Vacuum birefringence in strong magnetic fields: (I) Photon polarization tensor with all the Landau levels

Photons propagating in strong magnetic fields are subject to a phenomenon called the “vacuum birefringence” where refractive indices of two physical modes both deviate from unity and are different from each other. We compute the vacuum polarization tensor of a photon in a static and homogeneous magnetic field by utilizing Schwinger’s proper-time method, and obtain a series representation as a result of double integrals analytically performed with respect to proper-time variables. The outcome is expressed in terms of an infinite sum of known functions which is plausibly interpreted as summation over all the Landau levels of fermions. Each contribution from infinitely many Landau levels yields a kinematical condition above which the contribution has an imaginary part. This indicates decay of a sufficiently energetic photon into a fermion–antifermion pair with corresponding Landau level indices. Since we do not resort to any approximation, our result is applicable to the calculation of refractive indices in the whole kinematical region of a photon momentum and in any magnitude of the external magnetic field.     

Good point methods for computing prices and sensitivities of multi-asset European style options

Using number-theoretic methods, we investigate low-discrepancy sequences and weighted-sum estimators which outperform standard low-discrepancy techniques for pricing multi-asset European options on up to 5 underlying factors. The sequences used are simpler to implement than most low-discrepancy sequences, and computation time is considerably faster.     

Improved Compatibility of Styrene-Maleic Anhydride Copolymer/Polyethylene Blends Through Reactive Mixing

Abstract

To improve the compatibility of styrene-maleic anhydride copolymer/low density polyethylene (SMA/LDPE) blends, LDPE grafted with 2-hydroxyethyl methacrylate-isophorone diisocyanate (LDPE-g-HI) was prepared and blended with SMA of which anhydride was converted to carboxylic acid (SMAAc). The infrared spectra of LDPE-g-HI established the presence of isocyanate group. In the blend morphology, some adhesions between the two phases and much finer dispersions were observed in the SMAAc/LDPE-g-HI blends, indicating that chemical reactions took place during the melt blending. The lower heat capacity change at the glass transition temperature demonstrated that chemical bonds were produced in the SMAAc/LDPE-g-HI blends. From the results of the rheological test, it was found that strong positive deviation from the mixing rule occurred in viscosity for the SMAAc/LDPE-g-HI blends, concerning with good adhesion and finer dispersions. In the measurement of tensile property, the improved mechanical properties for the SMAAc/LDPE-g-HI blends were shown.     

DYE SENSITIZED TITANIA PHOTOVOLTAIC CELLS ON FLEXIBLE SUBSTRATES—CONCEPT TO COMMERCIALIZATION

ABSTRACT

Methods have been found for sintering titania nanoparticles at low temperature, e.g., <150°C, and for rapid sensitization of the sintered particles. This discovery means that dye-sensitized, titania solar cells can be made on flexible substrates, such as poly(ethylene terephthalate), in a continuous roll-to-roll manufacturing process. The ability to produce solar cells in a continuous fashion should substantially lower the cost of the cells compared to batch processed, on-glass cells. The combined attributes of spectral sensitivity, flexibility, light weight, impact resistance and low cost should find utility a variety of handheld appliances in both indoor and outdoor situations. In its most advanced state of development, this technology would find application in off-grid power generation and thus provide the opportunity of bringing solar generated electricity to rural areas of the world.     

Simulation of two‐phase flow–body interaction problems using direct forcing/fictitious domain–level set method

In the present paper, a direct forcing/fictitious domain (DF/FD)–level set method is proposed to simulate the twophase flow–body interaction. The DF/FD does not sacrifice accuracy and robustness by employing a discrete δ (Dirac delta) function to transfer quantities between the Eulerian nodes and Lagrangian points explicitly as the immersed boundary method. The advantages of this approach are the simple concept, the easy implementation and the utilization of original governing equation without modification. The main idea is to combine DF/FD method with the level set method in the Cartesian coordinates. We present the results of a number of test cases to illustrate the effectiveness of the proposed method for single‐phase flow–body interaction problem and the two‐phase flows with a stationary body. Eventually, the simulations of various water entry problems have been conducted to validate the capability and the accuracy of the present method on solving the twophase flow–body interaction. Consequently, the present results are found to be in good agreement with those of previous studies. Copyright © 2013 John Wiley & Sons, Ltd.     

Experimental and numerical investigation of aramid fibre reinforced laminates subjected to low velocity impact

The low velocity impact performance of domestic aramid fibre reinforced laminates is investigated experimentally and numerically. Laminates with different thicknesses are impacted by drop-weight test machine under different impact energies. The time histories of impact force are recorded and ultrasonic C-scan technology is used to inspect the internal damage of the laminates. Numerical simulation is conducted using finite element method (FEM), taking into account both intralaminar and interlaminar damage. The intralaminar damage model is based on the continuum damage mechanics (CDM) approach, which consists of the strain-based Hashin failure criteria and the exponential damage evolution law, and considers the nonlinear shear behaviour of the material. The interlaminar damage is simulated by interface elements with cohesive zone model. The numerical results show good agreements with the experiments, thus verifying the validity of the presented numerical model.     

Film-forming characteristics and thermal stability of low viscosity benzoxazines derived from melamine

A novel class of low-viscosity benzoxazines has been synthesized from melamine and formaldehyde with phenol or bisphenol A. The striking feature of the class of benzoxazines is the subtle combination of their inherently low viscosity at room temperature, good film-forming characteristics and high chemical and thermal stability mainly due to the introduction of melamine into the network of the polymers. The structure of the benzoxazines has been confirmed by proton nuclear magnetic resonance spectroscopy and fourier transform infrared spectroscopy. Thermal properties of polybenzoxazine have been studied by differential scanning calorimetry, dynamic mechanical analysis and thermogravimetric analysis. Transparent polybenzoxazine films were easily obtained under solvent-free conditions, exhibiting significantly improved toughness compared to the conventional polybenzoxazines. Our research may open a new path for overcoming the present drawbacks of polybenzoxazines such as high brittleness, the difficulties in preparing films and poor processibility via tailoring the structures and properties of amine in the benzoxazines.     

Low dose measurement with thick gate oxide MOSFETs

The low dose limit and the accuracy of high sensitivity MOS ionizing radiation dosimeters fabricated at LAAS-CNRS are investigated.     

Optimal control for reinitialization in finite element level set methods

A new optimal control problem that incorporates the residual of the Eikonal equation into its objective is presented. The formulation of the state equation is based on the level set transport equation but extended by an additional source term, correcting the solution so as to minimize the objective functional. The method enforces the constraint so that the interface cannot be displaced at least in the continuous setting. The system of first‐order optimality conditions is derived, linearized, and solved numerically. The control also prevents numerical instabilities, so that no additional stabilization techniques are required. This approach offers the flexibility to include other desired design criteria into the objective functional. The methodology is evaluated numerically in three different examples and compared with other PDE‐based reinitialization techniques. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximum likelihood estimation for second level fMRI data analysis with expectation trust region algorithm

The trust region method which originated from the Levenberg–Marquardt (LM) algorithm for mixed effect model estimation are considered in the context of second level functional magnetic resonance imaging (fMRI) data analysis. We first present the mathematical and optimization details of the method for the mixed effect model analysis, then we compare the proposed methods with the conventional expectation-maximization (EM) algorithm based on a series of datasets (synthetic and real human fMRI datasets). From simulation studies, we found a higher damping factor for the LM algorithm is better than lower damping factor for the fMRI data analysis. More importantly, in most cases, the expectation trust region algorithm is superior to the EM algorithm in terms of accuracy if the random effect variance is large. We also compare these algorithms on real human datasets which comprise repeated measures of fMRI in phased-encoded and random block experiment designs. We observed that the proposed method is faster in computation and robust to Gaussian noise for the fMRI analysis. The advantages and limitations of the suggested methods are discussed.