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For the application of nanoindentation on the nanoscale, the dislocation behavior affected by solid solution strengthening can be described microscopically, which contributes to comprehend the peculiarity of high-entropy alloys (HEAs). This study is to provide deeper insights into the dislocation motion within the plastic zone and reveal the material dependence of the plastic zone variation in multi-principal alloys through designed nanoindentation linear tests performed on face-centered cubic Ni, CoNi, CoCrNi, and FeCoCrNi metals and alloys. Indentation tests at various depths further confirmed that the scale factor, f , which was proposed to modify the Nix-Gao model, is governed by the material category. From this, a connection is established between f and pertinent parameters of dislocation activation process and distribution characteristics. As for the dislocation activation, the activation volume and theoretical strength are considered, and then the lattice distortion and strain gradient determine the dislocation distribution feature. Regarding the critical strengthening of adjacent indentations, a critical scale factor f eff of the strengthening boundary is defined, which is proportional to the indentation depth, and a large f eff is preferred for high-strength multi-principal HEAs and /or medium-entropy alloys (MEAs). Combining the f and the f eff of the four metals and alloys, a model describing the evolution of the indentation plastic zone is established, in which the plastic zone include three parts. For the inconsonant trends of f and f eff , a dislocation saturation zone is suggested to existing in the plastic zone. The Gradient plastic zone model proposed here graphically depicts the dislocations motion, as well as its reinforcement effect. Futhermore, this model lends credence to modify the framework which describes the mechanical response of materials under nanoindentation.

Recently, deep learning achieves competitive accuracy and robustness and dramatically improves the performance of target scale estimation through pre-trained special network branches. Yet, a fast and robust scale estimation method is still a challenging problem for visual object tracking. Early correlation filter tracking algorithm uses a multiscale search method to estimate the scale with the constant number of scale factors and invariant aspect ratio, which is redundant for the video frames with little or no scale change. Also, an independent network branch for target scale state is proposed, but the training network needs an abundance of datasets, and the effect is not very stable for the unseen target object. Aiming at the problems of existing scale estimation solutions, several variable scale learning methods are proposed to explore the scale change of the target. Firstly, we proposed a variable scale factor learning method, which makes us rid of the commonly used multiscale search with the flaws of fixed scale factors. Secondly, we used a multiscale aspect ratio solution to make up for invariant aspect ratio. Thirdly, the first and second scale methods were combined to propose a variable scale aspect ratio estimation method. Finally, the proposed scale estimation methods were embedded into the state-of-the-art ECO (Efficient Convolution Operators) and ATOM (Accurate Tracking by Overlap Maximization) trackers to replace the original scale methods for verifying the effectiveness of our proposed method. Extensive experiments on OTB100, UAV123, TC128 and LaSOT datasets demonstrate that the tracking performance can be improved effectively by using the proposed scale methods.

In this paper, the authors presented a new fractal microstrip patch antenna for Dedicated Short Range Communication (DSRC) (5.850–5.925 GHz) (IEEE 802.11p) service band. The proposed structure is obtained by etching the Minkowski boxes in all the four corners of a square geometry. Further, a square, obtained by imposing a scale factor of 50% of the existing sides, has been erased from each of the corners of the resultant structure. The final structure is obtained by superimposing this existing one with its $$45^\circ $$ rotated version. In order to get proper circular polarization and satisfactory S $$_{11}$$ characteristics from this structure, three diagonal grooves and four cross-coupled rectangular thin slits are carved from the resultant fractal geometry. A single layered Roger 5880 PCB laminated material is used to design the structure and simulated it using CST Microwave studio. The proposed antenna is a right-handed circularly polarized (RHCP) one with resonating frequency of 5.91 GHz. The measured CP gain of the antenna at resonating frequency is 5.58 dBic, and it gives a 3-dB axial bandwidth of 102 MHz which entirely covers the DSRC band. The measured radiation efficiency of the antenna is 94% and its computed aperture efficiency becomes 72%. The measured result of the prototype makes an excellent agreement with the simulated counterpart.

Current works on super-resolution have obtained satisfactory results since the advance of the convolution neural network. Nevertheless, most previous works use one network for one integer scale factor so ignore the super-resolution of the arbitrary scale factor. In this work, we propose a novel approach called Global Enhanced Upscale Network (GEUN) to tackle super-resolution with a single model adapting the arbitrary scale factor. In our GEUN, we propose the Global Enhanced Upscale module to replace the conventional upscale module. Our GEUN can upscale low-resolution images with an arbitrary scale factor through only one model. Extensive experimental results demonstrate the superiority of our GEUN.

In order to achieve wideband scaled measurement of low observable object scattering characteristics, the scaling design of the related absorbing material has been within the scope of researchers over recent years. In this work, a tunable material was designed to meet the wideband and high-precision requirements for scaling measurements. The material was produced using magnetorheological (MR) fluid, composed of silicon rubber and flaky carbonyl iron particles (CIPs), and an electric magnet. According to the results, applying the magnetic field made the CIPs in the MR fluid aligned with respect to different parallelism depth. Furthermore, the larger the field strength, the lower the permittivity and the higher the permeability. Based on the Maxwell–Garnett mixing rule, two parameters could be interpolated within a frequency range of 18–40 GHz. Changing the magnetic field resulted in the tunable absorbing property of the composite at frequencies of 2–40 GHz and the adjustable reflection loss in the region of −22 dB to –3 dB. While the thickness of the full-size absorbing coating was 0.7–0.9 mm at 10 GHz and a scale factor of 4, the designed material was as thick as 0.8 mm, and the average radar cross-section (RCS) error of coating plates was less than 0.5 dB. In addition, the scaled frequency band could be tunable within a range of 36–40 GHz as the absorber was as thin as 2 mm, and the mean RCS error was found to be less than 0.6 dB. Therefore, the MR fluid was shown to be a promising candidate for scaled measurements.

Scaled-down models have been extensively employed to study fluid flow phenomena in metallurgical ladles. The geometric scale factor in the models employed varies by one order of magnitude. A minimum value for the geometric scale factor for metallurgical ladles has not been reported before. In this study, mixing time in four different geometric scale ladles with one nozzle was measured as a function of gas flow rate, nozzle radial position, and oil thickness, using the electric conductivity method. Dynamic similarity was discussed in detail. Mixing time predicted and measured, according with dynamic similarity principles, was evaluated for the four ladles. The main finding from this work is that in principle dynamic, similarity can be achieved in all four ladles with different geometric scale ratios; however, it is evident that the experimental conditions can impose a limit to the geometric scale ratio.

In the milling process, chatter is easy to occur and has a very adverse impact on the quality of the workpiece and the production efficiency. A chatter feature extraction method based on optimized variational mode decomposition (OVMD) and multi-scale permutation entropy (MPE) was proposed to solve the problem that it is difficult to detect the machining chatter state during milling. The methodology presented in this article allows the occurrence of machining chatter to be effectively identified through real-time digital signal processing and analysis. First, in order to solve the problem of variational mode decomposition (VMD) parameter selection, an automatic selection method based on particle swarm optimization (PSO) and the maximum crest factor of the envelope spectrum (CE) was proposed. Then, the decomposed signal was reconstructed based on the energy ratio. In order to solve the problem that the single-scale permutation entropy (PE) cannot detect milling chatter well, the MPE was introduced to detect milling chatter. Finally, experimental verification was carried out, and the MPE of the reconstructed signals at different scales was extracted and analyzed. The results show that using the OVMD algorithm to process the signals can significantly improve the discrimination of MPE. With the increase of the scale factor, the MPE of the milling signals tends to decrease. At the same time, MPE is better than single-scale PE in chatter detection, and the MPE at scale factor of 4 is more conducive to chatter detection.

Rotating components such as rotating beams and plates are working in complex physical environments subjected to nonuniform distribution of their own materials, vibration caused by external excitation may result in work instability, structural fatigue and the like, so the dynamic analysis of rotating structures is of great significance. Based on the nonlocal elasticity theory and Timoshenko beam model, the vibration of a rotating functionally graded piezoelectric nanobeam is investigated. First, the dynamic governing equations and corresponding boundary conditions are derived by the Hamiltonian principle. Then, the governing equations and boundary conditions are discretized by the differential quadrature method. Subsequently, the vibration characteristics of nanobeams are analyzed after detailed numerical calculations. The effects of various parameters including rotational velocity, nonlocal parameter, functional gradient index, length–height geometry ratio and external voltage on the vibration characteristics under different boundary conditions are examined. Finally, the numerical results show that these parameters have non-negligible effects on the natural frequencies and modal shapes. The dynamics of rotating functionally graded nanobeams are affected by both external kinematic and voltage factors and inherent scale factor and their coupling effects. In particular, a nonlinear small-scale effect is observed for a rotating functionally graded piezoelectric nanobeam, which may be useful to the design and optimization of the nano-electro-mechanical system including the rotating structures.

To assess the safety of structures after the occurrence of an earthquake or decide about demolition or repair of structures, maximum residual interstory drift ratio (MRD) is one of the most important engineering demand parameters. For evaluating the probability of exceedance of MRD in structure from a specified limit, nonlinear dynamic analyses are performed by employing an intensity measure (IM). IMs link the structural seismic response analyses with the seismic hazard analysis. Employing an optimal IM in seismic evaluation of structures makes the results more realistic and reliable. The power of an IM to predict the seismic response of structures with low dispersion is called efficiency. Moreover, the ability of an IM for rendering the seismic response of structures independent from the other features of the ground motion is named sufficiency. In this study, the efficiency and sufficiency of some traditional and advanced IMs (including scalar and vector ones) for predicting MRD capacity of steel buckling restrained braced frames are evaluated. It is shown that all of the IMs considered do not have sufficiency with regard to scale factor (SF). Then, (Sa(T1),SaRatioOp‒D) as an optimal vector IM (optimized by multi-objective particle swarm optimization algorithm) having improved sufficiency with regard to SF is proposed.

The security of multimedia information is a prime concern in the present digital world. As a remedy, a robust color image watermarking in the transform domain using artificial intelligence is reported in this article. A color host image is secured by embedding a color watermark by utilizing the singular value decomposition and discrete wavelet transform. The color watermark information is scrambled with a chaotic map to give an additional stage of protection to overcome the problem of illegal copying and alteration of digital data by unauthorized users. All three RGB color channels of host singular values are modified with principal components of respective RGB information of scrambled watermark image. Ownership of data is provided by extracting the watermark in the presence of a secret key used while embedding process. To overcome the trade-off between the imperceptibility and robustness of the proposed algorithm artificial bee colony is used to optimize the scaling factor. The implementation of the proposed algorithm is performed on the MATLAB tool to compute the performance against the intentional and non-intentional image processing attacks. Comparative analysis with other related watermarking algorithms proves the robust, secure, and invisible nature of the proposed watermarking scheme.

Deep neural networks with single upsampling have achieved the improvement of performance for single image super-resolution. However, these networks lose a lot of details of low-resolution image in the reconstruction process. In this paper, we propose a gradual deep residual network for super-resolution (GDSR), which consists of multiple reconstruction network with 2 scale factor (2X reconstruction network). In 2X reconstruction network, a residual block connected by residual (RBR) is proposed to form a deep residual network, which is used to extract the depth features of low-resolution images; then the extracted features are upsampled into the features of high-resolution image by sub-pixel convolutional layer. GDSR gradually reconstructs high-quality high-resoluiton images from low-resolution images by multiple 2X reconstruction networks. Extensive experiments on benchmark datasets demonstrate that the proposed GDSR outperforms the state-of-the-art methods in terms of quantitative evaluation, visual evaluation, and execution time evaluation.

Under the influence of deep learning, many trackers have emerged recently. Among them, Siamese network reaches a pleasant balance between accuracy and speed, but its tracking performance still lags behind other trackers. In this paper, we have proposed a Hierarchical Correlation Siamese Network (HC-Siam) for object tracking. The tracker uses convolutional features of each layer to compare the correlation and identifies the position of the tracking object depending on the greatest correlation. Meanwhile, we have designed a Correlation Attention Module (CA-Module). For various objects, this module can assign different weights to the hierarchical correlation and help the network choose the distinct correlation from the hierarchical correlation. Besides, objects’ size and scale constantly varied during tracking, we claimed to use the separate scale factor in the wide and high directions to decrease the deformation of bounding boxes and increase the accuracy of our tracker. On the OTB dataset, the accuracy of HC-Siam is 6.5% higher than the baseline, and the speed of our tracker can reach 85 fps. On the VOT dataset, HC-Siam also has better performance in speed and accuracy.

To address the problems of insufficient detail extraction and long training time in the super-resolution reconstruction of chest X-ray images, a method of chest X-ray images super-resolution reconstruction using recursive neural network is proposed in this paper. Firstly, this paper designs a lightweight recursive network as the main branch, which solves the problem of training difficulty and time-consuming. Then, to overcome the lack of detail extraction in chest X-ray image, a detail complementary model is designed as another branch of the network to solve the problem of shallow information loss. Finally, the optimized activation function is used to reduce the loss of texture details and make the reconstructed image more complete and richer. When the scale factor is 2, the experimental results show that compared with other methods based on deep learning, such as the deep recursive neural network (DRCN), the details of chest X-ray images reconstructed by our method are more abundant. Specifically, the average value of PSNR and SSIM were improved by 0.17 dB and 0.0013 respectively. Moreover, the reconstruction speed of the images was increased by about 16% compared with DRCN.

This paper proposes an enhanced tightly-coupled sensor fusion scheme using a monocular camera and ultra-wideband (UWB) ranging sensors for the task of simultaneous localization and mapping. By leveraging UWB data, the method can achieve metric-scale, drift-reduced odometry and a map consisting of visual landmarks and UWB anchors without knowing the anchor positions. Firstly, the UWB configuration accommodates any degenerate cases with an insufficient number of anchors for 3D triangulation ( $$N\le 3$$ and no height data). Secondly, a practical model for UWB measurement is used, ensuring more accurate estimates for all the states. Thirdly, selected prior range measurements including the anchor-world origin and anchor–anchor ranges are utilized to alleviate the requirement of good initial guesses for anchor position. Lastly, a monitoring scheme is introduced to appropriately fix the scale factor to maintain a smooth trajectory as well as the UWB anchor position to fuse camera and UWB measurement in the bundle adjustment. Extensive experiments are carried out to showcase the effectiveness of the proposed system.

The fiber optic gyroscope (FOG) has a broad application prospect in the field of dynamic angle measurement. The scale factor, which is an important indicator of the FOG, directly determines the angle measurement precision. In this paper, the principles of angular velocity method and angular increment method, which have been commonly used in obtaining the scale factor, are introduced, and the error sources that affect the scale factor in both methods are analyzed in detail. The theoretical analysis results show that the main error sources of the scale factor are the relative error of the angular velocity benchmark generated by the rotary table and the value of the selected angular velocity benchmark in the angular velocity method. Other error sources need to be considered only at small angular velocity benchmark. Instead, the main error of the scale factor comes from the position precision of the rotary table in the angular increment method. Finally, the experiments on the scale factors of the FOG in both methods are carried out, and they are applied to the angle measurement experiments, respectively. The angle measurement results show that the deviation of the angle can be limited in 0.002° when the scale factor obtained by the angular increment method is adopted in angle measurement. It is an order of magnitude smaller than the angular velocity method. We can get the conclusion that the scale factor obtained by the angular increment method is more suitable for angle measurement than the angular velocity method.

In this paper, a structure for isolating packaging stress in a sandwich MEMS capacitive accelerometer is proposed and verified. The structure is designed and analyzed by finite element modeling (FEM) using ABAQUS. Two kinds of MEMS accelerometer, one with the stress isolation structure and the other without it, were simulated and compared. Simulation results show that the structure can reduce packaging stress and avoid uneven stress distribution. And then, MEMS accelerometers with and without the stress isolation structure are fabricated based on bulk micromachining technology and experimentally verified. The experimental results show that stabilities of the bias temperature coefficient and scale factor temperature coefficient of the MEMS accelerometer with the stress isolation structure are significantly improved. The comparison results demonstrate that the stress isolating structure is working and the packaging stress is successfully isolated.

In the paper, we consider solutions to the similarity transformation under different adjustment scenarios. We consider asymmetric cases, i.e., random errors included either in a target system (Gauss–Markov model, the most common case) or in a source system and a symmetric case when both systems are considered to be contaminated by random errors (Gauss–Helmert or errors-in-variables model). The presented solutions are based on Procrustes approach and all cases use point-wise weighting scheme. The asymmetric cases have closed-form solutions but the symmetric one, in the most general case considered herein, does not. In the latter case, weight matrices for a source and target systems are combined into one equivalent weight matrix which depends on a scale factor. This case is solved through a simple iterative process but there are some special instances which lead to closed-form solutions. The paper discusses the behavior of transformation parameters (rotations, translations, and a scale) under different adjustment scenarios.

Recent advanced deep learning studies have shown the positive role of feedback mechanism in image super-resolution task. However, current feedback mechanism only calculates residual errors of images with the same resolution without considering the useful features that may be carried by different resolution features. In this paper, to explore the potential of feedback mechanism, we design a new network structure (progressive up- and downsampling back-projection units) to construct a generative adversarial network for single image super-resolution and use progressive growing methodologies to train it. Unlike previous feedback structure, we use progressively increasing scale factor to build up- and down-projection units, which aims to learn fruitful features across scales. This method allows us to get more meaningful information from early feature maps. Additionally, we train our network progressively; in the process of training, we start from single layer network structure and add new layers as the training goes on. By this mean, the training process can be greatly accelerated and stabilized. Experiments on benchmark dataset with the state-of-the-art methods show that our network achieves 0.01 dB, 0.11 dB, 0.13 dB and 0.4 dB better PSNR results than that of RDN+, MDSR, D-DBPN and EDSR on 8 $$\times $$ enlargement, respectively, and also achieves favorable performance against the state-of-the-art methods on 2 $$\times $$ and 4 $$\times $$ enlargement.

The recent advances in deep convolutional neural networks (DCNNs) have convincingly demonstrated high-capability reconstruction for single image super-resolution (SR). However, it is a big challenge for most DCNNs-based SR models when the scaling factor increases. In this paper, we propose a novel Progressive Residual Network (PRNet) to integrate hierarchical and scale features for single image SR, which works well for both small and large scaling factors. Specifically, we introduce a Progressive Residual Module (PRM) to extract local multi-scale features through dense connected up-sampling convolution layers. Meanwhile, by embedding residual learning into each module, the relative information between high-resolution and low-resolution multi-scale features is fully exploited to boost reconstruction performance. Finally, the scale-specific features are fused to the reconstruction module for restoring the high-quality image. Extensive quantitative and qualitative evaluations on benchmark datasets illustrate that our PRNet achieves superior performance and in particular obtains new state-of-the-art results for large scaling factors such as 4 × and 8 ×.

In current adaptive steganography study, the distortion function is used to describe pixel modification distortion cost. Distortion cost can describe the influence of pixel modification to the cover. And it plays an important actor in adaptive stegaography. Based on previous researches, in this paper, an Anisotropic Distortion cost Update strategy (ADU strategy) is proposed to adaptively update the initial distortion cost (obtained by HILL .etc) to describe the interaction between multiple embedding modifications more accurately. Based on steanographic security theorty, it is proved that clustering modification strategy can improve steganographic security through theoretical derivation. And through study on steganalysis features, it is analyzed and proved that the determination of optimal modification method of the central pixel is anisotropic and much more complicated. Following these two proofs, the image gradient and thermal conductivity are used to quantify the anisotropy of 4 neighboring pixels. Then the optimal modification method of the central pixel is calculated. Finally, the distortion cost of the central pixel can be updated based on the optimal modification method. Experiments with the optimal embedding simulator show that the ADU strategy has better performance when the scaling factor is 2; the proposed ADU strategy can effectively improve the steganography schemes, especially for steganalytic performance with maxSRMd2 features.

The results of modeling and investigation of liquid distribution in mass-transfer devices having dumped packings are presented. A method of eliminating liquid accumulation on the walls of the devices having dumped packings is proposed and tested. Models of radial and longitudinal liquid mixing are developed with due regard for liquid spreading and uneven sprinkling over the device cross section. A relationship of the coefficient of longitudinal liquid phase mixing in unevenly sprinkled industrial-scale devices with the coefficient of longitudinal liquid phase mixing in the model device is established. The effect of scale factor on longitudinal liquid mixing in a packing layer decreases with increase of liquid spreading coefficients.

For the first time, the distribution of the lap-shear strength (σ) developed upon the contact of two amorphous bulk samples of poly(ethylene terephthalate) (PET) in the surroundings of the PET bulk glass transition temperature has been analysed as a function of healing temperature and healing time by using a Weibull statistical model. The Weibull parameters, Weibull modulus (m) and scale factor (σ0) of partially self-healed symmetric amorphous PET–PET interface have been estimated by analysing some tens of the lap-shear strength experimental data sets. It has been found that the σ0 values are very close to the corresponding mean σ values averaged for each test series, meaning that the Weibull analysis gives physically meaningful results. It has been shown that the majority of the σ experimental data sets can be described properly with the standard Weibull distribution function proposed for brittle solids. The m values for the PET–PET interface have been compared with those reported recently for the polymer–polymer interfaces of non-crystallizable amorphous polymers. The impact of the potential ability of an amorphous polymer to crystallize on the scatter in the measured interface lap-shear strength has been discussed.

Significant research has been conducted into image edge detection, usually focusing on gradient and higher order derivative approaches. Recent development in the field suggests the incorporation of scale factor in filter design; this is to increase robustness against noise and to facilitate the process of generating multilevel edge maps. While multifractal analysis technique uses scale factors, few researchers examine the effectiveness of this technique in image edge map generation due to its poor efficiency. Herein, we propose F-MED, a fast multifractal edge detector for grayscale images based on generating an edge map from different low frequency versions of the original image by means of frequency domain Gaussian low pass filters. The quality of results is evaluated subjectively via visual assessment and quantitatively using a set of full-reference and non-reference measures. Results show that the proposed F-MED can be leveraged to support not only high efficiency, but also quality improvement and high robustness against blurring effect and Rayleigh noise.

Whole-angle gyroscopes have broad prospects for development with inherent advantages of excellent scale factor, wide bandwidth and measurement range, which are restrictions on rate gyroscopes. Previous studies on the whole-angle mode are based mostly on the linear model of Lynch, and the essential nonlinearity of capacitive displacement detection is always neglected, which has significant negative effects on the performance. In this paper, a novel real-time calibration method of capacitive displacement detection is proposed to eliminate these nonlinear effects. This novel method innovatively takes advantage of the relationship between the first and third harmonic components of detective signals for calibration. Based on this method, the real-time calibration of capacitive displacement detection is achieved and solves the problems of traditional methods, which are usually related to the vibration amplitude, environmental variations and other factors. Furthermore, this novel calibration method is embedded into a whole-angle control system to restore the linear capacitive response in real time and then combined with a microshell resonator for the first time to exploit the enormous potential of an ultrahigh Q factor and symmetric structure. The effectiveness is proven because the angle drift is reduced significantly to improve the scale-factor nonlinearity by 14 times to 0.79 ppm with 0.0673°/h bias instability and a 0.001°/s rate threshold, which is the best reported performance of the MEMS whole-angle gyroscope thus far. More importantly, this novel calibration method can be applied for all kinds of resonators with the requirement of a linear capacitive response even under a large resonant amplitude.

In the present study, the dynamics of Y-shaped axially functionally graded nanoscale tubes transmitting flow with spinning motion in hygro-magnetic fields subjected to an axial load are surveyed based on the nonlocal strain gradient theory (NSGT). Scale-dependent dynamic equations are derived by exploiting Hamilton's principle. The generalized differential quadrature method is adopted, and the model equations are numerically solved. Backward and forward whirling frequencies, instability thresholds are obtained. Also, a parametric study is accomplished to explain the influence of key parameters such as axial material gradation, elbow inclination angle, complex environments, scale factor, spin and flow velocities on the system behavior. It is discovered that by considering simultaneous softening effects of axial load and moisture environments, the flutter condition could happen instead of divergence instability. Meanwhile, it is established that when the scale factor is greater than unity, the stabilizing effect of the strain gradient parameter dominates the system stability. Furthermore, the outcomes show that compared with homogeneous structures, it is possible to significantly enhance the stability performance of the axially graded systems by fine-tuning material characteristics.

We have discussed here a higher dimensional cosmological model and explained the recent acceleration with a Chaplygin type of gas. Dimensional reduction of extra space is possible in this case. Our solutions are general in nature because all the well known results of 4D Chaplygin driven cosmology are recovered when $d = 0$. We have drawn the best fit graph using the data obtained by the differential age method (CC) and it is seen that the graph favours only one extra dimension. That means the Chaplygin gas is apparently dominated by a 5D world. Relevant to point out that the final equation in this case are highly nonlinear in nature. Naturally it is not possible to obtain explicit solution of the 4D scale factor with time. To circumvent this difficulty, we consider a first order approximation of the key equation which has made it possible to get time explicit solution of 4D scale factor in exact form as well as the expression of extra dimensions. It may be pointed out that for large four dimensional scale factor this solution mimics $\Lambda$CDM model. An analysis of flip time is also studied both analytically and graphically in some detail. It clearly shows that early \emph{flip} occurs for higher dimensions. It is also seen that the rate of dimensional reduction is faster for higher dimensions. So we may conclude that the effect of compactification of extra dimension helps the acceleration., Comment: 14 Pages, 11 figures

In the current practice of probabilistic seismic hazard analysis (PSHA), the different estimates of ground motions predicted by ground motion models (GMMs) are attributed to epistemic uncertainty. The epistemic uncertainties arise from the lack of knowledge which is reflected in imperfect models and can be handled by either logic tree or backbone approaches. The use of backbone approach for PSHA provides a more robust estimation of the GMM contribution to the epistemic uncertainty. In this study, we quantify the epistemic uncertainty in the Iranian strong-motion data by a scale factor that can be calibrated to the recorded strong-motions. The scale factor is then added and subtracted from the backbone GMM to fairly cover the spread in the predictions from other GMMs. For this purpose, we used the Iranian strong-motion database that includes 865 records from 167 events up to 2013, with the moment magnitude range of 5.0 ≤ M ≤ 7.4, and distances up to 120 km including a variety of fault mechanisms. On the other hand, several candidate GMMs were selected from local, regional, and worldwide data. Then, we applied a data-driven method based on the deviance information criterion to rank the candidate GMMs and select the best GMM as the backbone model. The results of this study show that the epistemic uncertainty varies approximately from 0.1 to 0.3 in base-10 logarithmic units. It generally has minima in the magnitude range of prevalent data (M 5.5–6.5) and increases for small (M 4.5–5.5) and large earthquake magnitudes (M 6.5–7.5). The results also show that the scale factors generally grow with distance. Moreover, notable site effects are seen in the Iranian strong-motions. We conclude therefore that the proposed backbone GMMs along with the estimated scales factors of this study are promising for use in future earthquake hazard estimation in Iran, as they capture the recorded data and provide information on the upper and lower bounds of ground motion estimates.

The flower pollination algorithm (FPA) is an efficient metaheuristic optimization algorithm mimicking the pollination process of flowering species. In this study, FPA is applied, for the first time, to the optimum design of reinforced concrete (RC) cantilever retaining walls. It is found that FPA offers important savings with respect to conventional design approaches and that it outperforms genetic algorithm (GA) and the particle swarm optimization (PSO) algorithm in this design problem. Furthermore, parameter tuning reveals that the best FPA performance is achieved for switch probability values ranging between 0.4 and 0.7, a population size of 20 individuals and a Levy flight step size scale factor of 0.5. Finally, parametric optimum designs show that the optimum cost of RC retaining walls increases rapidly with the wall height and smoothly with the magnitude of surcharge loading.

In this paper, we report the effect of geometric parameters by calculating the capacitance scale factor of micromachined vibrating wheel on gimbal gyroscope with various shapes and mass conditions. The behavior of capacitance for vibratory torsional gyroscope with various shapes and mass conditions is investigated using MEMS+™. The structure dimensions of the gyroscope are optimized by matching frequencies in driving and sensing modes. The scale factor and linearity error extracted by calculated capacitance have been changed with various shapes condition unless the area of sensing electrodes and the mass of the gyroscope have been fixed. The mass ratio of gimbal and wheel structure is varied to minimize the linearity error.

Microelectromechanical systems’ (MEMS) inertial measurement unit (IMU) is widely used in many scenarios for its small size, low weight, and low-power consumptions. However, it possesses relatively low positioning accuracy compared with other high-grade IMUs, as errors accumulate quickly over time. This paper mainly focuses on the error characteristics of the gyro part of MEMS IMU by analyzing different kinds of error parameters. As there is no published standard for MEMS gyro error characterization, three dominant error parameters are selected and investigated, namely, scale factor, in-run bias stability, and angular random walk. In addition, Allan variance analysis is deployed as an important part of the scheme with relative results presented in this paper. Not only is theoretical analysis presented, but experimental verification is also carried out correspondingly with an ADIS16490 MEMS IMU. By comparison, we find that the results of in-run bias stability exceed the given features by up to ten times, while the rest of the results agree quite well with the given features. Possible reasons for the exceeding part are given. Calibration testing results not only provide concrete characterization for MEMS gyro errors, but also enhance the importance of overall calibration of MEMS IMU before use.

In recent years, the anomalous diffusion phenomenon has attracted attention from the scientific community due to the number of applications and development of experimental procedures to observe this phenomenon. From a mathematical point of view, anomalous diffusion can be described by empirical (algebraic models) and phenomenological models (differential models with integer or fractional order). Considering the empirical models, one of the ways to observe the presence of anomalous diffusion is to check if the particle concentration profiles collapse around the reference profile, defined in terms of a new independent variable that depends on spatial and temporal variables. This new variable (scale factor) is used to characterize the diffusion type (classical or anomalous). For phenomenological models, diffusivity is usually considered as a function of particle concentration to characterize anomalous diffusion. For both cases, an inverse problem needs to be formulated and solved to obtain the parameters for each methodology. In this context, the present contribution aims to formulate and solve two inverse anomalous diffusion problems related to empirical and phenomenological models. For this purpose, two experimental data sets and Differential Evolution (DE) are considered. The results obtained demonstrate that the DE strategy was able to find good estimates for the scale factor and for the parameters related to the phenomenological model.

For the first time, the response of the functionally graded (FG) hollow cylinder vessel with arbitrary material gradation in radial direction subjected to thermo-mechanical loads is investigated by employing differential transformation method (DTM). The coordinate transformation and proper scale factor are applied to eliminate redundant terms in DTM; as a result, fast convergence with less computational effort is observed. The elasticity modulus, thermal expansion coefficient, thermal conductivity and yield stress are assumed to be arbitrary functions of radius. The thick-walled FG reservoir is in steady-state condition, and strain hardening in plastic zone is neglected by using elastic–perfectly plastic behavior assumptions. The incompressible plastic deformation and plane-strain condition are considered to obtain radial displacement in the plastic zones. The effects of various parameters on commencement and propagation of possible plastic zones, yield pressure and yield temperature gradient are investigated. The analytical solutions for FG cylindrical container with conventional power law gradation are presented. In the case of arbitrary material gradation, the validity of the numerical procedure is proved by observing convergence and good agreement between results of DTM and results of finite element software Abaqus.

Fractal tubular structures (FTSs) can greatly increase the anti-crushing and energy absorption capacity of the material. To reveal this mechanism, fractal hexagonal tubes (FHTs) with self-similar fractal structure were designed and prepared. Compression experiments were carried out to verify the crushing modes of structures with different scale factors. Compared with the single-cell structure, FHTs have much greater mean crushing force (MCF). According to the experiments and the numerical simulations, when the side length of the second-order hexagon is 0.3 times of the length of the first-order primary hexagon, the FTS has the greatest peak force (PF) and MCF as well as the most excellent energy-absorbing ability. Three folding styles were revealed by the experiments and the numerical simulation when changing the scale factor, including the overall folding mode, the local foaling mode and the hybrid folding mode. Theoretical plastic models were built, which consistently predicted the MCF.

Statistical model calibration is a practical tool for computational model development processes. However, in optimization-based model calibration, the quality of the calibrated model is often unsatisfactory due to inefficiency and/or inaccuracy of calibration metrics. This paper proposes a new calibration metric, namely, probability residual (PR). PR quantifies the degree of agreement or disagreement between the computational response and experimental results. The PR metric is defined as the sum of the product of a scale factor and the squared residual. First, the scale factor defines the shape of the squared residual to maintain consistent sensitivity during the optimization process. Thus, the number of function evaluations can be reduced. Second, the mathematical form of the squared residuals is used to make convex optimization feasible. Therefore, the existence of a global minimum is guaranteed. To evaluate the performance of the proposed metric, numerical examples are shown in a case study. Various system functions—including linear, non-linear, and elliptical—are incorporated into the statistical model calibration. A case study that examines journal bearing rotor systems is presented to demonstrate the application of the proposed calibration metric to a real-world engineered system.

The scale factor for the use of power plants of a certain type refers to the fraction of their use in the overall energy balance of the system. Energy production by wind power plants depends directly on the wind conditions in a particular location and is stochastic in character. Increasing the fraction of these installations in the overall balance of a system also requires an increase in the power reserve capacity. Here the time a power system remains in the power deficit zone is estimated as a function of the fraction of wind power plants in the system structure. Two approaches to the placement of wind power units within a power system are compared– individual components and a system of a set of components. It is concluded that even within a small power system, combining geographically distributed components with favorable and unfavorable wind conditions into a system can have a positive effect on all the components within certain ranges of the scale factor.

Structurally parametric identification of the characteristics of the dispersion in the Friedmann–Robertson–Walker model and its approximations as models for cosmological distance scales are examined on the basis of the data on type SN Ia supernovae used to detect the “acceleration in the expansion of the universe.” It is shown that the deviations from the position characteristics of these models as a function of distance (the scale factor) are multiplicative. Estimates of the convolutions of the random and nonparametric unexcluded systematic components of the inadequacy errors of the Friedmann–Robertson–Walker model are obtained in the class of truncated distributions with zero curvature parameter and a Heckmann approximation with anisotropy and interpolation models taken into account.

Callaghan and White (2009) put forward the automated whitecap extraction (AWE) technique to determine the whitecap coverage (W). An improved AWE was used to analyze images collected in the South China Sea during 2012 and 2013 and in western Pacific during 2015 to determine W. The influences of meteorological and oceanographic factors on whitecap coverage were investigated in this study. It is found that W increases with wind speed. Scale factor and exponent of parameterization for W(U10) vary greatly in different models. Overall, there is a larger scatter of W at low wind speed than at high wind speed. W decreases with the increasing of wave age. Compared with wind speed, the scatter of W is smaller with wave age, which means the impact of wave age on the whitecap coverage is more robust under various environmental conditions. There is no significant dependence on SST and whitecap coverage seems to weakly decrease with SST. W decreases with the atmospheric stability. Relationship between W and wind speed change when swells are dominant. Swell can suppress wave breaking and decrease W. The effect is independent of the deflection angle between wind wave and swell.

The split Hopkinson pressure bar (SHPB) apparatus is frequently used to investigate the dynamic compression properties of various materials at strain rates from 102 to 104 s−1. Keeping the strain rate constant during loading is an important condition for obtaining accurate experimental results. However, we do not always need to take additional measures to control the constant strain rate loading conditions for materials with different dynamic response behaviors. To investigate the necessity of a constant strain rate condition in the SHPB test according to the different dynamic mechanical response behaviors of materials, a comprehensive numerical analysis scheme combined with the Cowper-Symonds plastic kinematic model was designed to perform the simulation tests. There are two factors primarily resulting in the errors in the calculated stress-strain response for the representative material model. One of them is the dynamic scale factor, which represents the strain rate sensitivity and controls the variation amplitude of flow stress with the change in strain rate. The other factor is the work-hardening rate, which affects the results by expanding the decrease in strain rate. This paper quantitatively describes the effects of strain rate sensitivity and the strain-hardening modulus on the accuracy of the reconstructed stress-strain behavior of a sample under a constant incident pulse. The conclusion presents several reference guides for the necessity of a constant strain rate condition for different dynamic response behaviors of materials based on the representative constitutive model.

In recent years, Lamb wave and piezoelectric transducers (PZTs) array based wavenumber filtering technique for damage estimation has been gradually studied. Compared with the time domain and frequency domain analysis of the Lamb wave signals, the wavenumber domain analysis is an effective approach to distinguish wave propagating direction and wave modes. However, the spatial resolution sampled by the PZTs is lower than that sampled by scanning laser Doppler vibrometer. As for the diameter of the PZT, it cannot be very small. In this paper, a new Lamb wave spatial sampling signal optimization method based on Morlet wavelet is proposed. Firstly, the frequency band parameter of the Morlet mother wavelet function is calculated by the Lamb wave excitation signal. Then, the sum of squared errors between the Lamb wave spatial sampling signal and the Morlet wavelet function fitting waveform at each scale factor and time factor is calculated. Finally, the scale factor and time factor corresponding to the least sum of squared errors can be judged to be the best match scale factor and time factor respectively, and the Morlet wavelet function fitting waveform in that scale factor and time factor can be seen as the optimized Lamb wave spatial sampling signal. The validation experiment performed on a glass fiber epoxy composite plate shows that the proposed method can improve the spatial resolution and length of the Lamb wave spatial sampling signal, and the sum of squared errors of this method is no more than 0.2.

We present a three-lane exclusion process that exhibits the same universal fluctuation pattern as generic one-dimensional Hamiltonian dynamics with short-range interactions, viz., with two sound modes in the Kardar-Parisi-Zhang (KPZ) universality class (with dynamical exponent $$z=3/2$$ z = 3 / 2 and symmetric Prähofer-Spohn scaling function) and a superdiffusive heat mode with dynamical exponent $$z=5/3$$ z = 5 / 3 and symmetric Lévy scaling function. The lattice gas model is amenable to efficient numerical simulation. Our main findings, obtained from dynamical Monte-Carlo simulation, are: (i) The frequently observed numerical asymmetry of the sound modes is a finite time effect. (ii) The mode-coupling calculation of the scale factor for the 5/3-Lévy-mode gives at least the right order of magnitude. (iii) There are significant diffusive corrections which are non-universal.

Soil, regarded as a homogeneous continuous medium in the classical soil mechanics, actually comprises mineral particles of different scales and has the basic characteristics of a heterogeneous discontinuous medium. During the deformation, particles of different scales contained in the soil demonstrate diverse deformation states and produce scale effects. At the same time, the rotation of the particles significantly changes the deformation and strength characteristics of the soil and produces a rotation effect. However, the current finite-element calculations are lacking in the calculation methods that take into account the effects of scale and rotation. In the previous work, one of the authors of this paper introduced an intrinsic scale factor and established a constitutive relationship according to the particle scale effect. Based on the constitutive formula of soil particle scale effect, the UEL subroutine of ABAQUS is used to express particle rotation by node rotation, and secondary development of the finite-element calculation program is carried out to solve the specific calculation problem of soil deformation scale effect caused by particle rotation. The results of a verification example involving a round hole display that the stress concentration factor of the hole decreases to a stable value with the increase of the intrinsic scale factor of the particles, which conforms to the influence mechanism of soil particle deformation and basically verifies the reliability of the secondary development program. Furthermore, using the secondary development program to calculate the stability of a slope illustrates that the shear band uncertainty and the element sensitivity in slope instability analysis are eliminated by considering the particle scale effect of the soil.

Dynamical aspects of cosmological model in an extended gravity theory have been investigated in the present work. We have adopted a simplified approach to obtain cosmic features, which in fact requires more involved calculations. A cosmological model is constructed using a hybrid scale factor that simulates a cosmic transit behaviour. The deceleration parameter and energy conditions have been obtained for the constructed model. Scalar fields have been reconstructed from the present model in the extended gravity. Different diagnostic methods have been applied to analyse the viability of the constructed model. The present model almost looks like a cosmological constant for a substantial cosmic time zone and does not show any slowing down feature in near future., Comment: 14 pages, 8 figures

The noise scale factor (NSF) is useful in calculating the random errors of lidar signals. A new method is proposed for estimating the NSF of lidar systems. Instead of measuring the solar background in the traditional method that demands special experiments or additional devices, the new method utilizes the molecular backscattered signal fragments of routinely observed lidar profiles to extract the light intensities and shot noises. Based on a 355 nm lidar system, experiments with the two methods have been carried out. The NSF calculated with the new method is 0.6473, very close to the value resulted from the traditional method, which is 0.6496. The experiments indicate that the new method is feasible and accurate. An example of calculating the random errors and signal to noise ratios (SNR) of lidar signals by using NSF is presented. Compared with the results calculated from multiple lidar profiles, the method using NSF eliminates the influence of aerosols and clouds.

Log-periodic quantum oscillations discovered in transition-metal pentatelluride give a clear demonstration of discrete scale invariance (DSI) in solid-state materials. The peculiar phenomenon is convincingly interpreted as the presence of two-body quasi-bound states in a Coulomb potential. However, the modifications of the Coulomb interactions in many-body systems having a Dirac-like spectrum are not fully understood. Here, we report the observation of tunable log-periodic oscillations and DSI in ZrTe5 and HfTe5 flakes. By reducing the flakes thickness, the characteristic scale factor is tuned to a much smaller value due to the reduction of the vacuum polarization effect. The decreasing of the scale factor demonstrates the many-body effect on the DSI, which has rarely been discussed hitherto. Furthermore, the cut-offs of oscillations are quantitatively explained by considering the Thomas-Fermi screening effect. Our work clarifies the many-body effect on DSI and paves a way to tune the DSI in quantum materials., Accepted by npj Quantum Materials

The GPS satellite transmitter antenna phase center offsets (PCOs) can be estimated in a global adjustment by constraining the ground station coordinates to the current International Terrestrial Reference Frame (ITRF). Therefore, the derived PCO values rest on the terrestrial scale parameter of the frame. Consequently, the PCO values transfer this scale to any subsequent GNSS solution. A method to derive scale-independent PCOs without introducing the terrestrial scale of the frame is the prerequisite to derive an independent GNSS scale factor that can contribute to the datum definition of the next ITRF realization. By fixing the Galileo satellite transmitter antenna PCOs to the ground calibrated values from the released metadata, the GPS satellite PCOs in the z-direction (z-PCO) and a GNSS-based terrestrial scale parameter can be determined in GPS + Galileo processing. An alternative method is based on the gravitational constraint on low earth orbiters (LEOs) in the integrated processing of GPS and LEOs. We determine the GPS z-PCO and the GNSS-based scale using both methods by including the current constellation of Galileo and the three LEOs of the Swarm mission. For the first time, direct comparison and crosscheck of the two methods are performed. They provide mean GPS z-PCO corrections of −186 ± 25 mm and −221 ± 37 mm with respect to the IGS values and +1.55 ± 0.22 ppb (parts per billion) and +1.72 ± 0.31 in the terrestrial scale with respect to the IGS14 reference frame. The results of both methods agree with each other with only small differences. Due to the larger number of Galileo observations, the Galileo-PCO-fixed method leads to more precise and stable results. In the joint processing of GPS + Galileo + Swarm in which both methods are applied, the constraint on Galileo dominates the results. We discuss and analyze how fixing either the Galileo transmitter antenna z-PCO or the Swarm receiver antenna z-PCO in the combined GPS + Galileo + Swarm processing propagates to the respective freely estimated z-PCO of Swarm and Galileo., Chinese Government Scholarship http://dx.doi.org/10.13039/501100010890, Helmholtz-Zentrum Potsdam Deutsches GeoForschungsZentrum - GFZ (4217)

In view of the problems of low precision, high energy consumption, and poor flexibility of the spatial characteristics analysis and vulnerability evaluation methods of agricultural land use environment, a principal component analysis–based spatial characteristics analysis and vulnerability evaluation method of agricultural land use environment is proposed. The remote sensing image of agriculture land was corrected. According to the Cartesian moments before and after image transformation, the scale factor, rotation angle, and translation parameters of image transformation are calculated, and these parameters are used to correct the agricultural land use image. The environment information data is obtained from the corrected image. On this basis, the dynamic degree of single and compound land use types is calculated. Two dynamic values are used to get the spatial characteristic values of agricultural land use. According to the eigenvalue, the evaluation index of land use vulnerability is calculated. Through principal component analysis, the comprehensive index of agricultural land vulnerability was obtained. Compare the index with the evaluation index to judge the level of land use vulnerability. The experimental results show that the method has high accuracy, low energy consumption, and the highest sensitivity coefficient of 0.99.

For rigid-perfect plastic solids, ideal plastic flow happens when all material elements follow minimum work paths and the two principal stretch lines are materially embedded. To describe its kinematics effectively, Lagrange convective orthogonal curvilinear system has to be constructed. Therefore, a numerical procedure for generating orthogonal body-fitted meshes has been developed and applied to non-steady plane-strain ideal plastic flow. The mapping between the Cartesian system and the orthogonal system is based on Laplace equations and Cauchy–Riemann condition. The numerical procedure takes into consideration of all the prescribed boundary curves instead of one as the boundary conditions, which has been adopted in earlier studies when using conventional characteristic line method. After each iteration step, the obtained boundary points are adjusted towards the orthogonality conditions until error tolerance requirement is met. For demonstration purpose, the numerical procedure is applied to the optimization of a bulk part under forging. The obtained orthogonal body-fitted meshes are in good agreement with previous methods. Then the optimal initial scale factor is also calculated based on this method and compared with earlier studies. Finally, the evolution of the intermediate shapes and frictional external boundary conditions is also calculated when there are no elastic dead zones.

With the development of MEMS gyroscope, acceleration sensitivity is becoming an important factor in application. The acceleration sensitivity would produce an obvious output error, and researchers mainly focus on bias acceleration sensitivity. Yet, in environment of high acceleration and angular rate, it is the scale factor acceleration sensitivity that influences the output most, and there is little research on it. In this paper, scale factor acceleration sensitivity of MEMS gyroscope in high acceleration environment is investigated with our established theoretical model and experimental measurement. Based on our proposed method of measuring the acceleration sensitivity in environment of high acceleration and angular rate, the MEMS tuning fork gyroscope is used for the measurement. The results show that the output error caused by acceleration can be up to − 30.1°/s and the scale factor acceleration sensitivity contributes the most. The coefficient of scale factor acceleration sensitivity is 35 ppm/g under 50g acceleration, and this coefficient increases linearly with acceleration that coincides with theoretical model. Lastly, some suggestions of decreasing scale factor acceleration sensitivity are given. This work is useful for the researchers to improve the performance of acceleration sensitivity of MEMS gyroscope.

Due to the so-called “size effect,” the tribological theory for traditional plastic forming processes cannot be applied directly to the micro/meso forming processes. Therefore, the friction behavior in micro/meso forming was systematically studied in this paper. Firstly, based on the open-close lubrication pockets model, a scale factor was introduced to modify the Wanheim/Bay friction model and a micro/meso forming friction model was established. The established friction model can be used in the numerical simulation of micro/meso forming processes. Secondly, the simulation and experiment of cylindrical upsetting without lubricant were carried out. Then, by comparing the simulation and experiment results, the calculation method of friction factor in Wanheim/Bay friction model was proposed. Finally, the simulation and experiment of cylindrical upsetting under the condition of liquid lubrication were also performed, and thus an approach to calculate the size factor in the established friction model for micro/meso forming was proposed. The friction model built in this paper and the methods to calculate the parameters in this model are of great importance for the quantitative study of size effect in micro/meso forming processes.

For its obvious high accuracy in a long term, rotary inertial navigation system becomes popular. However, as errors increasing with time are changed into periodic errors with zero mean, the accuracy of its azimuth angle decreases in view of short term and can’t fully satisfy the need of users such as flight control system. The precision of azimuth angle is studied by analyzing its influence factor and establishing the scale factor error model and drift models of fiber optic gyro and the measurement error model of photoelectric encoder. Correction for fiber optic gyro and photoelectric encoder based on their mutual assistance is designed to improve the short-term accuracy of rotary inertial navigation system’s azimuth angle. Experimental results in a fiber optic gyro based rotary inertial navigation system verify the proposed method.