Since the memory-dependent derivative (MDD) was developed in 2011, it has become a new branch of Fractional Calculus which is still in the ascendant nowadays. How to understand MDD and fractional derivative (FD)? What...
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Since the memory-dependent derivative (MDD) was developed in 2011, it has become a new branch of Fractional Calculus which is still in the ascendant nowadays. How to understand MDD and fractional derivative (FD)? What are the advantages and disadvantages for them? How do they behave in Modeling? These questions guide going deep into the illustration of memory effect. Though the FD is defined on an interval, it mainly reflects the local change. Relative to the FD, the physical meaning of MDD is much clearer. The time-delay reflects the duration of memory effect, and the kernel function reflects the dependent weight. The results show that the MDD is more suitable for temporal modeling. In addition, a numerical algorithm for MDD is also developed here. (C) 2020 Elsevier B.V. All rights reserved.
In this paper we study numerical computations of oxygen diffusion problems with a moving oxidation front on unbounded domains of planar, cylindrical and spherical geometrical shapes. A new domain transformation techni...
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In this paper we study numerical computations of oxygen diffusion problems with a moving oxidation front on unbounded domains of planar, cylindrical and spherical geometrical shapes. A new domain transformation technique of space variables and time variable is introduced in the application of the variable grid method for numerical computation of these problems. Some upper bound estimates of oxidation fronts are obtained. A numerical algorithm is proposed and discussed. (C) 1998 John Wiley & Sons, Ltd.
We discuss algorithms and numerical challenges in constructing and resolving spectral problems for photonic crystal surface-emitting lasers (PCSELs) with photonic crystal layers and large (up to several tens of mm(2))...
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We discuss algorithms and numerical challenges in constructing and resolving spectral problems for photonic crystal surface-emitting lasers (PCSELs) with photonic crystal layers and large (up to several tens of mm(2)) emission areas. We show that finite difference schemes created using coarse numerical meshes provide sufficient accuracy for several major (lowest-threshold) modes of particular device designs. Our technique is applied to the example of large-area all-semiconductor PCSELs, showing how it can be used to optimize device performance.
The conducted analytical, numerical and experimental studies for waiving of the elastic-viscous characteristics of elastic ropes are presented in the current report. The analytical studies are related to the creation ...
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The conducted analytical, numerical and experimental studies for waiving of the elastic-viscous characteristics of elastic ropes are presented in the current report. The analytical studies are related to the creation of a dynamic and mathematical model of a vibrating system, supported by such ropes. The numerical studies refer to the creation of a corresponding program and a simulation model. The experimental activities refer to the modification of an existing dynamic stand for the implementation of an experimental setting, corresponding to the initial dynamic model. Additional numerical activities are carried out in connection with the development of a programming module for receiving, processing and analysis of the results of the experimental studies. By applying of the combined procedure, the data for the resistance of randomly selected group of ropes, at different deformation in them, are received.
An algorithm is proposed that enables fast generation of a trajectory that brings the state of a deficient satellite from a given initial position to the neighborhood of a final desired one. The proposed algorithm is ...
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An algorithm is proposed that enables fast generation of a trajectory that brings the state of a deficient satellite from a given initial position to the neighborhood of a final desired one. The proposed algorithm is then used to design a discrete sampling-based state feedback control. Finally, simulations are done to test the robustness of the closed loop behaviour against several configurations of uncertainties and disturbances.
This paper proposes a kinematics algorithm in screw coordinates for articulated linkages. As the screw consists of velocity and position variables of a joint, the solutions of the forward and inverse velocities are th...
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This paper proposes a kinematics algorithm in screw coordinates for articulated linkages. As the screw consists of velocity and position variables of a joint, the solutions of the forward and inverse velocities are the functions of position coordinates and their time derivatives. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. Both the forward and the inverse kinematics have the similar calculation process in this method. Through examples of planar open-chain linkage, single closed-chain linkage and multiple closed-chain linkage, the kinematics algorithm is validated. It is particularly fit for developing numerical programmers for forward and inverse kinematics in the same procedures, including the velocity, displacement and acceleration which provide the fundamental information for dynamics of the linkage.
The article presents the results of a study of vibration process in pipelines conveying fluid or gas. A mathematical model pipeline was used in the form of cylindrical shell and a viscoelastic foundation in the form o...
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The article presents the results of a study of vibration process in pipelines conveying fluid or gas. A mathematical model pipeline was used in the form of cylindrical shell and a viscoelastic foundation in the form of two-parameter model of the Pasternak. The hereditary Boltzmann-Volterra theory of viscoelasticity is used to describe viscoelastic properties. The effects of the parameters of the Pasternak foundations, the singularity in the heredity kernels and geometric parameters of the pipeline on vibrations of structures with viscoelastic properties are numerically investigated. It is found that an account of viscoelastic properties of the pipeline material leads to a decrease in the amplitude and frequency of vibrations by 20-40%. It is shown that an account of viscoelastic properties of soil foundations leads to a damping of vibration process in pipeline.
For quasi-brittle rocks, a novel micromechanics-based fractional friction-damage coupling model is presented by combining the fractional plasticity theory and the micromechanical formulations for cracked solids. The p...
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For quasi-brittle rocks, a novel micromechanics-based fractional friction-damage coupling model is presented by combining the fractional plasticity theory and the micromechanical formulations for cracked solids. The plastic deformation is stemmed directly from the frictional sliding along microcracks while the damage is related to the initiation and propagation of microcracks. These two dissipation processes are inherently coupled. By applying the stress-fractional plasticity operation and the covariant transformation technique, a fractional operation instead of plastic potential is proposed to capture the non-orthogonal plastic flow. In addition, an energy release rate based damage criterion is adopted to describe material degradation. For numerical implementation, a novel explicit return mapping (ERM) integration algorithm is put forward. The predictive performance of the model is verified by comparisons with the associated model (fractional order alpha = 1) and laboratory observations from literatures. Moreover, the effectiveness of the ERM algorithm is assessed numerically.
The article presents a new method of automatic detection of subsidence troughs caused by underground coal mining. Land subsidence that results from mining leads to considerable damage to subsurface and surface infrast...
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The article presents a new method of automatic detection of subsidence troughs caused by underground coal mining. Land subsidence that results from mining leads to considerable damage to subsurface and surface infrastructure such as walls of buildings, road surfaces, and water relations in built-up areas. Within next 30 years, all coal mines are to be closed as part of the transformation of the mining industry in Poland. However, this is not going to solve the problem of subsidence in those areas. Thus, it is necessary to detect and constantly monitor such hazards. One of the techniques used for that purpose is DInSAR (differential interferometry synthetic aperture radar). It makes it possible to monitor land deformation over large areas with high accuracy and very good spatial and temporal resolution. Subsidence, particularly related to mining, usually manifests itself in interferograms in the form of elliptical interferometric fringes. An important issue here is partial or full automation of the subsidence detection process, as manual analysis is time-consuming and unreliable. Most of the proposed trough detection methods (i.e., Hough transform, circlet transform, circular Gabor filters, template recognition) focus on the shape of the troughs. They fail, however, when the interferometric fringes do not have distinct elliptical shapes or are very noisy. The method presented in this article is based on the analysis of the variability of the phase value in a micro-area of a relatively high entropy. The algorithm was tested for differential interferograms form the Upper Silesian Coal Basin (southern Poland). Due to mining, the studied area is particularly prone to various types of subsidence.
Here, an algorithm to efficiently compute the second-Born self-energy of many-body perturbation theory is described. The core idea consists in dissecting the set of all four-index Coulomb integrals into properly chose...
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Here, an algorithm to efficiently compute the second-Born self-energy of many-body perturbation theory is described. The core idea consists in dissecting the set of all four-index Coulomb integrals into properly chosen subsets, thus avoiding to loop over those indices for which the Coulomb integrals are zero or negligible. The scaling properties of the algorithm with the number of basis functions is discussed. The computational gain is demonstrated in the case of one-particle Kohn-Sham basis for organic molecules.
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