Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

The preparation and characterization of tin(IV) complexes of 2-quinolinecarboxaldehyde Schiff bases of S-methyl- and S-benzyldithiocarbazates and the X-ray crystal and molecular structures of the 2-quinolinecarboxaldehyde Schiff base of S-benzyldithi

New tin(IV) complexes of empirical formula, Sn(NNS)I-3 (NNS = anionic forms of the 2-quinolinecarboxaldehyde Schiff bases of S-methyl- and S-benzyldithiocarbazate) have been prepared and characterized by a variety of physico-chemical techniques. In the solid state, the Schiff bases exist as the thione tautomer but in solution and in the presence of tin(IV) iodide they convert to the thiol tautomer and coordinate to the tin atom in their deprotonated thiolate forms. The structures of the free ligand, Hqaldsbz and its triiodotin(IV) complex, [Sn(qaldsbz)I-3] have been determined by X-ray diffraction. The complex, [Sn(qaldsbz)I-3] has a distorted octahedral structure with the Schiff base coordinated to the tin atom as a uninegatively charged tridentate chelating agent via the quinoline nitrogen atom, the azomethine nitrogen atom and the thiolate sulfur atom. The three iodo ligands are coordinated meridionally to the tin atom. The distortion from an ideal octahedral geometry of [Sn(qaldsbz)I-3] is attributed to the restricted bite size of the tridentate Schiff base ligand. (C) 2004 Elsevier Ltd. All rights reserved.

Synthetic, EPR spectroscopic, magnetic and X-ray crystallographic structural studies on copper(II) complexes of the tridentate N2S donor ligand formed from 6-methyl-2-formylpyridine and S-methyldithiocarbazate (Hmpsme)

New copper(II) complexes of general empirical formula, Cu(mpsme)X center dot xCH(3)COCH(3) (mpsme = anionic form of the 6-methyl-2-formylpyridine Schiff base of S-methyldithiocarbazate; X = Cl, N-3, NCS, NO3; x = 0, 0.5) have been synthesized and characterized by IR, electronic, EPR and susceptibility measurements. Room temperature mu(eff) values for the complexes are in the range 1.75-2.1 mu(beta) typical of uncoupled or weakly coupled Cu(II) centres. The EPR spectra of the [Cu(mpsme)X] (X = Cl, N-3, NO3, NCS) complexes reveal a tetragonally distorted coordination sphere around the mononuclear Cu(II) centre. We have exploited second derivative EPR spectra in conjunction with Fourier filtering (sine bell and Hamming functions) to extract all of the nitrogen hyperfine coupling matrices. While the X-ray crystallography of [Cu(mpsme)NCS] reveals a linear polymer in which the thiocyanate anion bridges the two copper(II) ions, the EPR spectra in solution are typical of a magnetically isolated monomeric Cu(II) centres indicating dissociation of the polymeric chain in solution. The structures of the free ligand, Hmpsme and the {[Cu(mpsme)NO3] center dot 0.5CH(3)COCH(3)}(2) and [Cu(mpsme)NCS](n) complexes have been determined by X-ray diffraction. The {[Cu(mpsme)NO3]0.5CH(3)COCH(3)}(2) complex is a centrosymmetric dimer in which each copper atom adopts a five-coordinate distorted square-pyramidal geometry with an N2OS2 coordination environment, the Schiff base coordinating as a uninegatively charged tridentate ligand chelating through the pyridine and azomethine nitrogen atoms and the thiolate, an oxygen atom of a unidentate nitrato ligand and a bridging sulfur atom from the second ligand completing the coordination sphere. The [Cu(mpsme)(NCS)](n) complex has a novel staircase-like one dimensional polymeric structure in which the NCS- ligands bridge two adjacent copper(II) ions asymmetrically in an end-to-end fashion providing its nitrogen atom to one copper and the sulfur atom to the other. (c) 2005 Elsevier B.V. All rights reserved.

Ratiometric and nonratiometric Ca2+ indicators for the assessment of intracellular free Ca2+ in a breast cancer cell line using a fluorescence microplate reader

Transporters of Ca2+ are potential drug targets and Ca2+ is a useful signal in the assessment of G-protein-coupled receptor activation. Assays involving the assessment of intracellular Ca2+ using microplate readers most often use Ca2+ indicators which do not exhibit a spectra shift on Ca2+ binding (e.g. fluo-3). Indicators that do exhibit a spectral shift upon Ca2+ binding (e.g. fura-2) offer potential advantages for the calibration of intracellular Ca2+ levels. However, experimental limitations may limit the use of ratiometric dyes in microplate readers capable of screening. In this study, we compared the assessment of intracellular Ca2+ in adherent breast cancer cells using ratiometric and nonratiometric Ca2+ indicators. Our results demonstrate that both fluo-3 and fura-2 detect ATP dose-dependent increases in intracellular Ca2+ in the MCF-7 breast cancer cell line and that some of the limitations in the use of fura-2 appear to be overcome by the use of glass bottom microplates. The calibrated intracellular Ca2+ levels derived using fura-2 are consistent with those from microscopy and cuvette-based studies. Fura-2 may be useful in microplate studies, where cell lines with different properties are compared or where screening treatments lead to differences in the number of cells or dye loading. (C) 2003 Elsevier B.V. All rights reserved.

Analysis of the effect of transverse modes on free-space optical interconnect performance

Vertical-cavity surface-emitting lasers (VCSELs) and microlenses can be used to implement free space optical interconnects (FSOIs) which do not suffer from the bandwidth limitations inherent in metallic interconnects. A comprehensive link equation describing the effects of both optical and electrical noise is introduced. We have evaluated FSOI performance by examining the following metrics: the space-bandwidth product (SBP), describing the density of channels and aggregate bandwidth that can be achieved, and the carrier-to-noise ratio (CNR), which represents the relative strength of the carrier signal. The mode expansion method (MEM) was used to account for the primary cause of optical noise: laser beam diffraction. While the literature commonly assumes an ideal single-mode laser beam, we consider the experimentally determined multimodal structure of a VCSEL beam in our calculations. It was found that maximum achievable interconnect length and density for a given CNR was significantly reduced when the higher order transverse modes were present in Simulations. However, the Simulations demonstrate that free-space optical interconnects are still a suitable solution for the communications bottleneck, despite the adverse effects introduced by transverse modes.

Investigation of the Effect of Array Geometry on the Performance of Free-Space Optical Interconnects

The effect of transmitter and receiver array configurations on the stray-light and diffraction-caused crosstalk in free-space optical interconnects was investigated. The optical system simulation software (Code V) is used to simulate both the stray-light and diffraction-caused crosstalk. Experimentally measured, spectrally-resolved, near-field images of VCSEL higher order modes were used as extended sources in our simulation model. In addition, we have included the electrical and optical noise in our analysis to give more accurate overall performance of the FSOI system. Our results show that by changing the square lattice geometry to a hexagonal configuration, we obtain an overall signal-to-noise ratio improvement of 3 dB. Furthermore, system density is increased by up to 4 channels/mm2.