation transfer (CEST) is a magnetic resonance (MR) imaging method providing molecular image contrasts based on indirect detection of low concentrated solutes. Previous CEST studies focused predominantly on the imaging of single CEST exchange regimes (e.g., slow, intermediate or fast exchanging groups). In this work, we aim to establish a so-called comprehensive CEST protocol for 7 T, covering the different exchange regimes by three saturation B1 amplitude regimes: low, intermediate and high. We used the results of previous publications and our own simulations in pulseq-CEST to produce a 7 T CEST protocol that has sensitivity to these three B1 regimes. With postprocessing optimization (simultaneous mapping of water shift and B1, B0-fitting, multiple interleaved mode saturation B1 correction, neural network employment (deepCEST) and analytical input feature reduction), we are able to shorten our initially 40 min protocol to 15 min and generate six CEST contrast maps simultaneously. With this protocol, we measured four healthy subjects and one patient with a brain tumor. We established a comprehensive CEST protocol for clinical 7 T MRI, covering three different B1 amplitude regimes. We were able to reduce the acquisition time significantly by more than 50%, while still maintaining decent image quality and contrast in healthy subjects and one patient with a tumor. Our protocol paves the way to perform comprehensive CEST studies in clinical scan times for hypothesis generation regarding molecular properties of certain pathologies, for example, ischemic stroke or high-grade brain tumours.

The effect of structural damping on flow-induced vibration of a thin elliptical cylinder

This study experimentally investigates the influence of structural damping on the transverse flow-induced vibration (FIV) of an elastically mounted thin elliptical cylinder. The cylinder tested has an elliptical ratio of $\varepsilon = b/a = 5$ , where $a$ and $b$ are the streamwise and cross-flow dimensions, respectively, and a mass ratio (i.e. the total oscillating mass/the displaced fluid mass) of $17.4$ . The FIV response was characterised over a reduced velocity range of $2.30 \leq U^* = U/(\,{{f_{{nw}}}} b) \leq 10.00$ (corresponding to a Reynolds number range of $300 \leq \textit {Re} =(U b)/\nu \leq 1300$ ) and a structural damping ratio range of $3.62\times 10^{-3}\leq \zeta \leq 1.87\times 10^{-1}$ . Here, $U$ is the free stream velocity, ${{f_{{nw}}}}$ is the natural frequency of the system in quiescent fluid (water) and $\nu$ is the kinematic viscosity of the fluid. The FIV response was characterised by four wake–body synchronisation regimes (defined as the matching of the dominant fluid forcing and oscillation frequencies, and labelled regime I, regime II, regime III and the hyper branch) and a desynchronisation region, with the hyper branch representing a high amplitude regime not observed for a circular cylinder. Interestingly, the major vortex shedding mode was predominately two single opposite-signed vortices shed per body vibration cycle. Moreover, hydrogen-bubble-based flow visualisations revealed a secondary vortex street forming in the elongated shear layers associated with largest-scale vibration amplitudes ( $A^* = A/b$ up to $7.7$ ) in the hyper branch and regime II. As the structural damping ratio was increased beyond $1.92 \times 10^{-2}$ , the hyper branch was found to be suppressed. The results have potential ramifications for the efficient extraction of energy from free-flowing water sources, which has become increasingly topical over the last decade.

Multiple Fano Resonances in Dynamic Resonant Tunneling Processes

The existence of Fano resonances in dynamic resonant tunneling (RT) systems has been investigated. Fano resonances are characterized by the appearance of a 100% reflection coefficient in proximity to a high transmission coefficient. For a Fano resonance to appear, a bound state must exist. On the other hand, a resonant tunneling process is characterized by a high transmission and the existence of a quasi-bound state (QBS) instead of a bound one. It has been shown that, by narrowing the width of the barrier, the resonance energy of the QBS gradually decreases and eventually turns into a bound state. Consequently, in a dynamic RT process, there are two scenarios: either a bound state exists, in which case, Fano resonances exist for any barrier width, or a QBS exists, and the barrier should be narrow enough for the Fano resonance to appear. In both cases, the incoming particle’s frequency must be lower than the oscillating well’s frequency. In this work, these resonances are investigated in detail, and both exactly numerically and approximated analytical expressions are derived for both the weak and strong oscillating amplitude regimes. One of the conclusions is that, when the oscillating frequency is low enough, multiple Fano resonances can appear by varying the barrier’s width. Since these resonances are very sharp and zero transmission can easily be detected, this property can be used as a very accurate method for measuring the barrier’s width, even when the particle’s de-Broglie wavelength is much larger than the barrier’s width.

Automatized offline and online exploration to achieve a target dynamics in biohybrid neural circuits built with living and model neurons

Biohybrid circuits of interacting living and model neurons are an advantageous means to study neural dynamics and to assess the role of specific neuron and network properties in the nervous system. Hybrid networks are also a necessary step to build effective artificial intelligence and brain hybridization. In this work, we deal with the automatized online and offline adaptation, exploration and parameter mapping to achieve a target dynamics in hybrid circuits and, in particular, those that yield dynamical invariants between living and model neurons. We address dynamical invariants that form robust cycle-by-cycle relationships between the intervals that build neural sequences from such interaction. Our methodology first attains automated adaptation of model neurons to work in the same amplitude regime and time scale of living neurons. Then, we address the automatized exploration and mapping of the synapse parameter space that lead to a specific dynamical invariant target. Our approach uses multiple configurations and parallel computing from electrophysiological recordings of living neurons to build full mappings, and genetic algorithms to achieve an instance of the target dynamics for the hybrid circuit in a short time. We illustrate and validate such strategy in the context of the study of functional sequences in neural rhythms, which can be easily generalized for any variety of hybrid circuit configuration. This approach facilitates both the building of hybrid circuits and the accomplishment of their scientific goal.

KdV breathers on a cnoidal wave background

Using the Darboux transformation for the Korteweg–de Vries equation, we construct and analyze exact solutions describing the interaction of a solitary wave and a traveling cnoidal wave. Due to their unsteady, wavepacket-like character, these wave patterns are referred to as breathers. Both elevation (bright) and depression (dark) breather solutions are obtained. The nonlinear dispersion relations demonstrate that the bright (dark) breathers propagate faster (slower) than the background cnoidal wave. Two-soliton solutions are obtained in the limit of degeneration of the cnoidal wave. In the small amplitude regime, the dark breathers are accurately approximated by dark soliton solutions of the nonlinear Schrödinger equation. These results provide insight into recent experiments on soliton-dispersive shock wave interactions and soliton gases.

Prethermal Fragmentation in a Periodically Driven Fermionic Chain.

We study a fermionic chain with nearest-neighbor hopping and density-density interactions, where the nearest-neighbor interaction term is driven periodically. We show that such a driven chain exhibits prethermal strong Hilbert space fragmentation (HSF) in the high drive amplitude regime at specific drive frequencies ω_{m}^{*}. This constitutes the first realization of HSF for out-of-equilibrium systems. We obtain analytic expressions of ω_{m}^{*} using a Floquet perturbation theory and provide exact numerical computation of entanglement entropy, equal-time correlation functions, and the density autocorrelation of fermions for finite chains. All of these quantities indicate clear signatures of strong HSF. We study the fate of the HSF as one tunes away from ω_{m}^{*} and discuss the extent of the prethermal regime as a function of the drive amplitude.

Non-linear behavior of the transfer impedance of a Micro-Slit-Plate: effect of slit length in presence of a bias flow

The influence of the slit length and interactions between slits in a micro-slit plate (MSP) are investigated in the high amplitude regime. MSPs are plates with arrays of slit-shaped perforations, with width of the order of the acoustic viscous boundary layer thickness. The geometry discussed in this work is typical for fabrication by cutting and bending the plate, without removing material. Micro-slit plates designed with optimal acoustic properties in the linear regime will not be optimal when non-linear effects become significant resulting in vortex shedding. Impedance tube measurements of the transfer impedance on accurately manufactured micro-slit plates are compared to prediction by 2D incompressible Navier-Stokes model and to a quasi-steady theory. At moderately high amplitudes, the vortices remain close to the edges of the slit. The impedance of the plate is predicted within 20% by the model of a single isolated slit. At higher amplitudes, the vortices are traveling far away from the slit and a complex behavior. In this region, three-dimensional effects become important. For very high amplitudes, the vortices shed at neighboring slits start to interact, which affects the impedance.

Stability of exact solutions of the (2 + 1)-dimensional nonlinear Schrödinger equation with arbitrary nonlinearity parameter κ

In this work, we consider the nonlinear Schrödinger equation (NLSE) in 2+1 dimensions with arbitrary nonlinearity exponent κ in the presence of an external confining potential. Exact solutions to the system are constructed, and their stability as we increase the ‘mass’ (i.e., the L 2 norm) and the nonlinearity parameter κ is explored. We observe both theoretically and numerically that the presence of the confining potential leads to wider domains of stability over the parameter space compared to the unconfined case. Our analysis suggests the existence of a stable regime of solutions for all κ as long as their mass is less than a critical value M*(κ). Furthermore, we find that there are two different critical masses, one corresponding to width perturbations and the other one to translational perturbations. The results of Derrick’s theorem are also obtained by studying the small amplitude regime of a four-parameter collective coordinate (4CC) approximation. A numerical stability analysis of the NLSE shows that the instability curve M*(κ) versus κ lies below the two curves found by Derrick’s theorem and the 4CC approximation. In the absence of the external potential, κ = 1 demarcates the separation between the blowup regime and the stable regime. In this 4CC approximation, for κ < 1, when the mass is above the critical mass for the translational instability, quite complicated motions of the collective coordinates are possible. Energy conservation prevents the blowup of the solution as well as confines the center of the solution to a finite spatial domain. We call this regime the ‘frustrated’ blowup regime and give some illustrations. In an appendix, we show how to extend these results to arbitrary initial ground state solution data and arbitrary spatial dimension d.

Geometric imaginary and quasi-probability functions of multi-component Schrödinger cat state

Superposition is one of unusual features in quantum mechanics. This paper investigates the properties of multi-component Schrödinger cat state, generated by amplitude dispersion. The geometrical imaginary of the multi-component Schrödinger cat state is studied, and the entropy of the geometrical imaginary is proposed. This entropy is inverse proportional to the amplitude of the initial coherent state in the large amplitude regime. Additionally, the superposition of the multi-component cat state can be vividly displayed by the Wigner function and the Pegg–Barnett phase operator.

Bond performance of GFRP bars embedded in steel‐PVA hybrid fiber concrete subjected to repeated loading

AbstractThe bond performance of glass fiber‐reinforced polymer (GFRP) bars embedded in steel fiber–PVA hybrid fiber concrete plays an important role in their integration. In the present work, hybrid fiber concrete in different volume ratios of hybrid fibers with GFRP was investigated. Pullout tests with two amplitude regimes were conducted on hybrid fiber concrete specimens integrated with GFRP bars to investigate its ultimate bond strength, bond–slip curve, energy dissipation characteristics, and bond stiffness. The results indicate that when the total fiber volume ratio was fixed at 0.9%, the bond strength between the GFRP bars and hybrid fiber concrete increased gradually as the steel fiber volume increased, and the energy consumption increased gradually during the pullout. The slip corresponding to the ultimate bond strength under variable‐amplitude repeated loading is in good agreement with the experimental results under monotonic loading. The specimen P1S8 (0.1% PVA, 0.8% steel fiber) hybrid exhibited sufficient energy dissipation capacity and deformation capacity under repeated loads, and the bond stiffness is relatively higher and more stable during the loading and unloading stages.

Complex critical points and curved geometries in four-dimensional Lorentzian spinfoam quantum gravity

This paper focuses on the semiclassical behavior of the spinfoam quantum gravity in four dimensions. There has been long-standing confusion, known as the flatness problem, about whether the curved geometry exists in the semiclassical regime of the spinfoam amplitude. The confusion is resolved by the present work. By numerical computations, we explicitly find curved Regge geometries that contribute dominantly to the large-$j$ Lorentzian Engle-Pereira-Rovelli-Livine (EPRL) spinfoam amplitudes on triangulations. These curved geometries are with small deficit angles and relate to the complex critical points of the amplitude. The dominant contribution from the curved geometry to the spinfoam amplitude is proportional to ${e}^{i\mathcal{I}}$, where $\mathcal{I}$ is the Regge action of the geometry plus corrections of higher order in curvature. As a result, in the semiclassical regime, the spinfoam amplitude reduces to an integral over Regge geometries weighted by ${e}^{i\mathcal{I}}$, where $\mathcal{I}$ is the Regge action plus corrections of higher order in curvature. As a by-product, our result also provides a mechanism to relax the cosine problem in the spinfoam model. Our results provide important evidence supporting the semiclassical consistency of the spinfoam quantum gravity.

Room-temperature cost-effective in-situ grown MAPbBr3 crystals and their characterization towards optoelectronic devices

We report the in-situ, room-temperature synthesis of methylammonium lead bromide CH3NH3PbBr3 crystals using N-methyl formamide as a source of methylammonium (MA+) ions during the crystallization process to explore the structural, dielectric, and electronic properties of CH3NH3PbBr3 crystals for optoelectronic applications. Optical absorption and radio-luminescence measurements affirm the direct bandgap nature of the crystals. Impedance spectroscopy measurements with various applied AC voltages within the 20 Hz–10 MHz frequency range depict the influence of ionic motions on electrical transport across crystal planes. We have extracted electrical transport parameters in CH3NH3PbBr3 crystals from the Nyquist plots, which we found to be distinctly varied wherein two different AC voltage amplitude regimes, broadly for 10–50 mV and 100–500 mV AC voltage range.

Hinge-mode dynamics of periodically driven higher-order Weyl semimetals

We study the stroboscopic dynamics of hinge modes of a second-order topological material modeled by a tight-binding free fermion Hamiltonian on a cubic lattice in the intermediate drive frequency regime for both discrete (square pulse) and continuous (cosine) periodic drive protocols. We analyze the Floquet phases of this system and show that its quasienergy spectrum becomes almost gapless in the large drive amplitude regime at special drive frequencies. Away from these frequencies, the gapped quasienergy spectrum supports weakly dispersing Floquet hinge modes. Near them, these hinge modes penetrate into the bulk and eventually become indistinguishable from the bulk modes. We provide an analytic, albeit perturbative, expression for the Floquet Hamiltonian using Floquet perturbation theory (FPT) which explains this phenomenon and leads to analytic expressions of these special frequencies. We also show that in the large drive amplitude regime, the zero energy hinge modes corresponding to the static tight-binding Hamiltonian display qualitatively different dynamics at these special frequencies. We discuss possible local density of state measurement using a scanning tunneling microscope which can test our theory.

The influence of hydrogen on the low cycle fatigue behavior of strain-hardened 316L stainless steel

The present study focuses on the low cycle fatigue (LCF) behavior of strain-hardened 316L stainless steel under plastic strain control, aiming to understand the influence of internal hydrogen on fatigue performance and cyclic deformation behavior for energy-related technologies. The strain-hardened 316L specimens tested at plastic strain amplitudes between 0.1% and 0.7% with and without hydrogen displayed continuous cyclic softening. Internal hydrogen increased the cyclic strength of this steel, with a greater difference in strength at low plastic strain amplitudes. A Bauschinger analysis revealed that effective stresses represented the major contribution to the flow stress for all material conditions and amplitudes. At low plastic strain amplitudes, effective stresses were responsible for differences in cyclic strength between hydrogen precharged and non-charged specimens. In contrast, back stresses became more significant at high amplitudes, and more similar deformation structures were observed. Although internal hydrogen reduced the total LCF lifetime at all amplitudes, this degradation was more significant in the low amplitude regime. This result is attributed to high effective stresses that led to the onset of multiple slip at lower cumulative plastic strains in the hydrogen precharged condition compared to the non-charged condition at low amplitudes. In addition, the evolution of the apparent elastic response of the material suggests that the primary crack(s) nucleated at a smaller percentage of the total lifetime and propagated in fewer number of cycles in the hydrogen precharged than in the non-charged condition. Fracture surface and gage section observations revealed a transgranular crack path and planar slip traces in both material conditions, with internal hydrogen promoting multiple slip at lower values of cumulative plastic strain than in the non-charged condition.

A hysteretic loop phenomenon at strain amplitude dependent damping curves of pre-strained pure Mg during cyclic vibration

In this study, twins were introduced into pure Mg by pre-deformation, the strain amplitude dependent damping in pre-strained pure magnesium was investigated using cyclic vibration. The strain amplitude dependent damping curve exhibited a hysteretic loop as the strain amplitude was cycled. The damping value was greater during the high strain amplitude regime when the strain amplitude increased than when strain amplitude decreased. For the low strain amplitude regime, the opposite trend was observed. The results point to the damping behavior transitions between the two regimes occurring at a specific strain amplitude, increasing commensurately with increased pre-strain. This hysteretic loop phenomenon is attributed to the difference in mechanical energy consumed by the motion of the twin boundaries during cyclic vibration. The hysteretic loop indicates that twin dampening already exists. Therefore, the strain amplitude value of the intersection may be used as a reference parameter to detect twin damping.

Non-linear dynamics of hydrodynamic tori as a model of oscillations and bending waves in astrophysical discs

ABSTRACT Understanding oscillations and waves in astrophysical fluid bodies helps to elucidate their observed variability and the underlying physical mechanisms. Indeed, global oscillations and bending modes of accretion discs or tori may be relevant to quasi-periodicity and warped structures around compact objects. While most studies rely on linear theory, observationally significant, non-linear dynamics is still poorly understood, especially in Keplerian discs for which resonances typically demand a separate treatment. In this work, we introduce a novel analytical model which exactly solves the ideal, compressible fluid equations for a non-self-gravitating elliptical cylinder within a local shearing sheet. The aspect ratio of the ring is an adjustable parameter, allowing a continuum of models ranging from a torus of circular cross-section to a thin ring. We restrict attention to flow fields which are a linear function of the coordinates, capturing the lowest order global motions and reducing the dynamics to a set of coupled ordinary differential equations (ODEs). This system acts as a framework for exploring a rich range of hydrodynamic phenomena in both the large amplitude and Keplerian regimes. We demonstrate the connection between tilting tori and warped discs within this model, showing that the linear modes of the ring correspond to oppositely precessing global bending modes. These are further confirmed within a numerical grid based simulation. Crucially, the ODE system developed here allows for a more tractable investigation of non-linear dynamics. This will be demonstrated in a subsequent paper which evidences mode coupling between warping and vertical motions in thin tilted rings.

Nonlinear Damping of Standing Kink Waves Computed With Elsässer Variables

Abstract In a previous paper, we computed the energy density and the nonlinear energy cascade rate for transverse kink waves using Elsässer variables. In this paper, we focus on the standing kink waves, which are impulsively excited in coronal loops by external perturbations. We present an analytical calculation to compute the damping time due to the nonlinear development of the Kelvin–Helmholtz instability. The main result is that the damping time is inversely proportional to the oscillation amplitude. We compare the damping times from our formula with the results of numerical simulations and observations. In both cases we find a reasonably good match. The comparison with the simulations shows that the nonlinear damping dominates in the high amplitude regime, while the low amplitude regime shows damping by resonant absorption. In the comparison with the observations, we find a power law inversely proportional to the amplitude η −1 as an outer envelope for our Monte Carlo data points.