Fractional vortices and composite domain walls in flat nanomagnets

We provide a simple explanation of complex magnetic patterns observed in ferromagnetic nanostructures. To this end we identify elementary topological defects in the field of magnetization: ordinary vortices in the bulk and vortices with half-integer winding numbers confined to the edge. Domain walls found in experiments and numerical simulations in strips and rings are composite objects containing two or more of the elementary defects.     

Characterization of the signature of subwavelength variation from far-field irradiance

The dynamic signature of the subwavelength variation of a slit is shown to be determinable from far-field irradiance with a precision of better than 1 nm. One can increase the efficiency of measurement of the subwavelength's signature by adjusting the detection width over which the subwavelength variation is detected. The subwavelength variation of a rectangular aperture was also examined to show the general feasibility.     

1.5-mum emissions from laser-diode-pumped Nd-doped microchip solid-state lasers

1.5-mum emissions from Nd:YAG, Nd:YVO(4), and LiNdP(4) O>(12) microchip lasers pumped by laser diodes have been observed. These coherent emissions are attributed to the effect of high-energy modified lattice vibration owing to the existence of Nd ions as well as to stimulated intracavity Raman scattering enhanced by the microchip configuration. A four-wave mixing process involving two lasing fields and a Stokes field was identified as the generator of new adjacent 1.5-mu;m emission.     

Effects of packing density on the gas-transport properties of poly(phenolphthalein phthalate)s

The gas transport and other pertinent properties of three aromatic polyesters, made by reacting phenolphthalein with terephthaloyl chloride (PPha-tere), 50:50 terephthaloyl and isophthaloyl chlorides (PPha-50:50), and isophthaloyl chloride (PPha-iso), are reported. The glass transition temperatures of PPha-tere, PPha-50:50, and PPha-iso are 299, 279, and 249°C, respectively. Unexpectedly, the densities are 1.297, 1.298, and 1.304 g/cm³ in the same order; PPha-iso, therefore, has a higher packing density than PPha-tere. The permeability of PPha-tere to CO₂, CH₄, N₂, and O₂ is roughly 25% higher than that of PPha-50:50, and roughly 100% higher than that of PPha-iso. PPha-tere is roughly five times as permeable as polysulfone but has slightly higher permselectivities for the above gases. On the other hand, the solubilities of each gas in these three aromatic polyesters are roughly the same, suggesting that the higher permeability of PPha-tere is the result of a much larger gas diffusivity in the polymer. It is shown here that the significant difference in gas-diffusivity is a manifestation of the effects of packing density on the transport properties of glassy polymers.     

Psi‐series method for equality of random trees and quadratic convolution recurrences

An unusual and surprising expansion of the form as , is derived for the probability p_n that two randomly chosen binary search trees are identical (in shape, hence in labels of all corresponding nodes). A quantity arising in the analysis of phylogenetic trees is also proved to have a similar asymptotic expansion. Our method of proof is new in the literature of discrete probability and the analysis of algorithms, and it is based on the logarithmic psi‐series expansions for nonlinear differential equations. Such an approach is very general and applicable to many other problems involving nonlinear differential equations; many examples are discussed in this article and several attractive phenomena are discovered.Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 67–108, 2014     

Synthesis and characterization of chitosan‐modified polymethyl methacrylate latex particles

Stable chitosan‐modified polymethyl methacrylate (PMMA) latex particles were prepared by using 2,2′‐azobis(2‐amidinopropane) dihydrochloride (V‐50) as the cationic initiator. The polymerization rate (R_p) is controlled by the V‐50 concentration ([V‐50]) and R_p is less sensitive to the chitosan concentration ([C]) used in the synthesis work. The reaction system follows Smith–Ewart Case III kinetics due to the relatively large particles produced. The zeta potential data show that the isoelectric point (pI) of the latex particles is 10.7. The amounts of V‐50 (C_V‐50) and chitosan (C_c) ultimately incorporated into the particles correlate reasonably well with [V‐50] and [C], respectively. At pH 7, the quantity of the negatively charged bovine serum albumin (BSA, pI = 4.8) adsorbed on the positively charged chitosan‐free particles (Q) via the electrostatic interaction increases with increasing C_V‐50. However, Q is relatively insensitive to changes in C_c. This result implies that only the outermost region of the hairy chitosan‐modified particles is available for adsorption of the relatively large protein species. Colloidal stability shows a significant influence on the BSA adsorption process. © 1999 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 37: 1489–1499, 1999     

Hydrolytic stability and high Tg of polyimides derived from the novel 4,9‐bis[4‐(3,4‐dicarboxyphenoxy)phenyl]‐diamantane dianhydride

This work reports the synthesis and characterization of diamantane‐based polyimides obtained from 4,9‐bis[4(3,4‐dicarboxyphenoxy)phenyl]diamantane dianhydride and various aromatic diamines. Interestingly, the diamantane‐based polyimides were very stable to hydrolysis. This novel polyimide exhibits a low dielectric constant (2.65–2.77), low moisture absorption (<0.67%), good solubility, high T_g and unusually high thermal stability. Dynamic mechanical analysis (DMA) reveals that the diamantane‐based polyimides have high T_g ranging from 281 to 379 °C. The high‐temperature β₁ subglass transition around 285 °C was observed in polyimide 6a derived from 2,2′‐bis(trifluoromethyl)benzidine. This class of novel diamantane‐based polyimide is very promising for electronic applications, because of its good mechanical properties, good thermal stability, low dielectric constant, excellent hydrolytic resistance, and low moisture absorption. © 2009 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 47: 1673–1684, 2009     

Multiple-mode diffusion waves for viscous nonstrictly hyperbolic conservation laws

We study the large-time behaviors of solutions of viscous conservation laws whose inviscid part is a nonstrictly hyperbolic system. The initial data considered here is a perturbation of a constant state. It is shown that the solutions converge to single-mode diffusion waves in directions of strictly hyperbolic fields, and to multiple-mode diffusion waves in directions of nonstrictly hyperbolic fields. The multiple-mode diffusion waves, which are the new elements here, are the self-similar solutions of the viscous conservation laws projected to the nonstrictly hyperbolic fields, with the nonlinear fluxes replaced by their quadratic parts. The convergence rate to these diffusion waves isO(t ^–3/4+1/2p+) inL ^p , 1p, with >0 being arbitrarily small.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38