Higher-order Terms Research Articles

Nonlinear localized modes in a higher-order anisotropic ferromagnetic nanowire with octupole–dipole interaction

Increasing demand for advanced technologies that depends on magnetic phenomena, understanding and controlling the behavior of discrete breather in ferromagnetic nanowires are crucial for enhancing the efficiency and performance of such devices. The presence of octupole–dipole interactions signifies a unique aspect that could potentially influence the stability and localization of breather excitations. Hence, we adopted a multifaceted approach to investigate the Heisenberg anisotropic ferromagnetic nanowire discrete model with the following interactions: bilinear, octupole–dipole, anisotropy and its higher-order terms. The dynamics is governed by a discrete nonlinear Schrödinger equation (DNLS) arrived with the aid of Holstein–Primakoff transformation. This transformation was facilitated by utilizing the Glauber coherent representation of the boson operators. Subsequently, the dynamical equation is incorporated to the Modulational Instability (MI) analysis which is a systematical gateway to explore the breather excitation in the region of instability influenced by the octupole–dipole interaction coupling parameter. Then, we pictorially demonstrated that the octupole–dipole interaction plays a pivotal role in promoting the localization of discrete breather on the surface of the spin lattice sites in the discrete ferromagnetic nanowire. The energy density distribution also implies that the increase in octupole–dipole interaction results in the highly dense breather localization. The result shows that the increment in the octupole–dipole interaction parameter increases the amplitude of the localized breathers. These discrete breathers could hold immense promise for applications in magnetic storage and Spintronic devices, where maintaining stable localized modes is crucial for the device functionality. Our novelty lies in being pioneers in the exploration of a fully discrete model that encompasses higher-order interactions, such as the octupole–dipole interaction. We already have confirmed the existence of instability region on the discrete spin lattice by incorporating the octupole–dipole interaction [T. Pavithra, L. Kavitha, Prabhu and A. Mani, Modulational instability analysis in an isotropic ferromagnetic nanowire with higher order octopole-dipole interaction, in Nonlinear Dynamics and Applications: Proceedings of the ICNDA 2022 (Springer, 2022), p. 1209], we attempting to explore the generation of discrete breathers in a discrete anisotropic ferromagnetic nanowire. This effectively bridges the gap between theoretical understanding and practical implications, paving the way for innovative advancements in magnetic technology.

Third order nonlinear correlation of the electromagnetic vacuum at near-infrared frequencies

In recent years, electro-optic sampling, which is based on Pockel’s effect between an electromagnetic mode and a copropagating, phase-matched ultrashort probe, has been largely used for the investigation of broadband quantum states of light, especially in the mid-infrared and terahertz frequency range. The use of two mutually delayed femtosecond pulses at near-infrared frequencies allows the measurement of quantum electromagnetic radiation in different space-time points. Their correlation allows therefore direct access to the spectral content of a broadband quantum state at terahertz frequencies after Fourier transformation. In this work, we will prove experimentally and theoretically that when using strongly focused coherent ultrashort probes, the electro-optic sampling technique can be affected by the presence of a third-order nonlinear mixing of the probes’ electric field at near-infrared frequencies. Moreover, we will show that these third-order nonlinear phenomena can also influence correlation measurements of the quantum electromagnetic radiation. We will prove that the four-wave mixing of the coherent probes’ electric field with their own electromagnetic vacuum at near-infrared frequencies results in the generation of a higher-order nonlinear correlation term. The latter will be characterized experimentally, proving its local nature requiring the physical overlap of the two probes. The parameters regime where higher order nonlinear correlation results predominant with respect to electro-optic correlation of terahertz radiation is provided.

Containment control for second-order multi-agent systems with time-varying delays via variable-augmented-based free-weighting matrices

This paper investigates the containment control problem for multi-agent systems (MASs), where the time-varying communication delays are considered. The aim of this paper is to introduce new methods for the containment control research of MASs with time-varying delays. To obtain better results on maximum admissible upper bounds (MAUBs) of the delays to ensure the containment control, the variable-augmented-based free-weighting matrices (VABFWMs) method is introduced to avoid the higher-order terms of time-varying delays in estimating the derivative of the Lyapunov-Krasovskii functionals (LKFs). So our method no longer requires the quadratic function negative-determination lemma. In addition, by utilizing the proposed method, we design a containment controller to ensure that all followers are included into the convex hull formed by leaders. Finally, a numerical example is presented to illustrate the feasibility and superiority of our method.

Mitigation of the Brighter-fatter Effect in the LSST Camera

Thick, fully depleted charge-coupled devices are known to exhibit nonlinear behavior at high signal levels due to the dynamic behavior of charges collecting in the potential wells of pixels, called the brighter-fatter effect (BFE). The effect results in distorted images of bright calibration stars, creating a flux-dependent point-spread function that if left unmitigated, could make up a large fraction of the error budget in Stage IV weak-lensing (WL) surveys such as the Legacy Survey of Space and Time (LSST). In this paper, we analyze image measurements of flat fields and artificial stars taken at different illumination levels with the LSST Camera (LSSTCam) at SLAC National Accelerator Laboratory in order to quantify this effect in the LSSTCam before and after a previously introduced correction technique. We observe that the BFE evolves anisotropically as a function of flux due to higher-order BFEs, which violates the fundamental assumption of this correction method. We then introduce a new method based on a physically motivated model to account for these higher-order terms in the correction, and then we test the modified correction on both data sets. We find that the new method corrects the effect in flat fields better than it corrects the effect in artificial stars, which we suggest is the result of sub-pixel physics not included in this correction model. We use these results to define a new metric for the full-well capacity of our sensors and advise image processing strategies to further limit the impact of the effect on LSST WL science pathways.

Intraday volatility patterns from short-dated options

We propose a nonparametric estimator for the deterministic periodic component of volatility from short-dated options within an in-fill asymptotic setting. The estimator uses options with zero and one day to expiration sampled at high-frequency during a trading day. At each point in time, we aggregate the options to form nonparametric estimates of conditional risk-neutral expectations of future integrated return variation for the two available option tenors. A suitable ratio of these estimates removes the stochastic components of the conditional expectations of future volatility, up to asymptotically higher-order terms, and allows to form estimates of the deterministic periodic component of volatility. We derive a Central Limit Theorem for the estimator, with its rate of convergence determined from the mesh of the strike grid and the length of the time to expiration of the options. The newly-developed estimation procedure is applied to S&P 500 index options data.

Derivation of Key Attributes and Clusters of Korean Taekwondo Policies and Systems on Social Media: Comparative Big Data Analysis Based on Regime Change

This study analyzed the key attributes and clusters of policies and systems of Korean Taekwondo based on Park Geun-Hye and Moon Jae-in’s regime changes using big data, including 8,030 data points on social media over a period of 8 years. Frequency analysis, term frequency inverse document frequency analysis, and degree centrality analysis were performed using TEXTOM 4.5. In addition, a convergent and correlation analysis was performed using UCINET 6 to visualize related words and analyze clusters. Frequency, term frequency inverse document frequency, and degree centrality analyses revealed 30 high-order terms. A convergence of iterated correlations analysis of the derived words identified three common clusters: improvement, problem, and support. In addition, there were two distinct clusters in the Park Geun-hye government (research and sports policy), and three in the Moon Jae-in government (interview, thoughts, and athlete). The Korean government attempted to improve and address problems related to policies and systems for the development of Taekwondo. However, as Taekwondo policies and systems were implemented from different perspectives by each regime, systematic policies and systems could not be implemented.

Analytic auxiliary mass flow to compute master integrals in singular kinematics

The computation of master integrals from their differential equations requires boundary values to be supplied by an independent method. These boundary values are often desired at singular kinematical points. We demonstrate how the auxiliary mass flow technique can be extended to compute the expansion coefficients of master integrals in a singular limit in an analytical manner, thereby providing these boundary conditions. To illustrate the application of the method, we re-compute the phase space integrals relevant to initial-final antenna functions at NNLO, now including higher-order terms in their ϵ-expansion in view of their application in third-order QCD corrections.

Higher-order multi-scale computational approach and its convergence for nonlocal gradient elasticity problems of composite materials

A novel higher-order multi-scale computational approach for efficient nonlocal gradient elasticity simulation of composite materials is proposed in this paper. Based on the use of decoupling technique, raw fourth-order nonlocal gradient equations with periodically oscillatory coefficients are decoupled as the new second-order multi-scale equations for reducing the continuity requirements when implementing multi-scale simulation. Next, a novel macro-micro coupled multi-scale computational model with higher-order corrected terms is rigorously devised for high-resolution multi-scale and nonlocal analysis of composite materials via multi-scale asymptotic analysis. Then, the local error analysis of higher-order multi-scale solutions in the point-wise sense illustrates that establishing higher-order asymptotic corrected terms plays a vital role in investigating the micromechanical mechanisms. Moreover, a rigorous global error estimation with an explicit rate of higher-order multi-scale solutions is first derived in the energy norm sense. In addition, an efficient multi-scale numerical algorithm is presented to effectively simulate nonlocal gradient elasticity problems of composite materials based on finite element method (FEM). And we also derive the convergence estimation of the proposed numerical algorithm. Finally, numerical experiments are conducted to gauge the efficiency and accuracy of the proposed higher-order multi-scale method. This paper offers a unified higher-order two-scale computational framework for enabling nonlocal gradient elasticity behavior simulation of composite materials.

Characteristics differentiating problem representation synthesis between novices and experts.

Formulating a thoughtful problem representation (PR) is fundamental to sound clinical reasoning and an essential component of medical education. Aside from basic structural recommendations, little consensus exists on what characterizes high-quality PRs. To elucidate characteristics that distinguish PRs created by experts and novices. Early internal medicine residents (novices) and inpatient teaching faculty (experts) from two academic medical centers were given two written clinical vignettes and were instructed to write a PR and three-item differential diagnosis for each. Deductive content analysis described the characteristics comprising PRs. An initial codebook of characteristics was refined iteratively. The primary outcome was differences in characteristic frequencies between groups. The secondary outcome was characteristics correlating with diagnostic accuracy. Mixed-effects regression with random effects modeling compared case-level outcomes by group. Overall, 167 PRs were analyzed from 30 novices and 54 experts. Experts included 0.8 fewer comorbidities (p < .01) and 0.6 more examination findings (p = .01) than novices on average. Experts were less likely to include irrelevant comorbidities (odds ratio [OR] = 0.4, 95% confidence interval [CI] = 0.2-0.8) or a diagnosis (OR = 0.3, 95%CI = 0.1-0.8) compared with novices. Experts encapsulated clinical data into higher-order terms (e.g., sepsis) than novices (p < .01) while including similar numbers of semantic qualifiers (SQs). Regardless of expertise level, PRs following a three-part structure (e.g., demographics, temporal course, and clinical syndrome) and including temporal SQs were associated with diagnostic accuracy (p < .01). Compared with novices, expert PRs include less irrelevant data and synthesize information into higher-order concepts. Future studies should determine whether targeted educational interventions for PRs improve diagnostic accuracy.

Adaptive fixed-time dynamic surface tracking control for high-order nonstrict-feedback nonlinear switched systems

This paper considers the adaptive fixed-time neural tracking dynamic surface control (DSC) for high-order nonlinear switched systems. The uncertain nonlinear functions are approximated by neural networks (NNs). And the obstacles of high-order terms are eliminated by the adding a power integrator. A novel fixed-time convergence filter is proposed to refrain from the problem of repeated differentiation of virtual controllers. On the basis of the backstepping control algorithm and the common Lyapunov function (CLF) method, a novel adaptive fixed-time neural DSC strategy is developed. It is proven that the states in the closed-loop system are bounded and the tracking error converges to an area of zero in fixed time. The simulation experiments further verify the feasibility of the mentioned method.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom.

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

Nonlinear guided waves in the sandwich nanostructure coupled with piezoelectric actuator: Introducing machine learning approach to measure nonlinear phase velocities

In today's rapidly changing corporate environment, business executives are turning to cutting-edge technology to solve complex problems efficiently. A machine learning approach allows for a more thorough understanding and quantification of decision-making outcomes, leading to increased confidence in business decisions. In this work for the first time, machine learning approach and mathematical simulation are used to model nonlinear guided waves in the sandwich nanostructure coupled with piezoelectric actuator. Using mathematical modeling, the current work studies the nonlinear phase velocity in a sandwich nanoshell composed of a bi-directional functionally graded (BD-FG) core and piezoelectric patch. The modeling uses first-order shear deformation theory with the fairly thick hypothesis to describe the displacement fields of piezoelectric layers. For core layer, a higher order shear deformation theory with terms of higher order in the Taylor series expansion is presented. The nanosystem is accurately modeled using nonlocal strain gradient theory, incorporating nonlocal and length scale characteristics. The solution approach section outlines the multiple scale method for the time domain and the harmonic solution methodology for the displacement domain to address nonlinear equations. To reduce the computational expenses, a machine-learning approach is introduced to address the nonlinear vibration issue in the current study. Validating the conclusions of the current study by comparing them with machine-learning solutions and another published paper can confirm their accuracy. The results section presents the impacts of factors like area of piezoelectric patch, length scale, applied voltage, nonlocality, geometry condition and FG power index on the nonlinear phase velocity of the BD-FG nanoshell coupled with piezoelectric patch.

Surface wrinkling of a film coated to a graded substrate

We study the surface wrinkling of a stiff thin elastic film bonded to a compliant graded elastic substrate subject to compressive stress generated either by compression or growth of the bilayer. Our aim is to clarify the influence of the modulus gradient on the onset and surface pattern in this bilayer. Within the framework of finite elasticity, an exact bifurcation condition is obtained using the Stroh formulation and the surface impedance matrix method. Further analytical progress is made by focusing on the case of short wavelength limit for which the Wentzel–Kramers–Brillouin method can be used to resolve the eigenvalue problem of ordinary differential equations with variable coefficients. An explicit bifurcation condition is obtained from which the critical buckling load and the critical wavelength are derived asymptotically. In particular, we consider two distinct situations depending on the ratio β of the shear modulus at the substrate surface to that at infinity. If β is of O(1) or small, the parameters related to modulus gradient all appear in the higher-order terms and play an insignificant role in the bifurcation. In that case, it is the modulus ratio between the film and substrate surface that governs the onset of surface wrinkling. If, however, β≫1, the modulus gradient affects the critical condition through leading-order terms. Through our analysis we unravel the influence of different material and geometric parameters, including the modulus gradient, on the bifurcation threshold and the associated wavelength which can be of importance in many biological and technological settings.

Inclusion of higher-order terms in the border-collision normal form: Persistence of chaos and applications to power converters

The dynamics near a border-collision bifurcation are approximated to leading order by a continuous, piecewise-linear map. The purpose of this paper is to consider the higher-order terms that are neglected when forming this approximation. For two-dimensional maps we establish conditions under which a chaotic attractor created in a border-collision bifurcation persists for an open interval of parameters beyond the bifurcation. We apply the results to a prototypical power converter model to prove the model exhibits robust chaos.

Celestial self-dual Yang-Mills theory: a new formula and the OPE limit

Celestial holography is a new way to understand flat-space amplitudes. Self-dual theories, due to their nice properties, are good subjects to study celestial holography. In this paper, we developed a new formula to calculate the celestial color-ordered self-dual Yang-Mills amplitudes based on celestial Berends-Giele currents, which makes the leading OPE limit manifest. In addition, we explore some higher-order terms of OPE in the celestial self-dual Yang-Mills theory.

Fifth Forces from QCD Axions Scale Differently.

We reexamine the low-energy potential for a macroscopic fifth force generated from the exchange of two axions. The shift symmetry of the linear axion interactions leads to a potential falling off as V(r)∼1/r^{5}. We find that in the case of the QCD axion higher-order terms in the Lagrangian break the shift symmetry and lead to the dominant contribution to the potential scaling as V(r)∼1/r^{3}. These terms are generated by the same physics responsible for the axion mass, and therefore the new contributions to the potential induce a different force for external nucleons and leptons. We demonstrate how this result affects the sensitivity of searches for new long-range forces.

Interferometric near-infrared spectroscopy (iNIRS) reveals that blood flow index depends on wavelength.

Blood flow index (BFI) is an optically accessible parameter, with unit distance-squared-over-time, that is widely used as a proxy for tissue perfusion. BFI is defined as the dynamic scattering probability (i.e. the ratio of dynamic to overall reduced scattering coefficients) times an effective Brownian diffusion coefficient that describes red blood cell (RBC) motion. Here, using a wavelength division multiplexed, time-of-flight- (TOF) - resolved iNIRS system, we obtain TOF-resolved field autocorrelations at 773 nm and 855 nm via the same source and collector. We measure the human forearm, comprising biological tissues with mixed static and dynamic scattering, as well as a purely dynamic scattering phantom. Our primary finding is that forearm BFI increases from 773 nm to 855 nm, though the magnitude of this increase varies across subjects (23% ± 19% for N = 3). However, BFI is wavelength-independent in the purely dynamic scattering phantom. From these data, we infer that the wavelength-dependence of BFI arises from the wavelength-dependence of the dynamic scattering probability. This inference is further supported by RBC scattering literature. Our secondary finding is that the higher-order cumulant terms of the mean squared displacement (MSD) of RBCs are significant, but decrease with wavelength. Thus, laser speckle and related modalities should exercise caution when interpreting field autocorrelations.

The quasi-Gramian solution of a non-commutative extension of the higher-order nonlinear Schrödinger equation

The nonlinear Schrödinger (NLS) equation, which incorporates higher-order dispersive terms, is widely employed in the theoretical analysis of various physical phenomena. In this study, we explore the non-commutative extension of the higher-order NLS equation. We treat real or complex-valued functions, such as g 1 = g 1(x, t) and g 2 = g 2(x, t) as non-commutative, and employ the Lax pair associated with the evolution equation, as in the commutation case. We derive the quasi-Gramian solution of the system by employing a binary Darboux transformation. The soliton solutions are presented explicitly within the framework of quasideterminants. To visually understand the dynamics and solutions in the given example, we also provide simulations illustrating the associated profiles. Moreover, the solution can be used to study the stability of plane waves and to understand the generation of periodic patterns within the context of modulational instability.

On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods

Most of the Pth root algorithms exhibit high latency or small convergence rates when iteratively computing the roots. Here we present a slew of algorithms based on series expansions of binomial form, and exponential terms that show low latency or small computational cost for finding the Pth root. The latency decreases if the family of series taken are truncated at higher terms. We show that Babylonian method converges quadratically while the binomial series show an increase in convergence rate from quadratic, cubic and higher order O(t^N) convergence rate as the series is sequentially truncated at higher order terms.

Ising string beyond the Nambu-Goto action

A major result of the effective string theory (EST) description of confinement is the so-called “low-energy universality”, which states that the first few terms of the large distance expansion of any EST are universal and coincide with those of the Nambu-Goto action. Going beyond this approximation is one of the most interesting open problems in the EST. In the higher-order terms beyond Nambu-Goto several important pieces of physical information are encoded, which could improve our understanding of the physical mechanisms behind confinement and of the physical degrees of freedoms which originate the EST. In this paper we evaluate numerically the first two of these corrections in the case of the three-dimensional gauge Ising model. The first of them turns out to be negative; γ3=−0.00048(4), similar (but not equal) to the one recently measured in the SU(2) Yang-Mills theory in three dimensions and compatible with the bootstrap bound γ3≥−1768. Published by the American Physical Society 2024