A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Karman`s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

Influence of physical and geometrical parameters on three-dimensional load transfer mechanism at tunnel face

Three-dimensional discretizations used in numerical analyses of tunnel construction normally include excavation step lengths much shorter than tunnel cross-section dimensions. Simulations have usually worked around this problem by using excavation steps that are much larger than the actual physical steps used in a real tunnel excavation. In contrast, the analyses performed in this study were based on finely discretized meshes capable of reproducing the excavation lengths actually used in tunnels, and the results obtained for internal forces are up to 100% greater than those found in other analyses available in the literature. Whereas most reports conclude that internal forces depend on support delay length alone, this study shows that geometric path dependency (reflected by excavation round length) is very strong, even considering linear elasticity. Moreover, many other solutions found in the literature have also neglected the importance of the relative stiffness between the ground mass and support structure, probably owing to the relatively coarse meshes used in these studies. The analyses presented here show that relative stiffness may account for internal force discrepancies in the order of 60%. A dimensionless expression that takes all these parameters into account is presented as a good approximation for the load transfer mechanism at the tunnel face.

A geometrical approach of 3-D FEA for educational purposes applied to electrostatic fields

A geometrical approach of the finite-element analysis applied to electrostatic fields is presented. This approach is particularly well adapted to teaching Finite Elements in Electrical Engineering courses at undergraduate level. The procedure leads to the same system of algebraic equations as that derived by classical approaches, such as variational principle or weighted residuals for nodal elements with plane symmetry. It is shown that the extension of the original procedure to three dimensions is straightforward, provided the domain be meshed in first-order tetrahedral elements. The element matrices are derived by applying Maxwell`s equations in integral form to suitably chosen surfaces in the finite-element mesh.

Methods of Fourier optics in digital holographic microscopy

In this paper, processing methods of Fourier optics implemented in a digital holographic microscopy system are presented. The proposed methodology is based on the possibility of the digital holography in carrying out the whole reconstruction of the recorded wave front and consequently, the determination of the phase and intensity distribution in any arbitrary plane located between the object and the recording plane. In this way, in digital holographic microscopy the field produced by the objective lens can be reconstructed along its propagation, allowing the reconstruction of the back focal plane of the lens, so that the complex amplitudes of the Fraunhofer diffraction, or equivalently the Fourier transform, of the light distribution across the object can be known. The manipulation of Fourier transform plane makes possible the design of digital methods of optical processing and image analysis. The proposed method has a great practical utility and represents a powerful tool in image analysis and data processing. The theoretical aspects of the method are presented, and its validity has been demonstrated using computer generated holograms and images simulations of microscopic objects. (c) 2007 Elsevier B.V. All rights reserved.

MEMS-based incandescent microlamps for integrated optics applications

In this work we present the fabrication and operation of incandescent microlamps for integrated optics applications. This microlamp emits white and infrared light from a chromium resistor embedded in a free-standing silicon oxynitride (SiO(x)N(y)) cantilever that can be coupled to an optical waveguide. In fact, the chromium resistor is sandwiched between layers of SiO(x)N(y) that isolate it from the atmosphere, while electric current heats the resistor to incandescent temperatures. The same SiO(x)N(y) material used in the microlamp fabrication is also used to produce the optical waveguides to allow a monolithic integration of light source and optical circuit. Front-side bulk micromachining of the silicon substrate in potassium hydroxide (KOH) solution is used to fabricate the cantilevers that thermally isolate the resistors from the substrate, thus reducing the heat transfer and the current required to light the lamp.

Experimental study of the quantum driven pendulum and its classical analog in atom optics

We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck’s constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Molecular cocrystals of carboxylic acids. XXVII - An investigation into the use of triphenylphosphine oxide cocrystals for non-linear optics: the crystal structure of the adduct of triphenylphosphine oxide with N-methylpyrrole-2-carboxylic acid

Four adducts of triphenylphosphine oxide with aromatic carboxylic acids have been synthesized and tested for second-order non-linear optical properties. These were with N-methylpyrrole-2-carboxylic acid (I), indole-2-carboxylic acid (2), 3-dimethylaminobenzoic acid (3), and thiophen-2-carboxylic acid (4). Compound (1) produced clear, colourless crystals (space group P2(1)2(1)2(1) With a 9.892(1), b 14.033(1), c 15.305(1) Angstrom, Z 4) which allowed the structure to be determined by X-ray diffraction.

Optics of the developing fish eye: comparisons of Matthiessen's ratio and the focal length of the lens in the black bream Acanthopagrus butcheri (Sparidae, Teleostei)

Matthiessen's ratio (distance from centre of lens to retina: lens radius) was measured in developing black bream, Acanthopagrus butcheri (Sparidae, Teleostei). The value decreased over the first 10 days post-hatch from 3.6 to 2.3 along the nasal and from four to 2.6 along temporal axis. Coincidentally, there was a decrease in the focal ratio of the lens (focal length:lens radius). Morphologically, the accommodatory retractor lentis muscle appeared to become functional between 10-12 days post-hatch. The results suggest that a higher focal ratio compensates for the relatively high Matthiessen's ratio brought about by constraints of small eye size during early development. Combined with differences in axial length, this provides a means for larval fish to focus images from different distances prior to the ability to accommodate. (C) 1999 Elsevier Science Ltd. All rights reserved.

Quantum chaos in atom optics

I shall discuss the quantum and classical dynamics of a class of nonlinear Hamiltonian systems. The discussion will be restricted to systems with one degree of freedom. Such systems cannot exhibit chaos, unless the Hamiltonians are time dependent. Thus we shall consider systems with a potential function that has a higher than quadratic dependence on the position and, furthermore, we shall allow the potential function to be a periodic function of time. This is the simplest class of Hamiltonian system that can exhibit chaotic dynamics. I shall show how such systems can be realized in atom optics, where very cord atoms interact with optical dipole potentials of a far-off resonance laser. Such systems are ideal for quantum chaos studies as (i) the energy of the atom is small and action scales are of the order of Planck's constant, (ii) the systems are almost perfectly isolated from the decohering effects of the environment and (iii) optical methods enable exquisite time dependent control of the mechanical potentials seen by the atoms.

Utilizing encoding in scalable linear optics quantum computing

We present a scheme which offers a significant reduction in the resources required to implement linear optics quantum computing. The scheme is a variation of the proposal of Knill, Laflamme and Milburn, and makes use of an incremental approach to the error encoding to boost probability of success.