The uniform modulus of continuity of iterated Brownian motion

LetX be a Brownian motion defined on the line (withX(0)=0) and letY be an independent Brownian motion defined on the nonnegative real numbers. For allt0, we define theiterated Brownian motion (IBM),Z, by setting . In this paper we determine the exact uniform modulus of continuity of the process Z.Research supported by NSF grant DMS-9122242.     

Singularity spectrum of fractal signals from wavelet analysis: Exact results

The multifractal formalism for singular measures is revisited using the wavelet transform. For Bernoulli invariant measures of some expanding Markov maps, the generalized fractal dimensions are proved to be transition points for the scaling exponents of some partition functions defined from the wavelet transform modulus maxima. The generalization of this formalism to fractal signals is established for the class of distribution functions of these singular invariant measures. It is demonstrated that the Hausdorff dimensionD(h) of the set of singularities of Hölder exponenth can be directly determined from the wavelet transform modulus maxima. The singularity spectrum so obtained is shown to be not disturbed by the presence, in the signal, of a superimposed polynomial behavior of ordern, provided one uses an analyzing wavelet that possesses at leastN>n vanishing moments. However, it is shown that aC behavior generally induces a phase transition in theD(h) singularity spectrum that somewhat masks the weakest singularities. This phase transition actually depends on the numberN of vanishing moments of the analyzing wavelet; its observation is emphasized as a reliable experimental test for the existence of nonsingular behavior in the considered signal. These theoretical results are illustrated with numerical examples. They are likely to be valid for a large class of fractal functions as suggested by recent applications to fractional Brownian motions and turbulent velocity signals.     

Interaction of water with the regenerated cellulose membrane studied by DSC

One to three endothermal peaks atributted to melting of bulk and interfacial water were observed by DSC in the regenerated cellulose — water system. The profiles of thermal effects depend on water content, time of conditioning, film pretreatment and the conditions applied during the preceding freezing-thawing cycles. The occurrence might be deduced of melting-crystallisation processes. A large amount of non-freezable strongly bounded water was also detected. Although cellulose absorbs water quickly after immersion, the structural changes consisting on ordering of polymer fraction occur during further conditioning due to increase in strength of water binding. Using the membranes in the separation module at 90°C causes weakening of these bonds. Differences between interaction of particular cellulose films with water can be detected during the first, the second and the third heating. This revised version was published online in July 2006 with corrections to the Cover Date.     

Effect of molecular orientation distribution and crystallinity on the measurement of the crystal lattice modulus of nylon 6 by x-ray diffraction

The crystal lattice modulus of nylon 6 (-type) was measured by x-ray diffraction using nylon 6 films drawn up to five times. The measured crystal lattice modulus was 173–175 GPa for all specimens whose crystallinity and the Young's modulus were beyond 46% and 3.75 GPa, respectively. These results indicate that a state of homogenous stress can be achieved. In contrast, the values were scattered for the speciments whose crystallinity and Young's modulus are less than the above values. To study the origin, a numerical calculation of the crystal lattice modulus, as measured by x-ray diffraction, was carried out by considering effects on the orientation factors of molecular chains and crystallinity. In this calculation, a previously introduced model was employed, in which oriented crystalline layers are surrounded by oriented amorphous phases so that the strains of the two phases at the boundary are identical. The theoretical results calculated by the introduced model indicated that the crystal lattice modulus by x-ray diffraction is almost equal to the intrinsic crystal modulus if the morphology of the test specimen can be represented as a series model. In contrast, if a parallel model is more appropriate, the difference between the measured modulus and the intrinsic value can be pronounced. Such morphological dependence was found to be less pronounced with increasing high degree of molecular orientation and crystallinity.     

Underpotential deposition studies of copper on glassy carbon

Studies on the deposition and dissolution of copper from 0·5 M sulphuric acid solutions onto glassy carbon (GC) using potential sweep techniques indicated that an additional peak occurs at higher positive potentials than the bulk stripping peak. This peak is identified as due to the stripping of underpotential deposited (UPD) copper. Results of investigations on the effect of sweep rate, deposition potential and time of deposition on the peak characteristics of UPD and bulk deposited copper are also reported.     

Interaction of gas phase atomic hydrogen with Pt(111):Direct evidence for the formation of bulk hydrogen species

Employing hot tungsten filament to thermal dissociate molecular hydrogen,we generated gas phase atomic hydrogen under ultra-high vacuum(UHV)conditions and investigated its interaction with Pt(111) surface.Thermal desorption spectroscopy(TDS)results demonstrate that adsorption of molecular hy- drogen on Pt(111)forms surface Had species whereas adsorption of atomic hydrogen forms not only surface Had species but also bulk Had species.Bulk Had species is more thermal-unstable than surface Had species on Pt(111),suggesting that bulk Had species is more energetic.This kind of weakly- adsorbed bulk Had species might be the active hydrogen species in the Pt-catalyzed hydrogenation reactions.     

Mechanical properties and molecular mobility in oriented polyolefines

The static modulus of elasticity (E) and the correlation time of rotation ( _c ) of 2,-2,6,6-tetramethylpiperidine-1-oxyl are studied as a function of the temperature (210<T <350°K) for oriented films of isotactic polypropylene and polyethylene of high and low density.E and _c change both upon heating and polymer orientation; this result indicates that sample properties are influenced by the microstructure of the amorphous phase where probes are localized.     

Influence of Nucleation Agents Concentration on Crystallization Structure and Properties of Glass-ceramics

Deep color glass-ceramics is prepared by using gold tailings as the main raw material, and Cr2O3 is added as nucleation agent. Influence of different Cr2O3 additions on crystallization structure and properties of CaO-MgO-Al2O3-SiO2 glass-ceramics has been discussed so as to select optimum additions. DTA is employed to determine optimum crystallization and nucleation temperatures; XRD and SEM are used to characterize microstructure of each sample; and performance indexes, such as water absorption, bulk density, flexural strength and so on, are also determined. Experimental results show that when 3wt% Cr2O3 is introduced, fine glass-ceramics with diopside as the main crystal and Ca-Fe diopside as the second-crystal is obtained, and its corresponding performance indexes are as follows: water absorption 0.12%, bulk density 2.56 g/cm3, and flexural strength 70.01 Mpa.     

氢在钯单晶表面的解离与在体相的扩散

氢分子在金属表面的解离吸附与氢原子在金属体相的扩散是个典型的表面过程.前者在甲烷化及合成氨等基础化工反应中起着关键作用;后者常常导致金属材料的脆化与断裂,但过渡金属及其合金是安全和优良的储氢材料.因此,研究氢分子在金属表面的解离吸附与氢原子在金属体相的扩散,是多相催化与金属物理广泛感兴趣的课题,具有重要的理论和应用价值.本文采用分子动力学方法初步探讨了二者之间的关联.分子催化动力学为从微观层次上研究上述课题提供了一种理论方法.本文采用经过我们改进的半经验LEPS方法,计算了氢分子在Pd(100)和(110)晶面的解离和氢原子在钯表面与体相扩散的相互作用位能面,并根据计算结果探讨了其微观机理.     

NANOMECHANICAL MAPPING OF CARBON BLACK REINFORCED NATURAL RUBBER BY ATOMIC FORCE MICROSCOPY

Atomic force microscopy （AFM） has the advantage of obtaining mechanical properties as well as topographic information at the same time. By analyzing force-distance curves measured over two-dimensional area using Hertzian contact mechanics, Young＇s modulus mapping was obtained with nanometer-scale resolution. Furthermore, the sample deformation by the force exerted was also estimated from the force-distance curve analyses. We could thus reconstruct a real topographic image by incorporating apparent topographic image with deformation image. We applied this method to carbon black reinforced natural rubber to obtain Young＇s modulus distribution image together with reconstructed real topographic image. Then we were able to recognize three regions; rubber matrix, carbon black （or bound rubber） and intermediate regions. Though the existence of these regions had been investigated by pulsed nuclear magnetic resonance, this paper would be the first to report on the quantitative evaluation of the interfacial region in real space.