Spectral Description Research Articles

Spatial–Spectral Description of an Input Superconducting Converter of a Magnetocardiograph

Spatial–Spectral Description of an Input Superconducting Converter of a Magnetocardiograph

A method to assess linear self-predictability of physiologic processes in the frequency domain: application to beat-to-beat variability of arterial compliance.

The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

Physically accurate real-time synthesis of ocean waves for maritime simulators

The most efficient approach to the synthesis of multi-directional ocean waves is the so-called Fourier approach, based on a spectral description of waves in wavenumber space. According to this approach, 2D wavenumber spectra are transformed into spatial wave quantities by means of 2D Inverse Discrete Fourier Transforms. The Fourier approach is well described in literature, but the majority of works dealing with it are focused on graphical realism, and usually neglect the physical accuracy of the synthesized ocean scene. This paper presents a new implementation of the Fourier approach which exploits the equivalence between wavenumber and frequency/direction spectra to result in a flexible, performant and physically accurate model that is especially suitable for maritime simulators. In the proposed method, input wave spectra expressed in frequency/direction space are mapped at runtime on the wavenumber spectra used for the ocean synthesis. A GPU implementation based on the multi-band approach allows highly efficient real-time computations. The performance of the method is described in detail, investigating different configurations of the wavenumber spectrum and comparing the results obtained on different hardware. The physical accuracy is assessed by recording time series of synthesized wave elevations and using them to reconstruct a directional wave spectrum. Four benchmark spectra are examined, highlighting a very satisfactory match between the input and the reconstructed spectra, even for complex sea states with multiple wave systems originated from different sources.

Phase and defect diagrams based on spectral grain boundary segregation: A regular solution approach

Recent works have proposed the treatment of alloy defect states with thermodynamics analogous to phase thermodynamics, so they can be analyzed in a manner that is comparable to bulk phase diagrams. We refer to such diagrams containing both bulk phase and defect state information as “phase-and-defect diagrams.” Segregated grain boundaries (GBs) are an example of one such defect state, which enable, for example, the stabilization of nanocrystalline alloys. The recent development of spectral thermodynamic isotherms has demonstrated that a fully spectral description, which captures the complete distribution of local atomic environments in the grain boundary network, is necessary for accurate modeling of segregation behavior. To our knowledge, there is currently no spectral free energy formulation from which a phase-and-defect diagram of the segregated polycrystalline state can be produced. In this work, we present a spectral regular solution model of grain boundary segregation, from which we derive an analytical free energy function for the segregated polycrystalline state. We then use this free energy representation to construct a phase-and-defect diagram for a hypothetical alloy system, providing a framework for future efforts in developing spectral phase-and-defect diagrams.

Multi-scale dynamics of the interaction between waves and mean flows: From nonlinear WKB theory to gravity-wave parameterizations in weather and climate models

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for a new class of parameterizations of subgrid-scale gravity waves (GW) in weather and climate models. The development of this theory is reviewed here. It applies to all interesting regimes of atmospheric stratification, i.e., also to moderately strong stratification as occurring in the middle atmosphere, and thereby extends classic assumption for the derivation of quasi-geostrophic theory. At strong wave amplitudes a fully nonlinear theory arises that is complemented by a quasilinear theory for weak GW amplitude. The latter allows the extension to a spectral description that forms the basis of numerical implementations that avoid instabilities due to caustics, e.g., from GW reflection. Conservation properties are discussed, for energy and potential vorticity, as well as conditions under which a GW impact on the larger-scale flow is possible. The numerical implementation of the theory for GW parameterizations in atmospheric models is described, and the consequences of the approach are discussed, as compared to classic GW parameterizations. Although more costly than the latter, it exhibits significantly enhanced realism, while being considerably more efficient than an approach where all relevant GWs are to be resolved. The reported theory and its implementation might be of interest also for the efficient and conceptually insightful description of other wave-mean interactions, including those where the formation of caustics presents a special challenge.

Efficiency of Magnetohydrodynamic Wave Generation in Weakly Ionized Atmospheres

The generation of Alfvén and slow magnetoacoustic waves in weakly ionized atmospheres by excitation of the charges-only component of the two-fluid (charge and neutral) plasma is shown to be more or less efficient depending on the energy fraction initially allocated to the three stationary flow differential modes, which characterize the inter-species drift. This is explained via detailed analysis of the full 10-dimensional spectral description of two-fluid linear magnetohydrodynamics. Excitation via the velocity of the charges only is found to be very inefficient, in accord with previous results, while excitation via the magnetic field perturbation alone is highly efficient. All 10 eigenvalues and eigenvectors are presented analytically in the high collision frequency regime.

Soliton–mean field interaction in Korteweg–de Vries dispersive hydrodynamics

AbstractThe mathematical description of localized solitons in the presence of large‐scale waves is a fundamental problem in nonlinear science, with applications in fluid dynamics, nonlinear optics, and condensed matter physics. Here, the evolution of a soliton as it interacts with a rarefaction wave or a dispersive shock wave, examples of slowly varying and rapidly oscillating dispersive mean fields, for the Korteweg–de Vries equation is studied. Step boundary conditions give rise to either a rarefaction wave (step up) or a dispersive shock wave (step down). When a soliton interacts with one of these mean fields, it can either transmit through (tunnel) or become embedded (trapped) inside, depending on its initial amplitude and position. A topical review of three separate analytical approaches is undertaken to describe these interactions. First, a basic soliton perturbation theory is introduced that is found to capture the solution dynamics for soliton–rarefaction wave interaction in the small dispersion limit. Next, multiphase Whitham modulation theory and its finite‐gap description are used to describe soliton–rarefaction wave and soliton–dispersive shock wave interactions. Lastly, a spectral description and an exact solution of the initial value problem is obtained through the inverse scattering transform. For transmitted solitons, far‐field asymptotics reveal the soliton phase shift through either type of wave mentioned above. In the trapped case, there is no proper eigenvalue in the spectral description, implying that the evolution does not involve a proper soliton solution. These approaches are consistent, agree with direct numerical simulation, and accurately describe different aspects of solitary wave–mean field interaction.

Anharmonic effects on the reflectivity of CaS and MgS: a first-principles based study

We employ systematic calculations based on density functional theory to model the reflectivity of CaS and MgS in the infrared region. We show that in addition to the modeling using the harmonic approximation, an accurate spectral description requires the inclusion of anharmonic effects. Due to their conceptual simplicity, CaS and MgS are excellent systems for the explicit consideration of the anharmonicity, which we include here using a perturbative approach up to three-phonon scattering processes, and the consideration of isotopic disorder. All physical quantities, such as Born effective charges and dielectric constant, necessary for the calculation of the reflectivity within the Lorentz model are extracted from our first-principles computations. To validate our predicted optical and transversal modes, and reflectivity spectra, we compare them to available experimental results. We find that the overall agreement is good, which supports the importance of the inclusion of anharmonic terms in the modeling of optical properties in the infrared region.

Effective infrared spectral identification method via improved local binary patterns and spectral description representation

Infrared spectral identification task which is an essential branch of infrared spectroscopy, has been extensively studied. In this article, we proposed an efficient description representation model with the local binary pattern (LBP) strategy, and applied to infrared spectral searching and identification. The idea is motivated by the fact that spectral curve can be considered as a composition of micro-patterns such as peaks, troughs, valley and flat lines which are well described by LBP. The whole spectral lines are split into several small sections, and then extracted the spectral LBP features. The method is capable of extracting both the local and holistic spectral features and robust to random noise and baseline interferences. Experimental results on the public infrared spectral dataset demonstrate that the proposed spectral identification method can significantly raise performance when noise and baseline interferences are present.

A Model of Energy and Spectral Shape for the Internal Gravity Wave Field in the Deep Sea: The Parametric IDEMIX Model

Abstract The spectral description of the energy of oceanic internal gravity waves is generally represented by the Garrett–Munk (GM) model, a function with a power-law decrease of spectral energy in wavenumber–frequency space. Besides the slopes of these power laws, the spectrum is expressed as a function of energy and a bandwidth parameter that fixes the range of vertical modes excited in the respective state. Whereas concepts have been developed and agreed upon of what processes feed the wave spectrum and what dissipates energy, there is no explanation of what shapes the spectral distribution, i.e., how the power laws come about and what sets the bandwidth. The present study develops a parametric spectral model of energy and bandwidth from the basic underlying energy balance in terms of forcing, propagation, refraction, spectral transfer, and dissipation. The model is an extension of the IDEMIX (Internal Wave Dissipation, Energy and Mixing) models where bandwidth was taken as a constant parameter. The current version of the model is restricted to single-column mode and the slopes of the spectral power laws are fixed. A coupled system of predictive equations for energy and bandwidth (for up- and downward propagating waves) results. The equations imply that bandwidth relates to energy by a power law with an exponent given by the dynamical parameters. It agrees favorably with energy, bandwidth, and slope data from previously published fits of the GM model to Argo float observations. Numerical solutions of the coupled energy–bandwidth model in stand-alone modus are presented.

Absorption/Attenuation Spectral Description of ESKAPEE Bacteria: Application to Seeder-Free Culture Monitoring, Mammalian T-Cell and Bacteria Mixture Analysis and Contamination Description.

Despite numerous innovations, measuring bacteria concentrations on a routine basis is still time consuming and ensuring accurate measurements requires careful handling. Furthermore, it often requires sampling small volumes of bacteria suspensions which might be poorly representative of the real bacteria concentration. In this paper, we propose a spectroscopy measurement method based on a description of the absorption/attenuation spectra of ESKAPEE bacteria. Concentrations were measured with accuracies less than 2%. In addition, mixing the mathematical description of the absorption/attenuation spectra of mammalian T-cells and bacteria allows for the simultaneous measurements of both species' concentrations. This method allows real-time, sampling-free and seeder-free measurement and can be easily integrated into a closed-system environment.

The linear-time-invariance notion to the Koopman analysis: The architecture, pedagogical rendering, and fluid–structure association

This work augments a Linear-Time-Invariance (LTI) notion to the Koopman analysis, finding an invariant subspace on which consistent Koopman modes are expanded with fluid mechanics implications. The work also develops the Koopman-LTI architecture—a systematic procedure to associate fluid excitation and structure surface pressure by matching Koopman eigen tuples, establishing fluid–structure correspondences that examine fluid–structure interactions (FSIs) at new angles. The data-driven, modular architecture also exhibits the potential to evolve with advances in Koopman algorithms. A pedagogical prism wake example demonstrated that the Koopman-LTI generated a near-perfect linearization of nonlinear FSI dynamics involving inhomogeneous anisotropic turbulence, with mean and root-mean-squared errors of O−12 and O−9, respectively; the infinite-dimensional Koopman modes were also approximated with O−8 error. The subcritical wake during shear layer transition II was also reduced into only six dominant excitation-response Koopman duplets. The upstream and crosswind walls constitute a dynamically unified interface dominated by only two mechanisms. The downstream wall remains a distinct interface and is dominated by four other mechanisms. The complete revelation of the prism wake comes down to understanding the six mechanisms, which Part II [Li et al., “A parametric and feasibility study for data sampling of the dynamic mode decomposition: Range, resolution, and universal convergence states,” Nonlinear Dyn. 107(4), 3683–3707 (2022)] will address by investigating the physics implications of the duplets' in-synch phenomenological features. Finally, the analysis revealed z-velocity's marginal role in the convection-dominated free-shear flow, Reynolds stresses' spectral description of cascading eddies, wake vortices' sensitivity to dilation and indifference to distortion, and structure responses' origin in vortex activities.

Development of a Technique for the Spectral Description of Curves of Complex Shape for Problems of Object Classification

Vascular pathology symptoms can be determined by retinal image segmentation and classification. However, the retinal images from non-invasive diagnostics have a complex structure containing tree-like vascular beds, multiple segment boundaries, false segments, and various distortions. It should be noted that complex structure images’ segmentation does not always provide a single solution. Thus, the goal is to increase the efficiency of vascular diagnostics. This study aims to develop a technique for describing the geometric properties of complexly structured image segments used for classifying vascular pathologies based on retinal images. The advantages and disadvantages of the existing methods and algorithms of segmentation were considered. The most effective use areas of the mentioned methods and algorithms are revealed. Through detecting retinal thrombosis, the algorithm's efficiency for constructing a mathematical model of an arbitrary shape segment based on the morphological processing of binary and halftone images was justified. A modified variant of this algorithm based on the spectral analysis procedure of arbitrary shape boundary curves was used for the spectral description of complex shape curves for classifying vascular pathologies based on retinal images. Two approaches have been developed. The first one allows obtaining a closing segment of the curve from a symmetric mapping of the initial parametric curves. The second involves intelligent data processing and obtaining contours of minimum thickness, forming convex sets. The results of experiments confirm the possibility of practical use of the developed technique to solve problems of vascular pathology classification based on retinal images, showing the correct forecast probability was 0.93 with all associated risk factors. Doi: 10.28991/ESJ-2022-06-06-015 Full Text: PDF

Central measures of continuous graded graphs: the case of distinct frequencies

We define a class of continuous graded graphs similar to the graph of Gelfand–Tsetlin patterns, and describe the set of all ergodic central measures of discrete type on the path spaces of such graphs. The main observation is that an ergodic central measure on a subgraph of a Pascal-type graph can often be obtained as the restriction of the standard Bernoulli measure to the path space of the subgraph. This observation dramatically changes the approach to finding central measures also on discrete graphs, such as the famous Young graph. The simplest example of this type is given by the theorem on the weak limits of normalized Lebesgue measures on simplices; these are the so-called Cesàro measures, which are concentrated on the sequences with prescribed Cesàro limits (this limit parametrizes the corresponding measure). More complicated examples are the graphs of continuous Young diagrams with fixed number of rows and the graphs of spectra of infinite Hermitian matrices of finite rank. We prove existence and uniqueness theorems for ergodic central measures and describe their structure. In particular, our results (1) give a new spectral description of the so-called infinite-dimensional Wishart measures (in Biometrika 20A(1–2):32–52, 1928)—ergodic unitarily invariant measures of discrete type on the set of infinite Hermitian matrices; (2) describe the structure of continuous analogs of measures on discrete graded graphs. New problems and connections which appear are to be considered in new publications.

General $\delta$-shell interactions for the two-dimensional Dirac operator: self-adjointness and approximation

In this work we consider the two-dimensional Dirac operator with general local singular interactions supported on a closed curve. A systematic study of the interaction is performed by decomposing it into a linear combination of four elementary interactions: electrostatic, Lorentz scalar, magnetic, and a fourth one which can be absorbed by using unitary transformations. We address the self-adjointness and the spectral description of the underlying Dirac operator. In the non-critical case, we do so by providing a boundary triple, and in the critical purely magnetic case, by exploiting the phenomenon of confinement and super-symmetry. Moreover, we justify our model by showing that Dirac operators with singular interactions are limits in the strong resolvent sense of Dirac operators with regular potentials.

AGILE Observations of GRB 220101A: A “New Year's Burst” with an Exceptionally Huge Energy Release

We report the AGILE observations of GRB 220101A, which took place at the beginning of 2022 January 1 and was recognized as one of the most energetic gamma-ray bursts (GRBs) ever detected since their discovery. The AGILE satellite acquired interesting data concerning the prompt phase of this burst, providing an overall temporal and spectral description of the event in a wide energy range, from tens of kiloelectronvolts to tens of megaelectronvolts. Dividing the prompt emission into three main intervals, we notice an interesting spectral evolution, featuring a notable hardening of the spectrum in the central part of the burst. The average fluxes encountered in the different time intervals are relatively moderate, with respect to those of other remarkable bursts, and the overall fluence exhibits a quite ordinary value among the GRBs detected by MCAL. However, GRB 220101A is the second farthest event detected by AGILE, and the burst with the highest isotropic equivalent energy of the entire MCAL GRB sample, releasing E iso = 2.54 × 1054 erg and exhibiting an isotropic luminosity of L iso = 2.34 × 1052 erg s−1 (both in the 400 keV–10 MeV energy range). We also analyzed the first 106 s of the afterglow phase, using the publicly available Swift-XRT data, carrying out a theoretical analysis of the afterglow, based on the forward shock model. We notice that GRB 220101A is with high probability surrounded by a wind-like density medium, and that the energy carried by the initial shock shall be a fraction of the total E iso, presumably near ∼50%.

A rolling bearing status monitoring method based on subband spectral fuzzy description

Vibration signals provided by rotating machinery are informative signals about their operating states. By nature, the vibration signal behavior is non-stationary. To this end, the extraction of discriminating and fault-sensitive parameters is a major challenge in the field of monitoring rotating machines. Conventional fault diagnosis methods based on signal processing use statistical feature parameters in time domain, frequency domain and time-frequency representation. In this article, a new method is proposed for the detection and classification of bearing defects based on spectral subband using frequency membership functions. Statistical parameters including subband energy, Center frequency, root variance frequency and Shannon entropy are considered. Compared to the common features, the extracted parameters can provide discriminating information. These feature parameters are finally fed into a generalized RBF neural network system trained with the Resilient Backpropagation (Rprop) algorithm to classify seven pre-established fault types in ball bearings operating under multiple shaft speeds and load conditions. The results suggest that the proposed system can significantly improve the diagnostic performance in terms of accuracy and estimation of the bearing fault level.

Robust topology optimization of structures under uncertain propagation of imprecise stochastic-based uncertain field

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and standard deviation of compliance as well as the optimized topological layouts of a structure for various scenarios. In the proposed approach, the imprecise random field variables are determined utilizing parameterized p-boxes with different confidence intervals. The Karhunen–Loève (K–L) expansion is extended to provide a spectral description of the imprecise random field. The linear superposition method in conjunction with a linear combination of orthogonal functions is employed to obtain explicit mathematical expressions for the first and second order statistical moments of the structural compliance. Then, an interval sensitivity analysis is carried out, applying the Orthogonal Similarity Transformation (OST) method with the boundaries of each of the intermediate variable searched efficiently at every iteration using a Combinatorial Approach (CA). Finally, the validity, accuracy, and applicability of the work are rigorously checked by comparing the outputs of the proposed approach with those obtained using the particle swarm optimization (PSO) and Quasi-Monte-Carlo Simulation (QMCS) methods. Three different numerical examples with imprecise random field loads are presented to show the effectiveness and feasibility of the study.

Spectral description of Fredholm operators via polynomially Riesz operators perturbation

Abstract In this paper, we establish some spectral analysis in Fredholm theory involving the concept of a polynomially Riesz operators perturbation. Moreover, we apply the obtained results to analyze the incidence of some essential spectra of a perturbed operator via this kind of perturbation. Our approach allows us to investigate a new description in the theory of unbounded operator matrices defined with maximal domain via this kind of perturbation. Finally, we conclude by presenting some progress in the theory of polynomially operators and the theory of semi-Fredholm and semi-Browder operators.

A spectral description for extreme sea states offshore Denmark Part I: Power spectrum

A power spectral density function that describes extreme sea states in the Danish sector of the North Sea is developed. The power spectrum is specified in terms of the parameters: significant wave height, spectral peak period, and spectral second-moment period. The power spectral density function is a modified Torsethaugen spectrum, involving an expression for the peak enhancement factor that is dependent on the inverse of the square root of wave steepness and a high-frequency tail that decays at a rate which is dependent on the significant wave height and the ratio of the peak and second-moment periods. The new function was developed from Directional Waverider data measured at two sites in the Danish sector of the North Sea and validated with data from other sites offshore Denmark, primarily recorded with Saab WaveRadars. A companion paper describes a new directional spreading function, which together with the power spectral density function, provides a description of the complete frequency-direction spectrum of extreme sea states in the Danish sector of the North Sea.