Series solutions for steady unsaturated flow in irregular porous domains

For the most part, analytical solutions for steady unsaturated infiltration have been restricted to infinite and semi-infinite seepage geometries, using the quasi-linear approximation for the hydraulic conductivity. We provide analytical series methods to solve the steady quasi-linear flow equations, in finite irregular seepage geometries. Unlike the classical approach, the series method has been modified, to cater for arbitrary boundary geometry and surface recharge distributions. The matrix flux potential and the stream function both satisfy the same governing partial differential equation, and the stream function formulation is used to estimate the series coefficients. For a finite vadose zone, the stream function solution does not uniquely determine the matrix flux potential, when flux boundary conditions are used. Consequently, the stream function solution applies to a range of moisture distributions, for given infiltration and evapotranspiration rates through the surface.     

Formation and stability of a charged jet in a strong electric field

The shape of a charged jet is determined in the approximation of a strong electric field. The stability of the jet with respect to both axisymmetric and nonaxisymmetric perturbations of the sinusoidal type is investigated in the linear approximation. The domains of predominance of the axisymmetric and bending modes and the longitudinal partition mode are determined. Experimental data on the longitudinal partition of a polymeric jet into several daughter jets are given.     

Spatial and Dynamical Chaos Generated by Reaction–Diffusion Systems in Unbounded Domains

We consider in this article a nonlinear reaction–diffusion system with a transport term (L,∇ _x )u, where L is a given vector field, in an unbounded domain Ω. We prove that, under natural assumptions, this system possesses a locally compact attractor in the corresponding phase space. Since the dimension of this attractor is usually infinite, we study its Kolmogorov’s ɛ-entropy and obtain upper and lower bounds of this entropy. Moreover, we give a more detailed study of the spatio-temporal chaos generated by the spatially homogeneous RDS in . In order to describe this chaos, we introduce an extended (n + 1)-parametrical semigroup, generated on the attractor by 1-parametrical temporal dynamics and by n-parametrical group of spatial shifts ( = spatial dynamics). We prove that this extended semigroup has finite topological entropy, in contrast to the case of purely temporal or purely spatial dynamics, where the topological entropy is infinite. We also modify the concept of topological entropy in such a way that the modified one is finite and strictly positive, in particular for purely temporal and for purely spatial dynamics on the attractor. In order to clarify the nature of the spatial and temporal chaos on the attractor, we use (following Zelik, 2003, Comm. Pure. Appl. Math. 56(5), 584–637) another model dynamical system, which is an adaptation of Bernoulli shifts to the case of infinite entropy and construct homeomorphic embeddings of it into the spatial and temporal dynamics on . As a corollary of the obtained embeddings, we finally prove that every finite dimensional dynamics can be realized (up to a homeomorphism) by restricting the temporal dynamics to the appropriate invariant subset of .     

Mechanical properties of amphiphilic urethane acrylate ionomer hydrogels having heterophasic gel structure

Amphiphilic urethane acryale hydrogels containing ionic groups (dimethylolpropionic acid) were prepared by varying the molecular weight of the soft segment (polyether type) and the type of diisocyanate, and their mechanical properties were examined. They showed heterophasic gel structure composed of ionic hard domains induced by aggregation of the ionic groups and polyether soft domains comprising the urethane acrylate network. This heterophasic structure could be confirmed by dynamic mechanical analysis (DMA) and by wide-angle X-ray scattering analysis (WAXS); the crystallinity detected by WAXS and the transition peak of the ionic hard domains detected by DMA strongly suggested that there were ionic aggregates. These ionic aggregates acted as reinforcing fillers in the network, which eventually enhanced the tensile strength of the hydrogels. Above all, the tensile properties of the hydrogels were of interest in that the trends of the stress-strain curves were consistent with the rubbery ones. It is believed that the higher purity of the polyether soft domains resulted from the heterophasic gel structure imparting further elastomeric properties on the network. Received: 31 July 1998 Accepted in revised form: 15 October 1998     

Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains

The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007     

Nonoverlapping domain decomposition and additive splitting up methods for multidimensional parabolic problem

The explicit implicit domain decomposition methods are noniterative types of methods for nonoverlapping domain decomposition but due to the use of the explicit step for the interface prediction, the methods suffer from inaccuracy of the usual explicit scheme. In this article a specific type of first‐ and second‐order splitting up method, of additive type, for the dependent variables is initially considered to solve the two‐ or three‐dimensional parabolic problem over nonoverlapping subdomains. We have also considered the parallel explicit splitting up algorithm to define (predict) the interface boundary conditions with respect to each spatial variable and for each nonoverlapping subdomains. The parallel second‐order splitting up algorithm is then considered to solve the subproblems defined over each subdomain; the correction step will then be considered for the predicted interface nodal points using the most recent solution values over the subdomains. Finally several model problems will be considered to test the efficiency of the presented algorithm. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

High‐resolution solid‐state NMR study of the domain structure and molecular motion in drawn films of a vinylidene fluoride and trifluoroethylene copolymer with 73 mol % vinylidene fluoride

The heterogeneous higher order structure and molecular motion in a single crystalline film of a vinylidene fluoride (VDF) and trifluoroethylene (TrFE) copolymer with 73 mol % VDF was investigated with the ¹H–¹³C cross‐polarization/magic‐angle spinning NMR technique. A transient oscillation was observed in plots of the ¹³C peak intensity versus the contact time for the CH₂, CHF, and CF₂ groups. On the basis of the extended cross‐relaxation theory of spin diffusion, we determined that the oscillation behavior was caused by the TrFE‐rich segments in the chain and that the crystal consisted of VDF‐rich and TrFE‐rich domains. The former had TrFE‐rich segments in VDF and TrFE fractions of 0.24 and 0.27, respectively, and the latter had VDF‐rich segments in a VDF fraction of 0.49. The spin–lattice relaxation time T_1ρH in the rotating frame for each group was minimal in the three temperature regions of β, α_b, and α_c (↑) on heating and in the two temperature regions of α_1D and α_c (↓) on cooling. The α_c (↑) and α_c (↓) processes depended on the first‐order ferroelectric phase‐transition regions on heating and cooling, respectively. The motional modes for the other processes were confirmed by the T_1ρH minimum behavior of the VDF and TrFE groups in the TrFE‐rich domain and the VDF‐rich segments in the VDF‐rich domain. The β and α_b processes were attributed to the flip–flop motion of the TrFE‐rich segments and the competitive motion of the TrFE‐ and VDF‐rich segments in the ferroelectric phase, respectively. The α_1D process was due to the one‐dimensional diffusion motion of the conformational defects along the chain in the paraelectric phase, accompanied by the trans and gauche transformation of the VDF conformers of ttg⁺tg^? and g⁺tg^?tt. The effect of the competitive motion of the TrFE‐rich segment on the thermal stability of the VDF‐rich segment in the chain near the Curie temperature was examined. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1026–1037, 2002     

Potential flow around obstacles using the scaled boundary finite‐element method

The scaled boundary finite‐element method is a novel semi‐analytical technique, combining the advantages of the finite element and the boundary element methods with unique properties of its own. The method works by weakening the governing differential equations in one co‐ordinate direction through the introduction of shape functions, then solving the weakened equations analytically in the other (radial) co‐ordinate direction. These co‐ordinate directions are defined by the geometry of the domain and a scaling centre. The method can be employed for both bounded and unbounded domains. This paper applies the method to problems of potential flow around streamlined and bluff obstacles in an infinite domain. The method is derived using a weighted residual approach and extended to include the necessary velocity boundary conditions at infinity. The ability of the method to model unbounded problems is demonstrated, together with its ability to model singular points in the near field in the case of bluff obstacles. Flow fields around circular and square cylinders are computed, graphically illustrating the accuracy of the technique, and two further practical examples are also presented. Comparisons are made with boundary element and finite difference solutions. Copyright © 2003 John Wiley & Sons, Ltd.     

非光滑区域上非自治Navier-Stokes 方程非齐边界问题的吸引子

本文研究在2维Lipschitz区域上Navier-Stokes方程的非齐边界问题的长时间行为，在外力是时间的拟周期下，通过引入双参过程的概念，证明一致吸引子A的存在性，并给出一致吸引子A的Hausdorff维数的上界估计。     

Optimal competence set expansion using deduction graphs

A competence set is a collection of skills used to solve a problem. Based on deduction graph concepts, this paper proposes a method of finding an optimal process so as to expand a decision maker's competence set to enable him to solve his problem confidently. Using the concept of minimum spanning tree, Yu and Zhang addressed the problem of the optimal expansion of competence sets. In contrast, the method proposed here enjoys the following advantages: it can deal with more general problems involving intermediate skills and compound skills; it can find the optimal solution by utilizing a 0–1 integer program; and it can be directly extended to treat multilevel competence set problems, and thus is more practically useful.This work was supported by the National Science Council, Taipei, Taiwan, Republic of China, Grant No. NSC-81-0301-H-009-501.