Large Time Domain Research Articles

Electronic Synapses Enabled by an Epitaxial SrTiO3‐δ / Hf0.5Zr0.5O2 Ferroelectric Field‐Effect Memristor Integrated on Silicon

AbstractSynapses play a vital role in information processing, learning, and memory formation in the brain. By emulating the behavior of biological synapses, electronic synaptic devices hold the promise of enabling high‐performance, energy‐efficient, and scalable neuromorphic computing. Ferroelectric memristive devices integrate the characteristics of both ferroelectric and memristive materials and present a far‐reaching potential as artificial synapses. Here, it is reported on a new ferroelectric device on silicon, a field‐effect memristor, consisting of an epitaxial ultrathin ferroelectric Hf0.5Zr0.5O2 film sandwiched between an epitaxial highly doped oxide semiconductor SrTiO3‐δ and a top metal. Upon a low voltage of less than 2 V, the field‐effect modulation in the semiconductor enables to access multiple states. The device works in a large time domain ranging from milliseconds down to tens of nanoseconds. By gradually switching the polarization by identical pulses, the ferroelectric diode devices can dynamically adjust the synaptic strength to mimic short‐ and long‐term memory plasticity. Ionic contributions due to redox processes in the oxide semiconductor beneficially influence the device operation and retention.

Wavelet-based Edge Multiscale Parareal Algorithm for subdiffusion equations with heterogeneous coefficients in a large time domain

We present the Wavelet-based Edge Multiscale Parareal (WEMP) Algorithm, recently proposed in Li and Hu (2021), for efficiently solving subdiffusion equations with heterogeneous coefficients in long time. This algorithm combines the benefits of multiscale methods, which can handle heterogeneity in the spatial domain, and the strength of parareal algorithms for speeding up time evolution problems when sufficient processors are available. Our algorithm overcomes the challenge posed by the nonlocality of the fractional derivative in previous parabolic problem work by constructing an auxiliary problem on each coarse temporal subdomain to completely uncouple the temporal variable. We prove the approximation properties of the correction operator and derive a new summation of exponential to generate a single-step time stepping scheme, with the number of terms of O(|logτf|2) independent of the final time, where τf is the fine-scale time step size. We establish the convergence rate of our algorithm in terms of the mesh size in the spatial domain, the level parameter used in the multiscale method, the coarse-scale time step size, and the fine-scale time step size. Finally, we present several numerical tests that demonstrate the effectiveness of our algorithm and validate our theoretical results.

Relating peak optical luminosity and orbital period of stellar-mass black holes in X-ray binaries

ABSTRACT We compare the peak optical luminosity with the orbital period for a sample of 22 stellar-mass black hole candidates with good measurements of both quantities. We find that the peak absolute magnitude for the outbursts follows a linear relation with MV, peak = 3.48(± 0.85) − 3.89(± 0.91) logPorb, which corresponds to a $L_V \propto P_{orb}^{1.56\pm 0.36}$ power-law relation. Excluding V4641 Sgr which is a strong outlier and not likely to have outbursts produced by the standard disc instability model, in addition to BW Cir and V821 Ara – both of which have highly uncertain distances; the new correlation for the 19 sources is found to be MV, peak = 3.01 (± 0.93) − 3.21 (± 1.04) logPorb, which corresponds to $L_V \propto P_{orb}^{1.28 \pm 0.42}$. This is an analogous relationship to the ‘Warner relation’ between orbital period and peak luminosity found for cataclysmic variables. We discuss the implications of these results for finding black hole X-ray binaries in other galaxies and in our own Galaxy with the Large Synoptic Survey Telescope and other future large time domain surveys.

Multi-domain multivariate spectral collocation method for (2+1) dimensional nonlinear partial differential equations

The novelty of this work rests upon the use of the domain partitioning technique in time variable when discretizing the domain of solution in spectral collocation algorithm. The single domain multivariate spectral collocation based methods have been proven to be effective in solving time-dependent partial differential equations (PDEs) defined over small time domains. However, there is a significant loss of accuracy as time computational domain proliferates and also when the number of grid nodes approaches a definite particular number. Therefore, the establishment of the new innovative multi-domain multivariate spectral quasilinearisation method (MDMV-SQLM) is described for the purpose of solving (2+1) dimensional nonlinear PDEs defined on large time intervals. The main output of this study is confirmation that minimizing the size of time computational domain at each subinterval assures sufficiently accurate results that are attained using minimal number of nodal points and less computational time. The solution algorithm involves partitioning the time domain into multiple non-overlapping sub-domains, simplification of the nonlinear PDEs using the quasilinearisation method and assumption of approximate solutions using triple Lagrange interpolating polynomials with Chebyshev–Gauss–Lobatto (CGL) points. The multi-domain spectral collocation procedure is executed on the linear systems of algebraic equations, where the subsequent matrix systems are solved separately in every time sub-interval with the continuity equation essentially used in obtaining initial conditions in the next subintervals. MATLAB software is used to implement the solution algorithm and numerical results are demonstrated graphically and in tabular form. To highlight the efficaciousness and accuracy of the MDMV-SQLM, error estimates, condition numbers and computational time are presented for well known (2+1) dimensional nonlinear initial-Dirichlet boundary value problems. The adoption of the domain decomposition technique is efficacious in suppressing the numerical challenges linked to large matrices and ill-conditioned nature of the resulting coefficient matrix. Also, the communicated results confirm that the numerical scheme is computationally cheap, fast and yield extremely accurate and stable results with the aid of fewer number of grid points for large time domains.

Accurate Numerical Treatment on a Stochastic SIR Epidemic Model with Optimal Control Strategy

In this paper, a numerical study has been undertaken on the susceptible-infected-recovered (SIR) epidemic model that encompasses the mechanisms of the evolution of disease transmission; a prophylactic vaccination strategy in the susceptible populations, depending on the infective individuals. We furnish numerical and graphical simulation combined with explicit series solutions of the proposed model using the New Iterative Method (NIM) and Modified New Iterative Method (MNIM). The analytic-numeric New Iterative Method failed to deliver accurate solution for the large time domain. A new reliable algorithm based on NIM, the coupling of the Laplace transforms, and the New Iterative method is called Modified New Iterative Method (MNIM) which is presented to enhance the validity domain of NIM techniques. The convergence analysis of the MNIM has also been illustrated. The simulation results show that the vaccination strategy can slow down the spread of the epidemic rapidly. Numerical results illustrate the excellent performance of the MNIM and show that the modified method is much more accurate than the NIM.

Solution of a Complex Nonlinear Fractional Biochemical Reaction Model

This paper discusses a complex nonlinear fractional model of enzyme inhibitor reaction where reaction memory is taken into account. Analytical expressions of the concentrations of enzyme, substrate, inhibitor, product, and other complex intermediate species are derived using Laplace decomposition and differential transformation methods. Since different rate constants, large initial concentrations, and large time domains are unavoidable in biochemical reactions, different dynamics will result; hence, the convergence of the approximate concentrations may be lost. In this case, the proposed analytical methods will be coupled with Padé approximation. The validity and accuracy of the derived analytical solutions will be established by direct comparison with numerical simulations.

Mechanics of nonlinear internal flow induced vibration and stability analysis of a pre-tensioned single walled carbon nanotube using classical differential transform method with CAT and SAT after-treatment techniques

This paper explores nonlinear internal flow induced vibration and stability of a pre-tensioned nanotube (SWCNT) that rests on elastic foundations. During the process of modeling, the impact of nonlinear Winkler foundation is considered and incorporated. For simplicity, the established nonlinear partial differential equation (PDE) for the vibrating SWCNT is converted into ordinary differential equation (ODE) via the method of Galerkin decomposition. Thereafter, the ODE is solved via classical differential transform method (DTM). The obtained analytical solution is further treated by the application of CAT and SAT after-treatment techniques to enable it captures large time domain during dynamic response. The treated solution is then validated and used for parametric studies. The parametric studies show how nonlocal elastic theory produces more accurate results than the classical equivalent and also how the foundation parameter increases the frequency of the system. It also shows how an increase in pre-tension has similar effect as that of flow velocity as they both increase the nonlinear frequency ratio. It is envisioned that this work will serve as point of reference for subsequent investigations and studies in this research area.

Dynamics of nonlinear cantilever piezoelectric–mechanical system: An intelligent computational approach

In this study, a novel application of intelligent computing by the exploitation of a supervised neural networks (SNNs) optimized with the Levenberg–Marquardt method (LMM) is presented to study the dynamics of nonlinear cantilever piezoelectric–mechanical system (NCPMS) represented with a second-order system of ordinary differential equation. The dataset for NCPMS is created using Adams numerical solver for input and target parameters for continuous mapping of SNN model of the system. The training, testing, and validation processes are exploited for SNNs models learned by LMM to determine the solution of NCPMS for different scenarios based on variation of amplitude and phase of cantilever frequency for small- and large-time domains while keeping the tip mass, beam length, mass density, capacitance and load resistance constant. The performance of SNN to solve NCPMS is substantiated on measurement of achieved accuracy through mean squared error, error histogram illustrations and regression analyzes.

Analysis of Spatial and Temporal Distribution of Purinergic P2 Receptors in the Mouse Hippocampus

ATP and other nucleotides are important glio-/neurotransmitters in the central nervous system. They bind to purinergic P2X and P2Y receptors that are ubiquitously expressed in various brain regions modulating various physiological and pathophysiological processes. P2X receptors are ligand-gated ion channels mediating excitatory postsynaptic responses whereas P2Y receptors are G protein-coupled receptors mediating slow synaptic transmission. A variety of P2X and P2Y subtypes with distinct neuroanatomical localization provide the basis for a high diversity in their function. There is increasing evidence that P2 receptor signaling plays a prominent role in learning and memory and thus, in hippocampal neuronal plasticity. Learning and memory are time-of-day-dependent. Moreover, extracellular ATP shows a diurnal rhythm in rodents. However, it is not known whether P2 receptors have a temporal variation in the hippocampus. This study provides a detailed systematic analysis on spatial and temporal distribution of P2 in the mouse hippocampus. We found distinct spatial and temporal distribution patterns of the P2 receptors in different hippocampal layers. The temporal distribution of P2 receptors can be segregated into two large time domains, the early to mid-day and the mid to late night. This study provides an important basis for understanding dynamic P2 purinergic signaling in the hippocampal glia/neuronal network.

TTEM20AAR: a benchmark geophysical data set for unconsolidated fluvioglacial sediments

Abstract. Quaternary deposits are complex and heterogeneous. They contain some of the most abundant and extensively used aquifers. In order to improve the knowledge of the spatial heterogeneity of such deposits, we acquired a large (1500 ha) and dense (20 m spacing) time domain electromagnetic (TDEM) data set in the upper Aare Valley, Switzerland (available at https://doi.org/10.5281/zenodo.4269887; Neven et al., 2020). TDEM is a fast and reliable method to measure the magnetic field directly related to the resistivity of the underground. In this paper, we present the inverted resistivity models derived from this acquisition. The depth of investigation ranges between 40 and 120 m, with an average data residual contained in the standard deviation of the data. These data can be used for many different purposes: from sedimentological interpretation of quaternary environments in alpine environments, geological and hydrogeological modeling, to benchmarking geophysical inversion techniques.

Fink, a new generation of broker for the LSST community

ABSTRACT fink is a broker designed to enable science with large time-domain alert streams such as the one from the upcoming Vera C. Rubin Observatory Legacy Survey of Space and Time (LSST). It exhibits traditional astronomy broker features such as automatized ingestion, annotation, selection, and redistribution of promising alerts for transient science. It is also designed to go beyond traditional broker features by providing real-time transient classification that is continuously improved by using state-of-the-art deep learning and adaptive learning techniques. These evolving added values will enable more accurate scientific output from LSST photometric data for diverse science cases while also leading to a higher incidence of new discoveries which shall accompany the evolution of the survey. In this paper, we introduce fink, its science motivation, architecture, and current status including first science verification cases using the Zwicky Transient Facility alert stream.

Design of a hybrid NAR-RBFs neural network for nonlinear dusty plasma system

Robust modeling of a multimodal dynamic system is a challenging and fast-growing area of research. In this study, an integrated bi-modal computing paradigm based on Nonlinear Autoregressive Radial Basis Functions (NAR-RBFs) neural network model, a new family of deep learning with the strength of hybrid artificial neural network, is presented for the solution of nonlinear chaotic dusty system (NCDS) of tiny ionized gas particles arising in fusion devices, industry, astronomy, and space. In the proposed methodology, special transformations are introduced for a class of differential equations, which convert the local optimum to a global optimum. The proposed NAR-RBFs neural network model is implemented on bi-model NCDS represented with Van der Pol-Methiew Equation (VdP-ME) for different scenarios based on variation in dust gain production and loss for both small and large time domains. Excellent agreement for proposed bimodal computing paradigm by the result with the standard state of the arts numerical solvers is verified by attaining RMSE up to 1E−38 for the nonlinear VDP-ME. Accuracy of the proposed model in the critical time domain is also validated by convergence, stability and consistency analysis on statistics calculated from absolute error, root-mean-square error, and analysis of variance metrics.

Comparison of Splitting Methods for Deterministic/Stochastic Gross–Pitaevskii Equation

In this paper, we discuss the different splitting approaches to numerically solve the Gross–Pitaevskii equation (GPE). The models are motivated from spinor Bose–Einstein condensate (BEC). This system is formed of coupled mean-field equations, which are based on coupled Gross–Pitaevskii equations. We consider conservative finite-difference schemes and spectral methods for the spatial discretisation. Furthermore, we apply implicit or explicit time-integrators and combine these schemes with different splitting approaches. The numerical solutions are compared based on the conservation of the L 2 -norm with the analytical solutions. The advantages of the novel splitting methods for large time-domains are based on the asymptotic conservation of the solution of the soliton’s applications. Furthermore, we have the benefit of larger local time-steps and therefore obtain faster numerical schemes.

On the Multidomain Bivariate Spectral Local Linearisation Method for Solving Systems of Nonsimilar Boundary Layer Partial Differential Equations

In this work, a novel approach for solving systems of nonsimilar boundary layer equations over a large time domain is presented. The method is a multidomain bivariate spectral local linearisation method (MD-BSLLM), Legendre-Gauss-Lobatto grid points, a local linearisation technique, and the spectral collocation method to approximate functions defined as bivariate Lagrange interpolation. The method is developed for a general system of n nonlinear partial differential equations. The use of the MD-BSLLM is demonstrated by solving a system of nonlinear partial differential equations that describe a class of nonsimilar boundary layer equations. Numerical experiments are conducted to show applicability and accuracy of the method. Grid independence tests establish the accuracy, convergence, and validity of the method. The solution for the limiting case is used to validate the accuracy of the MD-BSLLM. The proposed numerical method performs better than some existing numerical methods for solving a class of nonsimilar boundary layer equations over large time domains since it converges faster and uses few grid points to achieve accurate results. The proposed method uses minimal computation time and its accuracy does not deteriorate with an increase in time.

Frequency-domain analytic method for efficient thermal simulation under curved trajectories laser heating

In the context of Computer Simulation, the problem of heat transfer analysis of thin plate laser heating is relevant for downstream simulations of machining processes. Alternatives to address the problem include (i) numerical methods, which require unaffordable time and storage computing resources even for very small domains, (ii) analytical methods, which are less expensive but are limited to simple geometries, straight trajectories and do not account for material non-linearities or convective cooling. This manuscript presents a parallel efficient analytic method to determine, in a thin plate under convective cooling, the transient temperature field resulting from application of a laser spot following a curved trajectory. Convergence of both FEA (Finite Element Analysis) and the analytic approaches for a small planar plate is presented, estimating a maximum relative error for the analytic approach below 3.5% at the laser spot. Measured computing times evidence superior efficiency of the analytic approach w.r.t. FEA. A study case, with the analytic solution, for a large spatial and time domain (1m×1m and 12s history, respectively) is presented. This case is not tractable with FEA, where domains larger than 0.05m×0.05m and 2s require high amounts of computing time and storage.

A multivariate spectral quasilinearisation method for entropy generation in a square cavity filled with porous medium saturated by nanofluid

We investigate flow in a square cavity filled with a porous medium saturated with a nanofluid and subjected to an applied magnetic field. The cavity walls, except the top, are at rest. The vertical walls of the cavity are adiabatic and bottom wall is kept at a fixed temperature. Flow is generated by the motion of the top wall. The entropy generated through fluid friction, heat and mass transfer is investigated. The equations in non-dimensional form are solved using a multivariate spectral quasilinearisation method. The applicability and accuracy of this is new method is confirmed by solving the cavity flow model equations. We show that this method may be used to solve nonlinear partial differential equations over a large time domain and in two space variables. The numerical results are given in terms of streamlines, isotherms, isoconcentration and entropy generation. The results show that flow behavior, heat and mass transfer are strongly affected by the Rayleigh, Eckert and Lewis numbers. The entropy generation, which increases with increasing Rayleigh number, is shown to depend primarily on the Brownian motion parameter.

Solving hyperbolic partial differential equations using a highly accurate multidomain bivariate spectral collocation method

In this article, the non-overlapping grids based multidomain bivariate spectral collocation method is applied to solve hyperbolic partial differential equations(PDEs) defined over large time domains. The article is among the very first works which consider the multidomain approach with respect to the time interval for hyperbolic PDEs. The proposed method is based on decomposing the time domain into smaller non-overlapping subintervals and solving the PDE independently on each of these subintervals. In this study, we aim at showing that the reduction in the size of the computational domain at each subinterval guarantees accurate results within a short computational time. In the solution process, the approximate solutions of the PDEs are approximated using bivariate Lagrange interpolating polynomials. The PDEs are discretized in both time and space variables using the spectral collocation, unlike previous studies where spectral collocation method has been applied on space variable only and finite difference based discretization in the time variable and vice versa. The resulting linear systems of algebraic equations are then solved independently at each subinterval with the continuity equation being employed to obtain initial conditions in subsequent subintervals. Finally, the approximate solutions of the PDEs are obtained by matching the solutions on different subintervals along common boundaries. The new error bound theorems and proofs for bivariate polynomial interpolation using Gauss–Lobatto nodes given explain the advantages of the proposed solution algorithm. The effectiveness and accuracy of the proposed method are demonstrated by presenting error analysis and the computational time for the solution of well known hyperbolic PDEs that have been reported in the literature. The method can be adopted and extended to solve problems in real life that are modeled by hyperbolic PDEs.

High-order integral nodal discontinuous Gegenbauer-Galerkin method for solving viscous Burgers' equation

ABSTRACTWe present a high-order integral nodal discontinuous Galerkin (DG) method to solve Burgers' equation. The method lays the first stone of a novel class of integral nodal DG methods exhibiting exponential convergence rates in both spatial and temporal directions; thus, producing highly accurate approximations using a significantly small number of collocation points. This useful result is proven theoretically under some mild conditions. The paper also introduces the first rigorous rounding-error analysis for the Gegenbauer integration matrices proving their stability feature. Two useful strategies were proposed to significantly reduce the errors in certain special cases and to handle problems with relatively large time domains. Extensive numerical comparisons with other competitive numerical methods manifest the superior accuracy and efficiency of the proposed numerical method. The established numerical method is so accurate in general for sufficiently smooth solutions to the extent that exact, or nearly exact solutions can be achieved using relatively small collocation points as the viscosity parameter .

Deep Convolutional Neural Networks and Learning ECG Features for Screening Paroxysmal Atrial Fibrillation Patients

In this paper, a novel computationally intelligent-based electrocardiogram (ECG) signal classification methodology using a deep learning (DL) machine is developed. The focus is on patient screening and identifying patients with paroxysmal atrial fibrillation (PAF), which represents a life threatening cardiac arrhythmia. The proposed approach operates with a large volume of raw ECG time-series data as inputs to a deep convolutional neural networks (CNN). It autonomously learns representative and key features of the PAF to be used by a classification module. The features are therefore learned directly from the large time domain ECG signals by using a CNN with one fully connected layer. The learned features can effectively replace the traditional ad hoc and time-consuming user's hand-crafted features. Our experimental results verify and validate the effectiveness and capabilities of the learned features for PAF patient screening. The main advantages of our proposed approach are to simplify the feature extraction process corresponding to different cardiac arrhythmias and to remove the need for using a human expert to define appropriate and critical features working with a large time-series data set. The extensive simulations and case studies conducted indicate that combining the learned features with other classifiers will significantly improve the performance of the patient screening system as compared to an end-to-end CNN classifier. The effectiveness and capabilities of our proposed ECG DL classification machine is demonstrated and quantitative comparisons with several conventional machine learning classifiers are also provided.

FDTD Simulation of Very Large Domains Applied to Radar Propagation Over the Ocean

A domain decomposition method for analyzing very large finite-difference time domains, tens of thousands of wavelengths long, is demonstrated by the application to the problem of radar scattering in the maritime environment. Success depends on the elimination of artificial scattering from the “sky” boundary which is ensured by an ultra-high-performance absorbing termination that eliminates this reflection at angles of incidence less than 0.03° off grazing. The results are cross validated against a parabolic equation (PE) method and a surface integral equation method on a 1.7 km sea surface problem, and to a PE method on propagation through an inhomogeneous atmosphere in a 4 km-long space, both at X-band. Further comparisons are made against boundary integral equation and PE methods from the literature in a 3.6 km space containing an inhomogeneous atmosphere above a flat sea at S-band. Details of the method are given for the 2-D problem. Application to 3-D is demonstrated by comparing the 2-D solution with the 3-D solution of a sea corridor 1.3 m wide, 2.25 m tall, by 110 m long.