共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, we present a semi-analytical approach to obtain the DEP force generated by parallel electrodes. By solving the electric potential equation using the separation of variables method, a solution was found in the form of a Fourier series with unknown coefficients. The unknown coefficients were determined by training a linear artificial neural network with the appropriate data satisfied on the boundary. This results of calculated electric field and DEP force for both planar electrode system and 3D electrode system are validated by comparison with the numerical results obtained using the commercial software CFD-ACE+. 相似文献
2.
M. M.R. Williams 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(2):245-255
In an earlier contribution to this journal [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)], we derived an integral
equation for the transmission of radiation through a slab of finite
thickness which incorporated internal reflection at the surfaces. Here we
generalise the problem to the case when there is a source on each face and
the reflection coefficients are different at each face. We also discuss
numerical and analytic solutions of the equation discussed in [M.M.R. Williams, Eur. Phys. J. B 47, 291 (2005)] when the
reflection is governed by the Fresnel conditions. We obtain numerical and
graphical results for the reflection and transmission coefficients, the
scalar intensity and current and the emergent angular distributions at each
face. The incident source is either a mono-directional beam or a smoothly
varying distribution which goes from isotropic to a normal beam. Of
particular interest is the philosophy of the numerical solution and whether
a direct numerical approach is more effective than one involving a more
elegant analytical solution using replication and the Hilbert problem. We
also develop the solution of this problem using diffusion theory and compare
the results with the exact transport solution.
An erratum to this article is available at . 相似文献
3.
Zhi Li & Paul Muir 《advances in applied mathematics and mechanics.》2013,5(4):528-547
In this paper we describe new B-spline Gaussian collocation software for solving two-dimensional
parabolic partial differential equations (PDEs) defined over a rectangular region. The numerical solution is represented as a bi-variate piecewise polynomial (using a tensor product
B-spline basis) with time-dependent unknown coefficients. These coefficients are determined by
imposing collocation conditions: the numerical solution is required to satisfy the PDE
and boundary conditions at images of the Gauss points mapped onto certain subregions of the spatial domain.
This leads to a large system of time-dependent
differential algebraic equations (DAEs) which is solved using the DAE solver, DASPK. We provide numerical results in which we use the new software, called BACOL2D, to solve three test problems. 相似文献
4.
The paper deals with the solution of the integral equation for particle transport in homogeneous material systems having plane and spherical symmetry. Emphasis is put on the explicit inclusion of anisotropic scattering (higher Legendre components of the scattering kernel). The present approach is based on a generalization of the Integral Transform method. The solution is represented as an expansion with respect to analytical basis functions with coefficients satisfying a certain linear system. The determination of this linear system and its matrix elements in a form convenient for numerical purposes is the central point of the paper. 相似文献
5.
In this Letter we propose a pseudospectral method for solving Thomas-Fermi equation which is a nonlinear ordinary differential equation on semi-infinite interval. This approach is based on rational Chebyshev pseudospectral method. This method reduces the solution of this problem to the solution of a system of algebraic equations. Comparison with some numerical solutions shows that the present solution is highly accurate. 相似文献
6.
We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes. 相似文献
7.
rf discharges are increasingly used in low pressure plasma processing, i.e. for etching, film deposition and sputtering. The modelling of such discharges is a very complex task, especially dependent on discharge conditions, however of large importance for the insight into the main physical processes and thus for their control to improve the final results. One main important aspect is the determination of the electron velocity distribution function and of relevant rate and transport coefficients. The paper contributes to the treatment of this problem. In the first part a systematic Fourier expansion of the kinetic equation and of the consistent particle, energy and momentum balance equation is described. Then, a mathematical analysis of the resulting ordinary differential equation system for the coefficients of the Fourier expansion is performed. Based upon this we succeeded to develop a numerical approach to calculate the physical relevant solution of this system. By this approach in addition to the harmonics of the distribution function that of relevant macroscopic quantities, as transport coefficients and collision frequencies, can be determined. In the second part of this paper this method will be applied to investigate the bulk plasma of a rf discharge in molecular hydrogen. 相似文献
8.
This article studies the response of a half-disk exposed to an external uniform static electric field. A semianalytical method is presented for computing the potential for a geometry consisting of two conjoined half-disks with different permittivities. The method is based on analytical series expansions with coefficients obtained as a numerical solution of a matrix equation. We consider the polarizability of a single dielectric half-disk and discuss a duality relation observed in 2D polarizability. We also study the surface plasmons supported by a negative-permittivity half-disk. 相似文献
9.
10.
D. L. Hovhannisyan A. H. Hovhannisyan G. D. Hovhannisyan K. A. Hovhannisyan 《Journal of Contemporary Physics (Armenian Academy of Sciences)》2010,45(6):251-257
We consider the effect of Raman inertial response of a medium on the stability of a first-order femtosecond soliton. Numerical solution to the high-order nonlinear Schrödinger equation, with the complex Raman term, describing propagation of a femtosecond optical soliton in a single-mode fiber, is obtained. It is shown that a soliton solution of the high-order nonlinear Schrödinger equation exists under certain conditions imposed on the equation coefficients. These conditions lead to limitations on the wavelength, fiber type, and the highest energy. Results of numerical solutions are in agreement with available experimental data. 相似文献
11.
We have developed a methodology for obtaining a Fokker-Planck equation for nonlinear systems with multiple stationary states that yields the correct system size dependence, i.e., exponential growth with system size of the relaxation time from a metastable state. We show that this relaxation time depends strongly on the barrier heightU(x) between the metastable and stable states of the system. For a Fokker-Planck (FP) equation to yield the correct result for the relaxation time from a metastable state, it is therefore essential that the free energy functionU(x) of the FP equation not only correctly locate the extrema of U(x), but also have the correct magnitudeU at these extrema. This is accomplished by so choosing the coefficients of the FP equation that its stationary solution is identical to that of the master equation that defines the nonlinear system.This work was supported in part by the National Science Foundation under Grant CHE 75-20624. 相似文献
12.
A suitable tool for the simulation of low frequency acoustic pulse signals propagating in a shallow sea is the numerical integration of the nonstationary wave equation. The main feature of such simulation problems is that in this case the sound waves propagate in the geoacoustic waveguide formed by the upper layers of the bottom and the water column. By this reason, the correct dependence of the attenuation of sound waves in the bottom on their frequency must be taken into account. In this paper we obtain an integro-differential equation for the sound waves in the viscoelastic fluid, which allows to simulate the arbitrary dependence of acoustic wave attenuation on frequency in the time domain computations. The procedure of numerical solution of this equation based on its approximation by a system of differential equations is then considered and the methods of artificial limitation of computational domain are described. We also construct a simple finite-difference scheme for the proposed equation suitable for the numerical solution of nonstationary problems arising in the shallow-sea acoustics. 相似文献
13.
Our purpose in this paper is to describe the wave propagation in media whose attenuation obeys a frequency power law. To achieve this, a frequency-domain wave equation was developed using previously derived causal dispersion relations. An inverse space and time Fourier transform of the solution to this algebraic equation results in a time-domain solution. It is shown that this solution satisfies the convolutional time-domain wave equation proposed by Szabo [J. Acoust. Soc. Am. 96, 491-500 (1994)]. The form of the convolutional loss operator contained in this wave equation is obtained. Solutions representing the propagation of both plane sinusoidal and transient waves propagating in media with specific power law attenuation coefficients are investigated as special cases of our solution. Using our solution, comparisons are made for transient one-dimensional propagation in a medium whose attenuation is proportional to frequency with recently obtained numerical solutions of Szabo's equation. These show good agreement. 相似文献
14.
Numerical solution of Helmholtz equation of barotropic atmosphere using wavelets 总被引:1,自引:0,他引:1 下载免费PDF全文
The numerical solution of the Helmholtz equation for barotropic atmosphere is estimated by use of the wavelet-Galerkin method. The solution involves the decomposition of a circulant matrix consisting up of 2-term connection coefficients of wavelet scaling functions. Three matrix decompositions, i.e. fast Fourier transformation (FFT), Jacobian and QR decomposition methods, are tested numerically. The Jacobian method has the smallest matrix-reconstruction error with the best orthogonality while the FFT method causes the biggest errors. Numerical result reveals that the numerical solution of the equation is very sensitive to the decomposition methods, and the QR and Jacobian decomposition methods, whose errors are of the order of 10^{-3}, much smaller than that with the FFT method, are more suitable to the numerical solution of the equation. With the two methods the solutions are also proved to have much higher accuracy than the iteration solution with the finite difference approximation. In addition, the wavelet numerical method is very useful for the solution of a climate model in low resolution. The solution accuracy of the equation may significantly increase with the order of Daubechies wavelet. 相似文献
15.
N. Calvo 《Physica D: Nonlinear Phenomena》2010,239(5):248-257
A shallow ice thermocoupled model for the complex nonlinear polythermal ice sheet dynamics is proposed and solved by means of efficient numerical methods. A novelty is the obstacle problem formulation associated to a nonlinear integro-differential equation (with nonlocal temperature dependent coefficients) for the ice sheet profile. This formulation is motivated by the free boundary feature and the influence of the temperature on the profile (fully nonisothermal model). Concerning the temperature equation, a dynamically prescribed surface temperature, obtained from an Energy Balance model corrected by the altitude effect, is posed. As the profile and temperature equations are fully coupled, a nonlinear PDE system governing the upper ice sheet profile, the velocity field, the temperature and the basal stress is stated. In addition to the numerical difficulties associated to the new profile equation, several techniques have been considered for the numerical solution of the temperature, velocity and basal magnitudes. Discussions concerning the nonlinear dynamics of the different involved magnitudes and the improvement in their computed values with respect to previous works are also presented. 相似文献
16.
Mustafa Gü lsu Yalç ın Ö ztü rk & Ayşe Anapali 《advances in applied mathematics and mechanics.》2013,5(6):872-884
In this article, we have introduced a Taylor collocation method,
which is based on collocation method for solving fractional Riccati
differential equation. The fractional derivatives are described in
the Caputo sense. This method is based on first taking the truncated
Taylor expansions of the solution function in the fractional Riccati
differential equation and then substituting their matrix forms into
the equation. Using collocation points, the systems of nonlinear
algebraic equation are derived. We further solve the system of
nonlinear algebraic equation using Maple 13 and thus obtain the
coefficients of the generalized Taylor expansion. Illustrative
examples are presented to demonstrate the effectiveness of the
proposed method. 相似文献
17.
M.M.R. Williams Matthew Eaton 《Journal of Quantitative Spectroscopy & Radiative Transfer》2010,111(5):696-707
The influence of uncertainty in the absorption and scattering coefficients on the solution and associated parameters of the radiative transfer equation is studied using polynomial chaos theory. The uncertainty is defined by means of uniform and log-uniform probability distributions. By expanding the radiation intensity in a series of polynomial chaos functions we may reduce the stochastic transfer equation to a set of coupled deterministic equations, analogous to those that arise in multigroup neutron transport theory, with the effective multigroup transfer scattering coefficients containing information about the uncertainty. This procedure enables existing transport theory computer codes to be used, with little modification, to solve the problem. Applications are made to a transmission problem and a constant source problem in a slab. In addition, we also study the rod model for which exact analytical solutions are readily available. In all cases, numerical results in the form of mean, variance and sensitivity are given that illustrate how absorption and scattering coefficient uncertainty influences the solution of the radiative transfer equation. 相似文献
18.
Numerical analysis of the one-dimensional heat equation subject to a boundary integral specification
B. Soltanalizadeh 《Optics Communications》2011,284(8):2109-2112
In this research a numerical technique is developed for the one-dimensional heat equation that combines classical and integral boundary conditions. New matrix formulation techniques with arbitrary polynomial bases are proposed for the numerical/analytical solution of this kind of partial differential equation. We give a simple and efficient algorithm based on an iterative process for numerical solution of the method. 相似文献
19.
Primak S 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):100-103
A compound representation of random processes is considered. Each independent component of such a process is considered as the solution of the proper stochastic differential equation (SDE). This guarantees that the process obtained is stationary and ergodic. The analytical expressions are developed for nonlinear coefficients of the generating SDE. Theoretical results are compared with numerical simulation. 相似文献
20.
The ensemble Kalman filter is a widely applied data assimilation technique useful for improving the forecast of computational models. The main computational cost of the ensemble Kalman filter comes from the numerical integration of each ensemble member forward in time. When the computational model involves a partial differential equation, the degrees of freedom of the solution in the discretization of the spatial domain are oftentimes used for the representation of the state of the system, and the filter is applied to this state vector. We propose a method of approximating the state of a partial differential equation in a representation space developed separately from the numerical method. This representation space represents a reparameterization of the state vector and can be chosen to retain desirable physical features of the solutions. We apply the ensemble Kalman filter to this representation of the state, and numerically demonstrate that acceptable results are obtained with substantially smaller ensemble sizes. 相似文献