A regularization of nonlinear diffusion equations in a multiresolution framework

We develop a regularization technique for Perona–Malik diffusion equations that relies on multiresolution techniques. The main result of this paper is to show that the chosen discretization overcomes the ill posedness of the nonlinear Perona–Malik model. The resulting algorithm is tested and the results are compared with pixel‐based methods. Copyright © 2007 John Wiley & Sons, Ltd.     

导引场下电磁泵浦自由电子激光的非线性理论

本文以Vlasov-Maxwell方程组为基础,用非线性动力学理论研究了存在导引场情况下电磁波泵浦的自由电子激光器的作用机制,导出了线性及非线性色散关系式,求出了非线性不稳定性增长率和自由电子激光的能量转换效率.结果表明,只要合理地选择参量条件,附加导引场可以大大提高自由电子激光的增长率和能量转换效率.     

Optical technique for classification, recognition and identification of obscured objects

The capability to classify, recognize and to identify objects from spatially low resolution images has high significance in security related applications especially in a case that recognition of camouflaged object is required.In this paper we present a novel approach in which the scenery containing obscured objects which we wish to classify, recognize or identify is illuminated by spatially coherent beam (e.g. laser) and therefore secondary speckles pattern is reflected from the objects. By special image processing algorithm developed for this research and which is basically based upon temporal tracking of the random speckle pattern one may extract the temporal signature of the object. And right after, to use it for its classification (e.g. its separation from the other objects in the scenery), its recognition and identification even in a case that the imager provides poor spatial resolution that by itself does not allow doing the specified detection related operations.     

Novel long chain unsaturated diisocyanate from fatty acid: Synthesis,characterization, and application in bio‐based polyurethane

A novel long chain linear unsaturated terminal diisocyanate, 1,16‐diisocyanatohexadec‐8‐ene (HDEDI) was synthesized from oleic acid via Curtius rearrangement. Its chemical structure was identified by FTIR, ¹H NMR, ¹³C NMR, and HRMS. This diisocyanate was used as a starting material for the preparation of entirely bio‐based polyurethanes (PUs) by reacting it with canola diol and canola polyol, respectively. The physical properties and crystalline structure of the PUs prepared from this diisocyanate were compared to their counterparts prepared from similar fatty acid‐derived diisocyanate, 1,7‐heptamethylene diisocyanate (HPMDI). The HDEDI based PUs demonstrated various different properties compared to those of HPMDI based PUs. For example, HDEDI based PUs exhibited a triclinic crystal form; whereas HPMDI based PUs exhibited a hexagonal crystal lattice. In addition, canola polyol‐HDEDI PU demonstrated a higher tensile strength at break than that of canola polyol‐HPMDI, attributed to the higher degree of hydrogen bonding associated with the former sample. Nevertheless, lower Young's modulus and higher elongation in canola polyol‐HDEDI PU were obtained because of the flexibility of the long chain introduced by the HDEDI diisocyanate. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 3302–3310, 2010     

Highly refractive polymer resin derived from sulfur‐containing aromatic acrylate

New sulfur‐containing polymers with high‐refractive indices and low birefringences have been developed as UV‐curable high‐refractive polymer resins. The polymers derived from 2,7‐bis[(2‐acryloylethyl)sulfanyl]thianthrene (2,7‐BAST) and 4,4′‐bis[(acryloyloxyethylthio)diphenylsulfide (4,4′‐BADS) were prepared by photopolymerization under UV irradiation. Transparent UV‐cured films were obtained in both cases. Both polymers showed good thermal stability, such as a 5% weight‐loss temperature at 355 °C under nitrogen and glass transition temperatures (T_g) in the range of 94–143 °C. They also showed high‐refractive indices of 1.6531 and 1.6645 at 632.8 nm and low birefringences of 0.0039 and 0.0069 in addition to high transparency in the visible region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2604–2609, 2010     

Three-photon excited PL spectroscopy and photo-generated Frenkel defects in wide-bandgap layered CdI2 semiconductors

We performed a three-photon excitation nonlinear photoluminescence (PL) spectroscopy in single crystals of wide-bandgap semiconductors (WBSs). The crystal temperature (TL)-dependent PL emission intensity (IPL) excited with different excitation power density (P) was measured. The PL emissions showed characteristics IPL with their maxima at around 520 nm. The IPL might be due to the presence of the photo-generated Frenkel defects (FDs) in WBSs. A detailed analysis of the PL spectra showed a third-order power law dependence of the maximum IPL on P for all the crystal temperature TL. The IPL was found to increase with decreasing TL. The results demonstrated the existence of the self-trapped excitons resulting from the presence of the FDs in the crystals.     

Diffusion Processes Associated with Nonlinear Evolution Equations for Signed Measures

In this paper, we explain how to associate a nonlinear martingale problem with some nonlinear parabolic evolution equations starting at bounded signed measures. Our approach generalizes the classical link made when the initial condition is a probability measure. It consists in giving to each sample-path a signed weight which depends on the initial position. After dealing with the classical McKean-Vlasov equation as an introductory example, we are interested in a viscous scalar conservation law. We prove uniqueness for the corresponding nonlinear martingale problem and then obtain existence thanks to a propagation of chaos result for a system of weakly interacting diffusion processes. Last, we study the behavior of the associated fluctuations and present numerical results which confirm the theoretical rate of convergence.     

Deformed soliton,breather,and rogue wave solutions of an inhomogeneous nonlinear Schrdinger equation

We use the 1-fold Darboux transformation (DT) of an inhomogeneous nonlinear Schro¨dinger equation (INLSE) to construct the deformed-soliton, breather, and rogue wave solutions explicitly. Furthermore, the obtained first-order deformed rogue wave solution, which is derived from the deformed breather solution through the Taylor expansion, is different from the known rogue wave solution of the nonlinear Schro¨dinger equation (NLSE). The effect of inhomogeneity is fully reflected in the variable height of the deformed soliton and the curved background of the deformed breather and rogue wave. By suitably adjusting the physical parameter, we show that a desired shape of the rogue wave can be generated. In particular, the newly constructed rogue wave can be reduced to the corresponding rogue wave of the nonlinear Schro¨dinger equation under a suitable parametric condition.     

Dynamics of surface dipole and tripole solitons in nonlocal nonlinear media with optical lattice field

We find the existence conditions for stationary dipole and tripole surface solitons formed at the interface of a nonlocal nonlinear medium and a lattice with linearly modulated frequency. We investigate how the degree of nonlocality, the depth, and the modulation frequency of the optical lattice field affect on the existence of the surface solitons and their dynamics. The relationship between the power and the model parameters is identified. The stability of the surface dipole and tripole solitons is numerically investigated.