共查询到20条相似文献,搜索用时 31 毫秒
1.
Mian Jiang Hua Deng 《Communications in Nonlinear Science & Numerical Simulation》2012,17(12):5240-5248
Spectral methods are among the most extensively used techniques for model reduction of distributed parameter systems in various fields, including fluid dynamics, quantum mechanics, heat conduction, and weather prediction. However, the model dimension is not minimized for a given desired accuracy because of general spatial basis functions. New spatial basis functions are obtained by linear combination of general spatial basis functions in spectral method, whereas the basis function transformation matrix is derived from straightforward optimization techniques. After the expansion and truncation of spatial basis functions, the present spatial basis functions can provide a lower dimensional and more precise ordinary differential equation system to approximate the dynamics of the systems. The numerical example shows the feasibility and effectiveness of the optimal combination of spectral basis functions for model reduction of nonlinear distributed parameter systems. 相似文献
2.
A. M. Romanovskaya 《Russian Mathematics (Iz VUZ)》2016,60(4):56-59
In the 80s of the XXth century the Riemann method for hyperbolic equations of the second order was extended to hyperbolic systems in general form with one spatial variable. In this paper, this result is extended to hyperbolic systems in general form with several spatial variables with time dependent coefficients. 相似文献
3.
Mian Jiang Jigang Wu Wenan Zhang Xuejun Li 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2018,24(3):258-274
Correct selection of spatial basis functions is crucial for model reduction for nonlinear distributed parameter systems in engineering applications. To construct appropriate reduced models, modelling accuracy and computational costs must be balanced. In this paper, empirical Gramian-based spatial basis functions were proposed for model reduction of nonlinear distributed parameter systems. Empirical Gramians can be computed by generalizing linear Gramians onto nonlinear systems, which results in calculations that only require standard matrix operations. Associated model reduction is described under the framework of Galerkin projection. In this study, two numerical examples were used to evaluate the efficacy of the proposed approach. Lower-order reduced models were achieved with the required modelling accuracy compared to linear Gramian-based combined spatial basis function- and spectral eigenfunction-based methods. 相似文献
4.
Ma Wenxiu 《数学年刊B辑(英文版)》1997,18(1):79-88
WEAKCONVERGENCEFORNONUNIFORMφMIXINGRANDOMFIELDSLUCHUANRONGAbstractLet{ξt,t∈Zd}beanonuniformφmixingstrictlystationaryrea... 相似文献
5.
6.
B.V. Rajarama Bhat Volkmar Liebscher Mithun Mukherjee 《Journal of Functional Analysis》2011,260(2):566-573
We prove that the spatial product of two spatial Arveson systems is independent of the choice of the reference units. This also answers the same question for the minimal dilation of the Powers sum of two spatial CP-semigroups: It is independent up to cocycle conjugacy. 相似文献
7.
Peter K. Moore 《Numerical Algorithms》2007,46(2):121-139
The performance of automatic codes for solving reaction–diffusion systems is controlled by a variety of parameters. Some of
them are invisible to the user while others can be modified. For the latter default values are available. The effects of four
such parameters are studied for a code that couples the method-of-lines in time with a high-order h-refinement finite element strategy in space. The key parameters considered are the ratio of the temporal error tolerance
to the spatial error tolerance, two parameters governing convergence of the iterative methods for the linear and nonlinear
systems, and the number of time steps between regridding. These parameters are typical in method-of-lines based codes. Computations
on a model problem demonstrate that both small and large temporal to spatial error ratios lead to performance degradation
as does less frequent regridding. They also show that insufficient convergence in the nonlinear solver can reduce the reliability
of the spatial error estimates. 相似文献
8.
ZHANGSHENGHAI 《高校应用数学学报(英文版)》1998,13(1):8-14
In this paper,nonnegative solutions for the degenerate elliptic systems are considered.First,nonnegative solutions for scalar equation with spatial discontinuities are studied. Then themethod developed for scalar equation is applied to study elliptic systems. At last,the existence criteria of nonnegative solutions of elliptic systems are given. 相似文献
9.
The purpose of this article is to study the Burgers and Black–Merton–Scholes equations with real time variable and complex spatial variable. The complexification of the spatial variable in these equations is made by two different methods which produce different equations: first, one complexifies the spatial variable in the corresponding (real) solution by replacing the usual sum of variables (translation) by an exponential product (rotation) and secondly, one complexifies the spatial variable in the corresponding evolution equation and then one searches for analytic and non-analytic solutions. By both methods, new kinds of evolution equations (or systems of equations) in two dimensional spatial variables are generated and their solutions are constructed. 相似文献
10.
Olympia E. Demesouka Konstantinos P. Anagnostopoulos 《European Journal of Operational Research》2019,272(2):574-586
Multicriteria spatial decision support systems (MC-SDSS) have emerged as an integration of geographical information systems (GIS) and multiple criteria decision aid (MCDA) methods for incorporating conflicting objectives and decision makers’ preferences into spatial decision models. In this paper, we present spatial UTASTAR (S-UTASTAR), a raster-based MC-SDSS for land-use suitability analysis. The multicriteria component of the system is based on the UTA-type disaggregation-aggregation approach. S-UTASTAR is applied in a raster-based case study concerning land-use suitability analysis to identify appropriate municipal solid waste landfill (MSW) sites in Northeast Greece. Moreover, robustness analysis tools are implemented to guarantee robust decision support results. More specifically, during the aggregation phase, the Stochastic Multiobjective Acceptability Analysis (SMAA) is used to indicate the frequency at which a site achieves the best ranking positions within a large set of alternative landfill sites. 相似文献
11.
S.M. Soskin R. Mannella O.M. Yevtushenko 《Communications in Nonlinear Science & Numerical Simulation》2010,15(1):16-23
We show that, in spatially periodic Hamiltonian systems driven by a time-periodic coordinate-independent (AC) force, the upper energy of the chaotic layer grows unlimitedly as the frequency of the force goes to zero. This remarkable effect is absent in any other physically significant systems. It gives rise to the divergence of the rate of the spatial chaotic transport. We also generalize this phenomenon for the presence of a weak noise and weak dissipation. We demonstrate for the latter case that the adiabatic AC force may greatly accelerate the spatial diffusion and the reset rate at a given threshold. 相似文献
12.
13.
Fran?ois Gay-Balmaz Jerrold E. Marsden Tudor S. Ratiu 《Journal of Nonlinear Science》2012,22(4):463-497
We present the material, spatial, and convective representations for elasticity and fluids with a free boundary from the Lagrangian reduction point of view, using the material and spatial symmetries of these systems. The associated constrained variational principles are formulated and the resulting equations of motion are deduced. In addition, we introduce general free boundary continua that contain both elasticity and free boundary hydrodynamics, extend for them various classical notions, and present the constrained variational principles and the equations of motion in the three representations. 相似文献
14.
We treat fourth order parabolic systems in divergence form with bounded measurable coefficients. We establish Hessian estimates for such parabolic systems by proving that the L p -regularity of the inhomogeneous terms exactly reflects in the regularity of the Hessian of the solutions for every ${p \in (1, \infty)}$ . The assumptions are that the coefficients are allowed to be merely measurable in one of spatial variables, but averaged in the other spatial variables and time variable. 相似文献
15.
A class of reaction-diffusion systems modeling plant growth with spatial competition in saturated media is presented. We show, in this context, that standard diffusion can not lead to pattern formation (Diffusion Driven Instability of Turing). Degenerated nonlinear coupled diffusions inducing free boundaries and exclusive spatial diffusions are proposed. Local and global existence results are proved for smooth approximations of the degenerated nonlinear diffusions systems which give rise to long-time pattern formations. Numerical simulations of a competition model with degenerate/non degenerate nonlinear coupled diffusions are performed and we carry out the effect of the these diffusions on pattern formation and on the change of basins of attraction. 相似文献
16.
本文运用地理加权回归(geographical weighted regression,GWR)方法,对1997-2002年期间中国地级市R&D知识溢出的空间非稳定性进行了实证分析。传统的OLS只是对参数进行"平均"或"全局"估计,不能反映参数在不同空间的空间非稳定性;GWR是一个简单、有效的技术,可以反映参数在不同空间的空间非稳定性。研究结果发现:在对R&D知识生产进行参数估计时,GWR模型与OLS模型有显著的差异;R&D知识生产的不同要素存在空间变异。 相似文献
17.
A reaction‐diffusion two‐predator‐one‐prey system with prey‐taxis describes the spatial interaction and random movement of predator and prey species, as well as the spatial movement of predators pursuing preys. The global existence and boundedness of solutions of the system in bounded domains of arbitrary spatial dimension and any small prey‐taxis sensitivity coefficient are investigated by the semigroup theory. The spatial pattern formation induced by the prey‐taxis is characterized by the Turing type linear instability of homogeneous state; it is shown that prey‐taxis can both compress and prompt the spatial patterns produced through diffusion‐induced instability in two‐predator‐one‐prey systems. 相似文献
18.
Nonlinear dynamical stochastic models are ubiquitous in different
areas. Their statistical properties are often of great interest, but
are also very challenging to compute. Many excitable media models
belong to such types of complex systems with large state dimensions
and the associated covariance matrices have localized structures. In
this article, a mathematical framework to understand the spatial
localization for a large class of stochastically coupled nonlinear
systems in high dimensions is developed. Rigorous \linebreak
mathematical analysis shows that the local effect from the diffusion
results in an exponential decay of the components in the covariance
matrix as a function of the distance while the global effect due to
the mean field interaction synchronizes different components and
contributes to a global covariance. The analysis is based on a
comparison with an appropriate linear surrogate model, of which the
covariance propagation can be computed explicitly. Two important
applications of these theoretical results are discussed. They are
the spatial averaging strategy for efficiently sampling the
covariance matrix and the localization technique in data
assimilation. Test examples of a linear model and a stochastically
coupled FitzHugh-Nagumo model for excitable media are adopted to
validate the theoretical results. The latter is also used for a
systematical study of the spatial averaging strategy in efficiently
sampling the covariance matrix in different dynamical regimes. 相似文献
19.
Evtim Zahariev John Mcphee 《Mathematical and Computer Modelling of Dynamical Systems: Methods, Tools and Applications in Engineering and Related Sciences》2013,19(4):417-435
An approach for solving the forward dynamics problem for mechanical systems with many closed kinematic chains is presented. The dynamic model takes the form of Differential-Algebraic Equations. An optimization method for stabilization of kinematic constraints using the pseudo-inverse mass matrix of the dynamic equations is suggested. The stabilization algorithm provides minimal deviations of the parameters and their velocities with respect to the solution of the differential equations. Estimation of independent coordinates is not required. The forward and inverse dynamic problems of a spatial mechanism and a spatial moving platform with many closed chains are solved. The effectiveness of the algorithm is analyzed. 相似文献
20.
V. M. Zhuravlev 《Theoretical and Mathematical Physics》2013,174(2):236-246
We present the theory of breaking waves in nonlinear systems whose dynamics and spatial structure are described by multidimensional nonlinear hyperbolic wave equations. We obtain a general relation between systems of first-order quasilinear equations and nonlinear hyperbolic equations of higher orders, which, in particular, describe electromagnetic waves in a medium with nonlinear polarization of an arbitrary form. We use this approach to construct exact multivalued solutions of such equations and to study their spatial structure and dynamics. The results are generalized to a wide class of multidimensional equations such as d’Alembert equations, nonlinear Klein-Gordon equations, and nonlinear telegraph equations. 相似文献