WIDE RANGE DETECTOR USING PARABOLIC CYLINDRICAL MIRROR FOR THz APPLICATIONS

A new, wide-band, high-speed and high-sensitivity THz detector has been developed. The prototype detector consists of a parabolic cylindrical mirror, a long wire antenna and a Schottky barrier diode. Direct detection measurements have shown a stable sensitivity of 150 ± 50 V/W for 1–2 THz without any adjustments. The long wire antenna was fixed at the focus of parabolic cylindrical mirror then it has been realized less operation steps, easy coupling to the external THz signals and a dramatic enhancement in the practicality of this system. The optically polished mirror and frosted surface one showed comparable sensitivities, thus easy polishing and less cost mirror fabrication can be applied for this system. The radiation pattern showed a maximum radiation angle of approximately 23° with its dominant main lobe, which was attributed to the wire antenna character and confirmed good agreements with classical antenna theory.     

Numerical analysis of a model of cure process for composites

We consider a composite material composed of fibres included in a resin which becomes solid when it is heated up (reaction of reticulation). The mathematical modelling of the cure process is given by a kinetic equation describing the evolution of the reaction of reticulation coupled with the heat equation. In this paper, we are interested in the computation of approximate solutions. We propose a family of discretized problems depending on two parameters (β₁, β₂) ε [0, 1]² which split the linear and non‐ linear terms in implicit and explicit parts. We prove the stability and convergence of the discretization for any (β₁, β₂) ε [½, 1 ] × [0, 1]. We present also some numerical results. Copyright © 2006 John Wiley & Sons, Ltd.     

Nonlinear degenerate parabolic equations with Neumann boundary condition

We study Neumann problem for a class of nonlinear degenerate parabolic PDE. A typical nonlinearity we have in mind is, for instance, β(u)=−1/u(u>0). We establish a necessary and sufficient condition on given data for existence of solution.     

The stress driven instability in elastic crystals: Mathematical models and physical manifestations

Summary Equilibrium equations and stability conditions for the simple deformable elastic body are derived by means of considering a minimum of the static energy principle. The energy is supposed to be sum of the volume (elastic) and the surface terms. The ability to change relative positions of different material particles is taken into account, and appropriate natural definitions of the first and second variations of the energy are introduced and calculated explicitly. Considering the case of negligible magnitude of the surface tension, we establish that an equilibrium state of a nonhydrostatically stressed simple elastic body (of any physically reasonable elastic energy potential and of any symmetry) possessing any small smooth part of free surface is always unstable with respect to relative transfer of the material particles along the surface. Surface tension suppresses the mentioned instability with respect to sufficiently short disturbances of the boundary surface and thus can probably provide local smoothness of the equilibrium shape of the crystal. We derive explicit formulas for critical wavelength for the simplest models of the internal and surface energies and for the simplest equilibrium configurations. We also formulate the simplest problem of mathematical physics, revealing peculiarities and difficulties of the problem of equilibrium shape of elastic crystals, and discuss possible manifestations of the above-mentioned instability in the problems of crystal growth, materials science, fracture, physical chemistry, and low-temperature physics.     

Local and non-local sources of airborne particulate pollution at Beijing--The ratio of Mg/Al as an element tracer for estimating the contributions of mineral aerosols from outside Beijing

A new element tracer technique has firstly been established to estimate the contributions of mineral aerosols from both inside and outside Beijing. The ratio of Mg/Al in aerosol is a feasible element tracer to distinguish between the sources of inside and outside Beijing. Mineral aerosol, inorganic pollution aerosol mainly as sulfate and nitrate, and organic aerosol are the major components of airborne particulates in Beijing, of which mineral aerosol accounted for 32%―67% of total suspended particles (TSP), 10%―70% of fine particles (PM2.5), and as high as 74% and 90% of TSP and PM2.5, respectively, in dust storm. The sources from outside Beijing contributed 62% (38%―86%) of the total mineral aerosols in TSP, 69% (52%―90%) in PM10, and 76% (59%―93%) in PM2.5 in spring, and 69% (52%―83%), 79% (52%―93%), and 45% (7%―79%) in TSP, PM10, and PM2.5, respectively, in winter, while only ～20% in summer and autumn. The sources from outside Beijing contributed as high as 97% during dust storm and were the dominant source of airborne particulates in Beijing. The contributions from outside Beijing in spring and winter are higher than those in summer, indicating clearly that it was related to the various meteorological factors.     

Comparative molecular field analysis (CoMFA) for phosphodiesterase (PDE) IV inhibitors

A comparative molecular field analysis (CoMFA) for phosphodiesterase (PDE) IV inhibitors has been performed to correlate their chemical structures with their observed biological activity. In this study, CoMFA model based on docking mode for active site of PDE IV can describe the relative change in magnitude of the steric and electrostatic fields as a function of the compounds. Pyridine N-oxide and pyridine group of each compound are aligned toward the metal ion in S2-sub pocket of PDE IV. The study provided a statistically valid model with good correlation and predictive power, and consequently we identified some key features that may be used to design new derivatives.     

Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

An $L^{\infty}$ Second Order Cartesian Method for 3D Anisotropic Interface Problems

A second order accurate method in the infinity norm is proposed for general three dimensional anisotropic elliptic interface problems in which the solution and its derivatives, the coefficients, and source terms all can have finite jumps across one or several arbitrary smooth interfaces. The method is based on the 2D finite element-finite difference (FE-FD) method but with substantial differences in method derivation, implementation, and convergence analysis. One of challenges is to derive 3D interface relations since there is no invariance anymore under coordinate system transforms for the partial differential equations and the jump conditions. A finite element discretization whose coefficient matrix is a symmetric semi-positive definite is used away from the interface; and the maximum preserving finite difference discretization whose coefficient matrix part is an M-matrix is constructed at irregular elements where the interface cuts through. We aim to get a sharp interface method that can have second order accuracy in the point-wise norm. We show the convergence analysis by splitting errors into several parts. Nontrivial numerical examples are presented to confirm the convergence analysis.     

On a double degenerate fourth-order parabolic equation

The existence of solutions to a fourth-order p-Laplacian equation with boundary degeneracy is studied. For the purpose of solving the corresponding non-degenerate (with respect to the coefficient of fourth-order term) regularized problem, a fourth-order semi-discrete elliptic problem with homogeneous boundary conditions is established and its existence and uniqueness are obtained by the functional minimization method. It follows that the approximate solutions of the non-degenerate parabolic problem are constructed and the corresponding existence and uniqueness are discovered by a limit procedure from the energy estimation method and a compactness argument. Finally, the existence and regularity of solutions for the problem with boundary degeneracy is obtained by using a regularization parameter vanishing limit.     

The Biological Effects of Forsythia Leaves Containing the Cyclic AMP Phosphodiesterase 4 Inhibitor Phillyrin

Forsythia fruit (Forsythia suspensa Vahl (Oleaceae)) is a common component of Kampo medicines for treating the common cold, influenza, and allergies. The main polyphenolic compounds in the leaves of F. suspensa are pinoresinol β-d-glucoside, phillyrin and forsythiaside, and their levels are higher in the leaves of the plant than in the fruit. It is known that polyphenolic compounds stimulate lipid catabolism in the liver and suppress dyslipidemia, thereby attenuating diet-induced obesity and polyphenolic anti-oxidants might attenuate obesity in animals consuming high-fat diets. Recently, phillyrin was reported as a novel cyclic AMP phosphodiesterase 4 (PDE4) inhibitor derived from forsythia fruit. It was expected that the leaves of F. suspensa might display anti-obesity effects and serve as a health food material. In this review, we summarized our studies on the biological effects of forsythia leaves containing phillyrin and other polyphenolic compounds, particularly against obesity, atopic dermatitis, and influenza A virus infection, and its potential as a phytoestrogen.