Non-uniform Problem Research Articles

An analytical model for saturated nonuniform laminar flow through rough fractures

Estimating the flow rate accurately through a single rough fracture poses a fundamental challenge. This study presents an analytical model for single-phase saturated nonuniform laminar flow through rough fractures. The flow analytical model of the fractures is constructed using homotopy thinning methods, average inertia approaches, and shortest path techniques, thereby simplifying the nonuniform flow problem to solving the integral of the incircle aperture function, from which the modified average Darcy velocity considering inertial effects is expressed. The flow equations in the global coordinates are then derived. The validity of the proposed model is verified by comparing it with flow simulations with the Navier–Stokes equations, perturbation solutions, previously corrected Reynolds equations, and experimental flow tests. The results obtained from the proposed model agree very well with those from simulations and experiments. The effective errors Di range within ±4.0% of the simulation results with an arithmetic mean of |Di| equal to 1.03%. As surface roughness increases, the proposed model can effectively capture the inertial behaviors arising from the nonuniform flow field. Compared to the previous corrected Reynolds equations and perturbation solutions, the proposed model demonstrates enhanced accuracy and applicability, introducing a new approach to address nonuniform flow problems in rough fractures with more complex geometries.

Novel path planning algorithm for laser powder bed fusion to improve the scan quality of triply periodic minimal surface structures

Traditional path planning methods, such as contour and raster methods, suffer from problems like uneven filling, overfilling, and underfilling in the sliced layers, resulting in poor continuity of the lattice melt pool, internal porosity defects, and severe powder adhesion at the contour edges, while research on path planning for three-periodic minimal surfaces lattices is relatively limited. In this study, a scanning path planning method based on lattice equations control is proposed, which differs from traditional contour paths and raster paths. The new paths are controlled by the isosurface parameters of the lattice equation and optimized using the traveling salesman problem, resulting in more uniform scanning paths. The new paths avoid the underfilling issue present in raster path and the sawtooth-shaped borders of raster path. Additionally, they circumvent the nonuniform scanning path problem caused by uneven wall thickness in contour path. Through visualizing the paths and conducting printing experiments on the lattice, it is found that the new path is more uniform compared to contour paths, effectively addressing the issue of overfilling. Compared to raster paths, the new path has smoother boundaries and reduces internal porosity and powder adhesion within the lattice. This research has important value in reducing internal porosity and external powder adhesion issues in three-period minimal surface (TPMS) lattice printing processes, further enhancing the manufacturing quality of TPMS lattices.

Numerical investigation and optimization of the melting performance of latent heat thermal energy storage unit strengthened by graded metal foam and mechanical rotation

In this paper, a combined passive graded metal foam and active mechanical rotation strategy is proposed to simultaneously solve the problem of slow melting rate and non-uniform phase change problem of the latent heat thermal energy storage (LHTES) technology. The enthalpy-porosity method and fixed grid structure are employed to numerically investigate the effects of porosity range, the number of graded layers, and the rotational angular velocity. Moreover, the response surface method (RSM) is further selected to optimize the structural parameters and obtain the function of melting performance and various factors. The result shows that there is an optimal porosity range and the total melting time decreases first and then increases with the increase of porosity range. When the porosity range is 12 % and the graded layer is three, it can shorten the melting time by 35.54 % and increase the thermal energy storage rate (TESR) by 51.57 %. In addition, the melting performance is gradually improved as the number of graded layers increases. The strengthening effect of graded metal foam with just four layers is close to that of the maximum layers considered in this paper. The trend of the influence of rotation speed on the melting performance of the LHTES unit is consistent with the porosity range, indicating the existence of the optimal rotational speed. The RSM optimization structure, with a 14.969 % porosity range, 5-layer graded number, and 2.267 rpm rotational speed, shortens the melting time by 42.42 % and increases the TESR by 62.75 % compared with the stationary case with uniform metal foam. This work verifies the effectiveness of active rotation coupling with passive graded porous structures, which could provide a new strengthening approach to enhance LHTES.

Randomized Nonuniform Sampling for Random Signals Bandlimited in the Special Affine Fourier Transform Domain

The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain.

Study of Nonclassical Transport by Applying Numerical Methods for Solving the Boltzmann Equation

This paper overviews the state of the art in the study of nonequilibrium gas flows with nonclassical transport, in which the Stokes and Fourier laws are violated (and, accordingly, the Chapman–Enskog method is inapplicable). For a reliable validation of anomalous transport effects, we use computational methods of different nature: the direct solution of the Boltzmann equation and direct simulation Monte Carlo. Nonclassical anomalous transport is manifested on scales of 5–10 mean free paths, which confirms the fact that a highly nonequilibrium flow is a prerequisite for the detection of the effects. Two-dimensional flow problems are considered, namely, the supersonic flow over a flat plate in the transient regime and the supersonic flow through membranes (lattices), where the flow behind the lattice corresponds to the spatially nonuniform relaxation problem. In this region, nonequilibrium distributions demonstrating anomalous transport are formed. The relationship of the effect with the second law of thermodynamics is discussed, the possibilities of experimental verification are considered, and the prospects of creating new microdevices on this basis are outlined.

Research on the deposition and properties characterization of novel conductive getter films on the inner wall of accelerator vacuum chamber

The new generation diffraction-limited storage ring has small vacuum chamber apertures, resulting in a distributed vacuum problem. Depositing a Ti-Zr-V NEG film layer on the inner face of vacuum chambers is an ideal solution for resolving the non-uniform vacuum distribution problem. However, Ti-Zr-V NEG coatings on the surface of the vacuum chamber increase its surface resistivity, which can intensify the wakefield impedance effect. This article proposes adding conductive Ag to the Ti-Zr-V NEG film. A novel Ti-Zr-V-Ag NEG film not only has good vacuum performance, but also has good conductivity. Ti-Zr-V-Ag NEG film is successfully prepared by magnetron sputtering. The activation kinetic processes and surface resistivity of Ti-Zr-V-Ag and Ti-Zr-V NEG films are detected in detail, and comparative research on the activation behavior and surface resistivity of Ti-Zr-V-Ag films deposited with various sputtering pressures is investigated. The results show that adding pure metallic silver to the Ti-Zr-V film effectively decreases the DC resistivity of the NEG films, and this reduction can be further enhanced by reducing the sputtering pressure. The activation kinetics behavior of the Ti-Zr-V-Ag film shows minor degradation compared with that of the Ti-Zr-V film.

Transduction from trees to graphs through folding

We introduce a fold operation that realises a tree-to-graph transduction by merging selected nodes in the input tree to form a possibly cyclic output graph. The work is motivated by the increasing use of graph-based representations in semantic parsing. We show that a suitable class of graphs languages can be generated by applying the fold operation to regular unranked tree languages. We investigate two versions of the fold operation, one that preserves a depth-first ordering between the edges, and one that does not. Finally, we demonstrate that the time complexity for the associated non-uniform membership problem is solvable in polynomial time for the order-preserving version, and NP-complete for the order-cancelling one.

A Fast Reduced-Order Model for Radial Integration Boundary Element Method Based on Proper Orthogonal Decomposition in the Non-Uniform Coupled Thermoelastic Problems

To efficiently address the challenge of thermoelastic coupling in functionally graded materials, we propose an approach that combines the radial integral boundary element method (RIBEM) with proper orthogonal decomposition (POD). This integration establishes a swift reduced-order model to transform the high-dimensional system of equations into a more manageable, low-dimensional counterpart. The implementation of this reduced-order model offers the potential for rapid numerical simulations of functionally graded materials (FGMs) under thermal shock loading. Initially, the RIBEM is utilized to resolve the thermal coupling issue within the FGMs. From these solutions, a snapshot matrix is constructed, capturing the solved temperature and displacement fields. Subsequently, the POD modes are established and a POD reduced-order model is constructed for the boundary element format of the thermally coupled problem. Finally, a system of low-order discrete differential equations is solved. Numerical experiments demonstrate that the results obtained from the reduced-order model closely align with those of the full-order model, even when considering variations in structural parameters or impact loads. Thus, the introduction of the reduced-order model not only guarantees solution accuracy but also significantly enhances computational efficiency.

An Optimal Iterative Learning Control Approach for Linear Systems With Nonuniform Trial Lengths Under Input Constraints

In practical applications of iterative learning control (ILC), the repetitive process may end up early by accident during the performance improvement along the trial axis, which yields the nonuniform trial length problem. For such practical systems, input signals are usually constrained because of some certain physical limitations. This article proposes an optimal ILC algorithm for linear time-invariant multiple-input–multiple-output (MIMO) systems with nonuniform trial lengths under input constraints. The optimal ILC framework is specifically modified for the nonuniform trial length problem, where the primal–dual interior point method is introduced to deal with the input constraints. Hence, the constraint handling capability are improved compared with the conventional counterparts for nonuniform trial lengths. Also, the monotonic convergence property of the proposed optimal ILC algorithm is obtained in the sense of mathematical expectation. Finally, the effectiveness of the proposed algorithm is verified on the numerical simulation of a mobile robot.

A posteriori error estimates for mixed approximations of degenerate elliptic problems

We consider the Raviart-Thomas mixed finite element approximation of non-uniform elliptic problems of the form −div(a∇u)=f where a=a(x) is in the Muckenhoupt class A2. We introduce an error estimator based on a local post-processing and prove its efficiency and reliability, generalizing to the degenerate case the theory developed in [24]. Finally, we present some numerical computations for a model problem showing the good behaviour of an adaptive procedure based on our estimator.

A framework for the efficient enhancement of non-uniform illumination underwater image using convolution neural network

In this paper, the non-uniform illumination enhancement problem of underwater images under the artificial light sources conditions is investigated based on Convolution Neural Network (CNN). First, we propose a trainable end-to-end enhancer called NUIENet, for enhancing the non-uniform illumination of underwater images. The proposed model consists of correction network and fusion layers. The correction network adopts the encoder–decoder structure with skip connections to enhance the features of different channels in the HSV domain, and then these enhanced features are fused by the fusion layers to obtain the desired high-quality images. Second, we built an underwater images dataset using Generative Adversarial Network (GAN) and Gaussian Function. Finally, both qualitative and quantitative experimental results show that the proposed method can produce better performance compared to other state-of-the-art enhancement methods on both real-word and synthetic underwater dataset.

Improved Approximation Algorithms for Matroid and Knapsack Means Problems

Both matroid means and knapsack means are variations of the classic [Formula: see text]-means problem in which we replace the cardinality constraint by matroid constraint or knapsack constraint respectively. In this paper, we give a 64-approximation algorithm for the matroid means problem and a [Formula: see text]-approximation algorithm for the knapsack means problem by using a simpler and more efficient rounding method. We improve previous 304 approximate ratio for the former and 20016 approximate ratio for the latter. In the rounding process, the application of integrality of the intersection of submodular (or matroid) polyhedra provides strong theoretical support. Moreover, we extend this method to matroid means problem with penalties, and give 64 and 880-approximate algorithms for uniform penalties and nonuniform penalties problem.

On a Response Matrix Solver for Slab-Geometry Neutral Particle Transport Problems in the Discrete Ordinates and Energy Multigroup Formulations Considering Non-Uniform Interior Sources

We present in this work an extension of the Response Matrix (RM) method for the numerical solution of slab-geometry neutral particle transport equation in the discrete ordinates (S) and energy multigroup formulations considering non-uniform sources. By using the term non-uniform we mean that the particle source is not spatially uniform inside the regions that compose the domain. The extended RM method, differently from the conventional RM method, is based on the solution of “source-independent” auxiliary problems (Green’s functions). The solution of these auxiliary problems is used in conjunction with the given non-uniform source to generate the sweeping matrices for the extended RM method. Numerical results with respect to both uniform and non-uniform source problems are given to illustrate the efficiency of the offered extended RM method.

Integrated Duty Cycle Control for Multiple Renewable Energy Sources in a Grid Connected System

Due to their abundance, affordability, and clean energy production, Renewable Energy Sources (RESs) have emerged as crucial sources of electricity production. As a result, considerable effort has been made to integrate renewable energy sources into the grid to help it meet energy demands. One of the challenges is the Maximum Power Extraction (MPE), where the maximum power needs to be extracted from each RES. The cost of implementation rises linearly with the number of RESs if the MPE arrangements are being made for each RES individually. Additionally, the MPE through multiple RES systems gets more challenging, especially when several PhotoVoltaic (PV) strings are connected and each PV string receive non-uniform irradiance. This paper proposes an integrated MPE control system for a multi-RES grid-connected system. The proposed solution uses a single microcontroller to maximize power from all sources to overcome the linearly growing cost problem. Moreover, we propose an improved Multi-Dimensional Cuckoo (MDC) algorithm for MPE to tackle the non-uniform irradiation problem with multi-string PV, in contrast to prior works with grid-connected multiple sources. The proposed technique is first put up against the individual MPE control system, and then it is put up against the Jaya algorithm that is documented in the literature for a typical one-dimensional MPE.

A scale-dependent hybrid algorithm for multi-dimensional time fractional differential equations

Time fractional differential model is an effective tool to characterize anomalous diffusion phenomena in hydrology and environmental science. Efficient numerical method is necessary to overcome the bottleneck of expensive computational cost for real-world application. Therefore, this paper proposes a scale-dependent hybrid algorithm to numerically solve multi-dimensional time fractional differential models. We employ the Hausdorff metric-based hybrid algorithm to discretize time terms of time fractional differential equations (FDEs) with variable step size, which is applicable to non-uniform time steps geological problems. Meantime, another advantage of the proposed algorithm is optimizing the computational process. The method only requires O( $$n_s$$ $$n_e$$ ) memory and O( $$n_s$$ $$n_t$$ $$n_e$$ ) computational cost while classical finite difference method relatively demands O( $$n_s$$ $$n_t$$ ) and O( $$n_s$$ $$n_t^2$$ ), where $$n_s$$ , $$n_t$$ and $$n_e$$ are the number of space nodes, time steps and exponentials, respectively. Furthermore, we adopt a meshless generalized finite difference method to discretize space terms of FDEs. Robustness and accuracy of the new algorithm are verified by two examples and a set of experimental data.

EFFICIENT RETINAL IMAGE ENHANCEMENT USING MORPHOLOGICAL OPERATIONS

Manual analysis of retinal images is a complicated and time-consuming task for ophthalmologists. Retinal images are susceptible to non-uniform illumination, poor contrast, transmission error, and noise problems. For the detection of retinal abnormalities, an efficient technique is required that can identify the presence of retinal complications. This paper proposes a methodology to enhance retinal images that use morphological operations to improve the contrast and bring out the fine details in the suspicious region. The enhancement plays a vital role in detecting abnormalities in the retinal images. Luminance gain metric ([Formula: see text] is obtained from Gamma correction on luminous channel of [Formula: see text]*[Formula: see text]*[Formula: see text] (hue, saturation, and value) color model of retinal image to improve luminosity. The efficiency and strength of the proposed methodology are evaluated using the performance evaluation parameters peak signal to noise ratio (PSNR), mean square error (MSE), mean absolute error (MAE), feature structural similarity index metric (FSIM), structural similarity index metric (SSIM), spectral residual index metric (SRSIM), Reyligh feature similarity index metric (RFSIM), absolute mean brightness error (AMBE), root mean square error (RMSE), image quality index (IQI), and visual similarity index (VSI). It has been revealed from the results and statistical analysis using the Friedman test that the proposed method outperforms existing state-of-the-art enhancement techniques.

Path Generation for Flexible Flank Polishing on Freeform Surfaces With Uniform Over-Cuts

One of the bottlenecks in flexible flank polishing is the non-uniform over-cuts problem caused by the difficulties of the polishing tool to conform to variable curvatures of the freeform surface along the polishing path. Consequently, it will significantly reduce the quality of finished surfaces and the service life of polishing tools. To solve the problem, a novel path generation method is proposed in this article, which not only gets the uniform over-cut at a single cutter location, but also keeps its uniformity over an entire polishing path. First, a tool orientation model is built on the freeform surface by analyzing the process of flexible flank polishing. Then, a novel indicator of over-cut uniformity is proposed with the developed Dupin indicatrix, and the tool orientation is determined by maximizing the indicator. Next, based on Taylor expansion, a polishing path generation method is presented with the consideration of over-cut uniformity. Finally, the proposed method is verified and analyzed relative to a comparison method by both virtual simulations and physical experiments. These results present a good consistency with each other and together provide strong support for the correctness, feasibility, and efficiency of the proposed method, which further contributes to surface quality and polishing tools service life.

Adaptive Superpixel-Based Disparity Estimation Algorithm Using Plane Information and Disparity Refining Mechanism in Stereo Matching

The motivation of this paper is to address the limitations of the conventional keypoint-based disparity estimation methods. Conventionally, disparity estimation is usually based on the local information of keypoints. However, keypoints may distribute sparsely in the smooth region, and keypoints with the same descriptors may appear in a symmetric pattern. Therefore, conventional keypoint-based disparity estimation methods may have limited performance in smooth and symmetric regions. The proposed algorithm is superpixel-based. Instead of performing keypoint matching, both keypoint and semiglobal information are applied to determine the disparity in the proposed algorithm. Since the local information of keypoints and the semi-global information of the superpixel are both applied, the accuracy of disparity estimation can be improved, especially for smooth and symmetric regions. Moreover, to address the non-uniform distribution problem of keypoints, a disparity refining mechanism based on the similarity and the distance of neighboring superpixels is applied to correct the disparity of the superpixel with no or few keypoints. The experiments show that the disparity map generated by the proposed algorithm has a lower matching error rate than that generated by other methods.

Robust k-center with two types of radii

In the non-uniform k-center problem, the objective is to cover points in a metric space with specified number of balls of different radii. Chakrabarty, Goyal, and Krishnaswamy [ICALP 2016, Trans. on Algs. 2020] (CGK, henceforth) give a constant factor approximation when there are two types of radii. In this paper, we give a constant factor approximation for the two radii case in the presence of outliers. To achieve this, we need to bypass the technical barrier of bad integrality gaps in the CGK approach. We do so using “the ellipsoid method inside the ellipsoid method”: use an outer layer of the ellipsoid method to reduce to stylized instances and use an inner layer of the ellipsoid method to solve these specialized instances. This idea is of independent interest and could be applicable to other problems.

Analysis of Non-Uniform Accreted Ice in Overhead Power Lines Using SAP2000

The design principles of overhead power lines cover the effect of external loads in the atmosphere (ice load and wind load) on the layout of power transmission systems. These additional loads are closely related to the geographical and meteorological characteristics of the land, so each country projects the additional loads on the power line design by considering its conditions. The ice load, which should be especially considered in mechanical calculations of power lines, causes forces on the conductor in the vertical direction. However, these vertical forces affect only one part of the conductor in the presence of partial ice, which generally occurs due to falling some ice in the power line to the ground for any reason or directly because of meteorological events and geographical features. The analysis of partial ice load is defined as the non-uniform accreted ice problem in the related studies. This study investigates the effect of non-uniform accreted ice on the conductor curve using data from Turkey. The results obtained from the non-linear model created using SAP2000 (Structural Analysis Program) are verified with the equations in the literature. The proposed model can be used to solve other problems by changing the parameters for cases in different countries.