Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems

We construct and analyze a mixed finite volume method on quadrilateral grids for elliptic problems written as a system of two first order PDEs in the state variable (e.g., pressure) and its flux (e.g., Darcy velocity). An important point is that no staggered grids or covolumes are used to stabilize the system. Only a single primary grid system is adopted, and the degrees of freedom are imposed on the interfaces. The approximate flux is sought in the lowest-order Raviart-Thomas space and the pressure field in the rotated- nonconforming space. Furthermore, we demonstrate that the present finite volume method can be interpreted as a rotated- nonconforming finite element method for the pressure with a simple local recovery of flux. Numerical results are presented for a variety of problems which confirm the usefulness and effectiveness of the method.

     

Compact Einstein warped product spaces with nonpositive scalar curvature

We study Einstein warped product spaces. As a result, we prove the following: if is an Einstein warped product space with nonpositive scalar curvature and compact base, then is simply a Riemannian product space.

     

Injection locked multi-section gain-coupled dual mode DFB laser for terahertz generation

A dual mode multi-section gain-coupled distributed feedback laser with tunable mode spacing is subharmonically injection locked at 0.315 THz. The injected signal consists of an optical comb with harmonics 35 GHz apart and a bandwidth of approximately 1.9 THz. The optical comb is a result of strong four-wave mixing in a highly-nonlinear dispersion-shifted fiber. In order to observe locking of the multi-section laser, the output is optically downconverted to RF frequencies using the same optical comb. The locked multi-section DFB laser is a coherent and tunable optical source suitable for continuous-wave terahertz generation systems.     

Oil Migration in Chocolate

Oil migration in filled chocolates limits shelf life due to texture changes and loss of visual appeal. Spatial and temporal oil concentration changes of a two-layer chocolate and peanut butter filling system, which models a filled chocolate, were monitored by magnetic resonance imaging. Formulations of chocolate varied with respect to particle size, milk fat content and emulsifier level. Sorption-time experimental data was used to establish the best fit diffusion coefficient for a Fickian diffusion model. On the basis of the comparison of spatial experimental data to the model, Fickian diffusion alone does not account for oil migration. Authors' address: Michael J. McCarthy, Department of Food Science and Technology, University of California, One Shields Avenue, Davis, CA 95616, USA     

Frequency domain optical tomography using a conjugate gradient method without line search

A conjugate gradient method without line search (CGMWLS) is presented. This method is used to retrieve the local maps of absorption and scattering coefficients inside the tissue-like test medium, with the synthetic data. The forward problem is solved with a discrete-ordinates finite-difference method based on the frequency domain formulation of radiative transfer equation. The inversion results demonstrate that the CGMWLS can retrieve simultaneously the spatial distributions of optical properties inside the medium within a reasonable accuracy, by reducing cross-talk between absorption and scattering coefficients.     

Evaluation of elastic modulus of cantilever beam by TA-ESPI

The paper proposes an evaluation technique for the elastic modulus of a cantilever beam by vibration analysis based on time average electronic speckle pattern interferometry (TA-ESPI) and Euler-Bernoulli equation. General approaches for the measurement of elastic modulus of a thin film are the Nano indentation test, Buldge test, Micro-tensile test, and so on. They each have strength and weakness in the preparation of the test specimen and the analysis of experimental results. ESPI is a type of laser speckle interferometry technique offering non-contact, high-resolution and whole-field measurement. The technique is a common measurement method for vibration mode visualization and surface displacement. Whole-field vibration mode shape (surface displacement distribution) at resonance frequency can be visualized by ESPI. And the maximum surface displacement distribution from ESPI can be used to find the resonance frequency for each vibration mode shape. And the elastic modules of a test material can be easily estimated from the measured resonance frequency and Euler-Bernoulli equation. The TA-ESPI vibration analysis technique can be used to find the elastic modulus of a material requiring simple preparation process and analysis.     

Shift-tolerance Property of Optical Security System using Phase-based Virtual Image

The shift-tolerance property of the encrypted image or the Fourier decrypting key in the Fourier space is proposed based on a phase-encoded virtual image. The encrypted data is obtained by the Fourier transform of the product of a phase-encoded virtual image to camouflage the original one and a random phase image. Therefore, even if unauthorized users analyze the encrypted image, they cannot reconstruct the required image. This virtual image protects the original one from being counterfeited and from unauthorized access. We demonstrate the robustness to data loss and shift of the encrypted data or the Fourier decrypting key in the proposed decryption technique using an interferometer.     

Quantum Dynamics of Systems Connected by a Canonical Transformation

Quantum Hamiltonian systems corresponding to classical systems related by a general canonical transformation are considered. The differential equation to find the unitary operator, which corresponds to the canonical transformation and connects quantum states of the original and transformed systems, is obtained. The propagator associated with their wave functions is found by the unitary operator. Quantum systems related by a linear canonical point transformation are analyzed. The results are tested by finding the wave functions of the under-, critical-, and over-damped harmonic oscillator from the wave functions of the harmonic oscillator, free-particle system, and negative harmonic potential system, using the unitary operator to connect them, respectively.