An Efficient Multiple-Dimensional Finite Element Solution for Water Flow in Variably Saturated Soils

Multiple-dimensional water flow in variably saturated soils plays an important role in ecological systems such as irrigation and water uptake by plant roots; its quantitative description is usually based on the Richards＇ equation. Because of the nonlinearity of the Richards＇ equation and the complexity of natural soils, most practical simulations rely on numerical solutions with the nonlinearity solved by iterations. The commonly used iterations for solving the nonlinearity are Picard and Newton methods with the former converging at first-order rate and the later at second-order rate. A recent theoretical analysis by the authors, however, revealed that for solving the diffusive flow, the classical Picard method is actually a chord-Newton method, converging at a rate faster than first order; its linear convergence rate is due to the treatment of the gravity term. To improve computational efficiency, a similar chord-Newton method as for solving the diffusive term was proposed to solve the gravity term. Testing examples for one-dimensional flow showed significant improvement. The core of this method is to produce a diagonally dominant matrix in the linear system so as to improve the iteration-toiteration stability and hence the convergence. In this paper, we develop a similar method for multiple-dimensional flow and compare its performance with the classical Picard and Newton methods for water flow in soils characterised by a wide range of van Genuchten parameters.

Non-linear dynamics analysis of in-plane motion for suspended cable under concentrated load

The non-linear equations of strings under a concentrated load were derived.The formulae of the linear frequency and the governing equation of the primary resonance were obtained by Galerkin and Multiple-dimensioned method.The reason of the loss of load in practical engineering was addressed.The bifurcation graphics and the relationship graphics of bifurcate point with concentrated load and the span length of the cable were obtained by calculating example.The results show that formula of the linear frequency of the suspended cable is different from that of the string.

Multiparameter encrypted orbital angular momentum multiplexed holography based on multiramp helicoconical beams

Optical orbital angular momentum(OAM)multiplexed holography has been implemented as an effective method for information encryption and storage.Multiramp helicoconical-OAM multiplexed holography is proposed and experimentally implemented.The mode selectivity of the multiramp mixed screw-edge dislocations,constant parameter K,and normalized factor are investigated,respectively,which demonstrates that those parameters can be used as additional coding degrees of freedom for holographic multiplexing.The combination of the topological charge and the other three parameters can provide a four-dimensional multiplexed holography and can enhance information capacity.

Uncertainty analysis and visualization of geological subsurface and its application in metro station construction

To visualize and analyze the impact of uncertainty on the geological subsurface,on the term of the geological attribute probabilities(GAP),a vector parameters-based method is presented.Perturbing local data with error distribution,a GAP isosurface suite is first obtained by the Monte Carlo simulation.Several vector parameters including normal vector,curvatures and their entropy are used to measure uncertainties of the isosurface suite.The vector parameters except curvature and curvature entropy are visualized as line features by distributing them over their respective equivalent structure surfaces or concentrating on the initial surface.The curvature and curvature entropy presented with color map to reveal the geometrical variation on the perturbed zone.The multiple-dimensional scaling(MDS)method is used to map GAP isosurfaces to a set of points in lowdimensional space to obtain the total diversity among these equivalent probability surfaces.An example of a bedrock surface structure in a metro station shows that the presented method is applicable to quantitative description and visualization of uncertainties in geological subsurface.MDS plots shows differences of total diversity caused by different error distribution parameters or different distribution types.