Nodal domain integration model of one-dimensional advection—diffusion

The nodal domain integration method is applied to a one-dimensional advection—diffusion mathematical model without a source term. Comparison of the resulting numerical model to the well known Galerkin finite element, subdomain, and finite difference domain models indicates that a single numerical statement can be developed which includes the Galerkin finite element, subdomain, and finite difference models as special cases.     

Truncation errors of selected finite difference methods for two-dimensional advection-diffusion equation with mixed derivatives

The spread of a passive contaminant in an open-channel reach is considered with use of a two-dimensional advection-diffusion equation with the included off-diagonal dispersion coefficients. This paper presents the calculation of truncation errors, namely numerical diffusion and numerical dispersion for various finite difference schemes. The accuracy of the considered finite-difference approximations is analysed by deriving and studying the relevant modified partial differential equation.     

Frequency domain analysis of time integration operators

The present paper analyses the error associated with the time integration operators in structural dynamics. It considers the time integration operators as digital recursive filters. The transfer functions of the discretized equations are derived and compared with the transfer function of the differential equation. This leads to a new approach for the accuracy analysis of the time integration operators, which is not restricted to the homogeneous part of the discretized equation. It can therefore be applied to the Duhamel Integral for which, as far as the author is aware, no error analysis has been reported so far. Results are presented for the Newmark's family integration operators. Various assumptions on the variation of the excitation between the sampling points in the Duhamel Integral are also analysed.     

A two-dimensional dam-break flood plain model

A simple two-dimensional dam-break model is developed for flood plain study purposes. Both a finite difference grid and an irregular triangle element integrated finite difference formulation are presented. The governing flow equations are approximately solved as a diffusion model coupled to the equation of continuity. Application of the model to a hypothetical dam-break study indicates that the approach can be used to predict a two-dimensional dam-break flood plain over a broad, flat plain more accurately than a one-dimensional model, especially when the flow can break-out of the main channel and then return to the channel at other downstream reaches.     

Simple two-dimensional model of propagation of magma-filled cracks

The direction of propagation of magma-filled cracks was theoretically examined for a two-dimensional model. The analytical result indicates that magma-filled cracks, which have magmatic pressures larger than a critical value, propagate in parallel with the maximum principal direction of far-field stress. This may give one of theoretical grounds to the dike method by which the regional stress field is estimated.     

Exact solution for two-dimensional flow to a well in an anisotropic domain

Although most current applications of the analytic element method are formulated for isotropic hydraulic conductivity, anisotropic domains can be modeled with analytic elements using the well-known coordinate transformation where one coordinate axis is scaled by the square root of the anisotropy ratio. If the standard analytic solution for steady radial flow to a well is used with this coordinate transformation, the resulting solution correctly models the far field but it does not meet the constant head boundary condition at the well radius. This could be a significant shortcoming if you are interested in the flow field close to the well or want to estimate the head at the pumping well. A new solution for two-dimensional steady flow to a well in an anisotropic domain is presented. This solution satisfies the governing equations exactly and meets the constant head boundary condition at the well radius exactly. It was derived using a conformal mapping.     

Ground-roll separation of seismic data based on morphological component analysis in two-dimensional domain

Ground roll is an interference wave that severely degrades the signal-to-noise ratio of seismic data and affects its subsequent processing and interpretation. In this study, according to differences in morphological characteristics between ground roll and reflected waves, we use morphological component analysis based on two-dimensional dictionaries to separate ground roll and reflected waves. Because ground roll is characterized by low-frequency, low-velocity, and dispersion, we select two-dimensional undecimated discrete wavelet transform as a sparse representation dictionary of ground roll. Because of a strong local correlation of the reflected wave, we select two-dimensional local discrete cosine transform as the sparse representation dictionary of reflected waves. A sparse representation model of seismic data is constructed based on a two-dimensional joint dictionary then a block coordinate relaxation algorithm is used to solve the model and decompose seismic record into reflected wave part and ground roll part.The good effects for the synthetic seismic data and application of real seismic data indicate that when using the model, strong-energy ground roll is considerably suppressed and the waveform of the reflected wave is effectively protected.     

Magnetic domain observations of nucleation processes in natural pyrrhotite and titanomagnetite

Magnetic domain patterns have been observed on particles of natural pyrrhotite and titanomagnetite undergoing hysteresis. These observations indicate that hysteresis properties are governed by two distinct mechanisms: (1) wall-pinning and (2) nucleation of reverse domains. Particles which are dominated by wall-pinning spontaneously nucleate reverse domains in saturation remanence (J_rs). The coercivity of such grains is determined by the presence of potential wells encountered by the wall in its traverse across the grain. However, many pseudosingle-domain particles (PSD) between 5 and 30 μm in diameter do not nucleate reverse domains in J_rs, but remain as saturated single-domains. These particles require a reverse field H_n to nucleate domain walls. When H_n is sufficiently large, the nucleating field controls magnetization reversal by driving the wall across the particle in a single Barkhausen jump, and the muscopic coercivity is nucleation-dominated.

The proportion P (w=0) of particles of a given size d which fail to nucleate walls in J_rs is found to be given by A exp(−Bd^1/2), where A and B are experimentally determined constants. The nucleation field H_n in pyrrhotite is observed to increase with decreasing grain size, exceeding 500 Oe in 5 μm particles.

The difficulty with which reverse domains are nucleated subsequent to saturation may thus provide a mechanism for achieving the high values of J_rs/J_s and coercive force observed in fine, pseudosingle-domain particles.     

Input-output model for runoff-sediment yield processes

Runoff (log-transformed) and sediment yield (log-transformed) sequences on a monthly or daily basis can be regarded as input and output for the watershed fluvial system. These sequences are nonstationary in general in different hydrological environments. Frequency and time domain analyses have shown that a parsimonious model can be built directly in terms of these nonstationary input-output sequences on a monthly and daily basis. A first-order dynamic model was found adequate to model the monthly runoff-sediment yield process; a second-order model adequately modeled the daily runoff-sediment yield process. The noise component in both cases possessed the characteristics of a white-noise sequence.     

Modelling floodplain flows using a two-dimensional finite element model

A prototype two-dimensional finite element flow model for depth-averaged free surface flows was developed for floodplain environments. Limited refinement of the model's physical representation was undertaken and the enhanced scheme applied to an 11 km river channel/floodplain reach in the U.K. Preliminary model results indicate that this modelling approach can be used to identify dynamic variations in the flow field parameters over length scales of the order of 10-100 m. Potentially, such data have the ability to permit detailed analysis of short-term floodplain sedimentary dynamics.     

A two-dimensional photochemical model of the stratosphere with Rayleigh scattering

Computations of concentrations of minor stratospheric gases using a two-dimensional model of the stratosphere are reported. The model includes Rayleigh scattering. This results in an increase in the photodissociation rate computation time by a factor of 1.5. The effect of ground albedo is assessed by comparing our results with a calculation of photolysis rates for a constant albedo with latitude. Comparison of results with a reference model including only molecular absorption are also made. The largest differences (50%) occur in NO and OH. An approximate expression for including the effects of Rayleigh scattering and surface reflectance in multi-dimensional models is suggested.     

光滑模型与尖锐边界结合的MT二维反演方法

如何得到快速稳定的反演结果和更清晰的地质体分界面等问题仍然是当前MT反演研究的一个重点.为了解决反演结果不能得到清晰的电性分界面的问题,本文在前人研究的基础上,基于OCCAM反演以及突出尖锐边界反演的思想,结合最小支撑梯度泛函,构建了新的反演目标函数,并利用共轭梯度法优化目标函数,实现了一种光滑模型与尖锐边界结合的MT二维反演方法.模型实验证明了该方法的准确性,通过与已发表的相关反演方法的结果进行比较,证明了该方法在光滑稳定的基础上可突出对尖锐电性边界的刻画.对广东徐闻地区的实测MT资料进行了处理,表明了该方法的适用性和效果.     

Developing land use scenario dynamics model by the integration of system dynamics model and cellular automata model

Models of land use change are useful tools for un-derstanding the analysis of the cause and conse-quences of land use changes, assessing the impacts of land use system on ecological system and supporting land use planning and policy[1,2]. Modeling land use scenario changes and its potential impacts on the structure and function of the ecosystem in the typical regions are regarded as one of the good ways to un-derstand the interactive mechanism between land use system and ecological system[3―10…     

Convergence and stability of step-by-step integration for model with negative-stiffness

The convergence and stability of step-by-step integration schemes used in the inelastic dynamic analysis of structures and their corresponding criteria were studied for a restoring force model with negative-stiffness. Convergence conditions and stability conditions 1, 2 or 3 were established. The numerical stability of the integration under negative-stiffness belongs to the category of relative stability; consequently, the concepts and the conclusions concerning numerical stability in the case of positive-stiffness (which belongs to absolute stability) cannot be used. Research into several step-by-step integration methods usually employed in inelastic dynamic analysis has shown great differences in numerical stability for models with negative-stiffness as compared with positive-stiffness models. The central difference method is convergent and unconditionally stable in the case of negative-stiffness, though it is only conditionally stable in the case of positive-stiffness. The Houbolt method satisfies the requirement for convergence; its stability, however, depends not only on the integration step size Δt but also on the stiffness ratio β for the model with negative-stiffness, unlike the unconditional stability for the model with positive-stiffness. The Newmark constant acceleration method is convergent and unconditionally stable in the case of negative-stiffness just like it is in the case of positive-stiffness.     

On the inadequacies of Long's model for steady two-dimensional stratified flows

Nonlinear analysis of two-dimensional steady flows with density stratification in the presence of gravity is considered. Inadequacies of Long's model for steady stratified flow over topography are explored. These include occurrence of closed streamline regions and waves propagating upstream. The usual requirements in Long's model of constant dynamic pressure and constant vertical density gradient in the upstream condition are believed to be the cause of these inadequacies. In this article, we consider a relaxation of these requirements, and also provide a systematic framework to accomplish this. As illustrations of this generalized formulation, exact solutions are given for the following two special flow configurations: the stratified flow over a barrier in an infinite channel; the stratified flow due to a line sink in an infinite channel. These solutions exhibit again closed-streamline regions as well as waves propagating upstream. The persistence of these inadequacies in the generalized Long's model appears to indicate that they are not quite consequences of the assumptions of constant dynamic pressure and constant vertical density gradient in Long's model, contrary to previous belief.

On the other hand, solutions admitted by the generalized Long's model show that departures from Long's model become small as the flow becomes more and more supercritical. They provide a nonlinear mechanism for the generation of columnar disturbances upstream of the obstacle and lead in subcritical flows to qualitatively different streamline topological patterns involving saddle points, which may describe the lee-wave-breaking process in subcritical flows and could serve as seats of turbulence in real flows. The occurrences of upstream disturbances in the presence of lee-wave-breaking activity described by the present solution are in accord with the experiments of Long (Long, R.R., “Some aspects of the flow of stratified fluids, Part 3. Continuous density gradients”, Tellus 7, 341--357 (1955)) and Davis (Davis, R.E., “The two-dimensional flow of a stratified fluid over an obstacle”, J. Fluid Mech. 36, 127–143 ()).     

Magnetotelluric dispersion relations in a two-dimensional model of the coastal effect

Numerical modeling is performed for seafloor magnetotelluric sounding in a 2-D offshore zone in a period range of 0.25–16 h. An anomaly of the seafloor longitudinal impedance observed at distances of 20–260 km from the shore is analyzed. Dispersion relations are violated for the longitudinal impedance within the anomalous zone.     

A two-dimensional horizontal wave propagation and mud mass transport model

The present study offers a two-dimensional horizontal wave propagation and morphodynamic model for muddy coasts. The model can be applied on a general three-dimensional bathymetry of a soft muddy coast to calculate wave damping, fluid mud mass transport and resulting bathymetry change under wave actions. The wave propagation model is based on time-dependent mild slope equations including the wave energy dissipation due to the wave-mud interaction of bottom mud layers as well as the combined effects of the wave refraction, diffraction and breaking. The constitutive equations of the visco-elastic–plastic model are adopted for the rheological behavior of fluid mud. The mass transport velocity within the fluid mud layer is calculated combining the Stokes’ drift, the mean Eulerian velocity and the gravity-driven mud flow. The results of the numerical model are compared against a series of conducted wave basin experiments, wave flume experiments and field observations. Comparisons between the computed results with both the field and laboratory data reveal the capability of the proposed model to predict the wave transformation and mud mass transport.