Time-domain Formulation Research Articles

Analytical solution for time integrals in diagrammatic expansions: Application to real-frequency diagrammatic Monte Carlo

The past years have seen a revived interest in the diagrammatic Monte Carlo (DiagMC) methods for interacting fermions on a lattice. A promising recent development allows one to now circumvent the analytical continuation of dynamic observables in DiagMC calculations within the Matsubara formalism. This is made possible by symbolic algebra algorithms, which can be used to analytically solve the internal Matsubara frequency summations of Feynman diagrams. In this paper, we take a different approach and show that it yields improved results. We present a closed-form analytical solution of imaginary-time integrals that appear in the time-domain formulation of Feynman diagrams. We implement and test a DiagMC algorithm based on this analytical solution and show that it has numerous significant advantages. Most importantly, the algorithm is general enough for any kind of single-time correlation function series, involving any single-particle vertex insertions. Therefore, it readily allows for the use of action-shifted schemes, aimed at improving the convergence properties of the series. By performing a frequency-resolved action-shift tuning, we are able to further improve the method and converge the self-energy in a non-trivial regime, with only 3-4 perturbation orders. Finally, we identify time integrals of the same general form in many commonly used Monte Carlo algorithms and therefore expect a broader usage of our analytical solution.

Time-Domain Studies of General Dispersive Anisotropic Media by the Complex-Conjugate Pole–Residue Pairs Model

A novel finite-difference time-domain formulation for the modeling of general anisotropic dispersive media is introduced in this work. The method accounts for fully anisotropic electric or magnetic materials with all elements of the permittivity and permeability tensors being non-zero. In addition, each element shows an arbitrary frequency dispersion described by the complex-conjugate pole–residue pairs model. The efficiency of the technique is demonstrated in benchmark numerical examples involving electromagnetic wave propagation through magnetized plasma, nematic liquid crystals and ferrites.

Adaptive Algorithm of Quasi-Stationary Periodic Processes Measurements Control

The aim of the work was to create an effective method of control of linear measuring systems functioning in the conditions of the prevailing influence of distortions caused by variability in time of measuring conversion parameters. The method and the algorithm of control of measurements of the quasi-stationary periodic process spectrum in frequency-domain and form in time-domain are presented, consisting in the simultaneous separate observation of the parameters of the process under probe and the parameters of the measuring system with the subsequent introduction of corrections. The control of system parameters is carried out using the artificial stationary polyharmonic sample impact. The spectra of the main and sample processes are not intersected. A synthesizing method of the form in time-domain of the sample impact process is presented. The main limitations and the range of conditions for the possible application of the method are determined, its effectiveness is shown on the example of the experimental data obtained during the low-frequency inductive electrical prospecting system functioning in alternating magnetic field measuring mode.

Minibatch least-squares reverse time migration in a deep-learning framework

Migration techniques are an integral part of seismic imaging workflows. Least-squares reverse time migration (LSRTM) overcomes some of the shortcomings of conventional migration algorithms by compensating for illumination and removing sampling artifacts to increase spatial resolution. However, the computational cost associated with iterative LSRTM is high and convergence can be slow in complex media. We implement prestack LSRTM in a deep-learning framework and adopt strategies from the data science domain to accelerate convergence. Our hybrid framework leverages the existing physics-based models and machine-learning optimizers to achieve better and cheaper solutions. Using a time-domain formulation, we find that minibatch gradients can reduce the computation cost by using a subset of total shots for each iteration. The minibatch approach not only reduces source crosstalk, but it is also less memory-intensive. Combining minibatch gradients with deep-learning optimizers and loss functions can improve the efficiency of LSRTM. Deep-learning optimizers such as adaptive moment estimation are generally well-suited for noisy and sparse data. We compare different optimizers and determine their efficacy in mitigating migration artifacts. To accelerate the inversion, we adopt the regularized Huber loss function in conjunction. We apply these techniques to 2D Marmousi and 3D SEG/EAGE salt models and find improvements over conventional LSRTM baselines. Our approach achieves higher spatial resolution in less computation time measured by various qualitative and quantitative evaluation metrics.

Implementation of Passive and Active Circuit Elements in Cylindrical Finite-Difference Time-Domain Formulation

The implementation of passive and active linear circuit elements in cylindrical finite-difference time-domain technique (CFDTD) is developed. The updating equations for active element such as a voltage sources and passive elements such as resistors, capacitors and inductors are represented for elements located along one of the cylindrical coordinate’s independent parameters. The analytical solutions for simple circuit configurations are computed and used as a reference to verify and confirm the accuracy of the developed CFDTD formulation and numerical results.

On the thermodynamic consistency of Quasi-linear viscoelastic models for soft solids

Originating in the field of biomechanics, Fung’s model of quasi-linear viscoelasticity (QLV) is one of the most popular constitutive theories employed to compute the time-dependent relationship between stress and deformation in soft solids. It is one of the simplest models of nonlinear viscoelasticity, based on a time-domain integral formulation. In the present study, we consider the QLV model incorporating a single scalar relaxation function. We provide natural internal variables of state, as well as a consistent expression of the free energy to illustrate the thermodynamic consistency of this version of the QLV model. The thermodynamic formulation highlights striking similarities between QLV and the internal-variable models introduced by Holzapfel and Simo. Finally, the dissipative features of compressible QLV materials are illustrated in simple tension.

Simplified FDTD Formulations for Magnetostatic Biased Graphene Simulations

Simplified finite difference time domain (FDTD) formulations are presented for magnetostatic biased graphene simulations. In this respect, graphene's anisotropic conductivity is incorporated into the FDTD algorithm by using the second-order Runge-Kutta (RK) scheme with the minimal additional computational resources. Moreover, the complex frequency shifted perfectly matched layer is combined with the presented RK-FDTD formulations to model open-space graphene structures. Numerical tests are included to validate the given formulations.

Nonlinear dispersive cell model for microdosimetry of nanosecond pulsed electric fields

For applications based on nanosecond pulsed electric fields (nsPEFs), the underlying transmembrane potential (TMP) distribution on the plasma membrane is influenced by electroporation (EP) of the plasma membrane and dielectric dispersion (DP) of all cell compartments which is important for predicting the bioelectric effects. In this study, the temporal and spatial distribution of TMP on the plasma membrane induced by nsPEFs of various pulse durations (3 ns, 5 ns unipolar, 5 ns bipolar, and 10 ns) is investigated with the inclusion of both DP and EP. Based on the double-shelled dielectric spherical cell model, the Debye equation describing DP is transformed into the time-domain form with the introduction of polarization vector, and then we obtain the time course of TMP by solving the combination of Laplace equation and time-domain Debye equation. Next, the asymptotic version of the Smoluchowski equation is included to characterize the EP of plasma membrane in order to observe more profound electroporation effects with larger pore density and electroporated areas in consideration of both DP and EP. Through the simulation, it is clearer to understand the relationship between the applied nsPEFs and the induced bioelectric effects.

Investigation of Sloshing Effects on Flexible Aircraft Stability and Response

The present paper provides an investigation of the effects of linear slosh dynamics on aeroelastic stability and response of flying wing configuration. The proposal of this work is to use reduced order model based on the theory of the equivalent mechanical models for the description of the sloshing dynamics. This model is then introduced into an integrated modeling that accounts for both rigid and elastic behavior of flexible aircraft. The formulation also provides for fully unsteady aerodynamics modeled in the frequency domain via doublet lattice method and recast in time-domain state-space form by means of a rational function approximation. The case study consists of the so-called body freedom flutter research model equipped with a single tank, partially filled with water, located underneath the center of mass of the aircraft. The results spotlight that neglecting such sloshing effects considering the liquid as a frozen mass may overshadow possible instabilities, especially for mainly rigid-body dynamics.

Time-domain finite element formulation of porous sound absorbers based on an equivalent fluid model

Time-domain finite element formulation of porous sound absorbers based on an equivalent fluid model

Wave propagation in two dimensional structures: An efficient solution method in time domain using exponential basis functions

In this paper, an efficient time domain formulation is proposed for computing time history dynamic responses of 2D structures, i.e. various types of trusses and frames. Unlike the methods using frequency domain, the proposed method employs the time weighted residual approach to solve the governing differential equations of the axial and flexural wave propagation problems, directly in time. Upon choosing the time step, the solution procedure begins with expressing the variation of axial and transverse displacement components, through the member’s length, as the summations of Fourier exponential basis functions in each time step. The unknown coefficients of the next steps are computed by the implementation of recurrent relations obtained based on a pre-integration process. The equilibrium and necessary continuity conditions at the common nodes/joints of adjacent elements are also fulfilled by introducing an innovative concept utilizing source functions. The role of these source functions is to simulate the boundary effects of the axial and flexural waves propagating within the structural members, simultaneously. The efficiency of the method is demonstrated in the dynamic analysis of some samples of truss and framed structures in terms of accuracy and computational time.

UWB Beam-Based Local Diffraction Tomography—Part II: The Inverse Problem

This two-part article is concerned with the medium reconstruction using the beam-based tomographic inverse scattering. This Part II is based on the results of Part I that has dealt with the preprocessing phase. Specifically, we defined there the beam-frame representation of the scattered field and the corresponding processing windows that transform the scattering data to the beam domain. We have also derived the “local time-domain diffraction tomography” relation according to which the beam-domain data are directly related to the local Radon transform (LRT) of the medium. This local transform can be inverted and is used here for the local reconstruction of the medium via beam-domain filtered backpropagation. In this article, we define the filtered backpropagated beam waves and then reconstruct the medium in any sub-domain of interest (DoI) by aggregating the contributions of the backpropagated beams that pass in or near that DoI. Specifically, we use the class of isodiffracting beam waves, namely, the isodiffracting Gaussian beams (ID-GBs) and the isodiffracting pulse beams (ID-PBs) for the frequency- and time-domain formulations, respectively. Explicit expressions for the filtered backpropagated reconstruction kernels are given. The efficacy of the beam-domain approach for local backpropagation and reconstruction is demonstrated via numerical examples of the synthetic noisy data.

An Efficient Numerical Formulation for Wave Propagation in Magnetized Plasma Using PITD Method

A modified precise-integration time-domain (PITD) formulation is presented to model the wave propagation in magnetized plasma based on the auxiliary differential equation (ADE). The most prominent advantage of this algorithm is using a time-step size which is larger than the maximum value of the Courant–Friedrich–Levy (CFL) condition to achieve the simulation with a satisfying accuracy. In this formulation, Maxwell’s equations in magnetized plasma are obtained by using the auxiliary variables and equations. Then, the spatial derivative is approximated by the second-order finite-difference method only, and the precise integration (PI) scheme is used to solve the resulting ordinary differential equations (ODEs). The numerical stability and dispersion error of this modified method are discussed in detail in magnetized plasma. The stability analysis validates that the simulated time-step size of this method can be chosen much larger than that of the CFL condition in the finite-difference time-domain (FDTD) simulations. According to the numerical dispersion analysis, the range of the relative error in this method is 10−6 to 5×10−4 when the electromagnetic wave frequency is from 1 GHz to 100 GHz. More particularly, it should be emphasized that the numerical dispersion error is almost invariant under different time-step sizes which is similar to the conventional PITD method in the free space. This means that with the increase of the time-step size, the presented method still has a lower computational error in the simulations. Numerical experiments verify that the presented method is reliable and efficient for the magnetized plasma problems. Compared with the formulations based on the FDTD method, e.g., the ADE-FDTD method and the JE convolution FDTD (JEC-FDTD) method, the modified algorithm in this paper can employ a larger time step and has simpler iterative formulas so as to reduce the execution time. Moreover, it is found that the presented method is more accurate than the methods based on the FDTD scheme, especially in the high frequency range, according to the results of the magnetized plasma slab. In conclusion, the presented method is efficient and accurate for simulating the wave propagation in magnetized plasma.

Fault Diagnosis of Nonlinear Analog Circuit Based on Generalized Frequency Response Function and LSSVM Classifier Fusion

For fault diagnosis of nonlinear analog circuit, a novel method based on generalized frequency response function (GFRF) and least square support vector machine (LSSVM) classifier fusion is presented. The sinusoidal signal is used as the input of analog circuit, and then, the generalized frequency response functions are estimated directly by the time-domain formulations. The discrete Fourier transform of measurement data is avoided. After obtaining the generalized frequency response functions, the amplitudes of the GFRFs are chosen as the fault feature parameters. A classifier fusion algorithm based on least square support vector machine (LSSVM) is used for fault identification. Two LSSVM multifault classifiers with different kernel functions are constructed as subclassifiers. Fault diagnosis experiments of resistor-capacitance (RC) circuit and Sallen Key filter are carried out, respectively. The results show that the estimated GFRFs of the circuit are accurate, and the fault diagnosis method can get high recognition rate.

Study on Tunable Magnetized Plasma Frequency Selective Surface Using JEC-FDTD Method

The tunability of traditional frequency selective surfaces (FSSs) is inconvenient using metal material patch as periodic element, utilizing genetic algorithms to model FSS layers obtaining desired filtering electromagnetic waves effect. However, plasma tube is used as an element of the frequency selection surfaces substituting traditional metal patch in this article. A 3-D finite-difference time-domain (FDTD) formulation for dispersive media called the JE convolution (JEC) method is derived using the convolution relationship between the current density $J$ and the electric field $E$ to simulate the interaction of incident wave and magnetized plasma FSS. Numerical experimental results show that the electron number density of magnetized plasma has a significant effect on the resonance frequency, which can be modulated to the desired filtering by varying the density in the magnetized plasma elements. Whereas the magnetized plasma FSSs behave exactly like a perfect electric conductor (PEC) increasing the electron number density to a certain degree. Thus, modulation based on the ionized electron number density of the magnetized plasma can be designed into a tunable plasma FSS. Both the collision model and the noncollision model of the magnetized plasma are proposed to research electromagnetic transmission characteristics of FSS. It shows that the collision frequency only affects the reflectivity while has no effect on the resonance frequency in the following numerical experiments. In addition, magnetization intensity of the plasma FSS is also taken into consideration. The users obtaining the desired resonance frequency and transmission characteristics of plasma FSS by simply tuning the plasma’s electron number density, collision frequency, and magnetization intensity. So the magnetized plasma FSS can not only improve the electromagnetic shielding effect but also facilitate the modulation and rapid response to achieve the desired filtering effect. What is more, the magnetized plasma FSS can be turned off to achieve transparency, which greatly expands the universality of magnetized plasma FSS.

Investigation on the full Mullins effect using time-dependent hyperelastic model with energy dissipation for rubber antivibration applications

Despite being investigated for many years, the Mullins effect is considered a major obstacle in understanding the behavior of rubber, especially in antivibration design and applications. It is important that not all current models relate the Mullins effect with a physical rubber property and the response is not measured in real time. In this paper, we propose a new method for antivibration applications. The full Mullins effect in the modified hyperelastic model, with stress softening and residual strain from the virgin state, is assumed to be a combination of damage, energy dissipation, and time-dependent characteristics. The measurable property of rubber (i.e. rebound resilience) is included. An industrial product, a circular rubber mount used for rail vehicles, is utilized for the experiment and simulation verification. The real-time history of the load and deflection calculated from the model is compared to the experimental data. In addition, the load-deflection responses of five consecutive cycles are extracted from the simulated historical data. To verify the proposed approach further, an overloading procedure 20% beyond specification is performed on three consecutive cycles. The comparisons between the simulation and the test data, in both the time-domain and load-deflection form, demonstrate the accuracy and reliability of the proposed approach. As the hyperelastic models are widely used in industry, the modification on existing models can be easily achieved and applied to antivibration applications.

Non-linear finite element modelling of light-to-heat energy conversion applied to solar nanofluids

Nanoparticles (NPs) exhibit remarkable photothermal conversion efficiency under optical illumination. This light-induced heating on NPs is interesting in many different applications, such as solar radiation absorption in nanofluids, which the present work focuses on. Consequently, mastering the temperature increase undergone by NPs and the surrounding media is extremely relevant today. As nanothermometry measurements of a single NP are hard to obtain, numerical simulations can contribute to better understand the physical phenomena involved in light-induced heating. In this vein, the current work presents theoretical and numerical formulations to predict the heating of optically excited NPs. Theoretically, a thermodynamic approach is conducted to obtain balance and constitutive equations. These equations are numerically discretised in the finite element method and implemented into a research code. The main novelty of the present work lies in developing, from a multiphysics perspective, a time domain formulation capable of modelling instantaneous dissipation that can be easily extended to account for more physical phenomena. Finally, the numerical model is validated by comparing analytical and numerical results, and maximum values of 0.0014 (%) of relative error between them are reached. Then some different analysis are performed for gold, silver and graphite NPs of 20 (nm) in diameter to characterise the temperature increase they produce in the surrounding medium (water) when optically excited at a wavelength of 400 (nm) and a laser intensity of 5 × 104(W/cm2) –silver NPs exhibiting the most significant temperature increase. The influence of NP concentration on the increase of temperature in nanofluids is numerically assessed as well by testing values of NP concentration up to a maximum of 0.052 (%), which considerably enhances temperature increase. In conclusion, the present numerical tool could be used to predict light-induced heating in NPs, which could complement and reduce the number of experiments for optimising the photothermal efficiency of solar nanofluids.

A Discrete Time Domain-Based MILP Framework for Control Parameter Tuning

The problem of tuning a fixed optimal set of parameters in time domain for dynamic systems is inherently nonlinear due to the product of tunable variables (controller gains and time constants) and time-dependent variables (bounded to the process), involved in equality constraints. This article presents a framework to transform such nonlinear problem into a mixed-integer linear problem through a binary-disjunctive representation of the problematic product between tunable and process-bounded variables, whereas addressing alternative linear representations to other nonlinearities such as saturation. A set of linear formulations in time domain are also developed to describe typical dynamic performance requirements, such as overshoot and settling time. The proposed framework was used to determine the optimal control parameters for disturbance rejection of the active power control loop in a photovoltaic generator with battery energy storage.

Direct Analysis of Three-Phase Induction Motor Considering Rotor Parameters’ Variation and Stator Belt Harmonics Effect

In this article, a novel procedure for the induction motor analysis is presented, avoiding the time-domain finite element problem formulation. The proposed technique closely links the mathematical model of the motor to the finite element simulations, concerning magneto-static and time-harmonic analyses. The target of the method is to include, in a rapid machine computation, also the effect of the slip frequency on the bars' current distribution and the induced currents in the cage due to the stator belt harmonics. The reported analysis example concerns the stand still operation of a double cage induction machine, where the rotor frequency is the grid frequency and the high stator current intensifies the role of the belt harmonics. A further application example concerns a flux weakening working point of a single cage induction motor in a variable speed drive. The aim of this work is to propose procedures to get a fast prediction of the induction motor performance, including also the principal parasitic effects, e.g. the rotor bars' skin effect and the stator belt harmonics, without using any time-domain analysis.

Cutting tool wear analysis using sound signal and simple microphone

Cutting tool is an important part of machining processes which in the operation frequently runs into wear. The wear cutting tool produces an imprecise product with low quality surface, may endanger machine tools by stimulating chatter. In this study, low cost and fast analysis of the wear of cutting tools in turning and drilling processes are proposed. For that purpose, the experimental set-up which consists of operating turning and drilling machine, simple microphone and Personal Computer (PC) with a sound card are set out. The wear of cutting tools are made by applying artificial wear. The sound data from normal and wear cutting tools of operating turning and drilling machines are recorded by using simple microphone and PC with a sound card. The obtained sound signals are then analyzed in the form of time and frequency domain, spectrogram by Wavelet Transform (WT). It is found that sound signals in time and frequency domain have a significant rise of amplitudes in wear conditions. The spectrograms exhibit the special contours which sign the existence of wear. The results demonstrate that the proposed method can analyze the cutting tool wear very well.