Global Analysis of the Flows of Fluids with Pressure-Dependent Viscosities

 To describe the flows of fluids over a wide range of pressures, it is necessary to take into account the fact that the viscosity of the fluid depends on the pressure. That the viscosity depends on the pressure has been verified by numerous careful experiments. While the existence of solutions local-in-time to the equations governing the flows of such fluids are available for small, special data and rather unrealistic dependence of the viscosity on the pressure, no global existence results are in place. Our interest here is to establish the existence of weak solutions for spatially periodic three-dimensional flows that are global in time, for a large class of physically meaningful viscosity-pressure relationships. (Accepted May 1, 2002) Published online November 15, 2002 Communicated by S. S. ANTMAN     

Quotients of uniform spaces

This paper develops the basic theory of quotients of uniform spaces via sufficiently nice group actions. We generalize and unify two fundamental constructions: quotients of topological groups via closed normal subgroups and quotients of metric spaces via actions by isometries. Basic results about inverse limits of topological groups are extended to inverse limits of group actions on uniform spaces, and notions of prodiscrete action and generalized covering map are introduced.     

Influence of load position on the stability of shallow arches

The influence of load position of lhe snap-through instability of shallow, circular, elastic arches is investigated. Results are obtained for pinned, clamped, and clamped-pinned end conditions. The worst load position is seen to depend on the arch rise.

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Zusammenfassung Der Eifluss der Kraftlage auf die Durchschgsinstabilität von flachen, elastischen Kreisbögen wird untersucht. Es sind Ergebnisse erhalten worden für Bögen mit gelenkigen eingespannten, und gelenkig-eingespannten Lagern. Die ungünstigste Kraftlage hängt von der Bogenhöhe ab.

     

Structural characterization of crystalline ternary inclusion compounds at the air-water interface

Crystalline ternary inclusion monolayers consisting of a two-dimensional hydrogen-bonded host network of guanidinium (G) ions and organosulfonate (S) amphiphiles, and biphenylalkane guests, can be generated at the air-water interface through synergistic structural enforcement by hydrogen bonding and host-guest packing. Surface pressure-area isotherms of the 4'-hexadecylbiphenyl-4-sulfonate (C16BPS) amphiphile in the presence of G, with or without guest, are characterized by lift-off molecular areas expected for the GS sheet based on single-crystal X-ray structures of homologous bulk crystals. Intercalation of biphenylalkane guests (4-C(n)()H(2)(n)()(+1)-C(6)H(4)-C(6)H(5), n = 1, 4, 6, 10, 16; denoted CnBP) between organosulfonate hydrophobes, which define pocketlike cavities in the GS monolayer host, afford ternary inclusion monolayers with a 1:1 host-guest stoichiometry. These inclusion monolayers are less compressible than the guest-free host, consistent with dense packing of the biphenylalkane moieties of the host and the biphenylalkane guests. The inclusion monolayers are distinguished from the amorphous guest-free host and from selected guanidinium-free mixed monolayers by structural characterization with grazing-angle incidence X-ray diffraction (GIXD). The GIXD data for the ternary (G)C16BPS:C16BP and (G)C16BPS:C6BP inclusion monolayers obtained upon compression are consistent with a rectangular unit cell. The dimensions of these unit cells and refinement of the GIXD data suggest a "rotated shifted ribbon" GS hydrogen-bonding motif similar to that observed in some bulk GS crystals, including (G)(ethylbiphenylsulfonate). GIXD reveals that (G)C16BPS:C16BP and (G)C16BPS:C6BP are more crystalline than the corresponding guanidinium-free mixed monolayers. The (G)C16BPS:C6BP inclusion monolayer is stable upon compression, even though the alkyl-alkyl host-guest interactions are reduced due to the shorter hexyl substituents of the guest, demonstrating an important reinforcing role for the hydrogen-bonded GS sheet. The structure of a C16BPS:tetracosane (C24) mixed monolayer is independent of G; the unit cell symmetry and dimensions suggest a structure governed by alkyl-alkane interactions that prohibit formation of a GS network. These results illustrate that the existence of ternary inclusion monolayers with an intact GS network requires guest molecules that are structurally homologous with the hydrophobes of the host, in this case biphenylalkanes. The observation of these inclusion compounds suggests an approach for introducing functional nonamphiphilic molecules to an air-water interface through inclusion in a well-defined host.     

Graphene growth on h-BN by molecular beam epitaxy

The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms.     

Postbuckling Analysis of Nonconservative Elastic Systems

Abstract

Previous work on the postbuckling and imperfection-sensitivity of elastic structures has concentrated on conservative systems. The results of Koiterand others have led to a general theory of nonlinear stability behavior for these systems. The theory must be modified when nonconservative forces are present, and this is the aim of the present paper.

Discrete, nonconservative, elastic systems which exhibit static (divergence) instability are considered. The nonlinear behavior in the neighborhood of a critical point is analyzed by means of a perturbation procedure. When the critical point is simple, the results are similar to those for conservative systems. When a coincident critical point exists, however, different types of behavior occur. In many cases there is no bifurcation at all, with only the fundamental (trivial) equilibrium path passing through the critical point. Imperfection-sensitivity is more severe than for the typical bifurcation points and can even occur when the perfect system has no bifurcation. The results are illustrated with the use of a nonlinear double pendulum model subjected to a partial follower load.     

Whirling of a forced cantilevered beam with static deflection. III: Passage through resonance

Nonstationary excitations of slender, elastic, cantilevered beams with equal principal moments of inertia are considered. The excitation frequency is slowly increased or decreased through a resonance of the first mode at a constant rate. Three resonances are investigated: primary resonance, superharmonic resonance of order two and subharmonic resonance of order two. After application of Galerkin's method with three modes, the nonlinear, nonstationary response of the first mode of the beam is determined by two methods: integration of the modulation equations obtained from the method of multiple scales, and direct numerical integration of the temporal equations of motion. Time histories are presented and the effects of excitation amplitude, rate of acceleration or deceleration through resonance, damping and initial conditions of the disturbance on the maximum response are studied. The effect of a persistent random disturbance is also examined. Although the excitation acts in the vertical plane, whirling occurs if the beam is subjected to out-of-plane disturbances.