Search results for: discrete spacetime

Authors: B. H. Aitchanov, Sh. K. Aitchanova, O. A. Baimuratov

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This paper is focused on dynamic pulse-frequency modulation (DPFM) control systems. Currently, the control law based on DPFM control signals is widely used in direct digital control subsystems introduced in the automated control systems of technological processes. Statistical analysis of automatic control systems is reduced to its construction of functional relationships between the statistical characteristics of the errors processes and input processes. Structural and dynamic Volterra models of digital pulse-frequency control systems can be used to develop methods for generating the dependencies, differing accuracy, requiring the amount of information about the statistical characteristics of input processes and computing labor intensity of their use.

Keywords: digital dynamic pulse-frequency control systems, dynamic pulse-frequency modulation, control object, discrete filter, impulse device, microcontroller

Procedia PDF Downloads 471

Authors: Varun Goel

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Solar energy is a good option among renewable energy resources due to its easy availability and abundance. The simplest and most efficient way to utilize solar energy is to convert it into thermal energy and this can be done with the help of solar collectors. The thermal performance of such collectors is poor due to less heat transfer from the collector surface to air. In this work, experimental investigations of single pass solar air heater having triangular duct and provided with roughness element on the underside of the absorber plate. V-shaped ribs are used for investigation having three different values of relative roughness pitch (p/e) ranges from 4-16 for a fixed value of angle of attack (α), relative roughness height (e/Dh) and a relative gap distance (d/x) values are 60°, 0.044 and 0.60 respectively. Result shows that considerable augmentation in heat transfer has been obtained by providing roughness.

Keywords: artificial roughness, solar air heater, triangular duct, V-shaped ribs

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Authors: Haijie Li, Xuping Zhang

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This paper presents a computationally efficient method for the modeling of robot manipulators with flexible links and joints. This approach combines the Discrete Time Transfer Matrix Method with the Finite Segment Method, in which the flexible links are discretized by a number of rigid segments connected by torsion springs; and the flexibility of joints are modeled by torsion springs. The proposed method avoids the global dynamics and has the advantage of modeling non-uniform manipulators. Experiments and simulations of a single-link flexible manipulator are conducted for verifying the proposed methodologies. The simulations of a three-link robot arm with links and joints flexibility are also performed.

Keywords: flexible manipulator, transfer matrix method, linearization, finite segment method

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Mahdi Zolfaghari, Seyed Hossein Hosseinian, Hossein Askarian Abyaneh, Mehrdad Abedi

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This paper presents a virtual active power filter (VAPF) using vehicle to grid (V2G) technology to maintain power quality requirements. The optimal discrete operation of the power converter of electric vehicle (EV) is based on recognizing desired switching states using the model predictive control (MPC) algorithm. A fast dynamic response, lower total harmonic distortion (THD) and good reference tracking performance are realized through the presented control strategy. The simulation results using MATLAB/Simulink validate the effectiveness of the scheme in improving power quality as well as good dynamic response in power transferring capability.

Keywords: electric vehicle, model predictive control, power quality, V2G technology, virtual active power filter

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Authors: Sabri Arik

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In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and Homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slopebounded activation functions. An important aspect of our results is their low computational complexity as the reported results can be verified by checking some properties symmetric matrices associated with the uncertainty sets of network parameters. The obtained results are shown to be generalization of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

Keywords: neural networks, delayed systems, lyapunov functionals, stability analysis

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Authors: Christoph Ramsauer, Jaydeep Karandikar, Tony Schmitz, Friedrich Bleicher

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Machining stability is an important limitation to discrete part machining. In this work, a networked implementation of milling stability optimization with Bayesian learning is presented. The milling process was monitored with a wireless sensory tool holder instrumented with an accelerometer at the Vienna University of Technology, Vienna, Austria. The recorded data from a milling test cut is used to classify the cut as stable or unstable based on the frequency analysis. The test cut result is fed to a Bayesian stability learning algorithm at the University of Tennessee, Knoxville, Tennessee, USA. The algorithm calculates the probability of stability as a function of axial depth of cut and spindle speed and recommends the parameters for the next test cut. The iterative process between two transatlantic locations repeats until convergence to a stable optimal process parameter set is achieved.

Keywords: machining stability, machine learning, sensor, optimization

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Authors: Tomoaki Hashimoto

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In recent decades, probabilistic constrained optimal control problems have attracted much attention in many research field. Although probabilistic constraints are generally intractable in an optimization problem, several tractable methods haven been proposed to handle probabilistic constraints. In most methods, probabilistic constraints are reduced to deterministic constraints that are tractable in an optimization problem. However, there is a gap between the transformed deterministic constraints in case of known and unknown probability distribution. This paper examines the conservativeness of probabilistic constrained optimization method with the unknown probability distribution. The objective of this paper is to provide a quantitative assessment of the conservatism for tractable constraints in probabilistic constrained optimization with the unknown probability distribution.

Keywords: optimal control, stochastic systems, discrete time systems, probabilistic constraints

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Authors: Andrey V. Timofeev

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This paper introduces an original method for guaranteed estimation of the accuracy of an ensemble of Lipschitz classifiers. The solution was obtained as a finite closed set of alternative hypotheses, which contains an object of classification with a probability of not less than the specified value. Thus, the classification is represented by a set of hypothetical classes. In this case, the smaller the cardinality of the discrete set of hypothetical classes is, the higher is the classification accuracy. Experiments have shown that if the cardinality of the classifiers ensemble is increased then the cardinality of this set of hypothetical classes is reduced. The problem of the guaranteed estimation of the accuracy of an ensemble of Lipschitz classifiers is relevant in the multichannel classification of target events in C-OTDR monitoring systems. Results of suggested approach practical usage to accuracy control in C-OTDR monitoring systems are present.

Keywords: Lipschitz classifiers, confidence set, C-OTDR monitoring, classifiers accuracy, classifiers ensemble

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Authors: Kaoutar Zellat, Tahar Kadri

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The purpose of new aseismic techniques is to provide an additional means of energy dissipation, thereby reducing the transmitted acceleration into the superstructure. In order to demonstrate the effectiveness of aseismic bearings technique and understand the behavior of seismically isolated bridges by such devices a three-span continuous deck bridge made of reinforced concrete is considered. The bridge is modeled as a discrete model and the relative displacements of the isolation bearing are crucial from the design point of view of isolation system and separation joints at the abutment level. The systems presented here are passive control systems and the results of some important experimental tests are also included. The results show that the base shear in the piers is significantly reduced for the isolated system as compared to the non isolated system in the both directions of the bridge. This indicates that the use of aseismic systems is effective in reducing the earthquake response of the bridge.

Keywords: aseismic bearings, bridge isolation, bridge, seismic response

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Authors: Mansour Al Qubeissi, Sergei S. Sazhin, Cyril Crua, Morgan R. Heikal

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This paper presents the application of the Discrete Component Model for heating and evaporation to multi-component biodiesel fuel droplets in direct injection internal combustion engines. This model takes into account the effects of temperature gradient, recirculation and species diffusion inside droplets. A distinctive feature of the model used in the analysis is that it is based on the analytical solutions to the temperature and species diffusion equations inside the droplets. Nineteen types of biodiesel fuels are considered. It is shown that a simplistic model, based on the approximation of biodiesel fuel by a single component or ignoring the diffusion of components of biodiesel fuel, leads to noticeable errors in predicted droplet evaporation time and time evolution of droplet surface temperature and radius.

Keywords: heat/mass transfer, biodiesel, multi-component fuel, droplet

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Authors: Yongxu Fu, Shaolong Wan

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We study the band degeneracy, defectiveness, as well as exceptional points of non-Hermitian systems and materials analytically. We elaborate on the energy bands, the band degeneracy, and the defectiveness of eigenstates under open boundary conditions based on developing a general theory of one-dimensional (1D) non-Hermitian systems. We research the presence of the exceptional points in a generalized non-Hermitian Su-Schrieffer-Heeger model under open boundary conditions. Beyond our general theory, there exist infernal points in 1D non-Hermitian systems, where the energy spectra under open boundary conditions converge on some discrete energy values. We study two 1D non-Hermitian models with the existence of infernal points. We generalize the infernal points to the infernal knots in four-dimensional non-Hermitian systems.

Keywords: non-hermitian, degeneracy, defectiveness, exceptional points, infernal points

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Authors: Broderick Crawford, Ricardo Soto, Natalia Berrios, Eduardo Olguin

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In this paper, we present a binary cat swarm optimization for solving the Set covering problem. The set covering problem is a well-known NP-hard problem with many practical applications, including those involving scheduling, production planning and location problems. Binary cat swarm optimization is a recent swarm metaheuristic technique based on the behavior of discrete cats. Domestic cats show the ability to hunt and are curious about moving objects. The cats have two modes of behavior: seeking mode and tracing mode. We illustrate this approach with 65 instances of the problem from the OR-Library. Moreover, we solve this problem with 40 new binarization techniques and we select the technical with the best results obtained. Finally, we make a comparison between results obtained in previous studies and the new binarization technique, that is, with roulette wheel as transfer function and V3 as discretization technique.

Keywords: binary cat swarm optimization, binarization methods, metaheuristic, set covering problem

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: Liang Zhao, Chong-quan Zhong

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In order to improve the control performance of vector inverter, an improved parameter identification solution for induction motor is proposed in this paper. Dc or AC voltage is applied to the induction motor using the SVPWM through the inverter. Then stator resistance, stator leakage inductance, rotor resistance, rotor leakage inductance and mutual inductance are obtained according to the signal response. The discrete Fourier transform (DFT) is used to deal with the noise and harmonic. The impact on parameter identification caused by delays in the inverter switch tube, tube voltage drop and dead-time is avoided by effective compensation measures. Finally, the parameter identification experiment is conducted based on the vector inverter which using TMS320F2808 DSP as the core processor and results show that the strategy is verified.

Keywords: vector inverter, parameter identification, SVPWM; DFT, dead-time compensation

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Authors: Joselito Medina Marin, Norberto Hernández Romero, Juan Carlos Seck Tuoh Mora, Erick S. Martinez Gomez

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The Flow Shop Scheduling Problem (FSSP) is a typical problem that is faced by production planning managers in Flexible Manufacturing Systems (FMS). This problem consists in finding the optimal scheduling to carry out a set of jobs, which are processed in a set of machines or shared resources. Moreover, all the jobs are processed in the same machine sequence. As in all the scheduling problems, the makespan can be obtained by drawing the Gantt chart according to the operations order, among other alternatives. On this way, an FMS presenting the FSSP can be modeled by Petri nets (PNs), which are a powerful tool that has been used to model and analyze discrete event systems. Then, the makespan can be obtained by simulating the PN through the token game animation and incidence matrix. In this work, we present an adaptive PN to obtain the makespan of FSSP by applying PN analytical tools.

Keywords: flow-shop scheduling problem, makespan, Petri nets, state equation

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Authors: Harpal Singh, Sakshi Batra

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The widespread and easy accesses to multimedia contents and possibility to make numerous copies without loss of significant fidelity have roused the requirement of digital rights management. Thus this problem can be effectively solved by Digital watermarking technology. This is a concept of embedding some sort of data or special pattern (watermark) in the multimedia content; this information will later prove ownership in case of a dispute, trace the marked document’s dissemination, identify a misappropriating person or simply inform user about the rights-holder. The primary motive of digital watermarking is to embed the data imperceptibly and robustly in the host information. Extensive counts of watermarking techniques have been developed to embed copyright marks or data in digital images, video, audio and other multimedia objects. With the development of digital video-based innovations, copyright dilemma for the multimedia industry increases. Video watermarking had been proposed in recent years to serve the issue of illicit copying and allocation of videos. It is the process of embedding copyright information in video bit streams. Practically video watermarking schemes have to address some serious challenges as compared to image watermarking schemes like real-time requirements in the video broadcasting, large volume of inherently redundant data between frames, the unbalance between the motion and motionless regions etc. and they are particularly vulnerable to attacks, for example, frame swapping, statistical analysis, rotation, noise, median and crop attacks. In this paper, an effective, robust and imperceptible video watermarking algorithm is proposed based on hybridization of powerful mathematical transforms; Fractional Fourier Transform (FrFT), Discrete Wavelet transforms (DWT) and Singular Value Decomposition (SVD) using redundant wavelet. This scheme utilizes various transforms for embedding watermarks on different layers by using Hybrid systems. For this purpose, the video frames are portioned into layers (RGB) and the watermark is being embedded in two forms in the video frames using SVD portioning of the watermark, and DWT sub-band decomposition of host video, to facilitate copyright safeguard as well as reliability. The FrFT orders are used as the encryption key that allows the watermarking method to be more robust against various attacks. The fidelity of the scheme is enhanced by introducing key generation and wavelet based key embedding watermarking scheme. Thus, for watermark embedding and extraction, same key is required. Therefore the key must be shared between the owner and the verifier via some safe network. This paper demonstrates the performance by considering different qualitative metrics namely Peak Signal to Noise ratio, Structure similarity index and correlation values and also apply some attacks to prove the robustness. The Experimental results are presented to demonstrate that the proposed scheme can withstand a variety of video processing attacks as well as imperceptibility.

Keywords: discrete wavelet transform, robustness, video watermarking, watermark

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

Procedia PDF Downloads 522

Authors: B. X. Tchomeni, A. A. Alugongo, T. B. Tengen

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In this paper, de Laval rotor system has been characterized by a hinge model and its transient response numerically treated for a dynamic solution. The effect of the ensuing non-linear disturbances namely rub and breathing crack is numerically simulated. Subsequently, three analysis methods: Orbit Analysis, Fast Fourier Transform (FFT) and Wavelet Transform (WT) are employed to extract features of the vibration signal of the faulty system. An analysis of the system response orbits clearly indicates the perturbations due to the rotor-to-stator contact. The sensitivities of WT to the variation in system speed have been investigated by Continuous Wavelet Transform (CWT). The analysis reveals that features of crack, rubs and unbalance in vibration response can be useful for condition monitoring. WT reveals its ability to detect non-linear signal, and obtained results provide a useful tool method for detecting machinery faults.

Keywords: Continuous wavelet, crack, discrete wavelet, high acceleration, low acceleration, nonlinear, rotor-stator, rub

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Authors: Ozden Saygili, Eser Cakti

Abstract:

The masonry building stock in Istanbul and in other cities of Turkey are exposed to significant earthquake hazard. Determination of the safety of masonry structures against earthquakes is a complex challenge. This study deals with experimental tests and non-linear dynamic analysis of masonry structures modeled through discrete element method. The 1:10 scale model of Mustafa Paşa Mosque was constructed and the data were obtained from the sensors on it during its testing on the shake table. The results were used in the calibration/validation of the numerical model created on the basis of the 1:10 scale model built for shake table testing. 3D distinct element model was developed that represents the linear and nonlinear behavior of the shake table model as closely as possible during experimental tests. Results of numerical analyses with those from the experimental program were compared and discussed.

Keywords: dynamic analysis, non-linear modeling, shake table tests, masonry

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Authors: Ramazan Kadiev, Arkadi Ponossov

Abstract:

Semidiscrete systems contain both continuous and discrete components. This means that the dynamics is mostly continuous, but at certain instants, it is exposed to abrupt influences. Such systems naturally appear in applications, for example, in biological and ecological models as well as in the control theory. Therefore, the study of semidiscrete systems has recently attracted the attention of many specialists. Stochastic effects are an important part of any realistic approach to modeling. For example, stochasticity arises in the population dynamics, demographic and ecological due to a change in time of factors external to the system affecting the survival of the population. In control theory, random coefficients can simulate inaccuracies in measurements. It will be shown in the presentation how to incorporate such effects into semidiscrete systems. Stability analysis is an essential part of modeling real-world problems. In the presentation, it will be explained how sufficient conditions for the moment stability of solutions in terms of the coefficients for linear semidiscrete stochastic equations can be derived using non-Lyapunov technique.

Keywords: abrupt changes, exponential stability, regularization, stochastic noises

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Authors: Shirin Jalili, Ramin Ghasemi Shayan

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Coarctation of the aorta (CoA) may be a common (CHD), which is the seventh most common sort of CHD. Still, this is often likely a think little off since the determination may be deferred, indeed within the pediatric populace. The choice for surgical repair incorporates resection of the contracted section with end-to-end or end-to-side anastomosis, subclavian fold aortoplasty, resection, and join the intervention, or prosthetic fix aortoplasty. Drastically expanded end-to-end repair or switched subclavian fold aortoplasty can be utilized when the coarctation expands to the distal arch. Swell angioplasty can be a palliative choice sometime recently the conclusive redress. Its objective is to stabilize high-risk patients that cannot be submitted to quick surgical intercession, such as untimely newborns. For disconnected and discrete coarctations, it can, as a rule, be drawn nearer and repaired by means of cleared out thoracotomy, extraction of the infected aorta (coarctectomy), and remaking, ordinarily by amplified end-to-end anastomosis. In this article, we need to supply a diagram of current proposals and strategies utilized to picture coarctations of the aorta.

Keywords: coarctation of the aorta, congenital heart disease, strategies, surgical repair

Procedia PDF Downloads 139

Authors: Walaa M.Abd-Elhafiez, Wajeb Gharibi

Abstract:

In this paper a novel color image compression technique for efficient storage and delivery of data is proposed. The proposed compression technique started by RGB to YCbCr color transformation process. Secondly, the canny edge detection method is used to classify the blocks into edge and non-edge blocks. Each color component Y, Cb, and Cr compressed by discrete cosine transform (DCT) process, quantizing and coding step by step using adaptive arithmetic coding. Our technique is concerned with the compression ratio, bits per pixel and peak signal to noise ratio, and produce better results than JPEG and more recent published schemes (like, CBDCT-CABS and MHC). The provided experimental results illustrate the proposed technique which is efficient and feasible in terms of compression ratio, bits per pixel and peak signal to noise ratio.

Keywords: image compression, color image, q-coder, quantization, edge-detection

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Authors: Chungkuk Jin, Moohyun Kim, Woo Chul Chung

Abstract:

This paper presents global performance and dynamic behaviors of a discrete-pontoon-type floating bridge with mooring lines in time domain under wind and wave excitations. The structure is designed for long-distance and deep-water crossing and consists of the girder, columns, pontoons, and mooring lines. Their functionality and behaviors are investigated by using elastic-floater/mooring fully-coupled dynamic simulation computer program. Dynamic wind, first- and second-order wave forces, and current loads are considered as environmental loads. Girder’s dynamic responses and mooring tensions are analyzed under different analysis methods and environmental conditions. Girder’s lateral responses are highly influenced by the second-order wave and wind loads while the first-order wave load mainly influences its vertical responses.

Keywords: floating bridge, mooring line, pontoon, wave excitation

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Authors: R. Hariti, M. Saighi, H. Saidani-Scott

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A numerical simulation of natural convection double diffusion, coupled with thermal radiation in unsteady laminar regime in a storage tank is carried out. The storage tank contains a liquefied natural gas (LNG) in its gaseous phase. Fluent, a commercial CFD package, based on the numerical finite volume method, is used to simulate the flow. The radiative transfer equation is solved using the discrete coordinate method. This numerical simulation is used to determine the temperature profiles, stream function, velocity vectors and variation of the heat flux density for unsteady laminar natural convection. Furthermore, the influence of thermal radiation on the heat transfer has been investigated and the results obtained were compared to those found in the literature. Good agreement between the results obtained by the numerical method and those taken on site for the temperature values.

Keywords: tank, storage, liquefied natural gas, natural convection, thermal radiation, numerical simulation

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Authors: Aliakbar Golshani, Armin Ramezanzad

Abstract:

Tensile strength which is an important parameter of the rock for engineering applications is difficult to measure directly through physical experiment (i.e. uniaxial tensile test). Therefore, indirect experimental methods such as Brazilian test have been taken into consideration and some relations have been proposed in order to obtain the tensile strength for rocks indirectly. In this research, to calculate numerically the tensile strength for granitic rocks, Particle Flow Code in three-dimension (PFC3D) software were used. First, uniaxial compression tests were simulated and the tensile strength was determined for Inada granite (from a quarry in Kasama, Ibaraki, Japan). Then, by simulating Brazilian test condition for Inada granite, the tensile strength was indirectly calculated again. Results show that the tensile strength calculated numerically agrees well with the experimental results obtained from uniaxial tensile tests on Inada granite samples.

Keywords: numerical simulation, particle flow code, PFC, tensile strength, Brazilian Test

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Authors: Guoliang Fan, Aiping Li, Xuemei Liu, Liyun Xu

Abstract:

The performance of the tightening equipment will decline with the working process in manufacturing system. The main manifestations are the randomness and discretization degree increasing of the tightening performance. To evaluate the degradation tendency of the tightening performance accurately, a complexity measurement approach based on Kolmogorov entropy is presented. At first, the states of performance index are divided for calibrating the discrete degree. Then the complexity measurement model based on Kolmogorov entropy is built. The model describes the performance degradation tendency of tightening equipment quantitatively. At last, a study case is applied for verifying the efficiency and validity of the approach. The research achievement shows that the presented complexity measurement can effectively evaluate the degradation tendency of the tightening equipment. It can provide theoretical basis for preventive maintenance and life prediction of equipment.

Keywords: complexity measurement, Kolmogorov entropy, manufacturing system, performance evaluation, tightening equipment

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Authors: Eugene Stepanov, Arcady Ponosov

Abstract:

To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Kun Xue, Lvlan Miu, Jiarui Li

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Jetting structures are widely found in particle rings or shells dispersed by the central explosion. In contrast, some explosive dispersal of particles only results in a dispersed cloud without distinctive structures. Employing the coupling method of the compressible computational fluid mechanics and discrete element method (CCFD-DEM), we reveal the underlying physics governing the formation of the jetting structure, which is related to the competition between the shock compaction and gas infiltration, two major processes during the shock interaction with the granular media. If the shock compaction exceeds the gas infiltration, the discernable jetting structures are expected, precipitated by the agglomerates of fast-moving particles induced by the heterogenous network of force chains. Otherwise, particles are uniformly accelerated by the interstitial flows, and no distinguishable jetting structures are formed. We proceed to devise the phase map of the jetting formation in the space defined by two dimensionless parameters which characterize the timescales of the shock compaction and the gas infiltration, respectively.

Keywords: compressible multiphase flows, DEM, granular jetting, pattern formation

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Authors: Kamel Al-Khaled

Abstract:

A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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