Evolution Of Amplitude Research Articles

Coarsening Dynamics of 2D Subaqueous Dunes

AbstractFluid flow over an initially flat granular bed leads to the formation of a surface‐wave instability. The sediment bed profile coarsens and increases in amplitude and wavelength as disturbances develop from ripples into dunes. We perform experiments and numerical simulations to quantify both the temporal evolution of bed properties and the relationship between the initial growth rate and the friction velocity u∗. Experimentally, we study underwater bedforms originating from a thin horizontal particle layer in a narrow and counter‐rotating annular flume. We investigate the role of flow speed, flow depth and initial bed thickness on dune evolution. Bedforms evolve from small, irregular disturbances on the bed surface to rapidly growing connected terraces (2D equivalent of transverse dunes) before splitting into discrete dunes. Throughout much of this process, growth is controlled by dune collisions which are observed to result in either coalescence or ejection (mass exchange). We quantify the coarsening process by tracking the temporal evolution of the bed amplitude and wavelength. Additionally, we perform Large Eddy Simulations (LES) of the fluid flow inside the flume to relate the experimental conditions to u∗. By combining the experimental observations with the LES results, we find that the initial dune growth rate scales approximately as . These results can motivate models of finite‐amplitude dune growth from thin sediment layers that are important in both natural and industrial settings.

The Fast Evolving, Tremendous Blue Superoutburst in ASASSN-21au Reveals a Dichotomy in the Outbursts of Long-period AM CVns

Abstract ASASSN-21au is an ultracompact accreting white dwarf binary (AM CVn type) with a period of ∼58 minutes. Using multiwavelength observations of the system, we discovered a dichotomy in the behavior of outbursts in AM CVns. The binary showed an initial increase in brightness that lasted for at least 82 days, followed by an additional increase that lasted two weeks. Afterward, ASASSN-21au went into superoutburst with a total duration of 19 days, showing an amplitude with respect to quiescence of ∼7.5 mag in g, with a precursor and an echo outburst. A correlation between X-rays, UV, and optical was identified for the first time in an AM CVn during this stage. The color evolution of ASASSN-21au indicates that during the superoutburst the dominant component was the accretion disk. The short duration, large amplitude, and color evolution of the superoutburst agree with expectations from the disk instability model. These characteristics are opposite to those observed in SDSS J080710+485259 and SDSS J113732+405458, which have periods of ∼53 minutes and ∼60 minutes, respectively. The initially slow increase in brightness in the light curve of ASASSN-21au and the behavior after the superoutburst favor a scenario in which changes in the mass-transfer rate led to disk instabilities, while the outburst mechanism of SDSS J080710+485259 and SDSS J113732+405458 has been attributed to enhanced mass transfer alone. Further observations are needed to understand the origin of this dichotomy.

Analytical prediction of delayed Hopf bifurcations in a simplified stochastic model of reed musical instruments

This paper investigates the dynamic behavior of a simplified single reed instrument model subject to a stochastic forcing of white noise type when one of its bifurcation parameters (the dimensionless blowing pressure) increases linearly over time and crosses the Hopf bifurcation point of its trivial equilibrium position. The stochastic slow dynamics of the model is first obtained by means of the stochastic averaging method. The resulting averaged system reduces to a non-autonomous one-dimensional Itô stochastic differential equation governing the time evolution of the mouthpiece pressure amplitude. Under relevant approximations the latter is solved analytically treating separately cases where noise can be ignored and cases where it cannot. From that, two analytical expressions of the bifurcation parameter value for which the mouthpiece pressure amplitude gets its initial value back are deduced. These special values of the bifurcation parameter characterize the effective appearance of sound in the instrument and are called deterministic dynamic bifurcation point if the noise can be neglected and stochastic dynamic bifurcation point otherwise. Finally, for illustration and validation purposes, the analytical results are compared with direct numerical integration of the model in both deterministic and stochastic situations. In each considered case, a good agreement is observed between theoretical results and numerical simulations, which validates the proposed analysis.

Analysis of nonlinear parity-time symmetric four-layer Bragg grating

The one dimensional PT (parity time) symmetric four-layer Bragg grating with gain and loss saturation effects is analyzed taking into account the evolution of the field amplitudes. The investigated structure has modulated real and imaginary parts of refractive index. The functional configurations of the Bragg grating have been considered, showing the behavior of this structure acting as a discrete device and as a component of an integrated circuit. The obtained characteristics illustrate the influence of the saturation effect on the intensity of the output wave at a given intensity of the incident plane wave for different values of gain and loss saturation intensities of the PT structure. The performed analysis shows the bistability of the structure and a strong influence of the incident wave intensity on the properties of light propagation nonreciprocity.

Magnetogenesis from baryon asymmetry during an early matter dominated era

In this paper, we study the simultaneous evolution of baryon asymmetry and hypermagnetic field amplitude assuming an early matter domination. We contrast our results to the conventional case where radiation domination during early universe is assumed. We show that the baryon asymmetry and the hypermagntic field amplitude can change by orders of magnitude if we assume a non-standard history of cosmology. That is because the Hubble rate determines which processes are efficient. We find that a change in Hubble rate can have a significant impact on when the weak sphalerons become active. As a result of a change in the evolution of baryonic asymmetry, alters the evolution of hypermagnetic field amplitude. It is known that if the hypermagnetic field amplitude is large enough, it can save the baryon asymmetry from diminishing. We show that whether a small seed of hypermagnetic field amplitude can be amplified to a large enough value will strongly depend on the history of cosmology.

Tricky Morphology: A New Species of Chamaecrista (Leguminosae) Shows Strong Morphological Convergence Among Not Closely Related Species Found in Similar Habitat

Abstract— Plants from Brazilian campos rupestres usually present morphological strategies that allow them to survive in extreme environments. However, in Chamaecrista (Leguminosae, Caesalpinioideae), one of the most diverse genera in the campos rupestres, needle-like leaflets are rare. Reviewing the species that present such leaf morphology, we describe Chamaecrista acicularis, a new species from the Canastra Range, in the southwestern region of the state of Minas Gerais, Brazil. Phylogenetic analyses revealed that C. acicularis is not closely related to other quite similar needle-like leafleted species and that this trait evolved convergently. We also present comments on the phylogenetic relationships of needle-like leafleted species as well as the evolution of the leaflet amplitude, and a detailed description of C. acicularis alongside illustrations, photos, geographical distribution, a key to the needle-like leafleted species and taxonomic notes on similar species. Additionally, we expand the description of Chamaecrista strictifolia and present an informal conservation status for all needle-like leafleted species.

Impact of two-photon absorption on two-dimensional solitons in silicon waveguides with a nonstationary potential*

We study the effects of weak two-photon absorption on two-dimensional (2D) solitons interaction in a silicon-based waveguide under a framework of coupled perturbed D nonlinear Schrödinger equations with a pure Kerr nonlinearity and a nonstationary potential. We extend the perturbative analysis for collisions of two one-dimensional solitons in silicon waveguides to derive the theoretical expressions for the amplitude evolution of a single perturbed soliton and for the abrupt amplitude downshift of a colliding soliton due to a fast interaction between two 2D solitons in silicon lattices. The theoretical calculations are then validated by the extensive simulations of the coupled perturbed D nonlinear Schrödinger model with periodic and non-periodic potentials. The simulations are implemented by using the accelerated imaginary-time evolution scheme and the split-step Fourier method. These results allow us to accurately capture the abrupt energy downshift of a colliding soliton in silicon-based two-dimensional waveguides.

Carleman estimates for the wave equation in heterogeneous media with non-convex interface

A wave equation whose main coefficient is discontinuous models the evolution of waves amplitude in a media composed of at least two different materials, in which the propagation speed is different. In our mathematical setting, the spatial domain where the partial differential equation evolves is an open bounded subset of R2 and the wave speed is assumed to be constant in each one of two sub-domains, separated by a smooth and possibly non-convex interface. This article is concerned with the construction of Carleman weights for this wave operator, allowing generalizations of previous results to the case of an interface that is not necessarily the boundary of a convex set. Indeed, using the orthogonal projection onto this interface, we define convex functions satisfying the transmission conditions imposed by the equation, such that, under usual hypothesis on the sign of the jump of the wave speed, can be used as Carleman weights.

Characteristics of Regular Pulse Bursts Generated From Lightning Discharges

In this work, we studied the waveforms of all lightning discharges from about 15 min. Eighty-three percent of all lightning discharges contain particular waveforms called regular pulse bursts (RPBs), which have regular microsecond-scale electric or magnetic field pulses. Maximum proportion of RPBs occur in middle or rear of lightning discharges. Prior to or after RPBs, there is always a chaotic pulse period. The analysis indicated that RPBs are caused by a secondary discharge in the fractured old breakdown channel, likeness to dart-stepped leader occuring in negative cloud-to-ground discharge (-CG). Four types of RPBs, namely, category of normal RPBs, category of back RPBs, category of symmetric RPBs, and category of reversal RPBs, were sorted in the light of the evolution of the pulse amplitude, interval between neighboring pulses and pulse polarity. In addition, the difference between normal RPBs and back RPBs was considered to be caused by the distance between neighboring charge pockets and the magnitude of the charge in every charge pocket. The symmetric RPBs were considered to be caused by a discharge channel with a large central charge area. Reversal RPBs were considered to be caused by a bending channel or superposition of two or more RPBs. We located some RPBs in a typical intra-cloud flash (IC) in three-dimensional. The analysis showed that the developing velocity of RPBs ranged from approximately 1.2 × 106 m/s to 3.0 × 106 m/s, which slower less than both of the dart leader or dart-stepped leader process from previous studies. And we found it is several meters to dozens of meters that the lengths range of discharge step which between two adjacent pulses.

Experimental 3-dimensional tracking of the dynamics of a single electron in the Fermilab Integrable Optics Test Accelerator (IOTA)

We present the results of experimental studies on the transverse and longitudinal dynamics of a single electron in the IOTA storage ring. IOTA is a flexible machine dedicated to beam physics experiments with electrons and protons. A method was developed to reliably inject and circulate a controlled number of electrons in the ring. A key beam diagnostic system is the set of sensitive high-resolution digital cameras for the detection of synchrotron light emitted by the electrons. With 60–130 electrons in the machine, we measured beam lifetime and derived an absolute calibration of the optical system. At exposure times of 0.5 s, the cameras were sensitive to individual electrons. Camera images were used to reconstruct the time evolution of oscillation amplitudes of a single electron in all 3 degrees of freedom. The evolution of amplitudes directly showed the interplay between synchrotron-radiation damping, quantum excitations, and scattering with the residual gas. From the distribution of measured single-electron oscillation amplitudes, we deduced transverse emittances, momentum spread, damping times, and beam energy. Estimates of residual-gas density and composition were calculated from the measured distributions of vertical scattering angles. Combining scattering and lifetime data, we also provide an estimate of the aperture of the ring. To our knowledge, this is the first time that the dynamics of a single electron are tracked in all three dimensions with digital cameras in a storage ring.

Spontaneous decay of artificial atoms in a three-qubit system

We study the evolution of qubits amplitudes in a one-dimensional chain consisting of three equidistantly spaced noninteracting qubits embedded in an open waveguide. The study is performed in the frame of single-excitation subspace, where the only qubit in the chain is initially excited. We show that the dynamics of qubits amplitudes crucially depend on the value of $kd$, where $k$ is the wave vector, $d$ is a distance between neighbor qubits. If $kd$ is equal to an integer multiple of $\pi$, then the qubits are excited to a stationary level. In this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of $kd$ the excitations of qubits exhibit the damping oscillations which represent the vacuum Rabi oscillations in a three-qubit system. In this case, the output spectrum of photon radiation is determined by a subradiant state which has the lowest decay rate. We also investigated the case with the frequency of a central qubit being different from that of the edge qubits. In this case, the qibits decay rates can be controlled by the frequency detuning between the central and the edge qubits.

Spontaneous decay of artificial atoms in a multi-qubit system

We consider a one-dimensional chain of N equidistantly spaced noninteracting qubits embedded in an open waveguide. In the frame of single-excitation subspace, we systematically study the evolution of qubits' amplitudes if the only qubit in the chain was initially excited. We show that the temporal dynamics of qubits' amplitudes crucially depend on the value of kd, where k is the wave vector, d is a distance between neighbor qubits. If kd is equal to an integer multiple of π, then the qubits are excited to a stationary level which scales as N−1. We show that in this case, it is the dark states which prevent qubits from decaying to zero even though they do not contribute to the output spectrum of photon emission. For other values of kd the excitations of qubits have the form of damping oscillations, which represent the vacuum Rabi oscillations in a multi-qubit system. In this case, the output spectrum of photon radiation is defined by a subradiant state with the smallest width.

Linear analysis of Atwood number effects on shear instability in the elastic\u2013plastic solids

The evolution of shear instability between elastic–plastic solid and ideal fluid which is concerned in oblique impact is studied by developing an approximate linear theoretical model. With the velocities expressed by the velocity potentials from the incompressible and irrotational continuity equations and the pressures obtained by integrating momentum equations with arbitrary densities, the motion equations of the interface amplitude are deduced by considering the continuity of normal velocities and the force equilibrium with the perfectly elastic–plastic properties of solid at interface. The completely analytical formulas of the growth rate and the amplitude evolution are achieved by solving the motion equations. Consistent results are performed by the model and 2D Lagrange simulations. The characteristics of the amplitude development and Atwood number effects on the growth are discussed. The growth of the amplitude is suppressed by elastic–plastic properties of solids in purely elastic stage or after elastic–plastic transition, and the amplitude oscillates if the interface is stable. The system varies from stable to unstable state as Atwood number decreasing. For large Atwood number, elastic–plastic properties play a dominant role on the interface evolution which may influence the formation of the wavy morphology of the interface while metallic plates are suffering obliquely impact.

An Analytical Spectral Model for Infragravity Waves over Topography in Intermediate and Shallow Water under Nonbreaking Conditions

AbstractThe theoretical model for group-forced infragravity (IG) waves in shallow water is not well established for nonbreaking conditions. In the present study, analytical solutions of the group-forced IG waves at O(β1) (β1 = hx/(Δkh), hx = bottom slope, Δk = group wavenumber, h = depth) in intermediate water and at in shallow water are derived separately. In case of off-resonance [β1μ−1 = O(β1), where is the resonant departure parameter, cg = group speed] in intermediate water, additional IG waves in quadrature with the wave group forcing (hereinafter, the nonequilibrium response or component) are induced at O(β1) relative to the equilibrium bound IG wave solution of Longuet–Higgins and Stewart (1962) in phase with the wave group. The present theory indicates that the nonequilibrium response is mainly attributed to the spatial variation of the equilibrium bound IG wave amplitude instead of group-forcing. In case of near-resonance [β1μ−1 = O(1)] in shallow water; however, both the equilibrium and nonequilibrium components are at the leading order. Based on the nearly-resonant solution, the shallow water limit of the local shoaling rate of bound IG waves over a plane sloping beach is derived to be ~h−1 for the first time. The theoretical predictions compare favorably with the laboratory experiment by Van Noorloos (2003) and the present numerical model results generated using SWASH. Based on the proposed solution, the group-forced IG waves over a symmetric shoal are investigated. In case of off-resonance, the solution predicts a roughly symmetric reversible spatial evolution of the IG wave amplitude, while in cases of near to full resonance the IG wave is significantly amplified over the shoal with asymmetric irreversible spatial evolution.

Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

We investigate the effect of horizontal periodic oscillation on the interfacial instability of two immiscible and viscous fluids of different densities in a fully saturated porous media. A linear stability analysis of the viscous and time-dependent basic flow leads to a periodic oscillator describing the evolution of the interfacial perturbation amplitude. The horizontal oscillation leads to the occurrence of two types of instability, the Kelvin–Helmholtz’s instability and the parametric resonance. These instabilities appear at the frontier between water and petroleum and have a practical interest in oil reservoir engineering. The results show that, an increase of the oscillation frequency destabilizes the Kelvin–Helmholtz instability and displaces the parametric instability regions toward the short wavelength perturbation. Also, we examine mainly how the other physical parameters of the system affect the instabilities for various permeability and porosity values of the porous medium as well as for relative heights of the two fluid layers.

Prediction on steady-oscillatory transition via Hopf bifurcation in a three-dimensional (3D) lid-driven cube

Massive computations of three-dimensional (3D) flow in subcritical flow state are carried out to investigate the transition from 3D steady flow to time-periodic oscillatory flow via Hopf bifurcation in a cube. Previous prediction of the steady-oscillatory transition in published works has been summarized. The transition point in lid-driven cavity has yet to come to consensus as the critical parameters are predicted in a wide range of values. The 3D unsteady governing equations are solved numerically using the spectral collocation method (SCM) in combination with the artificial compressibility method (ACM), SCM-ACM, a combined method with high accuracy that we developed. The temporal velocity evolution, amplitude evolution and dimensionless angular frequency are investigated. The accurate critical Reynolds number Recr is predicted by Richardson extrapolation. Results show that the initial conditions have significant effect to obtain the velocity which gradually approaches to steady state in the subcritical flow state, and appropriate initial conditions are given to efficiently obtain stable results by gradually increasing Re. Exponential decay of velocity amplitude becomes weaker with the increase of Re, and the decay rate is strictly linear against Re, while the dimensionless angular frequency remains constant. The Recr is affected by the number of nodes, which has also been observed by Feldman and Gelfgat [1] and Kuhlmann and Albensoeder [2], while the critical frequency is unaffected by the number of nodes in the present results. It also indicates that the Recr and the constant dimensionless angular frequency can be innovatively predicted with more accuracy and much fewer nodes. The improved point of steady-oscillatory transition in 3D lid-driven cube is Recr=1916.6 via Hopf bifurcation by Richardson extrapolation with dimensionless angular frequency ω=0.5752.

Effect of cavity on hypersonic flat-plate boundary layer instability

The effects of a cavity on hypersonic boundary layer instabilities are investigated experimentally. First- and second-mode wave amplitude evolution is determined using pressure sensors and high-resolution Schlieren technology. The results indicate that when a cavity is located downstream of the fast- and slow-mode synchronization points, it suppresses the second-mode wave and promotes first-mode wave growth. In contrast, when the cavity is located upstream of the synchronization point, the growth of the second-mode wave is promoted while that of the first-mode wave is suppressed. During disturbance evolution, nonlinear interactions are observed due to the phase-locked mechanism that relates the two unstable modes. The transition locations for various cases are confirmed using temperature-sensitive paint technology, and the influences of the cavity on the transition are explained from the perspective of unstable mode amplitude evolution.

Solitonic interactions for Rossby waves with the influence of Coriolis parameters

In the current study, the Rossby waves envelope near the equator is studied starting from a potential vorticity equation with the horizontal component of Coriolis parameter. Based on the equation, we first establish the amplitude evolution equation of the Rossby waves with complete Coriolis parameter and obtain rational function solutions by means of the subsidiary ordinary differential equation method with the help of chirp-free hypothesis. Then the 1-, 2-, 3-and N-soliton solutions are also obtained by the Hirota method. For these obtained solutions, they are rarely mentioned in fluid mechanics of ocean and atmospheric motion. On the other hand, these three-dimensional stereograms of the 1-, 2-soliton solutions are depicted with the physical parameter changing. The influence of each parameter on wave amplitude, the peak position and propagation direction of Rossby waves are discussed. The results show that the horizontal Coriolis parameter only alter the phase shift of the Rossby waves amplitude for the 1-soliton and 2-soliton solution. These results are of great significance for further theoretical research in geophysical fluid.

Time-domain formulation of electromagnetic scattering based on a polarization-mode expansion and the principle of least action

An approach to the full wave analysis of the time evolution of the polarization induced in the electromagnetic scattering from dispersive nonmagnetic particles is presented. It is based on the combination of the Hopfield model for the polarization field, the expansion of the polarization field in terms of static longitudinal and transverse modes of the particle, the expansion of the radiation field in terms of transverse wave modes of free space, and the principle of least action. The polarization field is linearly coupled to the electromagnetic field. The losses of the matter are described thorough a linear coupling of the polarization field to a bath of harmonic oscillators with a continuous range of natural frequencies. The set of linear ordinary differential integral equations of convolution type of the overall system is reduced by eliminating both the radiation degrees of freedom and the bath degrees of freedom, and the reduced system of equations is studied. The role played by the radiation field in the coupling between the longitudinal and transverse mode amplitudes of the polarization is described. The principal characteristics of the temporal evolution of the mode amplitudes are found as the particle size varies, including the impulse response. Results are presented for the analytically solvable spherical particle. The proposed approach leads to a general method for the analysis of the temporal evolution of the polarization field induced in dispersive particles of any shape, as well as for the computation of transients and steady states.

The Impact of the Mesoscale Ocean Variability on the Estimation of Tidal Harmonic Constants Based on Satellite Altimeter Data in the South China Sea

The estimation accuracy of tidal harmonic constants is of great significance to maritime traffic and port construction. However, due to the long sampling period of satellite altimeters, tidal signals alias the mesoscale ocean frequencies. As a result, the harmonic analysis is affected by mesoscale environmental noise. In this study, the influence of the mesoscale ocean variability (MOV) on the estimation of tidal harmonic constants was quantified by analyzing 25 years of altimeter data from the Topex/Poseidon (T/P) and Jason satellites in the South China Sea (SCS). The results indicated that the absolute amplitude differences (AADs) of the eight major tidal constituents before and after the mesoscale variability correction (MVC) were generally within 10 mm, and most were within 6 mm. For the relative impact, M2, O1, and K1 were not obviously affected by the MOV because of their large amplitudes, and the AADs generally accounted for less than ±10% of the amplitudes. As a tidal constituent with amplitude less than 2 cm in the SCS, the amplitude of K2 was significantly affected by the MOV, with the ratios of the AADs to its own amplitudes ranging from −64.79% to 95.99% in space. In terms of phase, the K2 tide was most affected by the MOV: 63% of the data points before and after correction were over ±5°, and the maximum and minimum values were 86.46° and −176.27°, respectively. The absolute phase differences of other tidal constituents before and after the MVC were generally concentrated within ±5°. The impact of the MOV on the evolution of tidal amplitudes in the SCS was also explored. It was found that the MOV can cause pseudo-rapid temporal variations of tidal amplitudes in some regions of the SCS.