Eigenmode Decomposition Research Articles

An examination of nonlinear collisionless magnetic reconnection through eigenmode decomposition

An examination of nonlinear collisionless magnetic reconnection through eigenmode decomposition

Localized Phonon Transport Study of GaN/SiO2 Core/shell Nanowires under Thermal-Stress Coupling.

In order to comprehensively explore the intricate mechanisms of thermo-mechanical interactions, this study employs the molecular dynamics method to investigate the influence of heat flux density, shell thickness and length, as well as stress on the radial interface phonon transport in GaN/SiO2 core/shell nanowire. Additionally, the surface eigenmode decomposition method is employed to analyze the interface phonon dispersion curves. The investigation reveals that with increasing heat flux density, internal thermal stresses intensify, leading to a complex distribution of thermal stresses within the system. Under the influence of thermal stress, the nonlinear acoustic properties interact with phonon scattering, resulting in the pronounced localization of interface phonons. Compressive stress causes an upshift in low-frequency phonons, while tensile stress induces a downward shift in the high-frequency optical branches at the interface. The localized phonon vibrations at the SiO2/GaN interface under nonuniform stress are identified as the primary cause for the abundant presence of nondispersive phonon modes at the radial interface. By elucidating the subtle interplay between lattice vibrations and stress fields, this study offers a novel and profound understanding of thermo-mechanical coupling effects, thereby providing innovative theoretical foundations for the design and performance management of thermoelectric devices.

Identification of the Aeromechanical Parameters of a Compressor Rotor from Blade Tip Timing Data

Abstract This article presents a maximum likelihood approach to identifying the mistuning, aerodynamic forcing functions, and aerodynamic influence coefficients of compressor rotor blades from noisy experimental measurements of blade deflection. The maximum likelihood estimation approach leads naturally to a nonlinear least squares optimization problem that can be solved using numerical optimization techniques such as quasi-Newton methods. An eigenmode decomposition approach is presented that permits the optimization objective function and gradient to be efficiently calculated so that the optimization is computationally feasible, even for experiments involving very large data sets. Simulation results show that the method has the potential to accurately identify the mistuning and aerodynamic nodal diameter forcing functions, but obtaining accurate results for influence coefficients may not be possible if there is significant disk flexibility. We demonstrate the method using both simulated and experimental blade vibration data from rotor 2 of the Purdue University three-stage axial compressor research facility collected using a light probe tip timing system as the rotor is slowly accelerated or decelerated through a Campbell diagram crossing.

Numerical research on the resonance frequency characteristics of the Sparkjet actuator using modal analysis

In this study, the resonance frequency characteristics of the SparkJet actuator are examined through numerical investigation using modal analysis. First, an eigenvalue problem is established to compute the resonance frequencies of the SparkJet actuator, considering its configuration, boundary conditions and internal physical phenomena. To validate the eigenvalue problem, computational fluid dynamics (CFD) simulation is conducted utilizing unsteady three-dimensional Navier-Stokes equations with plasma energy source term, assuming local thermal equilibrium (LTE). Subsequently, the resonance frequencies are obtained by performing fast Fourier transform (FFT) on the thrust and average pressure data obtained from the CFD. In our investigation of the resonance frequency characteristics, eigenmode decomposition on the pressure contour obtained from the CFD is conducted utilizing the eigenfunctions obtained from the eigenvalue problem and their orthogonality. The eigenmode decomposition enables us to quantitatively evaluate the contribution of each eigenfunction to the thrust. Comparisons between the frequencies corresponding to the eigenfunctions significantly influencing on the thrust and the resonance frequencies obtained by FFT reveal a maximum error of 5.29 % and an average error of 2.35 % Moreover, when the taper angle is relatively large (approximately 45∘ or more), eigenfunctions significantly influencing on the thrust can be categorized into two distinct geometric patterns. These physically represent the waves that propagate and reflect in the streamwise or radial direction within the SparkJet actuator. This observation implies that the complex interactions of shock waves within the SparkJet actuator can be reduced to a few waves with simple physical interpretations. This may potentially aid in analyzing the physical phenomena within the SparkJet actuator.

Geometric approach to nonequilibrium hasty shortcuts.

Complex and even non-monotonic responses to external control can be found in many thermodynamic systems. In such systems, nonequilibrium shortcuts can rapidly drive the system from an initial state to a desired final state. One example is the Mpemba effect, where preheating a system allows it to cool faster. We present nonequilibrium hasty shortcuts-externally controlled temporal protocols that rapidly steer a system from an initial steady state to a desired final steady state. The term "hasty" indicates that the shortcut only involves fast dynamics without relying on slow relaxations. We provide a geometric analysis of such shortcuts in the space of probability distributions by using timescale separation and eigenmode decomposition. We further identify the necessary and sufficient condition for the existence of nonequilibrium hasty shortcuts in an arbitrary system. The geometric analysis within the probability space sheds light on the possible features of a system that can lead to hasty shortcuts, which can be classified into different categories based on their temporal pattern. We also find that the Mpemba-effect-like shortcuts only constitute a small fraction of the diverse categories of hasty shortcuts. This theory is validated and illustrated numerically in the self-assembly model inspired by viral capsid assembly processes.

Generating high-efficiency swimming kinematics using hydrodynamic eigenmode decomposition

This paper explores the use of hydrodynamic eigenmode decomposition as a means of generating optimal swimming kinematics of slender three-dimensional bodies. The eigenvectors of the unsteady hydrodynamic system are used as basis functions for the response to external forcing, such as perturbations generated by the deformation of the body. Exploiting the orthogonality of the modes, we show that swimming according to a single appropriately selected hydrodynamic eigenmode results in high-efficiency swimming. To demonstrate this result, we use an inviscid three-dimensional vortex lattice model to investigate the hydrodynamic eigenmodes of a selection of geometries. We find that for all of the body geometries tested, hydrodynamic efficiency far exceeding that of pure heaving or pitching can be achieved. All eigenmodes tested produce high-efficiency motion, as long as the beat frequency is higher than the mode's “cut-in” frequency for thrust generation. The eigenmodes show qualitative similarity to swimming patterns observed in nature and also correspond well to the existing classifications of undulatory and oscillatory swimming. This study demonstrates that the hydrodynamic eigenmode analysis can generate high-efficiency swimming kinematics based only on information about the body and wake geometry, and as such, this method has significant potential for further development and application to autonomous underwater vehicle design.

Radiation from global topological strings using adaptive mesh refinement: Massive modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public code, GRChombo. We perform a quantitative investigation of massive radiation from single sinusoidally displaced string configurations, studying a range of string widths defined by the coupling parameter $\lambda$ over two orders of magnitude, effectively varying the mass of radiated particles $m_H \sim \sqrt{\lambda}$. We perform an in-depth investigation into the effects of AMR on massive radiation emission, including radiation trapping and the refinement required to resolve high frequency modes. We use quantitative diagnostic tools to determine the eigenmode decomposition, showing a complex superposition of high frequency propagating modes with different phase and group velocities. We conclude that massive radiation is generally strongly suppressed relative to the preferred massless channel, with suppression increasing at lower amplitudes and higher $\lambda$. Only in extreme nonlinear regimes (e.g.\ with relative amplitude $\varepsilon \sim 1.5$ and $\lambda < 1$) do we observe massive and massless radiation to be emitted at comparable magnitude. We find that massive radiation is emitted in distinct high harmonics of the fundamental frequency of the string, and we demonstrate that, for the sinusoidal configurations studied, massive radiation is exponentially suppressed with $\sqrt{\lambda}$ (i.e. the particle mass). Finally, we place these results in the context of axions and gravitational waves produced by cosmological cosmic string networks, and note that AMR provides a significant opportunity to explore higher $\lambda$ (thin string) regimes whilst using fewer computational resources.

Multispectral tunable symmetry-protected bound states in the continuum in all-dielectric split-ring resonator metasurfaces

Symmetry incompatible bound states in the continuum (BICs) are the non-radiating states that remain decoupled from the radiation continuum due to the symmetry mismatch. However, it has always been challenging to observe multiple symmetry-protected BICs in single resonator dielectric metasurfaces. This work reports multiple symmetry-protected BICs for both linear polarizations in all-dielectric metasurfaces made up of split-ring resonators (SRRs). Intensive numerical simulations predict that SRR can support a high-quality factor (Q) of 106 for standalone and with substrate in presence of asymmetry. However, for a realistic and practical scenario, a Q-factor of 8000 for standalone structures is achieved, which reduces by a factor of 1.25 in the presence of silica substrate. Even if the out-of-plane asymmetry is introduced either in the geometry or variation in the angle of incidence, BICs are transformed into quasi-BICs possessing Fano resonance. Eigenmode and multipole decomposition analysis confirm multiple BIC resonances; notable dominant contributions are from magnetic dipole, toroidal dipole, and electric and magnetic quadrupoles. Integrating monolayer graphene adds tunability to the metasurface, where distinct quasi-BIC modes can be employed to facilitate an excellent switching.

Rethinking the ill-posedness of the spectral function reconstruction — Why is it fundamentally hard and how Artificial Neural Networks can help

Reconstructing hadron spectral functions through Euclidean correlation functions are of the important missions in lattice QCD calculations. However, in a Källen–Lehmann (KL) spectral representation, the reconstruction is observed to be ill-posed in practice. It is usually ascribed to the fewer observation points compared to the number of points in the spectral function. In this paper, by solving the eigenvalue problem of continuous KL convolution, we show analytically that the ill-posedness of the inversion is fundamental and it exists even for continuous correlation functions. We discussed how to introduce regulators to alleviate the predicament, in which include the Artificial Neural Networks (ANNs) representations recently proposed by the Authors in [28]. The uniqueness of solutions using ANNs representations is manifested analytically and validated numerically. Reconstructed spectral functions using different regularization schemes are also demonstrated, together with their eigen-mode decomposition. We observe that components with large eigenvalues can be reliably reconstructed by all methods, whereas those with low eigenvalues need to be constrained by regulators.

Independently tunable bifunctional terahertz metasurface based on double-layer graphene

Artificial metasurfaces are one of the most promising candidates for realizing flexibly tunable devices. Here we propose a tunable bifunctional metasurface (TBM), which incorporates two layers of independently controllable hollow-patterned graphene that contribute to wideband linear polarization conversion mode and dual-band absorption mode, respectively. When working in linear polarization conversion mode, it can achieve the polarization conversion ratio (PCR) of over 96.1% and the relative bandwidth of about 42.2% in 3.98–6.11 THz; when operating in dual-band absorption mode, the absorptivity can reach 97.1% and 99.9% at 3.55 THz and 4.98 THz, respectively. The working mechanisms are elucidated through the eigenmode decomposition, transmission line model, surface current and field distributions. In addition, the influences of the chemical potential and relaxation time of graphene, main geometric parameters of the TBM, and incident angle of terahertz waves are discussed, implying that the TBM has excellent tunability and tolerance, and may provide a scheme for designing terahertz devices such as isolators, modulators and rotators.

Radiation from global topological strings using adaptive mesh refinement: Methodology and massless modes

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public numerical relativity code, GRChombo. We perform a quantitative investigation of the dynamics of single sinusoidally displaced string configurations, studying a wide range of string energy densities $\mu \propto \ln{\lambda}$, defined by the string width parameter $\lambda$ over two orders of magnitude. We investigate the resulting massless (Goldstone boson or axion) radiation signals, using quantitative diagnostic tools to determine the eigenmode decomposition. Given analytic radiation predictions, we compare the oscillating string trajectory with a backreaction model accounting for radiation energy losses, finding excellent agreement. We establish that backreaction decay is accurately characterised by the inverse square of the amplitude being proportional to the inverse tension $\mu$ for $3\lesssim \lambda \lesssim 100$. We conclude that analytic radiation modelling in the thin-string (Nambu-Goto) limit provides the appropriate cosmological limit for global strings. We contextualise these results with respect to axions and gravitational waves produced by cosmic string networks.

A Feedforward Neural Network for Modeling of Average Pressure Frequency Response

The Helmholtz equation has been used for modeling the sound pressure field under a harmonic load. Computing harmonic sound pressure fields by means of solving Helmholtz equation can quickly become unfeasible if one wants to study many different geometries for ranges of frequencies. We propose a machine learning approach, namely a feedforward dense neural network, for computing the average sound pressure over a frequency range. The data are generated with finite elements, by numerically computing the response of the average sound pressure, by an eigenmode decomposition of the pressure. We analyze the accuracy of the approximation and determine how much training data is needed in order to reach a certain accuracy in the predictions of the average pressure response.

Eigenmode Decomposition of the Diffusion Equation: Applications to Pressure-Rate Deconvolution and Reservoir Pore Volume Estimation

SummaryThis paper proposes the application of the eigenmode decomposition to the problem of pressure-rate deconvolution. The method enabled us to write the solution of the pressure-rate deconvolution as an infinite series of eigenmodes (eigenfunctions). Each eigenmode is associated with a hydraulic diffusion time scale (eigenvalue) that depends on the intrinsic reservoir properties. The set of eigenmodes forms a basis of the solution space and the analytical solution shows some desirable properties: It is smooth, physically constrained for a closed system, and some parameters have a physical interpretation. As a result, in both single and multiwell problems, the late-time unit slope appears naturally and the curvature penalty does not have to be imposed, thus addressing current knowledge gaps. As an additional contribution, we also propose a mathematically well-defined expression in terms of eigenfunctions to the concept of investigated volume during a well test and a procedure for untangling the single-well deconvolved response from interference effects of neighboring wells under certain conditions. Applications to the analysis of drillstem tests (DST) and reservoir characterization are presented.

Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature

Abstract The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of SU(2)L × SU(2)R symmetry breaking. However, the chiral condensate also breaks the axial U(1) symmetry, which is usually not studied as it is already broken by the anomaly and apparently has little impact on the transition. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial U(1) breaking contributes to the chiral phase transition. Employing a chirally symmetric lattice Dirac operator and its eigenmode decomposition, we separate the axial U(1) breaking effects from others. Our result in two-flavor QCD indicates that both of the connected and disconnected chiral susceptibilities are dominated by axial U(1) breaking at temperatures T ≳ 190 MeV after the quadratically divergent constant is subtracted.

Generation of four-mode cluster states based on cascade four-wave mixing process

As a crucial quantum resource for quantum computing and quantum information processing, cluster state has attracted extensive attention due to its unique entanglement properties and rich structures. In this work, we theoretically propose a scheme for generating four-mode entangled states based on cascaded four-wave mixing (FWM) process. The internal entanglement characteristics are studied by using the positivity under partial transposition criterion and eigenmode decomposition. In addition, the output entangled states are reconstructed and optimized by adjusting the relative phase of balanced homodyne detection and postprocessing the signal noise, and finally three four-mode cluster states with different structures are generated. Such a method can effectively reduce the excess noise induced by finite squeezing. Our theoretical results provide a reliable way of generating scalable continuous variable cluster states based on FWM process in atomic ensemble.

Varying fundamental constants principal component analysis: additional hints about the Hubble tension

ABSTRACT Varying fundamental constants (VFC; e.g. the fine-structure constant, αEM) can arise in numerous extended cosmologies. Through their effect on the decoupling of baryons and photons during last scattering and reionization, these models can be directly constrained using measurements of the cosmic microwave background (CMB) temperature and polarization anisotropies. Previous investigations focused mainly on time-independent changes to the values of fundamental constants. Here we generalize to time-dependent variations. Instead of directly studying various VFC parametrizations, we perform a model-independent principal component analysis (PCA), directly using an eigenmode decomposition of the varying constant during recombination. After developing the formalism, we use Planck 2018 data to obtain new VFC limits, showing that three independent VFC modes can be constrained at present. No indications for significant departures from the standard model are found with Planck data. Cosmic variance limited modes are also compared and simple forecasts for the Simons Observatory are carried out, showing that in the future improvements of the current constraints by a factor of ≃3 can be anticipated. Our modes focus solely on VFC at redshifts z ≥ 300. This implies that they do not capture some of the degrees of freedom relating to the reionization era. This aspect provides important new insights into the possible origin of the Hubble tension, hinting that indeed a combined modification of recombination and reionization physics could be at work. An extended PCA, covering both recombination and reionization simultaneously, could shed more light on this question, as we emphasize here.

Saturation physics of threshold heat-flux reduction

The saturation physics of ion-temperature-gradient-driven turbulence is examined in relation to the temperature-gradient variation of the heat flux, which can exhibit an upshift of the critical gradient for significant flux relative to the linear instability threshold. Gyrokinetic measurements of saturation properties and spectral energy transfer, which will be defined in Sec. II, are presented, indicating that the physics of saturation is fundamentally unchanged on either side of the upshifted gradient. To analyze heat transport below and above the upshifted critical gradient, a fluid model for toroidal ion-temperature-gradient turbulence is modified to include the kinetic instability threshold. The model and the heat flux are rendered in the eigenmode decomposition to track the dominant mode-coupling channel of zonal-flow-catalyzed transfer to a conjugate stable mode. Given linear and nonlinear symmetries, the stable mode level and the cross-correlation of the unstable and stable mode amplitudes are related to the unstable mode level via linear physics. The heat flux can then be written in terms of the unstable-mode level, which through a nonlinear balance depends on the eigenmode-dependent coupling coefficients and the triplet correlation time of the dominant coupled modes. Resonance in these quantities leads to suppressed heat flux above the linear threshold, with a nonlinear upshift of the critical gradient set by the resonance broadening of a finite perpendicular wavenumber and collisionality.

Efficient ensemble generation for uncertain correlated parameters in atmospheric chemical models: a case study for biogenic emissions from EURAD-IM version 5

Abstract. Atmospheric chemical forecasts heavily rely on various model parameters, which are often insufficiently known, such as emission rates and deposition velocities. However, a reliable estimation of resulting uncertainties with an ensemble of forecasts is impaired by the high dimensionality of the system. This study presents a novel approach, which substitutes the problem into a low-dimensional subspace spanned by the leading uncertainties. It is based on the idea that the forecast model acts as a dynamical system inducing multivariate correlations of model uncertainties. This enables an efficient perturbation of high-dimensional model parameters according to their leading coupled uncertainties. The specific algorithm presented in this study is designed for parameters that depend on local environmental conditions and consists of three major steps: (1) an efficient assessment of various sources of model uncertainties spanned by independent sensitivities, (2) an efficient extraction of leading coupled uncertainties using eigenmode decomposition, and (3) an efficient generation of perturbations for high-dimensional parameter fields by the Karhunen–Loéve expansion. Due to their perceived simulation challenge, the method has been applied to biogenic emissions of five trace gases, considering state-dependent sensitivities to local atmospheric and terrestrial conditions. Rapidly decreasing eigenvalues state that highly correlated uncertainties of regional biogenic emissions can be represented by a low number of dominant components. Depending on the required level of detail, leading parameter uncertainties with dimensions of 𝒪(106) can be represented by a low number of about 10 ensemble members. This demonstrates the suitability of the algorithm for efficient ensemble generation for high-dimensional atmospheric chemical parameters.

LED-based chromatic and white-light vortices of fractional topological charges

Based on an LED light source, we present an experimental scheme to produce chromatic and white-light optical vortices carrying fractional topological charges. In theory, we develop a general formula to simulate the propagation dynamics of such fractional chromatic and white-light vortices based on the eigenmode decomposition of orbital angular momentum within the Gaussian–Schell model. In the experiment, for the generation of the chromatic and white-light optical vortices, we use a phase-only spatial light modulator to prepare the desired holographic gratings and a prism to compensate for the dispersion for three primary colors (red, green, and blue). The experimental observations, e.g., the seal-healing effect of dislocation lines, are in good agreement with the simulation results. The present work extends the studies of fractional optical vortices not only from highly coherent to partially coherent region but also from monochromatic to chromatic (white-light) source, which may find potential applications in LED-based visible light communication and optical displaying.

Strength analysis in regulatory design documents and computational software

Modern building design standards have a long history. During this time, they have undergone a number of changes, but some of their provisions and recommendations, once proclaimed, remain unchanged. And although they do not meet the modern possibilities of computational analysis, but continue to exist due to the established tradition. In this paper, attention is paid to only some of the mentioned conflicts, which are related to the software implementation of regulatory requirements. The first of them is connected with two different parts in the process of design justification: calculation of the stress-strain state and verification of the accepted cross sections. It is noted that when the calculation model adopted for computer analysis of the structure does not correspond to the model that was meant when compiling the regulatory document, there may be contradictions or inaccuracies that cannot be resolved without decoding the approach adopted in the standards. Unfortunately, such a decoding is not provided in our rationing system. Another group of conflicts is connected with conducting the structural analysis taking into account geometrical and physical nonlinearity declared by standards. The matter is there are some problems that cannot be solved when using nonlinear calculation, for instance, dynamic analysis using eigenmode decomposition with the subsequent summation of modal reactions. The problem of choosing an unfavorable combination of loads is also in this list. In the final part of the article some proposals are formulated. This proposals aimed at eliminating contradictions between the desire to develop simple and understandable design rules and the ability of modern computer to solve problems without the use of dubious simplifications.