Patterns,fabric, anisotropy,and soil elasto-plasticity

This paper proposes a new method in the theory of soil plasticity – an advance on Hill [The Mathematical Theory of Plasticity, Clarendon Press, Oxford]. The method assumes that soil fabric consists of inter-locking, inter-twining, inter-laced, juxtaposed, and superposed elementary units called “patterns”. A mechanics of patterns is developed. As well as elastic and plastic components, a third strain-increment component is deduced which helps explain non-associated flow. The proposed method leads to explanations of critical states, anisotropy, sensitivity, the Bauschinger effect, and swept-out memory. All these appear in the method as near-inescapable features of plastic solids. Results are illustrated in detail for plane strain biaxial processes.     

Physiology,mechanics, and rheology

Biological systems possess rather specialized mechanical properties, acquired as part and parcel of the evolutionary development of the system as a whole. Their optimization permits the system to function physiologically in the context of a biologically essential, but mechanically often widely varying environment with adequate efficiency. The system's environment is its source of food and shelter; it represents the space in which it forages or preys on other creatures and in which it has to defend itself against still others. Thus, the system has to develop an adequately pliant, rheologically matched, energy-use efficient, mechanical interface between it and its surroundings. This must be an interface that both effectively excludes, but also effectively admits, the external. Internally, as well, it has to adapt the mechanical properties of cell and connective tissue to physiological function and the efficient performance of useful work. This will be illustrated by way of examples. Blood rheology is briefly discussed and put into the context of clinical hemorheology and epithelial protection; and function, by way of a mucus coating or a mucociliary clearance system, is reviewed in some detail. The importance of all aspects of rheological matching is demonstrated.Delivered as a Keynote Lecture at the Golden Jubilee Conference of the British Society of Rheology and Third European Rheology Conference, Edinburgh, 3–7 September, 1990.     

One-dimensional,time-dependent,homogeneous, two-phase flow in volcanic conduits

A one-dimensional, time-dependent, isothermal, homogeneous, two-phase flow model was developed to study magma ascent in volcanic conduits. The physical modeling equations were numerically solved by means of a TVD (total variation diminishing) predictor-corrector procedure and by means of a predictor-corrector technique based on the method of characteristics. The results from the transient model were verified with an analytical solution for wave propagation in conduits without friction and gravitational effects. The numerical solutions were also compared with those of a steady-state, homogeneous, two-phase model for basaltic and rhyolitic magma ascents in the fissures and circular conduits of Vesuvius and Mt St. Helens. An application of the model to magma decompression in conduits indicates very short times for gas exsolution, fragmentation, and shock wave propagation, implying that the modelling of gas exsolution should involve non-equilibrium kinetics effects. Future coupling of the transient magma ascent model with magma chamber and pyroclastic dispersion models should allow for more realistic simulations of the time-dependent behavior of real volcanic eruptions.     

Steady,oblique, detonation waves

Normal and oblique, steady planar detonation waves have been theoretically and computationally examined using the Zeldovich, von Neumann, Döring model. Combustion is between a methane/hydrogen mixture and dry air assuming, first, complete combustion, then an equilibrium solution. Prescribed parameters are the upstream values for the pressure, temperature, and Mach number, the fuel/air equivalence ratio, a hydrogen/methane ratio, and the detonation wave angle. For a given upstream state, the angle varies from its normal wave value in increments of 10 ^o to non-integer wave angles that correspond to the Chapman-Jouguet state for complete combustion and for an equilibrium solution. For each solution, detailed results are provided for the upstream state, the state just downstream of the shock, and the two downstream states. Over 340 solutions in a report (Emanuel and Tuckness 2002) are provided, thereby establishing, for the first time, comprehensive tables that can be used to provide quick estimates, establish trends, and check CFD results. This paper describes the basis for the model, briefly outlines the analytical and numerical method, and discusses several insights.     

Diffusion models for innovation: s-curves, networks, power laws, catastrophes, and entropy

This article considers models for the diffusion of innovation would be most relevant to the dynamics of early 21st century technologies. The article presents an overview of diffusion models and examines the adoption S-curve, network theories, difference models, influence models, geographical models, a cusp catastrophe model, and self-organizing dynamics that emanate from principles of network configuration and principles of heat diffusion. The diffusion dynamics that are relevant to information technologies and energy-efficient technologies are compared. Finally, principles of nonlinear dynamics for innovation diffusion that could be used to rehabilitate the global economic situation are discussed.     

COMPOSITION OF INDOOR AEROSOLS AT EMPEROR QIN''''S TERRA-COTTA MUSEUM, XI''''AN, CHINA, DURING SUMMER, 2004

Particle samples were collected in August 2004 both inside and outside Emperor Qin's Terra-Cotta Museum in Xi'an, China. Mass and chemical composition of total suspended particles (JSP, particles with aerodynamic diameter less than-30μm), PM2.5(particles with aerodynamic diameter <2.5μm) were determined. The average levels of indoor PM2.5 and TSP were 108.4 and 172.4 μg·m-3, respectively, with PM2.5 constituting 62.9% of the TSP mass. Sulfate ((32.4±6.2)%), organics ((27.7±8.0)%), and geological material ((12.5±3.4)%) dominated indoor PM2.5, followed by ammonium ((8.9±2.8)%), nitrate ((7.0±2.9)%), and elemental carbon (EC, (3.9±1.5)%). Particle size distribution varied with the number of tourists in the museum. The size of sulfate, organics, EC, nitrate, and ammonium was found to vary in the range of 0.43 to 3.3 μm in fraction. Ion balance indicated that the aerosol was acidic, with insufficient ammonium ions to neutralize the sulfuric and nitric acids. High concentrations of acidic aerosols will erode the Terra-cotta warriors and horses especially in the summer season with high temperature (30℃) and relative humidity (70%) and undesirable solar radiation inside the museum. More attention should be paid to protecting these precious antiques made 2000 years ago.     

Extended irreversible thermodynamics,generalized hydrodynamics,kinetic theory,and rheology

The gist of extended irreversible thermodynamics and generalized hydrodynamics is presented within the context of rheology of complex molecules (e.g., polymers) in this paper. Then, the constitutive equation for stress developed for polyatomic fluids in a previous paper is applied to rheology of polymeric fluids. This constitutive equation is fully consistent with the thermodynamic laws. It is shown that the collision bracket integrals appearing in the constitutive equation can be recast in terms of friction tensors of beads and equilibrium force-force correlation functions if the momentum relaxation is much faster than the configuration relaxation and there exist such relaxation times. The force-force correlation functions reduce to those related to the mean square radius of gyration of the polymer if the Hookean model is taken for forces. By treating the recast collision bracket integrals in the constitutive equation as empirical parameters, we analyze some experimental data on shear rate and elongation rate dependence of polymeric melts and obtain excellent agreement with experiment. We show that the empirical parameters can be related to the zero shear rate viscosity and the ratio of the secondary to the primary normal stress coefficient. Therefore, for the plane Couette flow geometry considered in the paper, the constitutive equation is completely specified by the limiting material functions at zero shear rate and relaxation times.Work supported in part by the Natural Sciences and Engineering Research Council of Canada and Fonds FCAR, Quebec. This paper was presented at the Symposium on Recent Developments in Structured Continua II held at Magog, Quebec, Canada, May 23–25, 1990.     

Diffusive coupling, dissipation, and synchronization

We consider the synchronization of diffusive coupled systems in situations where the synchronization is a consequence of the dissipation in the coupling as well as ones where there is an interaction between the inherent damping in the subsystems and the coupling. It is not required that the subsystems be identical, and they are allowed to have chaotic dynamics. Both discrete and continuous versions are discussed. We also consider coupled oscillators where the dynamics of each oscillator is determined by circuitry across a lossless transmission line.     

Computational grid,subgrid, and pixels

Free-surface flows in rivers, estuaries, and coastal areas are strongly dominated by the geometrical details of the study area. Nowadays, accurate bathymetric data are easily available on raster-based digital elevation models with an impressive spatial resolution. These data are often accessible as large two-dimensional arrays containing several millions of pixel values. Recent numerical methods are very efficient and rather accurate but far from being able to solve the governing differential equations on a computational grid with such a fine spatial resolution. In the present investigation, the unaltered pixel values from a digital elevation model are clustered to form subgrids of a coarser computational grid. Artificial cross-flow between disconnected areas is inhibited by introducing cell clones and edge clones. Each clone consists of directly connected pixels. It is shown how the resulting computational grid is able to resolve geometrical details of complex study areas to pixel resolution and for any grid size. As an example, the performance of the proposed algorithm is tested to simulate a typical tidal flow in the San Francisco Bay and the Sacramento-San Joaquin Delta area by using an extreme subgrid resolution given by a digital elevation model containing 196 000 000 pixels with 10 m pixel size.     

Chain recurrence,semiflows, and gradients

This paper is a study of chain recurrence and attractors for maps and semiflows on arbitrary metric spaces. The main results are as follows. (i) C. Conley's characterization of chain recurrence in terms of attractors holds for maps and semiflows on any metric space. (ii) An alternative definition of chain recurrence for semiflows is given and is shown to be equivalent to the usual definition. The alternative definition uses chains formed of orbit segments whose lengths are at least 1, while in the usual definition these lengths are required to be arbitrarily long. (iii) The chain recurrent set of a continuous semiflow is the same as the chain recurrent set of its time-one map. (iv) Conditions on a real-valued function are given that ensure that the semiflow generated by its gradient has only equilibria in its chain recurrent set. An example is given (onR ³) showing that a gradient flow may have nonequilibrium chain recurrent points if these conditions are violated.     

硫代磷酸三正辛酯的合成及其摩擦学性能研究

合成了一统代及四硫代磷酸三正辛酯，用电感耦合等离子体原子发射光谱仪、质谱仪和傅立叶转换红外光谱仪等表征了所合成的一硫代及四硫代磷酸三正辛酯的组成和结构，并在四球摩擦磨损试验机上考察了其在液体石蜡中的摩擦学性能；用扫描电子显微镜和X射线光电子能谱仪对钢球磨痕表面进行了分析表征。结果表明：所合成的一硫代磷酸酯具有比二烷基二硫代磷酸锌更优异的摩擦学性能，可以显著提高液体石蜡的承载能力和抗磨能力，并能在适当浓度和较高载荷（≥400N）下改善液体石蜡的减摩性能；而活性元素含量较高的四硫代磷酸酯对液体石蜡的极压、抗磨和减摩性能的影响不大，这可能是由于其导致腐蚀磨损所致，磨损表面分析结果表明，含添加剂的石蜡油在摩擦过程中发生腐蚀磨损，主要形成了由物理吸附膜和摩擦化学反应膜组成的复合膜。