Phase diagrams of Ising models on Husimi trees II. Pair Wand multisite interaction systems

We continue an earlier study of multisite interaction Ising spin models on Husimi trees. In particular, attention is given to systems with both a nearestneighbor pair interaction and three-site interactions. We use our calculations of the phase diagrams of the systems on Husimi trees as approximations of systems with the same interactions but on a regular lattice, e.g., the triangle lattice. Specific models where exact results are available are used as test cases. All of the work involves computation of quantities, such as the magnetization, by iterative processes. Hence we are dealing with a discrete map and for certain values of the interaction strengths we obtain for the magnetization diagram results involving period doubling, chaos, period-three windows, etc., all phenomena of recent interest in connection with dynamical systems and now associated with certain Ising spin systems.     

The attractor—basin portrait of a cellular automaton

Local space-time structures, such as domains and the intervening dislocations, dominate a wide class of cellular automaton (CA) behavior. For such spatially-extended dynamics regular domains, vicinities, and attractors are introduced as organizing principles to identify the discretized analogs of attractors, basins, and separatrices: structures used in classifying dissipative continuous-state dynamical systems. We describe the attractor-basin portrait of nonlinear elementary CA rule 18, whose global dynamics is largely determined by a single regular attracting domain. The latter's basin is analyzed in terms of subbasin and portal structures associated with particle annihilation. The conclusion is that the computational complexity of such CA is more apparent than real. Transducer machines are constructed that automatically identify domain and dislocation structures in space-time, count the number of dislocations in a spatial pattern, and implement an isomorphism between rule 18 and rule 90. We use a transducer to trace dislocation trajectories, and confirm that in rule 18, isolated dislocation trajectories, as well as a dislocation gas, agree extremely well with the classical model of annihilating diffusive particles. The CA efficiently transforms randomness of an initial pattern ensemble into a random walk of dislocations in space-time.     

N2（A）及N（2D）对IF（X）的传能研究

在微波放电系统中,对NH_3-F-F_2-CF_3I体系进行研究,结果表明,向IF(X)传能的诸多媒介中,N_2(A)及N(~2D)起着主要作用,并且这一结论在经微波激发后的N_2与CF_3I的直接反应中得到了进一步证实。     

我国运动稳定性研究的新进展

综述了近年来我国运动稳定性(包括力学系统、控制系统、人口系统、生态系统和大系统的稳定性)及其一般理论的研究进展。      

On general form of Navier-Stokes equations and implicit factored scheme

A general weak conservative form of Navier-Stokes equations expressed with respect to non-orthogonal Curvilinear coordinates and with primitive variables was obtained by using tensor analysis technique, where the contravariant and covariant velocity components were employed. Compared with the current coordinate transformation method, the established equations are concise and forthright, and they are more convenient to be used for solving problems in body-fitted curvilinear coordinate system. An implicit factored scheme for solving the equations is presented with detailed discussions in this paper. For n-dimensional flow the algorithm requires n-steps and for each step only a block tridiagonal matrix equation needs to be solved. It avoids inverting the matrix for large systems of equations and enhances the speed of arithmetic. In this study, the Beam- Warming’s implicit factored schceme is extended and developed in non-orthogonal curvilinear coordinate system.     

Rheological models for gypsum plaster pastes

Shear stress and shear rate data obtained for gypsum plaster pastes were correlated by means of different rheological models. The pastes were prepared from a commercial calcium sulfate hemihydrate at various water/plaster ratios ranging from 100/150 to 100/190. The tests were performed at 25°C using a rotating coaxial cylinder viscosimeter. The measurements were accomplished by applying a step-wise decreasing shear rate sequence. Discrimination among the models was made: (1) on the basis of the fitting goodness; (2) by checking the physical meaning of the calculated parameters; (3) on the basis of the stability of the parameters and of their prediction capacity beyond the limits of the experimental data. In the light of above, the Casson model seemed to be most effective for application to gypsum plaster pastes. K Consistency - n Power-law index - N Number of experimental data - P Number of parameters - Shear rate (s^–1) - ₀ Viscosity (Pa · s) - _d Dispersing medium viscosity (Pa · s) - _p Plastic viscosity (Pa · s) - Viscosity at zero shear rate (Pa · s) - Viscosity at infinite shear rate (Pa · s) - [] Intrinsic viscosity - ² Variance - Shear stress (Pa) - ₀ Yield stress (Pa) - Solid volume fraction - _m Maximum solid volume fraction     

Transient spherical flow of non-newtonian power-law fluids in porous media

The transient spherical flow behavior of a slightly compressible non-Newtonian, power-law fluids in porous media is studied. A nonlinear partial differential equation of parabolic type is derived. The diffusivity equation for spherical flow is a special case of the new equation. We obtain analytical, asymptotic and approximate solutions by using the methods of Laplace transform and weighted mass conservation. The structures of asymptotic and approximate solutions are similar, which enriches the theory of one-dimensional flow of non-Newtonian fluids through porous media.     

Sensitivity analysis of truss structures and its application to the fully stressed design

Based upon the theorems of structural variations this paper derives a set of expressions for calculating partial derivatives of internal forces, stresses and joint displacements with respect to bar areas for truss structures. Compared with the known formulas for finding the gradients of structural behaviours the calculation effort with the proposed expressions in this paper is usually smaller because the additional virtual loadings needed are relatively fewer. It is of practical significance to various optimization methods in which the calculation of gradients of behaviours is widely used. Moreover, applying the derived formulas to the fully stressed design (FSD), we obtain an improved iterative method for FSD. The numerical examples show that the new method considerably reduces the reanalysis number required to converge to an FSD in comparison with the simple stress ratio method.     

Anisotropic plastic stress fields at a rapidly propagating crack-tip

All the stress components at a rapidly propagating crack-tip in an elastic perfectly-plastic material are the functions of only. Making use of this condition and the equations of steady-state motion, stress-strain relations and Hill anisotropic yield condition, we obtain the general solutions in both the cases of anti-plane and in-plane strain. Applying these two general solutions to propagating Mode III and Mode I cracks, respectively, the anisotropic plastic stress fields at the rapidly propagating tips of Mode III and Mode I cracks are derived.