Experimental Investigations on the Thermal Diffusion Characteristics and Photoluminescence in Multiphase Micro Fluids Containing ZnO Micro Tubes and Fluorescein Dye

Optics and Spectroscopy - Scattering of light by disordered structures is normally detrimental to their applicability in many optoelectronic devices. However, some micro and nanostructures are...     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

Compatible relations on filters and stability of local topological properties under supremum and product

An abstract scheme using particular types of relations on filters leads to general unifying results on stability under supremum and product of local topological properties. We present applications for Fréchetness, strong Fréchetness, countable tightness and countable fan-tightness, some of which recover or refine classical results, some of which are new. The reader may find other applications as well.     

Line graphs of bipartite graphs with Hamiltonian paths

It is shown that, if t is an integer ≥3 and not equal to 7 or 8, then there is a unique maximal graph having the path P_t as a star complement for the eigenvalue ?2. The maximal graph is the line graph of K_m,m if t = 2m?1, and of K_m,m+1 if t = 2m. This result yields a characterization of L(G ) when G is a (t + 1)‐vertex bipartite graph with a Hamiltonian path. The graphs with star complement P_r ∪ P_s or P_r ∪ C_s for ?2 are also determined. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 137–149, 2003     

A Practical Solution to a Cargo Loading Problem at Bethlehem Steel

The optimum assignment of structural steel shapes to rail cars is an important logistical problem in the steel industry. In this paper, we discuss an application at Bethlehem Steel that not only involves weight and dimensional constraints, but also customer unloading constraints. The formulation is a generalized bin packing problem which is solved by modifying and extending the first fit decreasing algorithm. The solution algorithm, SOLID (for Structural Optimal Loading IDentification), has been used extensively for one of Bethlehem's high tonnage customers providing very good practical (implementable) results that achieve the desired goals. Bethlehem has enhanced this approach for use with other customers.     

On worst-case aggregation analysis for network location problems

Network location problems occur when new facilities must be located on a network, and the network distances between new and existing facilities are important. In urban, regional, or geographic contexts, there may be hundreds of thousands (or more) of existing facilities, in which case it is common to aggregate existing facilities, e.g. represent all the existing facility locations in a zip code area by a centroid. This aggregation makes the size of the problem more manageable for data collection and data processing purposes, as well as for purposes of analysis; at the same time, it introduces errors, and results in an approximating location problem being solved. There seems to be relatively little theory for doing aggregation, or evaluating the results of aggregation; most approaches are based on experimentation or computational studies. We propose a theory that has the potential to improve the means available for doing aggregation.This research was supported in part by the National Science Foundation, Grant No. DDM-9023392.     

The effect of nanoparticle shape on polymer‐nanocomposite rheology and tensile strength

Nanoparticles can influence the properties of polymer materials by a variety of mechanisms. With fullerene, carbon nanotube, and clay or graphene sheet nanocomposites in mind, we investigate how particle shape influences the melt shear viscosity η and the tensile strength τ, which we determine via molecular dynamics simulations. Our simulations of compact (icosahedral), tube or rod‐like, and sheet‐like model nanoparticles, all at a volume fraction ? ≈ 0.05, indicate an order of magnitude increase in the viscosity η relative to the pure melt. This finding evidently can not be explained by continuum hydrodynamics and we provide evidence that the η increase in our model nanocomposites has its origin in chain bridging between the nanoparticles. We find that this increase is the largest for the rod‐like nanoparticles and least for the sheet‐like nanoparticles. Curiously, the enhancements of η and τ exhibit opposite trends with increasing chain length N and with particle shape anisotropy. Evidently, the concept of bridging chains alone cannot account for the increase in τ and we suggest that the deformability or flexibility of the sheet nanoparticles contributes to nanocomposite strength and toughness by reducing the relative value of the Poisson ratio of the composite. The molecular dynamics simulations in the present work focus on the reference case where the modification of the melt structure associated with glass‐formation and entanglement interactions should not be an issue. Since many applications require good particle dispersion, we also focus on the case where the polymer‐particle interactions favor nanoparticle dispersion. Our simulations point to a substantial contribution of nanoparticle shape to both mechanical and processing properties of polymer nanocomposites. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1882–1897, 2007