SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

Computer computation of the method of multiple scales—dirichlet problem for a class of system of nonlinear differential equations

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales. Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼)     

A higher‐order accuracy lattice Boltzmann model for the wave equation

A lattice Boltzmann model with higher‐order accuracy for the wave motion is proposed. The new model is based on the technique of the higher‐order moment of equilibrium distribution functions and a series of lattice Boltzmann equations in different time scales. The forms of moments are derived from the binary wave equation by designing the higher‐order dissipation and dispersion terms. The numerical results agree well with classical ones. Copyright © 2008 John Wiley & Sons, Ltd.     

Well-posedness of the spatially homogeneous Landau equation for soft potentials

We consider the spatially homogeneous Landau equation of kinetic theory, and provide a differential inequality for the Wasserstein distance with quadratic cost between two solutions. We deduce some well-posedness results. The main difficulty is that this equation presents a singularity for small relative velocities. Our uniqueness result is the first one in the important case of soft potentials. Furthermore, it is almost optimal for a class of moderately soft potentials, that is for a moderate singularity. Indeed, in such a case, our result applies for initial conditions with finite mass, energy, and entropy. For the other moderately soft potentials, we assume additionally some moment conditions on the initial data. For very soft potentials, we obtain only a local (in time) well-posedness result, under some integrability conditions. Our proof is probabilistic, and uses a stochastic version of the Landau equation, in the spirit of Tanaka [H. Tanaka, Probabilistic treatment of the Boltzmann equation of Maxwellian molecules, Z. Wahrsch. Verw. Geb. 46 (1) (1978-1979) 67-105].     

Autoresonant asymptotics in an oscillating system with weak dissipation

We study a system of two first-order differential equations arising in averaging nonlinear systems over fast single-frequency oscillations. We consider the situation where the original system contains weak dissipative terms. We construct the asymptotic form of a two-parameter solution with an unbounded increasing amplitude. This result gives a key for understanding autoresonance in weak dissipative systems as a phenomenon of significant increase in the forced nonlinear oscillation initiated by a small external pumping. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 102–111, July, 2009.     

Studies of viscosities of dilute solutions of alkylamines in non-electrolyte solvents: III. Alkylamines in butanols at 303.15 K

Freezing in winter cereals is a complex phenomenon that can affect various plant tissues differently. To better understand how freezing affects specific tissue in the over wintering organ (crown) of winter cereal crops, non-acclimated oats (Avena sativa L.) were gradually frozen to ?3 °C and tissue damage during recovery was compared to plants that had been supercooled to ?3 °C and then frozen suddenly. Percentage of total water frozen, was the same whether crowns were frozen suddenly or gradually although the rate of freezing was considerably different. For example, all available water froze within 3 h in suddenly frozen crowns but it took more than 15 h for all available water to freeze in gradually frozen crowns. When plants were suddenly frozen, cells in the apical meristem were disrupted and apparently killed. In these plants re-growth was limited or non-existent. In contrast, the apical region of plants that were slowly frozen appeared undamaged but extensive vessel plugging was observed in cells of the lower crown, possibly from accumulation of phenolics or from microbial proliferation. These histological observations along with the calorimetric analysis suggested that the apical region was killed by intracellular freezing when frozen suddenly while the crown core was damaged by a process, which either induced production of putative phenolic compounds by the plant and/or permitted what appeared to be microbial proliferation in metaxylem vessels.     

Growth behavior of Cu/Al intermetallic compounds in hot‐dip aluminized copper

Hot‐dipped aluminum copper with plating auxiliary KF is introduced in this work. In this study, the intermetallic layer thickness varies with dipping temperature and time in a linear relationship. The main phases are identified to be CuAl₂ and K₃AlF₆ by means of X‐ray diffraction. The reaction equations are deduced according to the elements concentration gradient in cross section. The copper diffusion rate in liquid Al is calculated to be 1.13 × 10⁻¹² m²/s by Fick's second law in semi‐infinite solid model, and the obtained conductivity is 1.758–1.767 × 10⁻² Ω mm²/m. The results indicate that the interfacial bonding is in a good state and plating auxiliary KF aqueous solution. can significantly improve the substrate wettability. The appropriate hot‐dipping condition for the samples is 953–973 K for 4–8 s. Copyright © 2009 John Wiley & Sons, Ltd.     

Numerical examination of the extended phase‐space volume‐preserving integrator by the Nosé‐Hoover molecular dynamics equations

This article illustrates practical applications to molecular dynamics simulations of the recently developed numerical integrators [Phys Rev E 2006, 73, 026703] for ordinary differential equations. This method consists of extending any set of ordinary differential equations in order to define a time invariant function, and then use the techniques of divergence‐free solvable decomposition and symmetric composition to obtain volume‐preserving integrators in the extended phase space. Here, we have developed the technique by constructing multiple extended‐variable formalism in order to enhance the handling in actual simulation, and by constituting higher order integrators to obtain further accuracies. Using these integrators, we perform constant temperature molecular dynamics simulations of liquid water, liquid argon and peptide in liquid water droplet. The temperature control is obtained through an extended version of the Nosé‐Hoover equations. Analyzing the effects of the simulation conditions including time step length, initial values, boundary conditions, and equation parameters, we investigate local accuracy, global accuracy, computational cost, and sensitivity along with the sampling validity. According to the results of these simulations, we show that the volume‐preserving integrators developed by the current method are more effective than traditional integrators that lack the volume‐preserving property. © 2008 Wiley Periodicals, Inc. J Comput Chem, 2009