Exponential Variation Research Articles

Influence of the stoichiometric ratio of barrier layer alumina on the transport properties of Josephson junctions

In the field of quantum computing, the Josephson junction is one of the main components for generating superconducting qubits. The material defects present in the junction affect the stability and reproducibility of qubits, which consequently limits the performance of quantum computing. In this paper, we conduct a detailed study of the crystal structure of alumina at different stoichiometric ratios and its electrical properties using density-functional theory (DFT). Additionally, we simulate the amorphous structure at various stoichiometric ratios using molecular dynamics methods. Our results show that a decrease in the oxygen content in the crystalline alumina material leads to a linear reduction in the bandgap. We then construct Josephson junction models with different stoichiometric ratios of the barrier layer based on our study, and calculate the equilibrium conductance for each model using the Non-equilibrium Green’s Function (NEGF) method. Our results indicate that the structure of the barrier layer significantly affects the electrical properties of the Josephson junction. Moreover, the stoichiometric ratio of alumina is a critical parameter that results in exponential variations in the equilibrium conductance. In summary, we seek to elucidate the role that variations in the stoichiometric ratio of the oxide play in the transport properties of the junction. Our findings provide a theoretical basis for improving the stability and performance of superconducting qubits.

Exponential Variation of Irradiance in An Optically Active Water Medium for Potential Applications in Autonomous Underwater System

Exponential Variation of Irradiance in An Optically Active Water Medium for Potential Applications in Autonomous Underwater System

Demodulation of vibration signals for bearing fault detection using a method based on filtering and absolute value

A method for amplitude demodulation of vibration signals is proposed in your study, the method is designed for diagnosis and fault detection. The approach of the method starts by calculating the absolute values of the vibration signal data to make them all positive. Then, a low-pass filtering is applied to obtain an exponential variation of the data on the spectrum of the demodulated amplitude signal. The proposed method is applied to signals from the database, and subsequently, these signals are demodulated using both the proposed method and the Hilbert transform. Both methods reveal high-amplitude peaks at the same frequency values in the demodulated amplitude spectrum.

Analysis of free vibration characteristics of non-uniform graphene-reinforced axially functionally graded nanocomposite beam

This paper presents the changing effect on the free vibration behaviour of graphene-reinforced axially functionally graded nanocomposite (Gr-AFG) beam with non-uniform geometry. A generalized finite element method (GFEM) and Euler Bernoulli’s theory have been used for parametric analysis and the subsequent formulation of governing differential equations. The proposed approach (for uniform geometry) has been compared with the existing gradation schemes, e.g. ‘X’, ‘O’, ‘UD’, ‘A’, and ‘V’, and found to be well in agreement. Furthermore, a new harmonic ‘M’ function has been introduced in the current analysis, and the non-uniformity in the geometry has been implemented by varying the cross-section along the axial direction of the beam. The ‘M’ gradation in the axial direction results in an increase in the natural frequency with an increase in the slenderness ratio for the first four modes. Compared to uniform geometry, the non-uniform AFG-M beam with exponential geometry variation shows a lower fundamental frequency for all values of the slenderness ratio of the beam with an increase in the value of the exponent under C–S and C–C end support conditions.

An exponential variation based PSO for analog circuit sizing in constrained environment

This work presents an Exponential Variation based Particle Swarm Optimization (EV-PSO) algorithm to improve the convergence rate and find an optimal solution to analog circuit optimization problems in a constrained-driven environment. Existing evolutionary algorithms have a lower convergence rate leading to higher design time. This work introduces two novel parameters, ζ1 and ζ2, into the velocity update equation. These parameters dynamically vary with the number of iterations. The algorithm was implemented on the Python platform. The results have shown that, in comparison to the considered existing methods, the exponential variation of the parameters ζ1 and ζ2 in the proposed algorithms have a larger rate of convergence. The proposed EV-PSO has a convergence rate of 27 iterations, which is 57.8%, 65.38%, and 59.1% better than the conventional PSO, differential evolution (DE) and genetic algorithm (GA) respectively. The typical design obtained from the optimal solution is verified through the simulation using 45-nm CMOS technology. The optimal solution presented in this work meets the desired input specifications within the specified constrained environment.

The uniqueness of steady sonic–subsonic solution to hydrodynamic model for semiconductors

In this paper, we study the uniqueness of the stationary sonic–subsonic solution to the isentropic hydrodynamic model of semiconductors with sonic boundary. We provide a new method to improve the proof of the uniqueness of the steady-state sonic–subsonic solution, even for the general isentropic case. In detail, we apply the exponential variation method combining a series of modifications with respect to the degeneracy of electrons at the boundary. The proposed method in the present paper is much simpler and perfecter than the existing methods.

Numerical Simulation Study on the Influence of Fracture on Borehole Wave Modes: Insights from Fracture Width, Filling Condition, and Acoustic Frequency.

Unconventional reservoirs, such as shale and tight formations, have become increasingly vital contributors to oil and gas production. In these reservoirs, fractures serve as crucial spaces for fluid migration and storage, making their precise assessment essential. Array acoustic logging stands out as a pivotal method for evaluating fractures. To investigate the impact of fracture width, fracture-filling conditions, and acoustic frequency on compressional and shear waves, a three-dimensional variable mesh finite difference program was employed for acoustic logging numerical simulation. Firstly, numerical models representing fractured formations with varying fracture widths and distinct fluid-filling conditions were established, and array acoustic logging numerical simulations were conducted at different frequencies. Subsequently, the waveform data were processed to extract acoustic characteristic parameters, such as velocities and amplitude attenuations of compressional and shear waves. Finally, a quantitative analysis was conducted to examine the variation patterns of characteristic parameters of refracted compressional and shear waves in relation to fracture properties. The research results indicate that amplitude attenuation information derived from borehole wave modes is particularly sensitive to the changes in fracture properties. As fracture width increased, we observed a significant amplitude attenuation in both compressional and shear waves, proportional to the logarithm of the attenuation coefficients. Furthermore, when the fracture width was constant, gas-filled fractures exhibited more prominent amplitude attenuation than water-filled fractures, with shear wave attenuation being more sensitive to the filling material. Moreover, from a quantitative perspective, the analysis revealed that the attenuation coefficients of refracted compressional and shear waves exhibited an exponential variation with gas saturation. Notably, once fracture width and filling conditions were established, the amplitudes of compressional and shear waves at the dominant frequency of 40 kHz were significantly reduced compared to those at 8 kHz, accompanied by increased attenuation. Subsequent quantitative analysis revealed that, when the product of fracture width and dominant frequency remains constant, the corresponding attenuation coefficient ratios approach 1. This indicates that the attenuation process of acoustic propagation in fractured media follows the principle of acoustic similarity. The findings of this study provide reference for further research on fracture property evaluation methods based on array acoustic logging data.

Near-field scattering by the method of locally subsonic waves

A technique is developed for determining the sound field scattered by a compact body when it is close enough to an acoustic source to be in its near field. Our approach is based on the fact that large regions of many near fields may be well approximated at each point in space by a subsonic plane wave (also called an inhomogeneous plane wave, or an evanescent wave). Such a wave is defined by the property that in one direction it propagates with subsonic phase speed, while in a perpendicular direction it has exponential amplitude variation. Hence by defining a canonical problem, compact scattering of a subsonic plane wave, and solving it, we are able to give a unified analytical treatment of many near-field scattering problems. Our approach draws on the formulae of Rayleigh scattering (as applied to an incident field with complex wavenumber) and the asymptotic theory of the wave equation. For an arbitrary three-dimensional multipole, we determine in full detail how its subsonic wave structure depends on the spherical harmonic parameters ( m , n ) , and show that our approach has a very large region of validity.

Thermal buckling analysis of a new type of rectangular FG sandwich plates using a new higher-order shear deformation theory

This article presents a novel higher-order shear deformation Theory to investigate the thermal buckling behavior of a new type of functionally graded material (FGM) sandwich structure. The study focuses on a specific configuration of rectangular FGM sandwich plate, consisting of FGM face layers and FGM core layer subjected to temperature gradients varying linearly and non-linearly across the thickness. By employing the principle of virtual work, the governing equations are derived, involving only four unknown functions. The Navier procedure is then utilized to obtain closed-form solutions. In this study, the material properties and thermal expansion coefficient of the two face layers of the sandwich plate are assumed to vary in the thickness direction according to a simple power-law distribution. In contrast, the core layer is assumed to have an exponential variation along the thickness direction. The critical thermal buckling is influenced by various factors, including the thickness, and aspect ratios of the sandwich plate, the gradient index, the type of loading, and the type of sandwich plate. The effects of these variables on the critical buckling temperature are thoroughly examined and analyzed.

Investigation of coherent Fourier scatterometry as a calibration tool for determination of steep side wall angle and height of a nanostructure

Nanostructures with steep side wall angles (swa) play a pivotal role in various technological applications. Accurate characterization of these nanostructures is crucial for optimizing their performance. In this study, we propose a far-field detection method based on coherent Fourier scatterometry (CFS) for accurate quantification of steep swa and heights in cliff-like nanostructures. Our approach introduces a parameter termed ‘visibility’, derived from the unique far-field signatures of cliff-like nanostructures. This parameter serves as a quantitative metric for the calibration of swa and heights. The heightened sensitivity of our method is demonstrated, particularly when the incident polarization is perpendicular to the invariant direction of the nanostructure for swa calibration, while both polarization states exhibit sensitivity to height calibration. Furthermore, a comprehensive sensitivity analysis reveals the stable nature of our method, showcasing that even with fluctuations of ±10 nm in the position of the nanostructure, the resulting swa remains stable within a range of ±0.5∘ . The exponential variation of the visibility parameter with edge roundness is observed, with fluctuations in edge roundness within 10 nm resulting in swa variations within 1.7∘ for both polarization states. In experimental validations, our results demonstrate reasonable agreement between CFS-derived and AFM measurements. The AFM data for swa ( 77.99∘±1.37∘ ) and height (148.35 nm ±2.11 nm) are corroborated with CFS-derived value of swa ( 77.75∘±3.61∘ , 78.36∘±3.89∘ ) and height (149.42 nm ±1.66 nm, 150.05 nm ±1.04 nm) obtained from calibration curves for TM and TE incident beams, respectively. Overall, our findings underscore CFS as a potential and reliable tool for nanostructure characterization, offering precise measurements that are pivotal for advancing nanotechnology.

Multifunctional metasurface for ultrafast all-optical efficient modulation of terahertz wave

Metasurfaces have been widely used to terahertz (THz) modulators due to their unique electromagnetic (EM) modulation properties. However, to realize ultrafast and efficient control of the active metasurfaces remains a critical challenge. Herein, we first demonstrate a multifunctional metasurface modulator based on metal square rings, which have central rotational symmetry with local asymmetry. The former captures more EM energy to achieve strong enhancement of the local EM responses, and the latter generates high quality factor (Q-factor) Fano resonance. By scaling the unit structure, the resonant frequency shifts in an ultra-wideband range of ∼0.29-10 THz, which shows a linear relation between the Q-factor and the scaling factor, and an exponential variation between the full width at half maximum (FWHM) and the scaling factor. The results provide an effective approach to predict the frequency selection characteristics of the modulators in the THz regime. More importantly, by embedding the silicon into the specific position of the metasurface, external optical control results in the unit structure is constructed from meta-atom to molecularization model, the shifting of resonant frequency and the multi-level modulation of amplitude are realized, and the maximum modulation depth (MD) reaches ∼100 %. By systematically studying the dynamics of frequency and amplitude regulation, benefiting from the ultra-short relaxation time of the photo-carriers in silicon bridge, an ultrafast full recovery time of 2000 ps is achieved. Combined with the local field characteristics, the scaled unit structure achieves efficient modulation of the resonant frequency and amplitude under optical pumping, which provides a promising approach for the development of active metasurface modulator suitable for the whole THz band. This work demonstrates the viability of optical control molecularization of specific meta-atoms is applicable to the entire THz band, which has great potential use for future state-of-the-art THz modulators.

Analytical formulations of tunnel–soil–pile interaction under seismic excitations

AbstractTunnel–soil–pile interaction (TSPI) is a vital issue during seismic excitation because of the evaluation of the interactive structural behaviors of the tunnel. This study derives analytical formulae for the proposed TSPI model under transverse horizontal shear, vertical shear, and body waves, considering a series of piles along the tunnel's longitudinal axis. For this reason, the soil medium is considered to be an isotropic, homogeneous, elastic, and infinite. Also, the tunnel is assumed to be a beam element to connect to the series of piles by the linear elastic springs. Parametric studies of proposed formulae show the parabolic and exponential variations of tunnel forces and soil pressures when increases the number of piles. Also, recalculated tunnel moments of previous studies by using proposed formulae vary closely, which may indicate the accuracy of the present formulations. Similar variations are obtained for the previous field study verification by the present formulations. Therefore, the design charts and graphs are addressed in the present research which may be used as a standard to enhance this research in the future.

Expected spacing

The expected spacing, or average difference between consecutive order statistics, is known for uniform and exponential random variates. For other distributions, we can estimate it using the derivative of the inverse cumulative density (quantile) function, since passing a uniformly drawn value, whose spacing we know, through this function generates a random value from the distribution, and the difference between two such uniform values approximates the derivative. We calculate the spacing for two new distributions, the logistic and Gumbel, and show the estimator is exact for the first and approximate for the second. Comparing the estimators for six other distributions to numeric simulations shows they are also approximations, best in the middle of the order statistics with an error that goes inversely with the square of the sample size, but degrading in the tails.

Analysis of vibrational resonance in an oscillator with exponential mass variation

This study investigated vibrational resonance (VR) in a Duffing-type oscillator with position-dependent mass (PDM) distribution defined by spatially varying exponential function. The role of two PDM parameters, the fixed rest mass m0 and nonlinear strength k on observed resonances was investigated from the analytical and numerical computation of response amplitude Q, which is a measure of the amplification of a low-frequency (LF) signal through the introduction and modulation of a high-frequency (HF) signal in a weakly driven nonlinear system. The method of direct separation of motion was used to analytically compute the response amplitude, while the numerically computed response amplitude was obtained from the Fourier spectrum of the output signal. Single resonance peaks with good agreement between the numerically and the analytically computed responses were observed for the traditional HF-induced VR and the PDM-induced resonances. The results demonstrated that spatial mass perturbation can play the roles of HF signals typically used in traditional VR setups. The results of this investigation corroborate earlier reports that stated PDM parameters can complement the HF signal to control the observed resonance peaks. However, the exponentially varying PDM parameters did not initiate double or multiple resonances as reported for other mass distributions such as the regular mass function and the doubly-singular mass function. This study communicates that the nature of the PDM distribution actually determines the possibility of generating new peaks from observed resonances.

Self-similar pulse compression in a tapered Pb-silicate photonic crystal fiber at 2 µm

We report a 2-µm all-fiber nonlinear pulse compressor based on a tapered Pb-silicate photonic crystal fiber (PCF), which is capable of achieving large compression with low pedestal energy. A tapered Pb-silicate photonic crystal fiber with increased nonlinear coefficients is proposed for achieving self-similar pulse compression (SSPC) at 2 µm. The dynamic evolution of the fundamental order soliton is numerically analyzed based on the designed tapered fiber. After pulse compression in a tapered fiber with a length of 2.2 m, an initial 1.76 ps pulse can be compressed to 88 fs, increasing the peak power from 4.4 to 86 W with a compression factor of 20 and a quality factor of 98%. The results reveal that exponential variation yields superior compression performance and provides a promising solution for generating high-power femtosecond pulses at 2 µm.

Multivariate Forecasting Model for COVID-19 Spread Based on Possible Scenarios in Ecuador

So far, about 770.1 million confirmed cases of COVID-19 have been counted by August 2023, and around 7 million deaths have been reported from these cases to the World Health Organization. In Ecuador, the first confirmed COVID-19 case was registered on 19 February 2020, and the country’s mortality rate reached 0.43% with 12986 deaths, suggesting the need to establish a mechanism to show the virus spread in advance. This study aims to build a dynamic model adapted to health and socio-environmental variables as a multivariate model to understand the virus expansion among the population. The model is based on Susceptible-Infected-Recovered (SIR), which is a standard model in which the population is divided into six groups with parameters such as susceptible S(t), transit stage E(t), infected I(t), recovered R(t), deceased Me(t), infected asymptomatic Ia(t), infected symptomatic Is(t) and deceased by other causes M(t) to be considered and adapted. The model was validated by using consistent data from Chile and run by inconsistent data from Ecuador. The forecast error was analyzed based on the mean absolute error between real data and model forecast, showing errors within a range from 6.33% to 8.41% for Chile, with confidence a interval of 6.17%, then 3.87% to 4.70% range for Ecuador with a confidence interval of 2.59% until 23rd December 2020 of the database. The model forecasts exponential variations in biosecurity measures, exposed population, and vaccination.

Simultaneous Sensing and Actuating Capabilities of a Triple-Layer Biomimetic Muscle for Soft Robotics.

This work presents the fabrication and characterization of a triple-layered biomimetic muscle constituted by polypyrrole (PPy)-dodecylbenzenesulfonate (DBS)/adhesive tape/PPy-DBS demonstrating simultaneous sensing and actuation capabilities. The muscle was controlled by a neurobiologically inspired cortical neural network sending agonist and antagonist signals to the conducting polymeric layers. Experiments consisted of controlled voluntary movements of the free end of the muscle at angles of ±20°, ±30°, and ±40° while monitoring the muscle's potential response. Results show the muscle's potential varies linearly with applied current amplitude during actuation, enabling current sensing. A linear dependence between muscle potential and temperature enabled temperature sensing. Electrolyte concentration changes also induced exponential variations in the muscle's potential, allowing for concentration sensing. Additionally, the influence of the electric current density on the angular velocity, the electric charge density, and the desired angle was studied. Overall, the conducting polymer-based soft biomimetic muscle replicates properties of natural muscles, permitting simultaneous motion control, current, temperature, and concentration sensing. The integrated neural control system exhibits key features of biological motion regulation. This muscle actuator with its integrated sensing and control represents an advance for soft robotics, prosthetics, and biomedical devices requiring biomimetic multifunctionality.

Quantification of Vegetation Phenological Disturbance Characteristics in Open-Pit Coal Mines of Arid and Semi-Arid Regions Using Harmonized Landsat 8 and Sentinel-2

Open-pit mining activities inevitably affect the surrounding ecological environment. Therefore, it is crucial to clarify the disturbance characteristics of open-pit mining activities on the surrounding vegetation and scientifically implement ecological restoration projects. This study investigates the impact of open-pit coal mining in arid and semi-arid regions on surrounding vegetation from a vegetation phenology perspective. Initially, we construct a high-frequency time series of vegetation indices by Harmonized Landsat 8 and Sentinel-2 surface reflectance dataset (HLS). These time series are then fitted using the Double Logistic and Asymmetric Gaussian methods. Subsequently, we quantify three pivotal phenological phases: Start of Season (SOS), End of Season (EOS), and Length of Season (LOS) from the fitted time series. Finally, utilizing mine boundaries as spatial units, we create a buffer zone of 100 m increments to statistically analyze changes in phenological phases. The results reveal an exponential variation in vegetation phenological metrics with increasing distance from the mining areas of Heidaigou-Haerwusu (HDG-HEWS), Mengxiang (MX), and Xingda (XD) in northwest China. Then, we propose a method to identify the disturbance range. HDG-HEWS, MX, and XD mining areas exhibit disturbance ranges of 1485.39 m, 1571.47 m, and 671.92 m for SOS, and 816.72 m, 824.73 m, and 468.92 m for EOS, respectively. Mineral dust is one of the primary factors for the difference in the disturbance range. The HDG-HEWS mining area exhibits the most significant disruption to vegetation phenological metrics, resulting in a delay of 6.4 ± 3.4 days in SOS, an advancement of 4.3 ± 3.9 days in the EOS, and a shortening of 6.7 ± 3.5 days in the LOS. Furthermore, the overlapping disturbance zones of the two mining areas exacerbate the impact on phenological metrics, with disturbance intensities for SOS, EOS, and LOS being 1.38, 1.20, and 1.33 times those caused by a single mining area. These research results are expected to provide a reference for the formulation of dust suppression measures and ecological restoration plans for open-pit mining areas.

Impact of Non-Homogeneity on Vibration Dynamics of Orthotropic Visco-Elastic Plates with Exponential Thickness Variation

Impact of Non-Homogeneity on Vibration Dynamics of Orthotropic Visco-Elastic Plates with Exponential Thickness Variation

Dynamic fracture behavior for hole-initiated cracks in functionally graded magneto-electro-elastic bi-materials

In this article, the dynamic fracture behavior of hole-initiated cracks in functionally graded magneto-electro-elastic (FGMEE) bi-materials with exponential variation is studied by Green’s function method, and SH-wave is considered as an external load acting on the bi-materials. The mechanical model of the cracks is constructed through interface-conjunction and crack-deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm’s integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips is expressed. Numerical results clarified the factors that affect the DSIF, including wave number, incident angle, the geometry of the defect, and the gradient of the bi-materials. The accuracy of the present methods is examined by comparing the obtained results with the reference solutions. Compared with previous traditional numerical and analytical methods, the methods proposed in this paper are relatively more effective and applicable, and provide a new perspective for studying the fracture problems of FGMEE materials with more complex defects in practical engineering.