Search results for: Periodic Boundary Conditions (PBC)
3847 Non-reflection Boundary Conditions for Numerical Simulation of Supersonic Flow
Authors: A. Abdalla, A. Kaltayev
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This article presents the boundary conditions for the problem of turbulent supersonic gas flow in a plane channel with a perpendicular injection jets. The non-reflection boundary conditions for direct modeling of compressible viscous gases are studied. A formulation using the NSCBC (Navier- Stocks characteristic boundary conditions) through boundaries is derived for the subsonic inflow and subsonic non-reflection outflow situations. Verification of the constructed algorithm of boundary conditions is carried out by solving a test problem of perpendicular sound of jets injection into a supersonic gas flow in a plane channel.
Keywords: WENO scheme, non-reflection boundary conditions, NSCBC, supersonic flow.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 21893846 Periodic Solutions for a Delayed Population Model on Time Scales
Authors: Kejun Zhuang, Zhaohui Wen
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This paper deals with a delayed single population model on time scales. With the assistance of coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained. Furthermore, the better estimations for bounds of periodic solutions are established.
Keywords: Coincidence degree, continuation theorem, periodic solutions, time scales
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13413845 Periodic Solutions for a Two-prey One-predator System on Time Scales
Authors: Changjin Xu
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In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.
Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13613844 Fourier Galerkin Approach to Wave Equation with Absorbing Boundary Conditions
Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic
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Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 8753843 A Novel Approach to Positive Almost Periodic Solution of BAM Neural Networks with Time-Varying Delays
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In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.
Keywords: Delayed BAM neural networks, Hull theorem, Mmatrix, Almost periodic solution, Global exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14083842 Hydrodynamic Modeling of Infinite Reservoir using Finite Element Method
Authors: M. A. Ghorbani, M. Pasbani Khiavi
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In this paper, the dam-reservoir interaction is analyzed using a finite element approach. The fluid is assumed to be incompressible, irrotational and inviscid. The assumed boundary conditions are that the interface of the dam and reservoir is vertical and the bottom of reservoir is rigid and horizontal. The governing equation for these boundary conditions is implemented in the developed finite element code considering the horizontal and vertical earthquake components. The weighted residual standard Galerkin finite element technique with 8-node elements is used to discretize the equation that produces a symmetric matrix equation for the damreservoir system. A new boundary condition is proposed for truncating surface of unbounded fluid domain to show the energy dissipation in the reservoir, through radiation in the infinite upstream direction. The Sommerfeld-s and perfect damping boundary conditions are also implemented for a truncated boundary to compare with the proposed far end boundary. The results are compared with an analytical solution to demonstrate the accuracy of the proposed formulation and other truncated boundary conditions in modeling the hydrodynamic response of an infinite reservoir.Keywords: Reservoir, finite element, truncated boundary, hydrodynamic pressure
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 23013841 Multiple Positive Periodic Solutions to a Periodic Predator-Prey-Chain Model with Harvesting Terms
Authors: Zhouhong Li, Jiming Yang
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In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.
Keywords: Positive periodic solutions, Predator-prey-chain model, coincidence degree, harvesting term.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13003840 Four Positive Almost Periodic Solutions to an Impulsive Delayed Plankton Allelopathy System with Multiple Exploit (or Harvesting) Terms
Authors: Fengshuo Zhang, Zhouhong Li
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In this paper, we obtain sufficient conditions for the existence of at least four positive almost periodic solutions to an impulsive delayed periodic plankton allelopathy system with multiple exploited (or harvesting) terms. This result is obtained through the use of Mawhins continuation theorem of coincidence degree theory along with some properties relating to inequalities.Keywords: Almost periodic solutions, plankton allelopathy system, coincidence degree, impulse.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 7073839 Almost Periodic Sequence Solutions of a Discrete Cooperation System with Feedback Controls
Authors: Ziping Li, Yongkun Li
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In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.
Keywords: Discrete cooperation model, almost periodic solution, feedback control, Lyapunov function.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14393838 Existence and Exponential Stability of Almost Periodic Solution for Recurrent Neural Networks on Time Scales
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In this paper, a class of recurrent neural networks (RNNs) with variable delays are studied on almost periodic time scales, some sufficient conditions are established for the existence and global exponential stability of the almost periodic solution. These results have important leading significance in designs and applications of RNNs. Finally, two examples and numerical simulations are presented to illustrate the feasibility and effectiveness of the results.
Keywords: Recurrent neural network, Almost periodic solution, Global exponential stability, Time scale.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14043837 Periodic Solutions in a Delayed Competitive System with the Effect of Toxic Substances on Time Scales
Authors: Changjin Xu, Qianhong Zhang
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In this paper, the existence of periodic solutions of a delayed competitive system with the effect of toxic substances is investigated by using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales. New sufficient conditions are obtained for the existence of periodic solutions. The approach is unified to provide the existence of the desired solutions for the continuous differential equations and discrete difference equations. Moreover, The approach has been widely applied to study existence of periodic solutions in differential equations and difference equations.
Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13943836 A Numerical Study of Force-Based Boundary Conditions in Multiparticle Collision Dynamics
Authors: Arturo Ayala-Hernandez, Humberto H´ıjar
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We propose a new alternative method for imposing fluid-solid boundary conditions in simulations of Multiparticle Collision Dynamics. Our method is based on the introduction of an explicit potential force acting between the fluid particles and a surface representing a solid boundary. We show that our method can be used in simulations of plane Poiseuille flows. Important quantities characterizing the flow and the fluid-solid interaction like the slip coefficient at the solid boundary and the effective viscosity of the fluid, are measured in terms of the set of independent parameters defining the numerical implementation. We find that our method can be used to simulate the correct hydrodynamic flow within a wide range of values of these parameters.
Keywords: Multiparticle Collision Dynamics, Fluid-Solid Boundary Conditions, Molecular Dynamics.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 22203835 An Efficient Method for Solving Multipoint Equation Boundary Value Problems
Authors: Ampon Dhamacharoen, Kanittha Chompuvised
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In this work, we solve multipoint boundary value problems where the boundary value conditions are equations using the Newton-Broyden Shooting method (NBSM).The proposed method is tested upon several problems from the literature and the results are compared with the available exact solution. The experiments are given to illustrate the efficiency and implementation of the method.Keywords: Boundary value problem; Multipoint equation boundary value problems, Shooting Method, Newton-Broyden method.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17743834 Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks
Authors: Qianhong Zhang, Lihui Yang, Daixi Liao
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In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15073833 Almost Periodic Solution for an Impulsive Neural Networks with Distributed Delays
Authors: Lili Wang
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By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and effectiveness of the results.
Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 16053832 A Frequency Dependence of the Phase Field Model in Laminar Boundary Layer with Periodic Perturbations
Authors: Yasuo Obikane
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The frequency dependence of the phase field model(PFM) is studied. A simple PFM is proposed, and is tested in a laminar boundary layer. The Blasius-s laminar boundary layer solution on a flat plate is used for the flow pattern, and several frequencies are imposed on the PFM, and the decay times of the interfaces are obtained. The computations were conducted for three cases: 1) no-flow, and 2) a half ball on the laminar boundary layer, 3) a line of mass sources in the laminar boundary layer. The computations show the decay time becomes shorter as the frequency goes larger, and also show that it is sensitive to both background disturbances and surface tension parameters. It is concluded that the proposed simple PFM can describe the properties of decay process, and could give the fundamentals for the decay of the interface in turbulent flows.Keywords: Phase field model, two phase flows, Laminarboundary Layer
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15043831 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System
Authors: Daiming Wang
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In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.
Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14993830 Permanence and Almost Periodic Solutions to an Epidemic Model with Delay and Feedback Control
Authors: Chenxi Yang, Zhouhong Li
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This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.
Keywords: Permanence, Almost periodic solution, Epidemic model, Delay, Feedback control.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15393829 Almost Periodic Solution for a Food-limited Population Model with Delay and Feedback Control
Authors: Xiaoyan Dou, Yongkun Li
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In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.
Keywords: Almost periodic solution, food-limited population, feedback control, permanence.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 19493828 Exact Solution of the Ising Model on the 15 X 15 Square Lattice with Free Boundary Conditions
Authors: Seung-Yeon Kim
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The square-lattice Ising model is the simplest system showing phase transitions (the transition between the paramagnetic phase and the ferromagnetic phase and the transition between the paramagnetic phase and the antiferromagnetic phase) and critical phenomena at finite temperatures. The exact solution of the squarelattice Ising model with free boundary conditions is not known for systems of arbitrary size. For the first time, the exact solution of the Ising model on the square lattice with free boundary conditions is obtained after classifying all ) spin configurations with the microcanonical transfer matrix. Also, the phase transitions and critical phenomena of the square-lattice Ising model are discussed using the exact solution on the square lattice with free boundary conditions.Keywords: Phase transition, Ising magnet, Square lattice, Freeboundary conditions, Exact solution.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 18313827 Stability of Discrete Linear Systems with Periodic Coefficients under Parametric Perturbations
Authors: Adam Czornik, Aleksander Nawrat
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This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.Keywords: Exponential stability, time-varying linear systems, periodic systems.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 13993826 Periodic Storage Control Problem
Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan
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Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 12333825 Effects of Boundary Conditions on the Dynamic Values of Solid Structures
Authors: F. Kadioglu, M. Z. Polat, A. R. Gunay
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Correct measurement of a structural damping value is an important issue for the reliable design of the components exposed to vibratory and noise conditions. As far as a vibrating beam technique is concerned, the specimens under the test somehow are interacted with measuring and exciting devices, and also with boundary conditions of the test set-up. The aim of this study is to propose a vibrating beam method that offers a non-contact dynamic measurement of solid beam specimens. To evaluate the possible effects of the clamped portion of the specimens with clamped-free ends on the dynamic values (damping and the elastic modulus), the same measuring devices were used, and the results were compared to those with the free-free ends. First, the governing equations of beam specimens related to the free-free and clamped-free boundary conditions were expressed to be able to find their natural frequencies, flexural modulus and damping values. To get a clear idea of the sensitivity of the boundary conditions to the damping values at low, medium and high levels, representative materials were subjected to the tests. The results show that the specimens with low damping values are especially sensitive to the boundary conditions and that the most reliable structural damping values are obtained for the specimens with free-free ends. For the damping values at the low levels, a deviation of about 368% was obtained between the specimens with free-free and clamped-free ends, yet, for those having high inherent damping values, comparable results were obtained. It was obvious that the set-up with clamped-free boundary conditions was not able to produce correct/reliable damping values for the specimens with low inherent damping.
Keywords: Boundary conditions, damping, dynamic values, non-contact measuring systems, vibrating beam technique.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4433824 Existence and Exponential Stability of Almost Periodic Solution for Cohen-Grossberg SICNNs with Impulses
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In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.
Keywords: Almost periodic solution, exponential stability, neural networks, impulses.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 143233823 A Non-Standard Finite Difference Scheme for the Solution of Laplace Equation with Dirichlet Boundary Conditions
Authors: Khaled Moaddy
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In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.
Keywords: Standard finite difference schemes, non–standard schemes, Laplace equation, Dirichlet boundary conditions.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 6513822 Evaluating Spectral Relationships between Signals by Removing the Contribution of a Common, Periodic Source A Partial Coherence-based Approach
Authors: Antonio Mauricio F. L. Miranda de Sá
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Partial coherence between two signals removing the contribution of a periodic, deterministic signal is proposed for evaluating the interrelationship in multivariate systems. The estimator expression was derived and shown to be independent of such periodic signal. Simulations were used for obtaining its critical value, which were found to be the same as those for Gaussian signals, as well as for evaluating the technique. An Illustration with eletroencephalografic (EEG) signals during photic stimulation is also provided. The application of the proposed technique in both simulation and real EEG data indicate that it seems to be very specific in removing the contribution of periodic sources. The estimate independence of the periodic signal may widen partial coherence application to signal analysis, since it could be used together with simple coherence to test for contamination in signals by a common, periodic noise source.
Keywords: Partial coherence, periodic input, spectral analysis, statistical signal processing.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 14533821 Exponential Stability of Periodic Solutions in Inertial Neural Networks with Unbounded Delay
Authors: Yunquan Ke, Chunfang Miao
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In this paper, the exponential stability of periodic solutions in inertial neural networks with unbounded delay are investigated. First, using variable substitution the system is transformed to first order differential equation. Second, by the fixed-point theorem and constructing suitable Lyapunov function, some sufficient conditions guaranteeing the existence and exponential stability of periodic solutions of the system are obtained. Finally, two examples are given to illustrate the effectiveness of the results.
Keywords: Inertial neural networks, unbounded delay, fixed-point theorem, Lyapunov function, periodic solutions, exponential stability.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 15243820 Existence of Periodic Solutions in a Food Chain Model with Holling–type II Functional Response
Authors: Zhaohui Wen
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In this paper, a food chain model with Holling type II functional response on time scales is investigated. By using the Mawhin-s continuation theorem in coincidence degree theory, sufficient conditions for existence of periodic solutions are obtained.
Keywords: Periodic solutions, food chain model, coincidence degree, time scales.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 17063819 Defuzzification of Periodic Membership Function on Circular Coordinates
Authors: Takashi Mitsuishi, Koji Saigusa
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This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.
Keywords: Defuzzification, periodic membership function, polar coordinates transformation.
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 20693818 Generalization of Clustering Coefficient on Lattice Networks Applied to Criminal Networks
Authors: Christian H. Sanabria-Montaña, Rodrigo Huerta-Quintanilla
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A lattice network is a special type of network in which all nodes have the same number of links, and its boundary conditions are periodic. The most basic lattice network is the ring, a one-dimensional network with periodic border conditions. In contrast, the Cartesian product of d rings forms a d-dimensional lattice network. An analytical expression currently exists for the clustering coefficient in this type of network, but the theoretical value is valid only up to certain connectivity value; in other words, the analytical expression is incomplete. Here we obtain analytically the clustering coefficient expression in d-dimensional lattice networks for any link density. Our analytical results show that the clustering coefficient for a lattice network with density of links that tend to 1, leads to the value of the clustering coefficient of a fully connected network. We developed a model on criminology in which the generalized clustering coefficient expression is applied. The model states that delinquents learn the know-how of crime business by sharing knowledge, directly or indirectly, with their friends of the gang. This generalization shed light on the network properties, which is important to develop new models in different fields where network structure plays an important role in the system dynamic, such as criminology, evolutionary game theory, econophysics, among others.Keywords: Clustering coefficient, criminology, generalized, regular network d-dimensional.
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