A new approach to the solution of the Navier-Stokes equations

In the present paper a numerical algorithm is given for solving a standard problem in fluid dynamics, that of inviscid, irrotational, incompressible flow over an arbitrary symmetric profile. The purpose of the paper is to propose an alternative approach to solve certain fluid dynamic flows. This paper may be thought of as the first of a possible series of papers solving new and fundamental problems. In a sense, this new approach asks the question: what is the simplest and most efficient method of solving the problem considered by finite difference methods. It is believed that the following algorithm answers this question. Standard second-order finite difference techniques, such as SLOR and ADI, are used to solve numerically a mixed boundary value problem comprised of a pair of elliptic partial differential equations with constant coefficients.     

Arene-mercury complexes stabilized aluminum and gallium chloride: synthesis and structural characterization.

Reaction of HgCl(2) with 2 equiv of MCl(3) in an aromatic solvent yields Hg(arene)(2)(MCl(4))(2) where, arene = C(6)H(5)Me, M = Al (1), Ga (2); arene = C(6)H(5)Et, M = Al (3) and Ga (4); o-C(6)H(4)Me(2), M = Al (5), Ga (6); C(6)H(3)-1,2,3-Me(3), M = Al (7) and Ga (8). The solid-state structures of compounds 1-5 and 7 have been determined by X-ray crystallography. In the solid state, compounds 1-4 and 7 exist as neutral complexes in which two arenes are bound to the mercury, and the MCl(3) groups are bound through bridging chlorides to the mercury; compound 5 exists as a cation-anion pair [Hg(o-C(6)H(4)Me(2))(2)(AlCl(4))][AlCl(4)]. However, in solution compounds 1-8 all exist as neutral complexes. The structures of Hg(arene)(2)(AlCl(4))(2) and [Hg(arene)(2)(AlCl(4))](+) have been determined by DFT calculations [B3LYP level] to facilitate the assignment of the (13)C CPMAS NMR spectra and are in good agreement with the X-ray diffraction structures of compounds 1 and 5. Reaction of HgCl(2) with MCl(3) in benzene, m-xylene, and p-xylene results in the formation of liquid clathrates whose spectroscopic characterization is consistent with ionic structures, [Hg(arene)(2)(MCl(4))][MCl(4)]. The calculated energy difference between Hg(C(6)H(5)Me)(2)(AlCl(4))(2) and [Hg(C(6)H(5)Me)(2)(AlCl(4))][AlCl(4)] is discussed with respect to the structure of compound 5 in the solid state versus solution state and the proposed speciation in the liquid clathrates.     

Ergodic Control in L∞

The infinite horizon discounted L ^∞ problem is studied as the discount factor goes to zero. It is related to the limit of the finite horizon problem as the horizon becomes infinite. The deterministic problem with and without a running cost is considered.     

Analysis of the squeezing flow of dusty fluids

The current investigation deals with the study of the effect of introducing a small fraction of dust, by volume, to the fluid in a squeeze film on the viscous resistance to a steady moving disc. Expressions are obtained for the fluid-phase and the dust-phase velocity distributions and the dust particle number density. Analysis based on an iterative procedure indicates that the resistance to motion experienced by the moving disc increases due to the presence of dust.Nomenclature A arbitrary function of integration - B bulk concentration - F resistance to motion experienced by the disc (dusty fluid case) - F _c resistance to motion experienced by the disc (clean fluid case) - F* difference in resistance between the clean fluid and dusty fluid films - f mass concentration - h thickness of the squeeze film - K Stokes coefficient of resistance - m mass of a single dust particle - fluid viscosity coefficient - N dust particles number density - N ₀ dust particles number density at r=R - n iteration level - p fluid pressure in the squeeze film - P pressure in the surrounding - R radius of the disc - fluid density - (r, , y) cylindrical coordinates - t time - U fluid-phase velocity vector - V dust-phase velocity vector - ₁ fluid-phase radial velocity component - U ₂ dust-phase radial velocity component     

The classification of orthogonal electromagneto-fluid-dynamic flows

A theoretical analysis based on the equations of electromagneto-fluid-dynamics is undertaken in order to completely classify the flow geometries admitted by these equations. The steady two-dimensional flow of a viscous incompressible fluid of finite electrical conductivity and non-zero electric charge density is considered. The flow equations are formulated in terms of the streamfunction and magnetic flux function as independent variables. The exact analytical solution of the resulting equations is obtained when the magnetic field and the velocity field are everywhere orthogonal to each other. It is shown that the only possible flow is a uniform parallel flow.     

Simultaneous detection of 19 K‐ras mutations by free‐solution conjugate electrophoresis of ligase detection reaction products on glass microchips

We demonstrate here the power and flexibility of free‐solution conjugate electrophoresis (FSCE) as a method of separating DNA fragments by electrophoresis with no sieving polymer network. Previous work introduced the coupling of FSCE with ligase detection reaction (LDR) to detect point mutations, even at low abundance compared to the wild‐type DNA. Here, four large drag‐tags are used to achieve free‐solution electrophoretic separation of 19 LDR products ranging in size from 42 to 66 nt that correspond to mutations in the K‐ras oncogene. LDR‐FSCE enabled electrophoretic resolution of these 19 LDR‐FSCE products by CE in 13.5 min (E = 310 V/cm) and by microchip electrophoresis in 140 s (E = 350 V/cm). The power of FSCE is demonstrated in the unique characteristic of free‐solution separations where the separation resolution is constant no matter the electric field strength. By microchip electrophoresis, the electric field was increased to the maximum of the power supply (E = 700 V/cm), and the 19 LDR‐FSCE products were separated in less than 70 s with almost identical resolution to the separation at E = 350 V/cm. These results will aid the goal of screening K‐ras mutations on integrated “sample‐in/answer‐out” devices with amplification, LDR, and detection all on one platform.     

Stepwise synthesis of metal-organic frameworks: replacement of structural organic linkers

We demonstrate how a single-crystal to single-crystal transformation resulting from bridging-linker replacement is possible in extended 2D and 3D metal-organic frameworks (MOFs) by introducing pillared paddlewheel MOF structures into a solution containing dipyridyl linkers. No lateral movement of the layers was observed during this transformation, creating a templating effect from the "parent" structure to the "daughter" structure. A previously unattainable structure was obtained by a two-step synthetic method utilizing the bridging-linker replacement transformation method. Additionally, a bridging-linker insertion was observed when excess linker was used with the 2D MOF structure, inducing an overall 2D to 3D transformation.