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numerical solution to the Bloch equations:paramagnetic solutions under wideband continuous radio frequency irradiation in a pulsed magnetic field

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Chinese Physics C 2016年第8期40卷 174-184页

作者：陈文俊马洪余德曾小虎 School of Physics Huazhong University of Science and Technology School of Electronic Information and Communications Huazhong University of Science and Technology

A novel nuclear magnetic resonance （NMR） experimental scheme, called wideband continuous wave NMR （WB-CW-NMR）, is presented in this article. This experimental scheme has promising applications in pulsed magnetic fields, and can dramatically improve the utilization of the pulsed field. The feasibility of WB-CW-NMR scheme is verified by numerically solving modified Bloeh equations. In the numerical simulation, the applied magnetic field is a pulsed magnetic field up to 80 T, and the wideband continuous radio frequency （RF） excitation is a band-limited （0.68-3.40 GHz） white noise. ~lrthermore, the influences of some experimental parameters, such as relaxation time, applied magnetic field strength and wideband continuous RF power, on the WB-CW-NMR signal are analyzed briefly. Finally, a multi-channel system framework for transmitting and receiving ultra wideband signals is proposed, and the basic requirements of this experimental system are discussed. Meanwhile, the amplitude of the NMR signal, the level of noise and RF interference in WB-CW-NMR experiments are estimated, and a preliminary adaptive cancellation plan is given for detecting WB-CW-NMR signal from large background interference.

关键词： Bloch equations numerical solution pulsed magnetic fields wideband continuous radio frequencyirradiation relaxation time

numerical solution OF SHORELINE EVOLUTION NEAR COASTAL STRUCTURES

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Journal of Hydrodynamics 2003年第4期15卷 63-69页

作者： Cai Ze-wei, Song Xiao-gang, Ye Chun-yang Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo 315211, China Faculty of Arch. Ningbo Univ. Ningbo 315211 China

numerical analysis was made for shoreline evolution in the vicinity ofcoastal structures, including spur dike, detached breakwaters. The nonlinear partial differentialequation was derived, and numerical solutions were obtained by the finite difference method. Thenumerical results show good agreement with previous analytical results.

关键词： shoreline evolution numerical solution coastal structures

numerical solution of Euler-Lagrange Equation with Caputo Derivatives

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Advances in Applied Mathematics and Mechanics 2017年第1期9卷 173-185页

作者： Tomasz Blaszczyk Mariusz Ciesielski Czestochowa University of Technology Institute of Mathematicsal.Armii Krajowej 2142-201 CzestochowaPoland Czestochowa University of Technology Institute of Computer and Information Sciencesul.Dabrowskiego 7342-201 CzestochowaPoland

In this paper the fractional Euler-Lagrange equation is *** fractional equation with the left and right Caputo derivatives of order a∈(0,1]is transformed into its corresponding integral ***,we present a numerical solution of the integral form of the considered *** the basis of numerical results,the convergence of the proposed method is *** of numerical solutions of this equation are shown in the final part of this paper.

关键词： Fractional Euler-Lagrange equation fractional integral equation numerical solution Caputo derivatives

numerical solution of a mathematical model for water wavesin large coastal areas

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Acta Oceanologica Sinica 2000年第4期19卷 17-23页

作者： Zheng Yonghong Shen Yongming Xia Jin State Key Laboratory of Coastal and Offshore Engineering Dalian University of TechnologyDalian 116023China Dalian Design&Research Institute of Environmental Sciance Dalian 116023China

Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.

关键词： Water wave mathematical model numerical solution

Rheological Analysis of CNT Suspended Nanofluid with Variable Viscosity: numerical solution

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Communications in Theoretical Physics 2017年第6期67卷 681-687页

作者： Noreen Sher Akbar Zafar Hayat Khan DBS&H CEME National University of Sciences and Technology Department of Mathematics University of Malakand Dir (lower) Khyber Pakhtunkhwa

In this article, we discuss the two-dimensional stagnation-point flow of carbon nanotubes towards a stretching sheet with water as the base fluid under the influence temperature dependent viscosity. Similarity transformations are used to simplify the governing boundary layer equations for nanofluid. This is the first article on the stagnation point flow of CNTs over a stretching sheet with variable viscosity. A well known Reynold's model of viscosity is used. Single wall CNTs are used with water as a base fluid. The resulting nonlinear coupled equations with the relevant boundary conditions are solved numerically using shooting method. The influence of the flow parameters on the dimensionless velocity, temperature, skin friction, and Nusselt numbers are explored and presented in forms of graphs and interpreted physically.

关键词： two-dimensional flow variable nanofluid viscosity stagnation-point flow stretching sheet carbon nanotubes numerical solution

numerical solution of a Scalar One-Dimensional Monotonicity-Preserving Nonlocal Nonlinear Conservation Law

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Journal of Mathematical Research with Applications 2017年第1期37卷 1-18页

作者： Qiang DU Zhan HUANG Department of Applied Physics and Applied Mathematics Columbia University Department of Mathematics Penn State University

In this paper, we present numerical studies of a recently proposed scalar nonlocal nonlinear conservation law in one space dimension. The nonlocal model accounts for nonlocal interactions over a finite horizon and enjoys maximum principle, monotonicity-preserving and entropy condition on the continuum level. Moreover, it has a well-defined local limit given by a conventional local conservation laws in the form of partial differential equations. We discuss convergent numerical approximations that preserve similar properties on the discrete *** also present numerical experiments to study various limiting behavior of the numerical solutions.

关键词： nonlocal model nonlinear hyperbolic conservation laws maximum principle monotonicity preserving numerical solution

The　θ－Methods　in　numerical　solution　of　Systems　of　Differential　Equations　with　Two　Delay　Terms

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Journal of Systems Engineering and Electronics 1994年第3期5卷 32-40页

作者： Tian Hongjiong & Kuang Jiaoxun (Department of Mathematics, Shanghai Normal University, Shanghai 200234, China) Department of Mathematics Shanghai Normal University Shanghai 200234 China

This paper deals with the numerical solution of initial value problems for systems of differential equations with two delay terms. We investigate the stability of adaptations of the θ-methods in the numerical solution of test equations u'(t) = a 11 u(t) + a12v(t) + b11 u(t - τ1) + b12v(t-τ2,v'(t) = a21 u(t) + a22 v(t) + b21 u(t -τ1,) + b22 v(t -τ2), t>0,with initial conditionsu(t)=u0(t),v(t) =v0(t), t≤*** aij, bij∈C, τj >0, i,j = 1,2,, and u0(t), v0(t)are continuous and complex valued. Sufficient conditions for the asymptotic stability of test equation are derived. Furthermore, with respect to an appropriate definition of stability for the numerical method, it is proved that the linear θ-method is stable if and only if 1/2≤θ≤1 and the one-leg θ-method is stable if and only if θ= 1.

关键词： Delay differential equations numerical solution θ-methods Asymptotic stability Schur polynomial.

Existence and numerical solution for a Coupled System of Multi-term Fractional Differential Equations

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Journal of Donghua University(English Edition) 2015年第4期32卷 613-619页

作者：杨李凡叶海平 College of Science Donghua University

An initial value problem was considered for a coupled differential system with multi-term Caputo type fractional derivatives. By means of nonlinear alternative of Leray-Schauder and Banach contraction principle,the existence and uniqueness of solutions for the system were derived. Using a fractional predictorcorrector method, a numerical method was presented for the specified system. An example was given to illustrate the obtained results.

关键词： multi-term fractional differential equation Caputo derivative existence uniqueness numerical solution

Efficient numerical solution of the Modified Mild-Slope Equation

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China Ocean Engineering 2000年第2期15卷 161-174页

作者：潘军宁左其华王红川 Harbour and River Dept. Nanjing Hydraulic Research Institute Nanjing 210024 China Harbour and River Dept. NHRI Nanjing 210024 China

An efficient numerical model for wave refraction, diffraction and reflection is presented in this paper. In the model the modified time-dependent mild-slope equation is transformed into an evolution equation and an improved ADI method involving a relaxation factor is adopted to solve it. The method has the advantage of improving the numerical stability and convergence rate by properly determining the relaxation factor. The range of the relaxation factor making the differential scheme unconditionally stable is determined by stability analysis. Several verifications are performed to examine the accuracy of the present model. The numerical results coincide with the analytic solutions or experimental data very well and the computer time is reduced.

关键词： wave mild-slope equation numerical solution stability refraction diffraction reflection