Resonance Approximation Research Articles

THE RESONANCE APPROACH FOR THE PROCESS OF THE PHOTO-TRIDENT IN THE FIELD OF A LINEARLY POLARIZED ELECTROMAGNETIC WAVE

The process of the creation of an electron-positron pair at the scattering of a polarized high-energy photon (photo-trident) in the field of a monochromatic linearly polarized electromagnetic wave was investigated in the framework of the resonance approximation. This approximation allows to neglect the interference of amplitudes, i.e. resonance for each amplitude occurs in different kinematic regions. Despite these simplifications the expression for the probability for the investigated process, which has a second order in the fine structure constant, is sufficiently cumbersome. That is a consequence of the polarization properties of the intermediate state. And only for the case of linear polarization of the wave and an unpolarized initial photon, the probability of a photo-trident is factorized into the product of the probabilities of the first-order subprocesses into which the sequence of the studied process is divided.

Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery

Nonlinear Hierarchical Matrix Factorization-Based Tensor Ring Approximation for Multi-dimensional Image Recovery

Solving a class of infinite‐dimensional tensor eigenvalue problems by translational invariant tensor ring approximations

AbstractWe examine a method for solving an infinite‐dimensional tensor eigenvalue problem , where the infinite‐dimensional symmetric matrix exhibits a translational invariant structure. We provide a formulation of this type of problem from a numerical linear algebra point of view and describe how a power method applied to is used to obtain an approximation to the desired eigenvector. This infinite‐dimensional eigenvector is represented in a compact way by a translational invariant infinite Tensor Ring (iTR). Low rank approximation is used to keep the cost of subsequent power iterations bounded while preserving the iTR structure of the approximate eigenvector. We show how the averaged Rayleigh quotient of an iTR eigenvector approximation can be efficiently computed and introduce a projected residual to monitor its convergence. In the numerical examples, we illustrate that the norm of this projected iTR residual can also be used to automatically modify the time step to ensure accurate and rapid convergence of the power method.

Spin relaxation rate for baryons in a thermal pion gas

We study the relaxation dynamics of the spin polarization of baryons (nucleon and Λ baryon), in a thermal pion gas as a simple model of the hadronic phase of the QCD plasma produced in relativistic heavy-ion collisions. For this purpose, we formulate the quantum kinetic theory for the spin density matrix of baryons in the leading order of the gradient expansion. Considering the baryon-pion elastic scattering processes as the dominant interaction between baryons and thermal pions, we compute the spin relaxation rate of nucleons and Λ baryons in a pion gas up to temperature 200 MeV. In the case of nucleons, we evaluate the spin relaxation rate in the s-channel resonance approximation, based on the known experimental data on Δ resonances. We also estimate the spin relaxation rate for Λ baryons, based on experimental inputs and theoretical models for the low-energy Λπ scattering, including the chiral perturbation theory. Published by the American Physical Society 2024

Fröhlich resonance splitting in hybrid GaN nanowire-Ag nanoparticle structures

Plasmonic nanoparticles (NPs) have attracted significant attention due to their unique optical properties and broad optoelectronic and photonic applications. We investigate modifications of emission in hybrid structures formed by 60 nm silver NPs and GaN planar nanowires (NWs). Bare GaN NWs exhibit photoluminescence (PL) spectra dominated by broad bands peaking at ∼3.44 eV and ∼3.33 eV, attributed to basal plane stacking faults. In hybrids, two new narrow PL lines appear at 3.36 and 3.31 eV, resulting in PL enhancement at these energies. While the 3.36 eV line in hybrid structures can be explained using the Fröhlich resonance approximation based on the electric dipole concept, the appearance of two features at 3.36 and 3.31 eV indicates the splitting of resonance lines. This phenomenon is explained in framework of theoretical model based on the interaction of the dipole with its charge image, taking into account the quadrupole moment of the silver sphere and the quadrupole field of the charge image. A good agreement is obtained between the calculated Fröhlich resonance frequencies and the experimental PL lines in hybrid structures.

Resonant Modal Approximation of Time-Domain Elastic Scattering from Nano-Bubbles in Elastic Materials

Resonant Modal Approximation of Time-Domain Elastic Scattering from Nano-Bubbles in Elastic Materials

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We calculate the 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction rate which is an important constituent in nucleosynthesis networks and is contributed by resonant as well as non-resonant capture. For the resonant rate, we use the narrow resonance approximation whereas the non-resonant contribution is calculated with the Coulomb dissociation method for which we use finite-range distorted wave Born approximation theory. We then compare our calculated rate of 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B(n,γ)12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(n,\\gamma )^{12}$$\\end{document}B reaction with those reported earlier and with other charged particle reactions on 11\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{11}$$\\end{document}B.

Vector ring-like combined Akhmediev breathers for partially nonlocal nonlinearity under external potentials

Via the link between φp of a (3＋1)-dimensional variable-coefficient coupled partially nonlocal nonlinear Schrödinger system (NLSS) and Φ of constant-coefficient NLSS, considering the ring approximation and by means of the Darboux approach, we derive vector ring-like combined Akhmediev breathers(AB), including ring-like combined AB-doublet and ring-like combined AB with giant wave. From this breather solution, we find that physical quantities such as amplitude, width, center and phase are strongly affected by parameters of diffraction, linear potential and phase chirp. Moreover, we study the influence of parameters for radius and thickness on the form of vector ring-like combined AB.

Analyzing the backbone curve of piecewise-linear non-smooth systems using a generalized bilinear frequency approximation method

Estimating the resonant frequency of non-smooth systems with contacting elements is critical for the design, control, and health monitoring of various mechanical and aerospace structures. The nonlinearity caused by the intermittent contact excludes the use of efficient linear methods; hence, predicting vibration characteristics of these systems becomes computationally challenging. Furthermore, several numerical and analytical approaches that have been developed for analyzing smooth nonlinear systems cannot be applied to analyze non-smooth oscillators. To understand the dynamic properties of non-smooth dynamical systems, the bilinear frequency approximation (BFA) method, a classical analytical tool, was developed to estimate the nonlinear natural frequency of bilinear oscillators by using the linear characteristics of underlying linear subsystems to construct a closed-form analytical solution. However, the traditional BFA method is only applicable to systems in which the gap size between the contacting element is zero, which limits the capability of this efficient analytical technique. In this paper, a generalized BFA method is proposed to extend the capability of the method to capture the nonlinear natural frequency of high-dimensional non-smooth systems where either gaps or prestress exist. The generalized BFA method employs the natural frequencies, mode shapes, and modal amplitudes of the linear subsystems as well as the gap size at the contacting degrees of freedom (DOF) to estimate the nonlinear natural frequencies at different amplitude levels. The backbone curve of non-smooth oscillators can be efficiently constructed using the proposed analytical method. The generalized BFA method is demonstrated on a single-DOF system, a three-DOF system, and a finite element model (FEM) of a cantilever plate with contacting elements. The results show that the proposed method provides an accurate approximation of the backbone curve for the first resonance, which has the most dominant vibration response, with very low computational effort, but a rather poor approximation for higher resonances. The proposed technique can be integrated with high-dimensional FEMs to analyze the nonlinear resonance of complex structures. The performance of the method is validated both numerically and experimentally in this work.

Resonant escape induced by a finite time harmonic excitation.

The purpose of this paper is twofold. First, we obtain the critical forcing needed for a resonant escape in finite time in the presence of damping. Second, we adapt the isolated resonance approximation (AIR) method to find the escaping time and analyze the escape in finite time. Approximations of the escape time on both the phase and the parameter planes were obtained. In particular, a peculiar fractal-like boundary of the finite-time escape region was revealed. This discovery helps to better understand the limitations of AIR and explains the sensitivity of the numerical experiments to the integration time.

Effect of Plasmonic Ag Nanoparticles on Emission Properties of Planar GaN Nanowires.

The combination of plasmonic nanoparticles and semiconductor substrates changes the properties of hybrid structures that can be used for various applications in optoelectronics, photonics, and sensing. Structures formed by colloidal Ag nanoparticles (NPs) with a size of 60 nm and planar GaN nanowires (NWs) have been studied by optical spectroscopy. GaN NWs have been grown using selective-area metalorganic vapor phase epitaxy. A modification of the emission spectra of hybrid structures has been observed. In the vicinity of the Ag NPs, a new emission line appears at 3.36 eV. To explain the experimental results, a model considering the Fröhlich resonance approximation is suggested. The effective medium approach is used to describe the enhancement of emission features near the GaN band gap.

Classical simulation of variational quantum classifiers using tensor rings

In recent times, Variational Quantum Circuits (VQC) have been widely adopted to different tasks in machine learning such as Combinatorial Optimization and Supervised Learning. With the growing interest, it is pertinent to study the boundaries of the classical simulation of VQCs to effectively benchmark the algorithms. Classically simulating VQCs can also provide the quantum algorithms with a better initialization reducing the amount of quantum resources needed to train the algorithm. Even though Matrix Product State representations have been extensively used for quantum state approximation, their capacity is limited in simulating quantum circuits due to the exponential complexity in circuit depth. This manuscript proposes an algorithm that compresses the quantum state within a circuit using a noisy tensor ring representation which allows for the implementation of VQC based algorithms on a classical simulator at a fraction of the usual storage and computational complexity. Using the tensor ring approximation of the input quantum state, we propose a method that applies the parametrized unitary operations while retaining the low-rank structure of the tensor ring corresponding to the transformed quantum state, providing an exponential improvement of storage and computational time in the number of qubits and layers. This approximation is used to implement the tensor ring VQC (TRVQC) for the task of supervised learning on Iris and MNIST datasets to demonstrate the performance of the proposed method compared with the implementations from classical simulator using Matrix Product States (MPS). TRVQC has a test accuracy of 82.63% compared to the benchmark of 83.68% on Iris dataset whereas the former outperforms the latter on a reduced MNIST dataset with TRVQC having an accuracy of 83.73% compared to the benchmark 81.02%, showcasing the comparable performance of the proposed algorithm with the MPS framework.

Monte Carlo model for ion mobility and diffusion for characteristic electric fields in nanodosimetry

The quantification of the effects of space radiation for manned spaceflight can be approximated by nanodosimetric measurements. For the development of nanodosimetric detectors, a Monte Carlo model for ion mobility and diffusion for characteristic electric fields is presented.This model can be used to describe the interactions of ions in their parent gas based solely on commonly known input parameters, such as the ionization potential, kinetic diameter, molar mass, and polarizability of the gas. A model for approximating the resonant charge exchange cross section has been proposed, requiring only the ionization energy and mass of the parent gas as input parameters. The method proposed in this work was tested against experimental drift velocity data for a wide range of gases (helium, neon, nitrogen, argon, krypton, carbon monoxide, carbon dioxide, oxygen, propane). The transverse diffusion coefficients were compared to experimental values for helium, nitrogen, neon, argon, and propane gas.With the Monte Carlo code and resonant charge exchange cross section approximation model presented in this work, it is now possible to calculate an estimate of the drift velocities, transverse diffusion, and thus the ion mobility of ions in their parent gas. This is essential for further nanodosimetric detector development, as those parameters are often not well known for the gas mixtures used in nanodosimetry.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part II

We propose the further development of the resonant mode coupling approximation for the calculation of optical spectra of stacked periodic nanostructures in terms of the scattering matrix. We previously showed that given the resonant input and output vectors as well as background scattering matrices of two subsystems, one can easily calculate those for the combined system comprising two subsystems. It allows us to write a resonant approximation for the combined system and speed up the calculation significantly for typical wave scattering problems. This approach is best suitable for isolated resonances when the approximation of a constant background scattering matrix is reasonable. In this article, we aim at expanding the applicability of the resonant mode coupling approximation by utilizing more complicated approximations for the background matrices. In particular, we show that consideration of energy-dependent correction terms for the background matrices remarkably reduces the calculation error of the resonant parameters. Here we first consider a linear approximation of the background scattering matrices which is subsequently used as a base for a piecewise-linear approximation. We show that the latter allows one to keep the approximation error negligibly small with only a few sample points and to apply the resonant mode coupling approximation within almost arbitrary large energy ranges. Finally, we consider the approximation of background matrices by arbitrary matrix functions and propose a technique to derive resonant poles in this case. The methods described here could be considered an alternative approach for calculating the optical spectra of stacked systems.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part I

We develop the resonant mode coupling approximation to calculate the optical spectra of a stack of two photonic crystal slabs in terms of the scattering matrix. The method is based on the derivation of input and output resonant vectors in each slab in terms of the Fourier modal method in the scattering matrix form. We show that using the resonant mode coupling approximation of the scattering matrices of the upper and lower slabs, one can construct the total scattering matrix of the stack. The formation of the resonant output and input vectors of the stacked system is rigorously derived by means of an effective Hamiltonian. We demonstrate that the proposed procedure dramatically decreases the computation time without sufficient loss of accuracy. We believe that the proposed technique can be a powerful tool for fast-solving inverse scattering problems using stochastic optimization methods such as genetic algorithms or machine learning.

Near resonant approximation of the rotating stratified Boussinesq system on a 3-torus

Based on a novel treatment of near resonances, we introduce a new approximation for the rotating stratified Boussinesq system on three-dimensional tori with arbitrary aspect ratios. The rotation and stratification parameters are arbitrary and not equal. We obtain global existence for the proposed nonlinear system for arbitrarily large initial data. This system is sufficiently accurate, with an important feature of coupling effects between slow and fast modes. The key to global existence is a sharp counting of the relevant number of nonlinear interactions. An additional regularity advantage arises from a careful examination of some mixed type interaction coefficients. In a wider context, the significance of our near resonant approach is a delicate balance between the inclusion of more interacting modes and the improvement of regularity properties, compared to the well-studied singular limit approach based on exact resonance.

Escape dynamics of a particle from a purely nonlinear truncated quartic potential well under harmonic excitation

This paper focuses on the escape problem of a harmonically forced classical particle from a purely quartic truncated potential well. The latter corresponds to various engineering systems that involve purely cubic restoring force and absence of linear stiffness even under the assumption of small oscillations, such as pre-tensioned metal wires and springs, and compliant structural components made of polymer materials. This is in contrast to previous studies where the equivalent potential well could be treated as linear at first approximation under the assumption of small perturbations. Due to the strong nonlinearity of the current potential well, traditional analytical methods are inapplicable for describing the transient bounded and escape dynamics of the particle. The latter is analyzed in the framework of isolated resonance approximation by canonical transformation to action–angle variables and the corresponding reduced resonance manifold. The escape envelope is formulated analytically. Surprisingly, despite the essential nonlinearity of the well investigated, it exhibits a universal property of a sharp minimum due to the existence of multiple intersecting escape mechanisms. Unlike previous studies, three underlying mechanisms that govern the transient dynamics of the particle were identified: two maximum mechanisms and a saddle mechanism. The first two correspond to a gradual increase in the system’s response amplitude for a proportional increase in the excitation intensity, and the latter corresponds to an abrupt increase in the system’s response and therefore more potentially hazardous. The response of the particle is described in terms of energy-based response curves. The maximal transient energy is predicted analytically over the space of excitation parameters and described using iso-energy contours. All theoretical predictions are in complete agreement with numerical results.

Dynamics of a hybrid cubic vibro-impact oscillator and nonlinear energy sink

In the current work, we model the HCVI oscillator by a forced particle in a hybrid quartic-square potential well with infinite depth under periodic external forcing. The slow-flow dynamics of the system is analyzed in the framework of isolated resonance approximation by canonical transformation to action–angle (AA) variables and the corresponding reduced resonance manifold (RM). Two types of bifurcation are examined and described analytically. The former is associated with the SNO-regime and the HCVI-regime and vice versa, and the latter with reaching a chosen maximal transient energy level. Unlike previous studies, three underlying dynamical mechanisms that govern the occurrence of bifurcations are identified: two maximum mechanisms and one saddle mechanism. The first two correspond to a gradual increase in the system’s response amplitude for a proportional increase in the excitation intensity, and the latter corresponds to an abrupt increase in the system’s response and therefore more potentially hazardous when takes place in engineering systems and more effective for energy pumping when takes place in the HCVI-NES. Both mechanism types are universal for systems that undergo escape from a potential well. The maximal transient energy is predicted analytically over the space of excitation parameters and described using iso-energy contours. The response curves of the system are obtained analytically, allowing a full perspective on the HCVI-oscillator dynamical response, and the HCVI-NES performances and design optimization. All theoretical results are supported by numerical simulations.

Optical Mie Scattering by DNA-Assembled Three-Dimensional Gold Nanoparticle Superlattice Crystals

Programmable assemblies of gold nanoparticles engineered with DNA have intriguing optical properties such as Coulomb-interaction-driven strong coupling, polaritonic response in the visible range, and ultralow dispersion dielectric response in the infrared spectral range. In this work, we demonstrate the optical Mie resonances of individual microcrystals of DNA–gold nanoparticle superlattices. Broadband hyperspectral mapping of both transmission and dark-field scattering reveal a polarization-insensitive optical response with distinct spectral features in the visible and near-infrared ranges. Experimental observations are supported by numerical simulations of the microcrystals under a resonant effective medium approximation in the regime of capacitively coupled nanoparticles. The study identifies a universal characteristic optical response which is defined by a band of multipolar Mie resonances, which only weakly depend on the crystal size and light polarization. The use of gold superlattice microcrystals as scattering materials is of interest for fields such as complex nanophotonics, thermoplasmonics, photocatalysis, sensing, and nonlinear optics.

Fermions in graphene with magnetic field and time-oscillating potential

We study the Dirac fermions in graphene under a magnetic field and a scalar potential oscillating in time. Using the Floquet theory and resonance approximation, we show that the energy spectrum exhibits extra subbands resulting from the oscillating potential in addition to quantized Landau levels. The magnetic field and potential are discovered to greatly influence the generation of current density in the x and y-directions. Our numerical analysis reveals that the energy spectrum is symmetric and that the current density oscillates with varying amplitudes under various conditions.