An optimal theory for an expansion of flow quantities to capture the flow structures

An optimal theory on how database analysis to capture the flow structures has been developed in this paper, which include the POD method as its special case. By means of the remainder minimization method in the Sobolev space, for more general optimal conditions the new theory has the potential to overcome an inherent limitation of the POD method, i.e., it cannot be used to the situations in which the optimal condition is other than the inner product global one. As an example, using the new theory, the database of a two-dimensional flow over a backward-facing step is analyzed in detail, with velocity and vorticity bases.

General Solution to Two-Dimensional Nonslipping JKR Model with a Pulling Force in an Arbitrary Direction

In this paper, a generalized JKR model is investigated, in which an elastic cylinder adhesively contacts with an elastic half space and the contact region is assumed to be perfect bonding. An external pulling force is acted on the cylinder in an arbitrary direction. The contact area changes during the pull-off process, which can be predicted using the dynamic Griffith energy balance criterion as the contact edge shifts. Full coupled solution with an oscillatory singularity is obtained and analyzed by numerical calculations. The effect of Dundurs' parameter on the pull-off process is analyzed, which shows that a nonoscillatory solution can approximate the general one under some conditions, i.e., larger pulling angle (pi/2 is the maximum value), smaller a/R or larger nondimensional parameter value of Delta gamma/E*R. Relations among the contact half width, the external pulling force and the pulling angle are used to determine the pull-off force and pull-off contact half width explicitly. All the results in the present paper as basic solutions are helpful and applicable for experimenters and engineers.

The scattering of general SH plane wave by interface crack between two dissimilar viscoelastic bodies

The scattering of general SH plane wave by an interface crack between two dissimilar viscoelastic bodies is studied and the dynamic stress,intensity factor at the crack-tip is computed. The scattering problem can be decomposed into two problems: one is the reflection and refraction problem of general SH plane waves at perfect interface (with no crack); another is the scattering problem due to the existence of crack. For the first problem, the viscoelastic wave equation, displacement and stress continuity conditions across the interface are used to obtain the shear stress distribution at the interface. For the second problem, the integral transformation method is used to reduce the scattering problem into dual integral equations. Then, the dual integral equations are transformed into the Cauchy singular integral equation of first kind by introduction of the crack dislocation density function. Finally, the singular integral equation is solved by Kurtz's piecewise continuous function method. As a consequence, the crack opening displacement and dynamic stress intensity factor are obtained. At the end of the paper, a numerical example is given. The effects of incident angle, incident frequency and viscoelastic material parameters are analyzed. It is found that there is a frequency region for viscoelastic material within which the viscoelastic effects cannot be ignored.

Damage analysis of tetragonal perovskite structure ceramics implicated by asymptotic field solutions and boundary conditions

Cracking of ceramics with tetragonal perovskite grain structure is known to appear at different sites and scale level. The multiscale character of damage depends on the combined effects of electromechanical coupling, prevailing physical parameters and boundary conditions. These detail features are exhibited by application of the energy density criterion with judicious use of the mode I asymptotic and full field solution in the range of r/a = 10(-4) to 10(-2) where r and a are, respectively, the distance to the crack tip and half crack length. Very close to the stationary crack tip, bifurcation is predicted resembling the dislocation emission behavior invoked in the molecular dynamics model. At the macroscopic scale, crack growth is predicted to occur straight ahead with two yield zones to the sides. A multiscale feature of crack tip damage is provided for the first time. Numerical values of the relative distances and bifurcation angles are reported for the PZT-4 ceramic subjected to different electric field to applied stress ratio and boundary conditions that consist of the specification of electric field/mechanical stress, electric displacement/mechanical strain, and mixed conditions. To be emphasized is that the multiscale character of damage in piezoceramics does not appear in general. It occurs only for specific combinations of the external and internal field parameters, elastic/piezoelectric/dielectric constants and specified boundary conditions. (C) 2002 Published by Elsevier Science Ltd.

Comparative mechanisms of photosynthetic carbon acquisition in Hizikia fusiforme under submersed and emersed conditions

The economic seaweed Hizikia fusiforme (Harv.) Okamura (Sargassaceae, Phaeophyta) usually experiences periodical exposures to air at low tide. Photosynthetic carbon acquisition mechanisms were comparatively studied under submersed and emersed conditions in order to establish a general understanding of its photosynthetic characteristics associated with tidal cycles. When submersed in seawater, H fusiforme was capable of acquiring HCO3- as a source of inorganic carbon (Ci) to drive photosynthesis, while emersed and exposed to air, it used atmospheric CO2 for photosynthesis. The pH changes surrounding the H fusiforme fronds had less influence on the photosynthetic rates under emersed condition than under submersed condition. When the pH was as high as 10.0, emersed H fusiforme could photosynthesize efficiently, but the submersed alga exhibited very poor photosynthesis. Extracellular carbonic anhydrase (CA) played an important role in the photosynthetic acquisitions of exogenous Ci in water as well as in air. Both the concentrations of dissolved inorganic carbon in general seawater and CO2 in air were demonstrated to limit the photosynthesis of H fusiforme, which was sensitive to O-2. It appeared that the exogenous carbon acquisition system, being dependent of external CA activity, operates in a way not enough to raise intracellular CO2 level to prevent photorespiration. The inability of H fusiforme to achieve its maximum photosynthetic rate at the current ambient Ci levels under both submersed and emersed conditions suggested that the yield of aquaculture for this economic species would respond profitably to future increases in CO2 concentration in the sea and air.

Conditions for the local manipulation of all bipartite Gaussian states

We provide a general, necessary, and sufficient condition for the possibility of transforming a mixed bipartite Gaussian state with arbitrarily many modes to another one under arbitrary local Gaussian channels, which do not include classical communication. Moreover, by means of this condition we present a necessary criterion that can be used to check the possibility of a state transformation between two mixed Gaussian states. At the same time, we prove that our criterion can be reduced to the Eisert-Plenio criterion when the mode number is chosen as 1 per side.

Conditions for the local manipulation of tripartite Gaussian states

We present the normal form of the covariance matrix for three-mode tripartite Gaussian states. By means of this result, the general form of a necessary and sufficient criterion for the possibility of a state transformation from one tripartite entangled Gaussian state to another with three modes is found. Moreover, we show that the conditions presented include not only inequalities but equalities as well.

Faddeev-Jackiw canonical path integral quantization for a general scenario, its proper vertices and generating functionals

We generalize the Faddeev-Jackiw canonical path integral quantization for the scenario of a Jacobian with J=1 to that for the general scenario of non-unit Jacobian, give the representation of the quantum transition amplitude with symplectic variables and obtain the generating functionals of the Green function and connected Green function. We deduce the unified expression of the symplectic field variable functions in terms of the Green function or the connected Green function with external sources. Furthermore, we generally get generating functionals of the general proper vertices of any n-points cases under the conditions of considering and not considering Grassmann variables, respectively; they are regular and are the simplest forms relative to the usual field theory.

Entanglement conditions for mixed SU(2) and SU(1,1) systems

We derive a class of inequalities for detecting entanglement in the mixed SU(2) and SU(1, 1) systems based on the Schrodinger-Robertson indeterminacy relations in conjugation with the partial transposition. These inequalities are in general stronger than those based on the usual Heisenberg uncertainty relations for detecting entanglement. Furthermore, based on the complete reduction from SU(2) and SU(1,1) systems to bosonic systems, we derive some entanglement conditions for two-mode systems. We also use the partial reduction to obtain some inequalities in the mixed SU(2) (or SU(1, 1)) and bosonic systems.

Direct conversion of methane under nonoxidative conditions

Direct conversion of methane into hydrogen and valuable chemicals under nonoxidative conditions is a process severely limited thermodynamically. However, the movement from the present era of fossil fuels into the coming hydrogen energy age makes it an interesting and important approach compared with the direct conversion of methane under the aid of oxidants. This paper gives a brief overview of the direct conversion of CH4 under nonoxidative conditions. At the same time, our understanding of methane dehydroaromatization over Mo/HZSM-5 catalysts for the simultaneous formation of hydrogen and light aromatics is discussed in general, while the bifunctionality of Mo/HZSM-5 catalysts and the role of carbonaceous deposits formed during the reaction are reviewed in more detail. A perspective of the topic from both academic points of view and potential industrial applications is also presented. (C) 2003 Elsevier Science (USA). All rights reserved.

A Facile and Efficient One-Pot Synthesis of Substituted Quinolines from alpha-Arylamino Ketones Under Vilsmeier Conditions

An efficient one-pot synthesis of substituted quinolines from alpha-arylamino ketones in the presence of PBr3 in DMF has been developed. This general protocol provides a novel and facile access to substituted quinolines by sequential Vilsmeier-Haack reaction, intramolecular cyclization and aromatization reactions of alpha-arylamino ketones. PBr3 plays a dual role in the quinoline synthesis: as a key component of the Vilsmeier reagent (PBr3/DMF) and as a reducing reagent.