Three-dimensional Bayesian optical diffusion tomography with experimental data

Reconstructions of a three-dimensional absorber embedded in a scattering medium by use of frequency domain measurements of the transmitted light in a single source-detector plane are presented. The reconstruction algorithm uses Bayesian regularization and iterative coordinate descent optimization, and it incorporates estimation of the detector noise level, the source-detector coupling coefficient, and the background diffusion coefficient in addition to the absorption image. The use of multiple modulation frequencies is also investigated. The results demonstrate the utility of this algorithm, the importance of a three-dimensional model, and that out-of-plane scattering permits recovery of three-dimensional features from measurements in a single plane.     

A note on rearrangement of Fourier series

We give an example of a permutation of integers which preserves all convergent Fourier series and makes some divergent Fourier series converge.     

The thermodynamics of elastic deformation—I: Equation of state for solids

The isobaric and isothermal volume derivatives of In B, In μ and In μ' are investigated, where B, μ and μ' are the isothermal bulk modulus and the two shear moduli, respectively, of a cubic crystal. In the case of the bulk modulus, the temperature independence of αB (where α is the volume thermal expansion) for a large number of materials, ensures that the derivatives are constant and approximately equal, while for the shear moduli, evidence is advanced that the isothermal derivatives are constant along an isotherm, but not along an isobar except at high temperatures near the melting point. The relationships satisfied by the bulk modulus enable the explicit temperature and pressure dependence of the molar volume, V, thermal expansion, and bulk modulus to be determined. The most adequate representation of the volume dependence of the Grüneisen parameter, γ, appears to be that γ/V is independent of volume between the Debye and melting temperatures.     

An optimal process of femtosecond laser cutting of NiTi shape memory alloy for fabrication of miniature devices

The mechanical properties of NiTi shape memory alloy (SMA) components are sensitive to thermal influence during laser machining. To make the femtosecond laser cutting of NiTi material meet the strict fabrication requirements for miniature SMA devices with high precision, complex patterns and minimal heat affected zone (HAZ) along with high throughput, we report an optimal process of sideways-movement path planning in this article. Femtosecond laser processing of NiTi SMA using the fundamental wavelength of 775 nm from a Ti:sapphire laser along with its second and third harmonic irradiations were systematically investigated. We observed that the main impact of ultrashort laser pulse induced air breakdown on materials processing was beam widening. The laser beam at fundamental wavelength suffered less widening than its harmonic wavelengths. Femtosecond laser machining of metals is still basically a thermal mechanism. High ablation rates at higher laser fluences causes significant recast formation, while lower fluences resulted in better cutting quality at the expense of efficiency. The optimal process involving the method of sideways-movement path planning enables recast-free high-precision features at higher laser fluences with better throughput.     

Effects of anisotropy,order parameter,and viscosity on translational self-diffusion in nematic liquid crystals

A theory developed for the translational diffusion in nematic liquids crystals shows a dependence on the viscosities, order parameter, and molecular structure. Theoretical results for self-diffusion in p-azoxyanisole at 125°C are D^{∥ = 4.3 × 10?6, D⊥ = 3.1 × 10?6 c2/s}, andD^∥/D^⊥ = 1.4.     

A two-stage iterative process for the synthesis of poly-oxazoles

[reaction: see text]. Methodology has been developed to prepare bis-oxazoles via a two-stage iterative process. The sequence begins with C(2)-chlorination of a lithiated oxazole using hexachloroethane. Generation of the C(2)-C(4)(') bond by S(N)Ar substitution with TosMIC anion, followed by conversion to the heterocycle in a one-pot reaction with glyoxylic acid monohydrate, affords the desired bis-oxazole in good yield and purity. The two-stage process allows for efficient synthesis of a tris-oxazole and the first iterative preparation of a tetra-oxazole.     

Asymmetric synthesis of cis-5-substituted pyrrolidine 2-phosphonates using metal carbenoid NH insertion and delta-amino beta-ketophosphonates

Cis-5-substituted pyrrolidine phosphonates, proline surrogates, are prepared by a highly stereoselective intramolecular metal carbenoid N-H insertion from a sulfinimine-derived delta-amino alpha-diazo beta-ketophosphonate. [reaction: see text]