47,597 results
Search Results
202. On an m-dimensional system of quantum inclusions by a new computational approach and heatmap.
- Author
-
Ghaderi, Mehran and Rezapour, Shahram
- Subjects
FIXED point theory ,DIFFERENTIAL equations ,BOUNDARY value problems ,RESEARCH personnel ,PHENOMENOLOGICAL theory (Physics) - Abstract
Recent research indicates the need for improved models of physical phenomena with multiple shocks. One of the newest methods is to use differential inclusions instead of differential equations. In this work, we intend to investigate the existence of solutions for an m-dimensional system of quantum differential inclusions. To ensure the existence of the solution of inclusions, researchers typically rely on the Arzela–Ascoli and Nadler's fixed point theorems. However, we have taken a different approach and utilized the endpoint technique of the fixed point theory to guarantee the solution's existence. This sets us apart from other researchers who have used different methods. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables, and some figures. The paper ends with an example. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
203. Solutions to a discrete resonance problem with eigenparameter-dependent boundary conditions.
- Author
-
Gao, Chenghua, Yang, Enming, and Li, Huijuan
- Subjects
BOUNDARY value problems ,LYAPUNOV-Schmidt equation ,DIGITAL technology ,ARTIFICIAL intelligence ,ALGORITHMS - Abstract
In this paper, we considered the existence of solutions to a discrete second-order resonance problem with eigenparameter-dependent boundary conditions. We first transformed the resonance problem into its corresponding equivalent system using the Lyapunov-Schmidt method. In addition, using Schauder's fixed-point theorem and the connectivity theories of the solution set of compact vector fields, we obtained the existence and multiplicity of solutions to the second-order discrete resonance problem with eigenparameter-dependent boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
204. Nontrivial solutions for a Hadamard fractional integral boundary value problem.
- Author
-
Zhang, Keyu, Sun, Qian, and Xu, Jiafa
- Subjects
BOUNDARY value problems ,FRACTIONAL integrals ,ARTIFICIAL intelligence ,ALGORITHMS ,DIGITAL technology - Abstract
In this paper, we studied a Hadamard-type fractional Riemann-Stieltjes integral boundary value problem. The existence of nontrivial solutions was obtained by using the fixed-point method when the nonlinearities can be superlinear, suberlinear, and have asymptotic linear growth. Our results improved and generalized some results of the existing literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
205. Multiple positive solutions for a singular tempered fractional equation with lower order tempered fractional derivative.
- Author
-
Zhang, Xinguang, Jiang, Yongsheng, Li, Lishuang, Wu, Yonghong, and Wiwatanapataphee, Benchawan
- Subjects
BOUNDARY value problems ,FIXED point theory ,ALGORITHMS ,MACHINE learning ,ARTIFICIAL intelligence ,DIGITAL technology - Abstract
Let α ∈ (1 , 2 ] , β ∈ (0 , 1) with α − β > 1. This paper focused on the multiplicity of positive solutions for a singular tempered fractional boundary value problem { − 0 R D t α , λ u (t) = p (t) h (e λ t u (t) , 0 R D t β , λ u (t)) , t ∈ (0 , 1) , 0 R D t β , λ u (0) = 0 , 0 R D t β , λ u (1) = 0 , where h ∈ C ([ 0 , + ∞) × [ 0 , + ∞) , [ 0 , + ∞)) and p ∈ L 1 ([ 0 , 1 ] , (0 , + ∞)). By applying reducing order technique and fixed point theorem, some new results of existence of the multiple positive solutions for the above equation were established. The interesting points were that the nonlinearity contained the lower order tempered fractional derivative and that the weight function can have infinite many singular points in [ 0 , 1 ]. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
206. An $ {\varepsilon} $-approximate solution of BVPs based on improved multiscale orthonormal basis.
- Author
-
Zhang, Yingchao, Jia, Yuntao, and Lin, Yingzhen
- Subjects
ORTHONORMAL basis ,BOUNDARY value problems - Abstract
In the present paper, we construct a set of multiscale orthonormal basis based on Legendre polynomials. Using this orthonormal basis, a new algorithm is designed for solving the second-order boundary value problems. This algorithm is to find numerical solution by seeking ε -approximate solution. Moreover, we prove that the order of convergence depends on the boundedness of u (m) (x) . In addition, third numerical examples are provided to validate the efciency and accuracy of the proposed method. Numerical results reveal that the present method yields extremely accurate approximation to the exact solution. Meanwhile, compared with the other algorithms, the results obtained demonstrate that our algorithm is remarkably effective and convenient. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
207. A novel iterative scheme for solving delay differential equations and third order boundary value problems via Green's functions.
- Author
-
Okeke, Godwin Amechi, Udo, Akanimo Victor, Alqahtani, Rubayyi T., Kaplan, Melike, and Ahmed, W. Eltayeb
- Subjects
BOUNDARY value problems ,NONEXPANSIVE mappings ,DELAY differential equations ,GREEN'S functions - Abstract
In this paper, we constructed a novel fixed point iterative scheme called the Modified-JK iterative scheme. This iteration process is a modification of the JK iterative scheme. Our scheme converged weakly to the fixed point of a nonexpansive mapping and strongly to the fixed point of a mapping satisfying condition (E). We provided some examples to show that the new scheme converges faster than some existing iterations. Stability and data dependence results were proved for this iteration process. To substantiate our results, we applied our results to solving delay differential equations. Furthermore, the newly introduced scheme was applied in approximating the solution of a class of third order boundary value problems (BVPs) by embedding Green's functions. Moreover, some numerical examples were presented to support the application of our results to BVPs via Green's function. Our results extended and generalized other existing results in literature. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
208. ITERATIVE SCHEMES FOR PROBABILISTIC DOMAIN DECOMPOSITION.
- Author
-
MORÓN-VIDAL, JORGE, BERNAL, FRANCISCO, and SPIGLER, RENATO
- Subjects
BOUNDARY value problems ,HELMHOLTZ equation ,STATISTICAL errors - Abstract
Probabilistic domain decomposition (PDD) is an alternative paradigm for solving boundary value problems (BVPs) in parallel with excellent scalability properties, thanks to its reliance on stochastic representations of the BVP. However, there are cases when the latter is less numerically convenient, or unknown. Semilinear elliptic BVPs and the Helmholtz equation are prominent examples of either class. In this paper, we overcome this issue by designing suitable iterative schemes for either problem. These schemes not only retain the desirable properties of PDD but also are optimally suited for pathwise variance reduction, resulting in a systematic, nearly cost-free reduction of the statistical error through the iterations. Numerical tests carried out on the supercomputer Marconi100 are presented. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
209. Existence of Three Weak Solutions for a Class of Quasi-Linear Elliptic Operators with a Mixed Boundary Value Problem Containing p(·)-Laplacian in a Variable Exponent Sobolev Space.
- Author
-
Junichi Aramaki
- Subjects
BOUNDARY value problems ,LAPLACIAN matrices ,HYPOTHESIS ,NONLINEAR partial differential operators ,MATHEMATICS - Abstract
In this paper, we consider a mixed boundary value problem to a class of nonlinear operators containing p(·)-Laplacian. More precisely, we are concerned with the problem with the Dirichlet condition on a part of the boundary and the Steklov boundary condition on an another part of the boundary. We show the existence of at least three weak solutions under some hypotheses on given functions and the values of parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
210. Positive Solutions for Third Order Three-Point Boundary Value Problems with p-Laplacian.
- Author
-
Xingfang Feng and Hanying Feng
- Subjects
FIXED point theory ,BOUNDARY value problems ,DIFFERENTIAL equations ,MATHEMATICS ,EXAMPLE - Abstract
In this paper, the existence of positive solutions of the following third-order three-point boundary value problem with p-Laplacian {(Φ
p (u"(t)))' + f(t, u(t)) = 0, t (0, 1), u(0) = au(η), u(1) = au(η), u"(0) = 0, is studied, where Φp(s) = |s|p- 2s, p > 1. By using the fixed point index method, we establish sufficient conditions for the existence of at least one or at least two positive solutions for the above boundary value problem. The main result is demonstrated by providing an example as an application. [ABSTRACT FROM AUTHOR]- Published
- 2024
- Full Text
- View/download PDF
211. Generalized Boussinesq System with Energy Dissipation: Existence of Stationary Solutions.
- Author
-
Baranovskii, Evgenii S. and Shishkina, Olga Yu.
- Subjects
ENERGY dissipation ,BOUNDARY value problems ,NONLINEAR differential equations ,PARTIAL differential equations ,STEADY-state flow ,MONOTONE operators ,MASS transfer - Abstract
In this paper, we investigate the solvability of a boundary value problem for a heat and mass transfer model with the spatially averaged Rayleigh function. The considered model describes the 3D steady-state non-isothermal flow of a generalized Newtonian fluid (with shear-dependent viscosity) in a bounded domain with Lipschitz boundary. The main novelty of our work is that we do not neglect the viscous dissipation effect in contrast to the classical Boussinesq approximation, and hence, deal with a system of strongly nonlinear partial differential equations. Using the properties of the averaging operation and d-monotone operators as well as the Leray–Schauder alternative for completely continuous mappings, we prove the existence of weak solutions without any smallness assumptions for model data. Moreover, it is shown that the set of all weak solutions is compact, and each solution from this set satisfies some energy equalities. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
212. A uniformly convergent computational method for singularly perturbed parabolic partial differential equation with integral boundary condition.
- Author
-
Wondimu, Getu Mekonnen, Duressa, Gemechis File, Woldaregay, Mesfin Mekuria, and Dinka, Tekle Gemechu
- Subjects
BOUNDARY value problems ,PARABOLIC differential equations ,FINITE difference method ,EULER method ,FINITE differences ,BOUNDARY layer (Aerodynamics) - Abstract
This paper presents a numerical method for a class of singularly perturbed parabolic partial differential equations with integral boundary conditions (IBC). The solution to the considered problem exhibits pronounced boundary layers on both the left and right sides of the spatial domain. To address this challenging problem, we propose the use of the implicit Euler method for time discretization and a finite difference method on a well-designed piecewise uniform Shishkin mesh for spatial discretization. The integral boundary condition is approximated using Simpson's 13rule. The presented method demonstrates almost second-order uniform convergence in the discretization of the spatial derivative and first-order convergence in the discretization of the time derivative. To validate the applicability and accuracy of the proposed method, two illustrative examples are employed. The computational results not only accurately reflect the theoretical estimations but also highlight the method's effectiveness in capturing the intricate features of singularly perturbed parabolic partial differential equations with integral boundary conditions. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
213. Convergence analysis of compact finite difference method for the solution of anti-periodic boundary value problems.
- Author
-
Saqib, Abdul Baseer, Loghmani, Ghasem Barid, and Heydari, Mohammad
- Subjects
BOUNDARY value problems ,FINITE differences ,DERIVATIVES (Mathematics) - Abstract
The main objective of this paper is to introduce the fourth and sixth-order compact finite difference methods for solving anti-periodic boundary value problems. Compact finite difference formulas can approximate the derivatives of a function more accurately than the standard finite difference formulas for the same number of grid points. The convergence analysis of the proposed method is also investigated. This analysis shows how the error between the approximate and exact solutions decreases as the grid space is reduced. To validate the proposed method's accuracy and efficiency, some computational experiments are provided. Moreover, a comparison is performed between the standard and compact finite difference methods. The experiments indicate that the compact finite difference method is more accurate and efficient than the standard one. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
214. Solvability Criterion for a System Arising from Monge–Ampère Equations with Two Parameters.
- Author
-
Wang, Liangyu and Li, Hongyu
- Subjects
MONGE-Ampere equations ,CONVEX geometry ,BOUNDARY value problems - Abstract
Monge–Ampère equations have important research significance in many fields such as geometry, convex geometry and mathematical physics. In this paper, under some superlinear and sublinear conditions, the existence of nontrivial solutions for a system arising from Monge–Ampère equations with two parameters is investigated based on the Guo–Krasnosel'skii fixed point theorem. In the end, two examples are given to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
215. Multiplicity of Solutions for Discrete 2 n -TH Order Periodic Boundary Value Problem with φ p -Laplacian.
- Author
-
Zuo, Jiabin, Hammouti, Omar, and Taarabti, Said
- Subjects
BOUNDARY value problems ,LAPLACIAN operator ,CRITICAL point theory ,MULTIPLICITY (Mathematics) - Abstract
The purpose of this paper is to investigate the existence and multiplicity of nontrivial solutions with the φ p -Laplacian for the discrete 2 n -th order periodic boundary value issue. To support these conclusions, we have employed variational techniques and contemporary critical point theory. A few new findings are expanded upon and enhanced. We give an example to show how our key findings can be applied. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
216. Learning Fuel-Optimal Trajectories for Space Applications via Pontryagin Neural Networks.
- Author
-
D'Ambrosio, Andrea and Furfaro, Roberto
- Subjects
PONTRYAGIN'S minimum principle ,SPACE trajectories ,BOUNDARY value problems ,TANGENT function ,MACHINE learning ,HYPERBOLIC functions - Abstract
This paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control problems through indirect methods. Specifically, PoNNs learn to solve the Two-Point Boundary Value Problem derived from the application of the Pontryagin Minimum Principle to the problem's Hamiltonian. Within PoNNs, the Extreme Theory of Functional Connections (X-TFC) is leveraged to approximate states and costates using constrained expressions (CEs). These CEs comprise a free function, modeled by a shallow neural network trained via Extreme Learning Machine, and a functional component that consistently satisfies boundary conditions analytically. Addressing discontinuous control, a smoothing technique is employed, substituting the sign function with a hyperbolic tangent function and implementing a continuation procedure on the smoothing parameter. The proposed methodology is applied to scenarios involving fuel-optimal Earth−Mars interplanetary transfers and Mars landing trajectories. Remarkably, PoNNs exhibit convergence to solutions even with randomly initialized parameters, determining the number and timing of control switches without prior information. Additionally, an analytical approximation of the solution allows for optimal control computation at unencountered points during training. Comparative analysis reveals the efficacy of the proposed approach, which rivals state-of-the-art methods such as the shooting technique and the adaptive Gaussian quadrature collocation method. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
217. Existence Solutions for a Singular Nonlinear Problem with Dirichlet Boundary Conditions on Exterior Domains.
- Author
-
Ali, Mageed and Iaia, Joseph
- Subjects
BOUNDARY value problems ,PARTIAL differential equations ,CONTINUOUS functions ,PARAMETER estimation ,MATHEMATICAL models - Abstract
Copyright of Kirkuk Journal of Science is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
- Published
- 2024
- Full Text
- View/download PDF
218. Existence and Uniqueness of Some Unconventional Fractional Sturm–Liouville Equations.
- Author
-
Gholizadeh Zivlaei, Leila and Mingarelli, Angelo B.
- Subjects
STURM-Liouville equation ,BOUNDARY value problems ,EXISTENCE theorems ,DIFFERENTIAL equations ,EQUATIONS - Abstract
In this paper, we provide existence and uniqueness results for the initial value problems associated with mixed Riemann–Liouville/Caputo differential equations in the real domain. We show that, under appropriate conditions in a fractional order, solutions are always square-integrable on the finite interval under consideration. The results are valid for equations that have sign-indefinite leading terms and measurable coefficients. Existence and uniqueness theorem results are also provided for two-point boundary value problems in a closed interval. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
219. On singular φ-Laplacian BVPs of nonlinear fractional differential equation.
- Author
-
Temar, Bahia, Saifi, Ouiza, and Djebali, Smaïl
- Subjects
NONLINEAR differential equations ,LAPLACIAN operator ,FRACTIONAL differential equations ,NONLINEAR boundary value problems ,BOUNDARY value problems ,FIXED point theory ,BANACH spaces - Abstract
This paper investigates the existence of multiple positive solutions for a class of φ-Laplacian boundary value problem with a nonlinear fractional differential equation and fractional boundary conditions. Multiple solutions are proved under slight conditions on a possibly degenerating source term. Approximation techniques together with the fixed point index theory a on cone of a Banach space are employed. Some illustrating examples of are also supplied. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
220. Holographic Euclidean thermal correlator.
- Author
-
He, Song and Li, Yi
- Subjects
BOUNDARY value problems ,CORRELATORS ,STRAINS & stresses (Mechanics) ,MAXWELL equations ,THERMAL stresses ,HORIZON ,BLACK holes - Abstract
In this paper, we compute holographic Euclidean thermal correlators of the stress tensor and U(1) current from the AdS planar black hole. To this end, we set up perturbative boundary value problems for Einstein's gravity and Maxwell theory in the spirit of Gubser-Klebanov-Polyakov-Witten, with appropriate gauge fixing and regularity boundary conditions at the horizon of the black hole. The linearized Einstein equation and Maxwell equation in the black hole background are related to the Heun equation of degenerate local monodromy. Leveraging the connection relation of local solutions of the Heun equation, we partly solve the boundary value problem and obtain exact two-point thermal correlators for U(1) current and stress tensor in the scalar and shear channels. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
221. Plasticity-Induced Heating: Revisiting the Energy-Based Variational Model.
- Author
-
Hartmann, Christoph and Obermeyer, Michael
- Subjects
HEATING ,MATERIAL plasticity ,BOUNDARY value problems ,STRAIN rate ,MANUFACTURING processes - Abstract
Temperature evolution during plastic deformation is of great importance for the design of manufacturing processes, as well as for the analysis and prediction of tool wear. However, the results from experimental- and numerical-type research are still often contradictory. In this paper, we analyze methods for estimating plasticity-induced heating directly from displacement fields that can be recorded during experiments or extracted from simulation results. In terms of computational methodology, the thermodynamically motivated energy-based variational formulation of the coupled thermo-mechanical boundary-value problem is adapted to the problem at hand. Since an analysis of this variational formulation exhibits challenges and distinct inconsistencies with respect to the problem at hand, an alternative approach is proposed. This alternative approach is essentially a purely thermal finite element simulation, and it is conducted using a heat source term that is empirically based on the fraction of irreversible deformation work converted to heat. Our approach estimates plasticity-induced heating based on the strain and strain rate data derived from displacement fields. We therefore incorporate thermo-visco-plastic constitutive behavior (Johnson–Cook) with a thermodynamically motivated model that specifies the fraction of plastic work converted to heat (the Taylor–Quinney coefficient). [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
222. IMPROVED AND VECTORISED MATLAB-BASED ALGORITHMS FOR SERIAL AND PARALLEL IMPLEMENTATION OF FINITE ELEMENT METHOD IN LINEAR ELASTICITY.
- Author
-
Sadjiep Tchuigwa, Baurice Sylvain, Krmela, Jan, Pokorny, Jan, and Krmelova, Vladimira
- Subjects
- *
FINITE element method , *BOUNDARY value problems , *SPARSE matrix software , *DEGREES of freedom - Abstract
This paper presents two improved algorithms for efficient sequential and parallel implementation of the Finite element method (FEM) for both linear and nonlinear boundary value problems. The proposed algorithms address some weak points, such as the overuse of for-loops and serial computing caused by dependencies in constructing fundamental expressions (global stiffness matrix, mass matrix, global force vector, etc.) resulting from the finite element method. By taking advantage of the concepts of sparse matrix representation, vectorization, and the physical architecture of modern computing resources, the proposed methods are free from mesh partitioning techniques or similar approaches and enable the use of all available CPU cores/threads without synchronization. Moreover, these algorithms are also adapted to deal with meshes involving elements of any order in both 2D and 3D. Two tests from NAFEMS benchmarks are implemented in MATLAB to verify the accuracy and stability of the proposed algorithms in both serial and parallel processing. According to serial and parallel computing results, the proposed algorithms perform better than the standard sparse assembly strategy and behave linearly with the mesh size but at a smaller rate than the latter. In parallel processing, the algorithms are also demonstrated to be accurate and achieve an efficiency of at least 60% in 2D and 70% with two cores/threads when the mesh size is greater than 10,000. Moreover, the simulations revealed that the performance gap between the proposed algorithm and the classical sparse algorithm is more pronounced in 2D than in 3D due to the increase in degrees of freedom. [ABSTRACT FROM AUTHOR]
- Published
- 2024
- Full Text
- View/download PDF
223. ON A NEW ARITHMETHIC ADDITIVE FUNCTION RELATED TO THE GENERALIZED DIVISORS OF AN INTEGER.
- Author
-
BOUDERBALA, MIHOUB
- Subjects
INTEGERS ,BOUNDARY value problems ,DIFFERENTIAL equations ,FIXED point theory ,DERIVATIVES (Mathematics) - Abstract
The main purpose of this paper is to define a new additive function related to generalized divisors of an integer and to study some of its properties. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
224. Low-Thrust multi-revolutionary trajectories to geostationary orbit using angular independent variable.
- Author
-
Oo, Paing Soe Thu
- Subjects
ORBITS (Astronomy) ,BOUNDARY value problems ,TRAJECTORY optimization ,DIFFERENTIAL equations ,CONTINUATION methods ,INDEPENDENT variables ,MAXIMUM principles (Mathematics) - Abstract
In this paper, the problem of optimization of multi-revolutionary transfers of a spacecraft with a fixed angular range of auxiliary longitude and the free transfer time from a given initial orbit to geostationary orbit in a central Newtonian gravitational field is considered. The purpose of the optimization is to calculate the program of control of the vector of the thrust, which provided optimal multi-revolutionary trajectories to the final orbit with the minimum cost of the propellant. The magnitude of thrust is assumed to be constant. The optimized control is the vector control program of thrust, including its direction and periods of operation. For mathematical modeling of the spacecraft motion, differential equations in equinoctial elements are used, and as an independent variable, an auxiliary longitude is used, introduced in such a way that the differential equation for it coincides with the differential equation for true longitude in unperturbed motion. An approach based on the Pontryagin maximum principle is proposed to solve the trajectory optimization problem. Using the maximum principle, the problem of optimizing the multi-revolutionary transfer of spacecraft with limited thrust is reduced to a two-point boundary value problem and the boundary value problem is solved by the method of continuation on parameter. To get the goal, the problems of optimizing the multi-revolutionary transfer with limited power and limited thrust are considered. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
225. Invariant manifolds to read impulsive transfer to the Earth-Moon L2 halo orbit based on invariant manifolds.
- Author
-
Rui, Zhou
- Subjects
INVARIANT manifolds ,LAGRANGIAN points ,ORBITS (Astronomy) ,ORBITAL transfer (Space flight) ,BOUNDARY value problems ,LUNAR exploration ,CONTINUATION methods - Abstract
Spacecraft insertion into halo orbits around the Luna-Earth libration point L2 is necessary for the lunar exploration programs, especially for solving problems of studying the far side of the Moon by using landing vehicles. The paper proposes a new method for calculating the transfer trajectories to such halo orbits. Considered two flight sachems: conventional transfer and transfer with ballistic capture. A numerical method has been developed for solving the problems. It consists in inserting invariant manifolds of halo orbits and calculating two-impulse trajectories from an initial circular earth orbit to the insertion point of this stable manifold. The problem of transfer orbit calculation is reduced to calculating the transfer trajectory between the LEO and a given entry point to the stable manifold. For solving the boundary value problem, the parameter continuation method is used, which based on Newtonian homotopy between the solutions of the unperturbed and perturbed boundary value problems. And a hybrid algorithm for optimizing the insertion point of the manifold for trajectories with ballistic capture is proposed, the numerical examples are given. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
226. A FEM in frequency domain for a transient electric field in non-sinusoidal steady state under the non-sinusoidal periodic voltage.
- Author
-
Wen, Teng, Wei, Xiaoyun, Li, Xuebao, Cao, Boyuan, and Zhao, Zhibin
- Subjects
ELECTRIC transients ,ELECTRIC fields ,INSULATED gate bipolar transistors ,BOUNDARY value problems ,FINITE element method ,STEADY state conduction ,TRANSISTORS - Abstract
Purpose: This paper aims to focus on the finite element method in the frequency domain (FD-FEM) for the transient electric field in the non-sinusoidal steady state under the non-sinusoidal periodic voltage excitation. Design/methodology/approach: Firstly, the boundary value problem of the transient electric field in the frequency domain is described, and the finite element equation of the FD-FEM is derived by Galerkin's method. Secondly, the constrained electric field equation on the boundary in the frequency domain (FD-CEFEB) is also derived, which can solve the electric field intensity on the boundary and the dielectric interface with high accuracy. Thirdly, the calculation procedures of the FD-FEM with FD-CEFEB are introduced in detail. Finally, a numerical example of the press-packed insulated gate bipolar transistor under the working condition of the repetitive turn-on and turn-off is given. Findings: The FD-CEFEB improves numerical accuracy of electric field intensity on the boundary and interfacial charge density, which can be achieved by modifying the existing FD-FEMs' code in appropriate steps. Moreover, the proposed FD-FEM and the FD-CEFEB will only increase calculation costs by a little compared with the traditional FD-FEMs. Originality/value: The FD-CEFEB can directly solve the electric field intensity on the boundary and the dielectric interface with high accuracy. This paper provides a new FD-FEM for the transient electric field in the non-sinusoidal steady state with high accuracy, which is suitable for combined insulation structure with a long time constant. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
227. Complex Boundary Value Problems of Nonlinear Differential Equations 2014.
- Author
-
Xinguang Zhang, Yong Hong Wu, Dragoş-Pãtru, Covei, and Xinan Hao
- Subjects
LAPLACE transformation ,BOUNDARY value problems ,NONLINEAR differential equations - Published
- 2014
- Full Text
- View/download PDF
228. A continuous model of magnetic moment distribution in a system with bilinear and biquadratic coupling.
- Author
-
Omelchenko, Pavlo, Wadge, Elliot, Besler, Juliana, Girt, Erol, and Heinrich, Bret
- Subjects
MAGNETIC moments ,MAGNETIC structure ,BOUNDARY value problems ,ATOMIC models ,DATA analysis - Abstract
In this paper, we present a continuous model as an analog to the discrete atomic model often used in the interpretation/analysis of magnetometry studies of magnetic structures with bilinear and/or biquadratic coupling. For a typical set of parameters, the continuous model is shown to be nearly indistinguishable from its discrete counterpart; validating it for data analysis purposes. Furthermore, we also find a very simple analytic expression which can approximately solve the continuous model and also provides insight into the behaviors of the magnetic moment within the magnetic structure. The main advantage of the continuous model is that numerically it can be solved as a boundary value problem, which can be significantly faster than the energy minimization required for the discrete model improving computational speed and allowing for much more rapid data analysis. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF
229. Coupled systems with Ambrosetti-Prodi-type differential equations.
- Author
-
Minhós, F., Carapau, F., and Rodrigues, G.
- Subjects
DIFFERENTIAL equations ,BOUNDARY value problems ,TOPOLOGICAL degree - Abstract
In this paper, we consider some boundary value problems composed by coupled systems of second-order differential equations with full nonlinearities and general functional boundary conditions verifying some monotone assumptions. The arguments apply the lower and upper solutions method, and defining an adequate auxiliary, homotopic, and truncated problem, it is possible to apply topological degree theory as the tool to prove the existence of solution. In short, it is proved that for the parameter values such that there are lower and upper solutions, then there is also, at least, a solution and this solution is localized in a strip bounded by lower and upper solutions. As far as we know, it is the first paper where Ambrosetti-Prodi differential equations are considered in couple systems with different parameters. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
230. 3-D forward modelling for DC resistivity method based on smooth multiscale finite-element algorithm.
- Author
-
Qi, Yanfu, Li, Xiu, Jing, Xu, Sun, Naiquan, Qi, Zhipeng, and Zhou, Jianmei
- Subjects
PARTIAL differential equations ,UNDERGROUND construction ,BOUNDARY value problems ,PROBLEM solving - Abstract
SUMMARY: When the conventional finite-element method is used to simulate the 3-D direct-current (DC) resistivity response over a conductive earth with large complex structures, it requires finely discretized mesh to accurately represent the underground structures. Directly solving the current-conduction problem on the fine mesh will lead to a huge amount of calculation. In this paper, we develop a fast 3-D forward modelling method for DC resistivity method based on smooth multiscale finite-element algorithm. Instead of using the conventional polynomial basis functions, we construct the multiscale basis functions by solving the local boundary-value problems of partial differential equation in parallel on the multiscale meshes. The multiscale basis functions can capture the small-scale heterogeneous information in coarse cells and reflect it to the large scale by assembling macro matrix of coarse mesh. Thus, it enables us to quickly obtain the accurate solution by solving the original current-conduction problem with complex structures on coarse mesh. We further adopt the oversampling technology to improve the forward modelling accuracy. Besides, by combining with the gradient smoothing technology, we avoid establishing the continuous form of multiscale basis functions and their spatial derivative integral operation to rapidly assemble the macro matrix. Finally, the reliability of the proposed algorithm is verified by applying our code to the 3-D complex models and comparing it with the conventional finite-element method. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
231. Existence and Uniqueness of Local Regular Solution to the Schrödinger Flow from a Bounded Domain in R3 into S2.
- Author
-
Chen, Bo and Wang, Youde
- Subjects
LANDAU-lifshitz equation ,BOUNDARY value problems ,RICCATI equation ,HARMONIC maps ,RIEMANNIAN manifolds - Abstract
In this paper, we show the existence and uniqueness of local regular solutions to the initial-Neumann boundary value problem of the Schrödinger flow from a smooth bounded domain Ω ⊂ R 3 into S 2 (namely Landau–Lifshitz equation without dissipation). The proof is built on a parabolic perturbation method, an intrinsic geometric energy argument, the symmetric (algebraic) properties of S 2 and some observations on the behaviors of some geometric quantities on the boundary of the domain manifold.It is based on methods from Ding and Wang (one of the authors of this paper) for the Schrödinger flows of maps from a closed Riemannian manifold into a Kähler manifold as well as on methods by Carbou and Jizzini for solutions of the Landau–Lifshitz equation. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
232. Using asymptotic homogenization to determine effective thermo-viscoelastic properties of fibrous composites with interphase layer.
- Author
-
Vlasov, Alexander Nikolaevich, Volkov-Bogorodsky, Dmitriy Borisovich, and Savatorova, Viktoria
- Subjects
ASYMPTOTIC homogenization ,FIBROUS composites ,YOUNG'S modulus ,MECHANICAL behavior of materials ,PARAMETRIC equations ,BOUNDARY value problems - Abstract
In this paper, we apply the method of asymptotic homogenization in parametric space in order to determine thermo-viscoelastic properties of materials composed of cylindrical fibers surrounding by an intermediate layer separating them from viscoelastic matrix. We use the Maxwell model of viscoelasticity. The volumetric fraction and physical properties of the layer can vary. There is a possibility of a contrast between the properties of fibers, the layer, and the matrix. Our approach allows us to treat temperature as a parameter and study the response of mechanical characteristics on the change in temperature. We perform the Fourier transform of governing equations and then implement asymptotic homogenization of the resulting equations in parametric space. Microscopic boundary value problem is defined on a periodic cell consisting of a fiber surrounded by a layer and embedded in the matrix. Macroscopic equations are derived for the complex Young's and shear moduli. Effective viscoelastic properties of the material are computed for different values of the frequency of harmonic oscillations and for various temperatures. This paper discusses how effective storage and loss Young's and shear moduli depend on volumetric fraction and mechanical properties of the material of the layer. The obtained results can provide information on how concentration, structure and properties of inclusions can affect the effective storage and loss Young's and shear moduli. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
233. (ω , ρ)-BVP Solutions of Impulsive Differential Equations of Fractional Order on Banach Spaces.
- Author
-
Fečkan, Michal, Kostić, Marko, and Velinov, Daniel
- Subjects
FRACTIONAL differential equations ,BANACH spaces ,BOUNDARY value problems ,IMPULSIVE differential equations - Abstract
The paper focuses on exploring the existence and uniqueness of a specific solution to a class of Caputo impulsive fractional differential equations with boundary value conditions on Banach space, referred to as (ω , ρ) -BVP solution. The proof of the main results of this study involves the application of the Banach contraction mapping principle and Schaefer's fixed point theorem. Furthermore, we provide the necessary conditions for the convexity of the set of solutions of the analyzed impulsive fractional differential boundary value problem. To enhance the comprehension and practical application of our findings, we conclude the paper by presenting two illustrative examples that demonstrate the applicability of the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
234. Neumann boundary value problems for elliptic operators with measure-valued coefficients.
- Author
-
Wei, Rong, Yang, Saisai, and Zhang, Tusheng
- Subjects
BOUNDARY value problems ,ELLIPTIC operators - Abstract
In this paper, we prove that there exists a unique weak solution to the Neumann boundary value problem for second order elliptic operators whose coefficients are signed measures. We will give a probabilistic representation of the solution. The heat kernel estimates and reflected diffusion processes play important roles. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
235. Upper and Lower Solution Method for a Singular Tempered Fractional Equation with a p -Laplacian Operator.
- Author
-
Zhang, Xinguang, Chen, Peng, Tian, Hui, and Wu, Yonghong
- Subjects
LAPLACIAN operator ,OPERATOR equations ,EQUATIONS ,BOUNDARY value problems - Abstract
In this paper, we consider the existence of positive solutions for a singular tempered fractional equation with a p-Laplacian operator. By constructing a pair of suitable upper and lower solutions of the problem, some new results on the existence of positive solutions for the equation including singular and nonsingular cases are established. The asymptotic behavior of the solution is also derived, which falls in between two known curves. The interesting points of this paper are that the nonlinearity of the equation may be singular in time and space variables and the corresponding operator can have a singular kernel. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
236. Dynamic interaction between complex defect and crack in functionally graded magnetic-electro-elastic bi-materials.
- Author
-
An, Ni, Song, Tian-shu, and Hou, Gangling
- Subjects
BOUNDARY value problems ,FUNCTIONALLY gradient materials ,NUMERICAL analysis ,INTEGRAL equations ,MECHANICAL models ,PROBLEM solving - Abstract
This paper aims to develop an effective theoretical method for analyzing the interaction of interfacial crack and complex defect in functionally graded magnetic-electro-elastic bi-materials with exponential variation under the action of anti-plane incident SH-wave. The boundary value problem of interest is solved by Green's function method. The mechanical model of the cracks is constructed through interface conjunction and crack deviation techniques, thereby simplifying the crack problem to solving a series of the first kind of Fredholm's integral equations, from which the dynamic stress intensity factor (DSIF) at the crack tips of the left crack are expressed. The validity of the present method is verified by comparing with a single crack model in previous work. Through the analyses of numerical cases, it can be concluded that the DSIF is related with 3 factors:the geometry of complex defect and crack, the characteristics of incident wave and the inhomogeneity of materials. Comparing with dual integral equations in dealing with asymmetric defects, the method in this paper is relatively more flexible and applicable, also it comes up with a new way to study fracture problems in functionally graded magnetic-electro-elastic materials with more complex defects. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
237. EXISTENCE OF SOLUTIONS FOR IMPULSIVE BOUNDARY VALUE PROBLEMS ON INFINITE INTERVALS.
- Author
-
DOĞRU AKGÖL, Sibel
- Subjects
BOUNDARY value problems ,NONLINEAR boundary value problems - Abstract
The paper deals with the existence of solutions for a general class of second-order nonlinear impulsive boundary value problems defined on an infinite interval. The main innovative aspects of the study are that the results are obtained under relatively mild conditions and the use of principal and nonprincipal solutions that were obtained in a very recent study. Additional results about the existence of bounded solutions are also provided, and theoretical results are supported by an illustrative example. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
238. Neumann boundary value problem for the Beltrami equation in a ring domain.
- Author
-
GENÇTÜRK, İlker
- Subjects
BOUNDARY value problems ,NEUMANN problem ,SINGULAR integrals ,EQUATIONS - Abstract
In this paper, the Neumann boundary value problem for the Beltrami operator is explicitly solved in a circular ring domain, solvability conditions for this problem are also given in explicit forms. Moreover, the Neumann problem for second-order operators with the Bitsadze/Laplace operator as the main part as combinations of the Cauchy-Riemann and the Beltrami operators is investigated. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
239. (I q)–Stability and Uniform Convergence of the Solutions of Singularly Perturbed Boundary Value Problems.
- Author
-
Vrabel, Robert
- Subjects
BOUNDARY value problems ,DIFFERENTIAL equations ,ORDINARY differential equations - Abstract
In this paper, using the notion of ( I q )–stability and the method of a priori estimates, known as the method of lower and upper solutions, the sufficient conditions guaranteeing uniform convergence of solutions to the solution of a reduced problem on the entire interval [ a , b ] have been established for four different types of boundary conditions for a singularly perturbed differential equation ε y ″ = f (x , y , y ′) , a ≤ x ≤ b . In the second part of the paper, by employing the Peano phenomenon, we analyzed the structure of the solutions of the reduced problem f (x , y , y ′) = 0 . [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
240. On coupled system of nonlinear Ψ-Hilfer hybrid fractional differential equations.
- Author
-
Mali, Ashwini D., Kucche, Kishor D., and Vanterler da Costa Sousa, José
- Subjects
FRACTIONAL differential equations ,INITIAL value problems ,BOUNDARY value problems ,HYBRID systems ,NONLINEAR systems ,BANACH algebras - Abstract
This paper is dedicated to investigating the existence of solutions to the initial value problem (IVP) for a coupled system of Ψ-Hilfer hybrid fractional differential equations (FDEs) and boundary value problem (BVP) for a coupled system of Ψ-Hilfer hybrid FDEs. Analysis of the current paper depends on the two fixed point theorems involving three operators characterized on Banach algebra. In the view of an application, we provided useful examples to exhibit the effectiveness of our achieved results. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
241. Eventual smoothness of generalized solutions to a singular chemotaxis system for urban crime in space dimension 2.
- Author
-
Qiu, Zixuan and Li, Bin
- Subjects
CHEMOTAXIS ,BOUNDARY value problems ,GENERALIZATION ,MATHEMATICAL models ,MATHEMATICAL formulas - Abstract
This paper is concerned with a chemotaxis system in a two-dimensional setting as follows: { u t = Δ u − χ ∇ ⋅ (u ∇ ln v) − κ u v + r u − μ u 2 + h 1 , v t = Δ v − v + u v + h 2 , with the parameters χ , κ , μ > 0 and r ∈ R , and with the given functions h 1 , h 2 ≥ 0. This model was originally introduced by Short et al for urban crime with the particular values χ = 2 , r = 0 and μ = 0 , and the logistic source term r u − μ u 2 was incorporated into ( ⋆) by Heihoff to describe the fierce competition among criminals. Heihoff also proved that the initial-boundary value problem of ( ⋆) possesses a global generalized solution in the two-dimensional setting. The main purpose of this paper is to show that such a generalized solution becomes bounded and smooth at least eventually. In addition, the long-time asymptotic behavior of such a solution is discussed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
242. Positive weak solutions for heterogeneous elliptic logistic BVPs with glued Dirichlet-Neumann mixed boundary conditions.
- Author
-
Cano-Casanova, Santiago
- Subjects
BOUNDARY value problems ,MATHEMATICAL analysis - Abstract
This article concerns the existence of positive weak solutions of a heterogeneous elliptic boundary value problem of logistic type in a very general annulus. The novelty of this work lies in considering non-classical mixed glued boundary conditions. Namely, Dirichlet boundary conditions on a component of the boundary, and glued Dirichlet-Neumann boundary conditions on the other component of the boundary. In this paper we perform a complete analysis of the existence of positive weak solutions of the problem, giving a necessary condition on the parameter for the existence of them, and a sufficient condition for the existence of them, depending on the -parameter, the spatial dimension and the exponent of the reaction term. The main technical tools used to carry out the mathematical analysis of this work are variational and monotonicity techniques. The results obtained in this paper are pioners in the field, because up the knowledge of the autor, this is the first time where this kind of logistic problems have been analyzed. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
243. SOLVABILITY FOR ITERATIVE SYSTEMS OF HADAMARD FRACTIONAL BOUNDARY VALUE PROBLEMS.
- Author
-
KRUSHNA, B. M. B., RAJU, V. V. R. R. B., PRASAD, K. R., and SRINIVAS, M. A.
- Subjects
HILBERT'S tenth problem ,HADAMARD matrices ,BOUNDARY value problems ,FIXED point theory ,KERNEL (Mathematics) - Abstract
In this paper, we consider an iterative system of Hadamard fractional boundary value problems. The sufficient conditions are derived for the existence of at least one positive solution by utilizing Guo-Krasnosel'skii fixed point theorem. The obtained results in the paper are illustrated with an example for their feasibility. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
244. Global existence and exponential stability of solutions for thermodiffusion equations of type III.
- Author
-
Zhang, Ming
- Subjects
EXPONENTIAL stability ,THERMOPHORESIS ,PARTIAL differential equations ,INITIAL value problems ,BOUNDARY value problems - Abstract
In this paper, we consider an initial boundary value problem for the one-dimensional thermodiffusion equations of type III. By the semigroup approach and the energy method, we establish the global existence and exponential stability for the solutions in a bounded region. The main work of this paper is to extend the study of thermodiffusion equations to the model of type III, which can be used as a reference for the study of other types of partial differential equations. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
245. Vallée-Poussin Theorem for Equations with Caputo Fractional Derivative.
- Author
-
Bohner, Martin, Domoshnitsky, Alexander, Padhi, Seshadev, and Srivastava, Satyam Narayan
- Subjects
CAPUTO fractional derivatives ,GREEN'S functions ,DERIVATIVES (Mathematics) ,FUNCTIONAL differential equations ,FRACTIONAL differential equations ,DIFFERENTIAL inequalities - Abstract
In this paper, the functional differential equation (D C a + α x) (t) + ∑ i = 0 m (T i x (i)) (t) = f (t) , t ∈ [ a , b ] , with Caputo fractional derivative D C a + α is studied. The operators T
i act from the space of continuous to the space of essentially bounded functions. They can be operators with deviations (delayed and advanced), integral operators and their various linear combinations and superpositions. Such equations could appear in various applications and in the study of systems of, for example, two fractional differential equations, when one of the components can be presented from the first equation and substituted then to another. For two-point problems with this equation, assertions about negativity of Green's functions and their derivatives with respect to t are obtained. Our technique is based on an analog of the Vallée-Poussin theorem for differential inequalities, which is proven in our paper and gives necessary and sufficient conditions of negativity of Green's functions and their derivatives for two-point problems: there exists a positive function v satisfying corresponding boundary conditions and the inequality (D C a + α ν) (t) + ∑ i = 0 m (T i v (i)) (t) < 0 , t ∈ [ a , b ] . Choosing the function v, we obtain explicit sufficient tests of sign-constancy of Green's functions and its derivatives. It is demonstrated that these tests cannot be improved in a general case. Influences of delays on these sufficient conditions are analyzed. It is demonstrated that the tests can be essentially improved for "small" deviations. [ABSTRACT FROM AUTHOR]- Published
- 2023
- Full Text
- View/download PDF
246. Editorial: Overview and Some New Directions.
- Author
-
Zeng, Shengda, Migórski, Stanislaw, and Liu, Yongjian
- Subjects
HOPF bifurcations ,GEOMETRIC function theory ,SYSTEMS theory ,QUANTUM field theory ,NONLINEAR dynamical systems ,BOUNDARY value problems - Abstract
The notion of competing HT ht -Laplacians with weights is considered for the first time. They are driven by a degenerated HT ht -Laplacian with weights and a competing HT ht -Laplacian with weights, respectively. Finally, the authors indicate how the result can be extended to HT ht -equations ( HT ht ). This research aims to present a linear operator HT ht by utilizing the I q i -Mittag-Leffler function and to introduce the subclass of harmonic HT ht -convex functions HT ht related to the Janowski function. [Extracted from the article]
- Published
- 2023
- Full Text
- View/download PDF
247. Fractional p -Laplacian Equations with Sandwich Pairs.
- Author
-
Sousa, Jose Vanterler da C.
- Subjects
FRACTIONAL differential equations ,BOUNDARY value problems ,EQUATIONS - Abstract
The main purpose of this paper was to consider new sandwich pairs and investigate the existence of a solution for a new class of fractional differential equations with p-Laplacian via variational methods in ψ -fractional space H p α , β ; ψ (Ω) . The results obtained in this paper are the first to make use of the theory of ψ -Hilfer fractional operators with p-Laplacian. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF
248. B-Spline Finite Element Method for Solving Linear System of Second-Order Boundary Value Problems.
- Author
-
Yazdani, A. and Gharbavi, S.
- Subjects
LINEAR systems ,FINITE element method ,BOUNDARY value problems ,ORDINARY differential equations ,GALERKIN methods - Abstract
In this paper, we solve a linear system of second-order boundary value problems by using the quadratic B-spline finite element method (FEM). The performance of the method is tested on one model problem. Comparisons are made with both the analytical solution and some recent results.The obtained numerical results show that the method is efficient. [ABSTRACT FROM AUTHOR]
- Published
- 2023
249. Numerical Study of the Influence of the Heater Position upon the Heat Transfer during Pyrolysis Process Used for End-of-life Tires Treatment.
- Author
-
Filipova, M., Georgiev, I. R., and Zheleva, I.
- Subjects
PYROLYSIS ,ENVIRONMENTAL protection ,BOUNDARY value problems - Abstract
One of the most dangerous waste in the world are the End-of-Life tires (EOLT). They are waste that does not practically decompose in nature. Because of this their sound treatment is needed for environment protection. Pyrolysis process is one of the possible methods for such a treatment. Globally, around 23% of all EOLT are processed through pyrolysis, whereas in the Republic of Bulgaria only 5% are processed by pyrolysis. It is clear that for Bulgaria this method still has a good potential for usage, development and further research. The pyrolysis process, used for EOLT treatment, usually is 3D and non-stationary. Thus it is very complicated for modeling and studying. Following [3] an adequate mathematical model of the heat transfer during the pyrolysis process used for the treatment of the End-of-Life tires (EOLT) has been presented in our previous paper [1].There a numerical algorithm in MATLAB for solving the respective mathematical initial and boundary value problems has been also developed. Some results for the temperature field for several characteristic periods of operation of pyrolysis station are presented and commented in this paper [1]. In our next paper [2] we have examined the influence of the heating upon the heat transfer during the pyrolysis process used for EOLT treatment. This paper deals with studying the influence of the heater position upon the heat transfer during EOLT treatment by pyrolysis process. The results for temperature fields, temperature isolines and gradients at some specific moments of time and for two different initial heating functions are graphically presented and commented. Results from this modeling can be used in the real pyrolysis stations for more precise displacement of heathers and measurement devices and for designing of automated management of the process. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
250. Reconciling semiclassical and Bohmian mechanics. II. Scattering states for discontinuous potentials.
- Author
-
Trahan, Corey and Poirier, Bill
- Subjects
ENERGY levels (Quantum mechanics) ,EXCITED state chemistry ,NUCLEAR physics ,BOUNDARY value problems ,QUANTUM theory ,PHYSICS - Abstract
In a previous paper [B. Poirier, J. Chem. Phys. 121, 4501 (2004)] a unique bipolar decomposition, Ψ=Ψ
1 +Ψ2 , was presented for stationary bound states Ψ of the one-dimensional Schrödinger equation, such that the components Ψ1 and Ψ2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Ψ itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well behaved, even when Ψ has many nodes or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step potential, and square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a companion paper [C. Trahan and B. Poirier, J. Chem. Phys. 124, 034116 (2006), following paper]. [ABSTRACT FROM AUTHOR]- Published
- 2006
- Full Text
- View/download PDF
Discovery Service for Jio Institute Digital Library
For full access to our library's resources, please sign in.