Asymptotic Amplitude Research Articles

Defect Solutions of the Nonreciprocal Cahn-Hilliard Model: Spirals and Targets.

We study the defect solutions of the nonreciprocal Cahn-Hilliard model. We find two kinds of defects, spirals with unit magnitude topological charge, and topologically neutral targets. These defects generate radially outward traveling waves and thus break the parity and time-reversal symmetry. For a given strength of nonreciprocity, spirals and targets with unique asymptotic wave number and amplitude are selected. We use large-scale simulations to show that at low nonreciprocity α, disordered states evolve into quasistationary spiral networks. With increasing α, we observe networks composed primarily of targets. Beyond a critical threshold α_{c}, a disorder-order transition from defect networks to traveling waves emerges. The transition is marked by a sharp rise in the global polar order.

Optimal Amplitude–Density Synthesis of Linear Aperiodic Arrays

New deterministic procedures for the design of linear aperiodic arrays are described which permit exploiting, in a combined way, both the positions and the excitation amplitudes of the array elements obtaining a pattern which optimally fits, in terms of a weighted L2 norm, the pattern of a reference linear continuous aperture. A first numerical procedure is based on alternating optimization of positions and amplitudes by means of closed-form convex projectors. Sufficient conditions for the solution to be optimal are established. A second numerical procedure is based on a domino-like sequential determination of the unknowns which can be iterated to convergence. Additionally, analytical asymptotic expressions for the optimal inter-element spacing and amplitude are derived by means of variational techniques. The optimal asymptotic inter-element spacing is demonstrated to be proportional to the reference tapering to the power (-2/3) while the optimal asymptotic array amplitude is proportional to the reference tapering to the power (1/3). For aperiodic arrays with equiamplitude excitation it is proved that the optimal inter-element spacing is proportional to the reference tapering to the power (-1). Based on these asymptotic dependencies, closed-form analytical solutions are obtained for amplitudes and positions of the elements. Several numerical results confirm the effectiveness and accuracy of the new procedures.

Accessing chiral-even quark generalised parton distributions in the exclusive photoproduction of a γπ± pair with large invariant mass in both fixed-target and collider experiments

We compute the exclusive photoproduction of a γπ± pair using the collinear factorisation framework, in the kinematic regime where the pair has a large invariant mass and the meson has a sufficiently large transverse momentum to not resonate with the outgoing nucleon. This exclusive channel presents a new avenue for the investigation of GPDs. It is particularly interesting as the high centre of mass energies available at future experiments will allow the study of GPDs at small skewness ξ. We compute the scattering amplitude of the process, at leading twist and leading order in αs, which is used to estimate its cross-section and linear polarisation asymmetries with respect to the incoming photon, for JLab 12-GeV, COMPASS, future EIC and LHC (in ultra-peripheral collisions) kinematics. We find that the order of magnitude of estimates are sufficiently large for a dedicated experimental analysis to be performed, especially at JLab. We also compare the results from an asymptotic distribution amplitude (DA) to those using a recently proposed holographic DA.

The short-term recovery of sprint cycling performance

Short-term sprint cycling performance recovery was investigated, with consideration to the Match Sprint. Fifteen strength-trained men (age: 24 ± 6 years; height: 1.81 ± 0.08 m; body mass: 83.4 ± 8.4 kg) were first familiarised with an 18 s sprint. During the baseline trial, blood lactate concentration, tissue saturation index, and oxygen uptake were monitored following a single sprint. In the remaining trials, the recovery duration (45, 90, 135, 180, 360, and 720 s) between two sprints was varied. Peak (PPO) and mean (MPO) power output were computed for each sprint. The recovery percentage of MPO and the recovery time-course of the physiological variables were modelled using one- and two-phase exponential functions. Statistical significance was set a priori at p < 0.05. Effects of sprint number, recovery time, and a sprint number × recovery time interaction were found for both PPO and MPO. Post hoc tests revealed significant differences between sprints at all time-points for both variables. The time constant (τ), 130.6 ± 95.6 s, of the one-phase exponential function (asymptotic amplitude [A0] = 97.4 ± 2.5%), suggested that performance recovery had stabilised within 12 minutes. However, the parameters of the two-phase function indicated that recovery was incomplete (A0 = 87.7 ± 6.4%, A1 = 11.9 ± 5.2%, τ0 = 56.3 ± 33.3 s, τ1 = 458.2 ± 283.3 s). The τ for MPO recovery was not significantly correlated with any of the physiological variables. The reduction in sprint cycling performance throughout the tested time-period could be meaningful for athletes competing in the Match Sprint.

DETERMINATION, ANALYSIS AND SYNTHESIS OF THE ROOTS OF VALID ALGEBRAIC EQUATIONS USING LOGARITHMIC AMPLITUDE-PHASE FREQUENCY CHARACTERISTICS

The article considers the method of approximate determination, analysis and synthesis of the roots of real algebraic equations of high order. The solution of such problems is relevant in the case of designing information-measuring and control systems, studying the dynamics of movement of various mechanisms (industrial robots, quadrocopters, etc.), determining the trajectories of aircraft, etc. The analytical solution of such problems is limited to equations of the third (sometimes fourth) degree, in other cases it is necessary to use either special sequential algorithms or packages of applied computer programs such as "Wolfram.Matematica", which allow only to find the roots of the equations, but not to synthesize them. The proposed method is based on the application for the decomposition of the studied polyomial (corresponding to the equation) into the simplest multipliers corresponding to aperiodic and/or oscillatory links, asymptotic logarithmic amplitude and phase-frequency characteristics. The form and values of the roots of the equation are proposed to be judged by the slopes at the fracture points of the logarithmic amplitude and phase-frequency characteristics of the polyparticle under study. The construction of logarithmic amplitude and phase-frequency characteristics is carried out by discarding the "small" terms of the polygamy at separate frequency intervals. A feature of the method is the possibility of its use both in conjunction with the computer and without it. Manual use of the method assumes that the user has a calculator and a ruler. The method allows to determine not only the roots of real algebraic equations (both real and complex), but also to establish a visual relationship between the coefficients for the terms of the equations with the type and values of the roots and purposefully change the necessary coefficients to change the parameters and type of roots. The possibilities of the method are not limited to solving real algebraic equations with positive coefficients and integer powers, it shows quite satisfactory results for equations with mixed coefficients and fractional powers. The method is quite simple, clear, has a small error in the case of far spaced roots, but in the case of closely spaced roots, its error increases, although it remains quite acceptable. The article presents the substantiation of the method, shows numerous examples of its capabilities, compares the results obtained with the results obtained with the help of the package of applied computer programs "Wolfram.Matematica".

Perturbative connection formulas for Heun equations

Connection formulas relating Frobenius solutions of linear ODEs at different Fuchsian singular points can be expressed in terms of the large order asymptotics of the corresponding power series. We demonstrate that for the usual, confluent and reduced confluent Heun equation, the series expansion of the relevant asymptotic amplitude in a suitable parameter can be systematically computed to arbitrary order. This allows to check a recent conjecture of Bonelli-Iossa-Panea Lichtig-Tanzini expressing the Heun connection matrix in terms of quasiclassical Virasoro conformal blocks.

Examining AGN UV/Optical Variability beyond the Simple Damped Random Walk

We present damped harmonic oscillator (DHO) light-curve modeling for a sample of 12,714 spectroscopically confirmed quasars in the Sloan Digital Sky Survey Stripe 82 region. DHO is a second-order continuous-time autoregressive moving-average process, which can be fully described using four independent parameters: a natural oscillation frequency (ω 0), a damping ratio (ξ), a characteristic perturbation timescale (τ perturb), and an amplitude for the perturbing white noise (σ ϵ ). The asymptotic variability amplitude of a DHO process is quantified by σ DHO—a function of ω 0, ξ, τ perturb, and σ ϵ . We find that both τ perturb and σ ϵ follow different dependencies with rest-frame wavelength (λ RF) on either side of 2500 Å, whereas σ DHO follows a single power-law relation with λ RF. After correcting for wavelength dependence, σ DHO exhibits anticorrelations with both the Eddington ratio and the black hole mass, while τ perturb—with a typical value of days in the rest frame—shows an anticorrelation with the bolometric luminosity. Modeling active galactic nuclei (AGN) variability as a DHO offers more insight into the workings of accretion disks close to the supermassive black holes at the center of AGN. The newly discovered short-term variability (characterized by τ perturb and σ ϵ ) and its correlation with bolometric luminosity pave the way for new algorithms that will derive fundamental properties (e.g., Eddington ratio) of AGN using photometric data alone.

Estimating asymptotic phase and amplitude functions of limit-cycle oscillators from time series data.

We propose a method for estimating the asymptotic phase and amplitude functions of limit-cycle oscillators using observed time series data without prior knowledge of their dynamical equations. The estimation is performed by polynomial regression and can be solved as a convex optimization problem. The validity of the proposed method is numerically illustrated by using two-dimensional limit-cycle oscillators as examples. As an application, we demonstrate data-driven fast entrainment with amplitude suppression using the optimal periodic input derived from the estimated phase and amplitude functions.

Rayleigh–Taylor and Richtmyer–Meshkov instabilities in the presence of an inclined magnetic field

A unified and analytical model is developed to study the effects of an inclined magnetic field on magneto-Rayleigh–Taylor (MRT) and magneto-Richtmyer–Meshkov (MRM) instabilities in ideal magnetohydrodynamics. Unlike either a horizontal or a vertical magnetic field is present, the decay modes possess decaying and oscillation behaviors together. The vorticity transportation is analyzed. The dispersion relations are derived, and some interesting phenomena are observed. For a small R that represents the ratio of the magnetic field strength, or equivalently, the inclination θ, the growth rate of MRT instabilities resembles the case when a vertical magnetic field is present. For a large R, the growth rate resembles to the case when a horizontal magnetic field exists. The maximum growth rate becomes strongly dependent on At instead of on R. Furthermore, analytical expression is obtained for the MRM instability by using the impulsive accelerated model. The decaying and oscillating rates of the perturbed amplitude are explicitly related to θ. For two limiting cases, with either the vertical or the horizontal magnetic field existing, our results retrieve previous one of the theoretical analyses and numerical simulations. Generally, the asymptotic amplitude becomes independent of the wave number of the initial perturbation in the MRM instability. These findings regarding magneto-hydrodynamic interfacial instabilities in an inclined magnetic field could provide physical insights for magnetically driven targets and astrophysical observations. This analytical model is easily expanded to investigate the effects of finite thickness of magnetic slab and sheared magnetic field in relevant to high-energy-density physics and to astrophysics.

Rational Form of Amplitude and Its Asymptotic Factorization

We provide arguments for the use of the rational form of unitarization, its relation with the diffraction peak shrinkage and asymptotics of the inelastic cross-section. The particular problems of the Regge model and the exponential form of unitarization with a factorized eikonal are discussed as well. A central role belongs to the asymptotic amplitude factorization resulting from Mandelstam analyticity and its symmetry over the scattering variables.

Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.

Asymptotic safety and quantum gravity amplitudes

Application of the Weinberg's conditions of asymptotic safety to amplitudes and not to couplings of the effective action can help to uniquely define the running in the UV and avoid some of the asymptotic safety program problems. As it turns out the requirement for a quantum gravity to be defined by S-matrix, that obeys the Weinbergs asymptotic safety criteria is a very restrictive one. The idea is illustrated by the 4-graviton amplitude in string theory and its symmetries.

Improving Damped Random Walk Parameters for SDSS Stripe 82 Quasars with Pan-STARRS1

Abstract We use the Panoramic Survey Telescope and Rapid Response System 1 Survey (Pan-STARRS1, PS1) data to extend the Sloan Digital Sky Survey (SDSS) Stripe 82 quasar light curves. Combining PS1 and SDSS light curves provides a 15 yr baseline for 9248 quasars—5 yr longer than prior studies that used only SDSS. We fit the light curves with the damped random walk (DRW) model—a statistical description of their variability. We correlate the resulting DRW model parameters: asymptotic variability amplitude SF∞, and characteristic timescale τ, with quasar physical properties—black hole mass, bolometric luminosity, and redshift. Using simulated light curves, we find that a longer baseline allows us to better constrain the DRW parameters. After adding PS1 data, the variability amplitude is a stronger function of the black hole mass and has a weaker dependence on quasar luminosity. In addition, the characteristic timescale τ dependence on quasar luminosity is marginally weaker. We also make predictions for the fidelity of DRW model parameter retrieval when light curves will be further extended with Zwicky Transient Facility and Rubin Observatory Legacy Survey of Space and Time data. Finally, we show how updated DRW parameters offer an independent method of discovering changing-look quasar candidates (CLQSOs). The candidates are outliers in terms of differences in magnitude and scatter between the SDSS and PS1 segments. We identify 40 objects (35 newly reported) with a tenfold increase in the variability timescale between SDSS and SDSS–PS1 data due to a large change in brightness (over 0.5 mag)—characteristic for CLQSOs.

Asymptotic Behavior of Small Perturbations for Unsteady Motion an Ideal Fluid Jet

The stability problem of unsteady rotating circular jet motion of an ideal fluid is reduced to solving an initial-boundary value problem for Poincare–Sobolev type equation with an evolutionary condition on the jet free initial boundary. The solution of this problem is constructed by the method of variables separation. The asymptotic amplitudes behavior perturbations of the free jet boundary at t → ∞ is found. The results obtained are compared with the known results on the stability of the potential jet motion

Pion light-cone distribution amplitude from the pion electromagnetic form factor

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_\pi(Q^2)$ and the integrated modulus of the timelike form factor. For $F_\pi(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BaBar collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single $a_2\neq 0$ is disfavoured by the fit. Considering the models with $a_{n>2}\neq 0$, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals $a_2 (1 \mbox{GeV}) = (0.22 - 0.33) $, $a_4 (1 \mbox{GeV}) = (0.12 - 0.25) $. The higher moments starting from $a_{8}$ are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab $F_\pi$ collaboration.

Isochoric heat capacity of near- and supercritical benzene and derived thermodynamic properties

As part of a continuing study of the critical and supercritical phenomena in fluids and fluid mixtures, one- (CV1) and two-phase (CV2) isochoric heat capacities, densities (ρS) and phase-transition temperatures (TS) of benzene were measured in the critical and supercritical regions. Measurements were made in the immediate vicinity of the liquid-gas phase transition and the critical points in order to accurately determine of the phase transition properties (TS,ρS,CV1, and CV2). The measurements cover the temperature range from (347 to 616) K for 10 liquid and vapor isochores between (265 and 653) kg·m−3 at pressure up to 7.5 MPa. The measurements were performed using a high-temperature, high-pressure, nearly constant-volume adiabatic calorimeter. The standard uncertainties of the density, temperature, and isochoric heat capacity, CV, measurements are estimated to be 0.1%, 0.02 K, and 1.5%, respectively. The measured one- (CV1) and two-phase (CV2) isochoric heat capacities along the critical isochore and the saturated liquid (ρS') and vapor (ρS") densities near the critical point were used to accurately estimate the theoretically meaningful asymptotic critical amplitudes (A0±and B0) and related amplitudes for other properties (Γ0+, D0, ξ0), and their universal relations, A0+/A0−, A0+Γ0+B02, αA0+Γ0+B0−2, D0Γ0+B0δ−1, ξ0αA0+vC1/3. Saturated liquid and vapor densities (ρS′,ρS″) together with measured two-phase CV2 data were used to estimate the values of asymmetric parameters a3 (complete scaling parameter) and b2 of the coexistence curve singular diameter. Experimentally determined asymptotical critical amplitudes (A0±and B0 fluid-specific parameters) were used to check and confirm the predictive capability of the universal correlation in terms of their dependence on the acentric factor ω based on the generalized corresponding states principle. The measured values of two-phase CV2 as a function of the specific volume V along various isotherms were used to calculate second temperature derivatives of vapor pressure d2PSdT2 and chemical potential d2μdT2 and to estimate the value of Yang-Yang anomaly strength parameter Rμ = − 0.683 for benzene. The contributions of the vapor pressure, CVP=VCTd2PSdT2, and the chemical potential, CVμ=−Td2μdT2, to the measured total two-phase CV2 were derived from the measurements.

Effect of suction on laminar-flow control in subsonic boundary layers with forward-/backward-facing steps

In a subsonic boundary layer, a forward-facing step (FFS) or a backward-facing step (BFS) usually destabilizes the oncoming Tollmien–Schlichting (T-S) waves, leading to a promotion of laminar–turbulent transition. This paper studies a laminar-flow control strategy by introducing wall suction immediately ahead of the FFS or behind the BFS. The impact of the step–suction combination on an oncoming T-S wave is quantified by a transmission coefficient, defined as the ratio of the asymptotic amplitude downstream of the step and suction to that upstream. In order to solve this problem, a local scattering theory based on the large-Reynolds number (large-R) asymptotic framework and a Harmonic linearized Navier–Stokes approach, that calculates the perturbation field at finite Reynolds numbers, are employed. The latter approach is confirmed to be accurate by comparing its results with direct numerical simulations, and the results given by the two approaches agree when the Reynolds number is asymptotically large. According to the large-R triple-deck formulism, a few control parameters, such as the Mach number, Reynolds number, and wall temperature, disappear, which makes a systematical parametric study possible. The destabilizing effect of a step increases with its height, while the stabilizing effect of suction increases with its flux. For a step with a moderate height, suction with a small flux is sufficient to compensate the destabilizing effect of the step.

Supercritical CO2: Properties and Technological Applications - A Review

The main goal of the present paper is to assess the available information so as to obtain a general procedure for dealing with the critical enhancement of the thermodynamic and transport properties of supercritical CO2 and CO2 containing binary mixtures for practical and scientific applications. The present review provides comprehensive analysis of the thermodynamic and transport properties of supercritical carbon dioxide and CO2 containing binary mixtures (experiment and theory) and their various technological and scientific applications in different natural and industrial processes. The available information for the thermodynamic and transport properties (experiment and theory) enhancement (anomaly) of supercritical carbon dioxide and SC CO2 + solute mixtures is comprehensively reviewed. The effect of long-range order parameter fluctuations on the thermodynamic and transport properties of supercritical fluids (SC CO2) will be discussed. Simplified scaling type equation based on mode-coupling theory of critical dynamics with two critical amplitudes and one cutoff wave number as fluid-specific parameters was used to accurately predict of the transport properties of supercritical carbon dioxide. The recommended values of the specific parameters (asymptotic critical amplitudes) of the carbon dioxide for practical (prediction of the thermodynamic and transport properties of the supercritical CO2 for technological applications) and scientific use were provided. The role of the critical line shapes of the carbon dioxide containing binary mixture (SC CO2+solvent) in determination of the critical behavior of the mixture near the critical point of pure supercritical solvent (CO2) is discussed. Krichevskii parameter concept for a description of thermodynamic behavior of dilute near-critical SC CO2+solute mixtures is also discussed. The structural and thermodynamic properties of the carbon dioxide containing binary mixtures near the critical point of pure solvent (CO2) are discussed.

On some implications of the BaBar data on the γ⁎η′ transition form factor

At leading-twist accuracy the form factors for the transitions from a virtual photon to the η or η′ can be expanded into a power series of the variable ω, being related to the difference of the two photon virtualities. The series possess the remarkable feature that only the Gegenbauer coefficients of the meson distribution amplitudes of order l≤m contribute to the term ∼ωm. Thus, for ω→0 only the asymptotic meson distribution amplitude contributes, allowing for a test of the mixing of the η and η′ decay constants. Employing the Gegenbauer coefficients determined in an analysis of the form factors in the real photon limit, we present predictions for the γ⁎η and γ⁎η′ form factors and compare them to the BaBar data.

One- and two-phase isochoric heat capacities and saturated densities of 2-propanol in the critical and supercritical regions

One- (CV1) and two-phase (CV2) liquid + vapor equilibrium isochoric heat capacities, densities (ρS), and phase-transition temperatures (TS) of 2-propanol were measured in the critical region. Measurements were made in the immediate vicinity of the liquid–gas phase transition and critical point in order to accurately determine the locus of phase-transition properties (TS, ρS, CV1, and CV2). Additional measurements were made over an extended temperature range from (317 to 525) K for 9 liquid and 3 vapor isochores between (234 and 697) kg⋅m−3 at pressure up to 6.5 MPa. The measurements were performed using a high-temperature, high-pressure, nearly constant-volume adiabatic piezo-calorimeter. The standard uncertainty of the density, temperature, and isochoric heat capacity (CV) measurements is estimated to be 0.1%, 0.02 K, and 1.5%, respectively. The measured one- (CV1) and two-phase (CV2) isochoric heat capacities along the critical isochore and the saturated liquid (ρS') and vapor (ρS'') densities near the critical point were used to derive theoretically meaningful asymptotic critical amplitudes (A0± and B0) and related amplitudes for other properties (Γ0+,D0,ξ0) and their universal relations, A0+/A0-, A0+Γ0+B02, αA0+Γ0+B0-2, D0Γ0+B0δ-1, ξ0αA0+vC1/3 and the asymmetric parameters a3 and b2 of the coexistence curve singular diameter. Experimental two-phase heat capacities CV2 as a function of specific volume V , along various isotherms, were used to calculate second temperature derivatives of vapor pressure d2PSdT2 and chemical potential d2μdT2 and to estimate the value of the Yang-Yang anomaly strength parameter Rμ for 2-propanol. The relative contributions of the vapor pressure, CVP=VCTd2PSdT2, and the chemical potential, CVμ=-Td2μdT2, to the measured total two-phase CV2 were estimated.