Rotational bands in 169Re

Based on the systematic investigation of the data available for nuclei with A≥ 40, a Z ^1/3-dependence for the nuclear charge radii is shown to be superior to the generally accepted A ^1/3 law. A delicate scattering of data around R _c/Z ^1/3 is inferred as owing to the isospin effect and a linear dependence of R _c/Z ^1/3 on N/Z (or (N - Z)/2) is found. This inference is well supported by the microscopic Relativistic Continuum Hartree-Bogoliubov (RCHB) calculation conducted for the proton magic Ca, Ni, Zr, Sn and Pb isotopes including the exotic nuclei close to the neutron drip line. With the linear isospin dependence provided by the data and RCHB theory, a new isospin-dependent Z ^1/3 formula for the nuclear charge radii is proposed. Received: 23 September 2001 / Accepted: 21 January 2002     

Nonlinear spring model for frictional stick-slip motion

Frictional stick-slip dynamics is discussed using a model of one oscillator pulled by a nonlinear spring force. We focus our attention on the nonlinear spring parameter k₀. The dynamics of the model is carefully studied, both numerically and analytically. Our numerical investigation, which involves bifurcation diagrams, shows a rich spectrum of dynamical behavior including periodic, quasi-periodic and chaotic states. On the other hand, and for a good selection of parameters , the motion of the particle involves periodic stick-slip, erratic and intermittent motions, characterized by force fluctuations, and sliding. This study suggests that the transition between each of motion strongly depends on the nonlinear parameter k₀. The system also displays resonance at fractional frequencies of the oscillator.     

Equivalence of some integrals and modulus of smoothness

Let f∈C(R). We are interested in lower and upper bounds of the integrals

     

In-situ TiC particle reinforced Ti–Al matrix composites: Powder preparation by mechanical alloying and Selective Laser Melting behavior

Mechanical alloying of Ti–Al–graphite elemental powder mixture was performed to synthesize nanocomposite powder with Ti(Al) solid solution matrix reinforced by in-situ formed TiC particles. The evolutions in phases, microstructures, and compositions of milled powders with the applied milling times were investigated. It showed that with increasing the milling time, the starting irregularly shaped powder underwent a successive change in its morphology from a flattened shape (10 h) to a highly coarsened spherical one (15 h) and, eventually, to a fine, equiaxed and uniform one (above 25 h). The prepared TiC/Ti(Al) composite powder was nanocrystalline, with the estimated average crystallite size of 12 nm and of 7 nm for Ti(Al) and TiC, respectively. Formation mechanisms behind the microstructural development of powders were elucidated. The Ti(Al) solid solution is formed through a gradual and progressive solution of Al into Ti lattice. The formation of TiC is through an abrupt, exothermic, and self-sustaining reaction between Ti and C elements. Selective Laser Melting (SLM) of as-prepared TiC/Ti(Al) composite powder was performed. The TiC particle reinforced TiAl₃ (a major phase) and Ti₃AlC₂ (a minor phase) matrix composite part was obtained after SLM. Although a slight grain growth occurred as relative to as-milled powder, the SLM processed composites still exhibited a refined microstructure.     

Shape memory effect of thermoplastic segmented polyurethanes with self-complementary quadruple hydrogen bonding in soft segments

This paper describes the fact that a kind of thermoplastic shape memory polyurethane with self-complementary quadruple hydrogen bonding units in soft segments can present a significant shape memory effect under the usually used thermodynamic programming condition. Compared with the control sample, it was observed that the introduction of self-complementary quadruple hydrogen bonding into soft segments increases the glass transition temperature from 28.3 ^° C to 73.3 ^° C. Therefore, the temporary deformation can be fixed well after cooling at room temperature; subsequently thermal responsive shape memory recovery can be triggered by heating up to 86 ^° C. The immediate shape recovery ratio and shape fixity ratio can be 95.8% and 95.9%. Even after 24 hours relaxation for the stretched films, the corresponding R_r and R_f can be 94% and 60%. In contrast, the sample without quadruple hydrogen bonding shows that the elasticity and the deformation cannot be fixed after 24 hours relaxation. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.     

Multicyclicity of unbounded normal operators and polynomial approximation in C

A remarkable and much cited result of Bram [J. Bram, Subnormal operators, Duke Math. J. 22 (1955) 75-94] shows that a star-cyclic bounded normal operator in a separable Hilbert space has a cyclic vector. If, in addition, the operator is multiplication by the variable in a space L²(m) (not only unitarily equivalent to it), then it has a cyclic vector in L^∞(m). We extend Bram's result to the case of a general unbounded normal operator, implying by this that the (classical) multiplicity and the multicyclicity of the operator (cf. [N.K. Nikolski, Operators, Functions and Systems: An Easy Reading, vol. 2, Math. Surveys Monogr., vol. 93, Amer. Math. Soc., Providence, 2002]) coincide. It follows that if m is a sigma-finite Borel measure on C (possibly with noncompact support), then there is a nonnegative finite Borel measure τ equivalent to m and such that L²(C,τ) is the norm-closure of the polynomials in z.     

Chemical degradation of crosslinked ethylene-propylene-diene rubber in an acidic environment. Part II. Effect of peroxide crosslinking in the presence of a coagent

An investigation on the time-dependent chemical degradation of ethylene-propylene diene rubber containing 5-ethylidene-2-norbornene as diene cured by peroxide crosslinking in the presence of a coagent in an acidic environment (20% Cr/H₂SO₄) has been made. Two types of rubber, with comparable monomer composition, but having significant differences in molar mass and levels of long chain branching were tested. Dicumyl peroxide and triallylcyanurate under similar conditions were used for curing the rubbers. The molecular mechanisms of chemical degradation at the surface were studied using X-ray photoelectron spectroscopy and attenuated total reflectance Fourier transform infrared spectroscopy, which demonstrate that several oxygenated species evolve during exposure. The primary process of degradation is hydrolytic attack on the crosslink sites, which is manifested by a decrease in crosslink density. The surface degradation is found to be strong enough to alter the bulk mechanical properties as observed by the change in retention in tensile strength, elongation at break, modulus at 50% elongation and, the change in micro-hardness. Retention in modulus at 50% elongation is found to follow a negative linear correlation with decrease in crosslink density. With higher molar mass and level of long chain branching more crosslinking occurs and thus comparatively more hydrolytic attack ensues. Scanning electron microscopy shows that the surface topography is significantly altered upon exposure and supports the notion of the dependence of degradation on the crosslinking density of the samples. Importantly, the coagent used in this study is shown to enhance the chemical degradation through formation of weaker sites for hydrolysis. The results also show that upon prolonged exposure the resulting oxygenated species tend to combine with each other.     

Confinement-induced instability and adhesive failure between dissimilar thin elastic films

When two thin soft elastomeric films are separated from each other, an elastic instability develops at the interface. Although similar instability develops for the case of a soft film separating from a rigid adherent, there are important differences in the two cases. For the single-film case, the wavelength of instability is independent of any material properties of the system, and it scales only with thickness of the film. For the two-film case, a co-operative instability mode develops, which is a non-linear function of the thicknesses and the elastic moduli of both films. We investigate the development of such instability by energy minimization procedures. Understanding the nature of this instability is important, as it affects the adhesive compliance of the system and thus the energy release rate in the debonding of soft interfaces.     

Surface-functionalized nanoparticles with liquid-like behavior: The role of the constituent components

Ionically modified silica nanoparticles with large counter anions (sulfonate, isostearate) at two silica volume fractions (13 and 27%) form a viscous fluid and a glass but not crystalline solids. Dielectric spectroscopy, Brillouin scattering and shear rheometry were employed to investigate these new nanoparticle-based fluids. The glass transition temperature and hence the local dynamics are governed by the large counter anions, whereas the flow properties can be controlled by the spatial correlation between the nanoparticles, e.g. by tuning the volume fraction of hard cores and local interactions between segments in the soft corona. Liquid-like ordering of the cores was revealed by X-ray scattering and found to influence significantly the macroscopic flow properties of these salts.     

New information on the T1/2 = 47 s isomer in the 136I nucleus

The ¹³⁶I nucleus, populated in the spontaneous fission of ²⁴⁸Cm, was studied by means of prompt γ-ray spectroscopy using the EUROGAM2 array. The observation in this work of the 42.6keV prompt-γ, M1 + E2 transition de-exciting the 7^- level in ¹³⁶I indicates that this level, interpreted as the configuration, does not correspond to the T = 47s, β-decaying isomer in ¹³⁶I. The isomer is placed 42.6keV below the 7^- level. It has spin 6^- and is interpreted as the configuration. This and other members of both multiplets can be reproduced properly only if one assumes that the πd_5/2 orbital in ¹³⁶I is located 400keV lower than in ¹³³Sb. Possible mechanisms causing this effect are discussed.