Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G ^∗(iν). The experimental data are available in the frequency window ν∈[ν_min,ν_max] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor h( n) = \fracG"( n)G￠(n)\eta( \nu) = \frac{G'( \nu )}{G'(\nu )} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G ^∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (G _k ,τ _k ,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).     

Coarsening of δ-Ni<Subscript>2</Subscript>Si precipitates in a Cu–Ni–Si alloy

The coarsening behavior of rod-shaped and spherical δ-Ni₂Si precipitates in a Cu–1.86 wt% Ni–0.45 wt% Si alloy during aging at 823–948 K has been investigated by measuring both precipitate size by transmission electron microscopy (TEM) and solute concentration in the Cu matrix by electrical resistivity. The rod-shaped δ precipitates have an elongated shape along 〈[`5] 5 8 \overline{5} 5 8 〉_m and a {110}_m habit-plane facet. The coarsening theory of a spherical precipitate in a ternary alloy developed by Kuehmann and Voorhees (KV) has been modified to a case of rod-shaped precipitates. The coarsening kinetics of average size of the rod-shaped and spherical δ precipitates with aging time t obey the t ^1/3 time law, as predicted by the modified KV theory. The kinetics of depletion of the supersaturation with t are coincident with the predicted t ^−1/3 time law. Application of the modified KV theory has enabled calculation of the energies of sphere, {110}_m and rod-end interfaces from the data on coarsening alone. The energy of the {110}_m interface having a high degree of coherency to the Cu matrix is estimated to be 0.4 J m⁻², the incoherent sphere-interface energy 0.6 J m⁻², and the rod-end interface energy 5.2 J m⁻².     

Response of a viscous liquid layer to pitching-and roll-excitation in zero-gravity environment

The response of a viscous liquid layer to pitching- and roll excitation has been determined. For a simplified analytical treatment the no-slip condition at the top and the bottom of the liquid column has been abandoned in the pitching case. The response of the free liquid surface displacement and the velocity distribution has been determined as a function of the reduced frequency ωa²/ν for various surface tension parameters σa/ρv². Due to viscosity the resonance amplitudes are finite and disappear for higher modes and shorter liquid layers. The velocity distribution, effective moment of inertia and effective damping was obtained for the liquid layer in roll excitation.     

Viscosity and supercooling of Fe-Cr (≤40 at % Cr) melts

We have studied the composition dependences of the kinematic viscosity (ν) and supercooling (Δt) of Fe-Cr melts at chromium contents of up to 40 at %. The results indicate that there is a minimum in viscosity at 5 at % Cr, a maximum at 12 at % Cr, and a sharp rise in the crystallization tendency of the solid solution in this composition range. The Δt(x) and ν(x) data obtained can be understood in terms of the composition dependence of the bonding energy, which is governed by the geometric and chemical short-range order in the atomic arrangement. Using a probabilistic approach to evaluation of various short-range order configurations and the experimental viscosity and supercooling data at chromium contents of 2.5 and 30 at %, we have calculated Δt(x) and ν(x) up to 40 at % Cr.     

Induction time approach to surface induced crystallization in polyethylene/poly (ɛ-caprolactone) melt

The surface induced crystallization of poly (ɛ-caprolactone) (PCL) on an ultra-high modulus polyethylene (PE) fibre was investigated using a new approach based on the induction timet _i. This approach allows estimation of the free energy difference function Δσ as it appears in the theory of heterogeneous nucleation. The classical approach based on the rate of heterogeneous nucleationl is not applicable to transcrystallization because the nucleation density at the fibre surface cannot be measured. A relationship betweenl andt _i is proposed and a theoretical justification is presented. Good agreement between the two approaches is obtained for a verification case where bothl andt _i can be determined. A transcrystalline growth rate study yields an estimate of the parameter σσ_e for PCL of 680 erg²cm⁻⁴. The maximum growth rateg ^* is also obtained. The results obtained indicate the influence of certain parameters on the appearance of transcrystallinity. It is also shown how the interfacial morphology can be controlled by the knowledge of the variations of the induction time with temperature.     

A modular integration and multiresolution framework for image interpretation

In this paper, we give a generalized formulation for a vision problem in the framework of modular integration and multiresolution. The developed framework is used to solve the high-level vision problem of scene interpretation. The formulation essentially involves the concept of reductionism and multiresolution, where the given vision taskν is broken down into simpler subtasksν ₁,ν ₂, …,ν _m. Moreover, instead of solving the vision taskν ^Ω =ν at the finest resolution Θ, we solve the synergetically coupled vision subtasks at coarser resolutions (Ω −N) for Θ ≥N>0 and use the results obtained at resolution (Θ −N) to solveν ^{Ω −N+1}, the vision task at resolution (Θ −N+1). Image interpretation is a two-phased analysis problem where some salient features or objects in an image are identified by segmenting the image and the objects in the segmented image are interpreted based on their spatial relationships. We present a solution to the joint segmentation and interpretation problem in the proposed generalized framework. For the interpretation part we exploit the Markov Random Field (MRF) based image interpretation scheme developed by Modestino and Zhang. Experimental results on both indoor and outdoor images are presented to validate the proposed framework.     

Hardness of metallic crystals

This paper presents a new formula for calculating the hardness of metallic crystals, resulted from the research on the critical grain size with stable dislocations. The formula is H = 6 kG/[π(1 − ν)e ^η ], where H is the hardness, k the coefficient, G the shear modulus, ν the Poisson’s ratio, η a function of the radius of an atom (r) and the electron density at the atom interface (n). The formula will not only be used to testify the critical grain size with stable dislocations, but also play an important role in the understanding of mechanical properties of nanocrystalline metals.     

Microstructure of a vacuum diffusion layer in the joint of Fe—Al alloy with low-carbon steel

On the interface of diffusively bonded Fe—16Al and Q235, we observe the formation of a well-pronounced layer formed by FeAl, Fe₃Al, and α-Fe(Al) solid solutions. This layer can decrease the diffusion activation energy (facilitating the diffusion of elements and, hence, accelerating its growth). The formation of the diffusion layer is preceded by a latent period t ₀ and its thickness x increases with time according to the parabolic law: x ² = 4.8·10⁴ exp[−133,020/(RT)](t−t ₀). Published in Fizyko-Khimichna Mekhanika Materialiv, Vol. 41, No. 5, pp. 74–78, September–October, 2005.     

The effects of native and light induced defects on optoelectronic properties of hydrogenated amorphous silicon–germanium (a-SiGe:H) alloy thin films

Effects of native and light induced defects states in hydrogenated amorphous silicon–germanium alloy thin films with different Ge concentrations have been investigated by using steady-state photoconductivity, dual beam photoconductivity (DBP), transmission spectroscopy and photothermal deflection spectroscopy (PDS) techniques. In the annealed state, sub-bandgap absorption spectra obtained from both PDS and DBP overlap very well at energies above 1.4 eV. However, differences in α (hν) spectrum exist in the lower energy part of absorption spectrum. The α (hν) value measured at 1.0 eV is the lowest for 10% Ge sample and increases gradually as Ge content of the sample increases. In the light soaked state, time dependence of photoconductivity decay obeys to t ^−x power law, where x changes from 0.30 to 0.60 for samples with low Ge content and 0.05–0.1 for samples with high Ge content. Correspondingly, the increase of the sub-bandgap absorption coefficient at lower energies obeys to t ^y power law, where y values are lower than the x value of the same sample. It can be inferred that sub-bandgap absorption and photoconductivity measurements are not controlled by the same set of defects created in the bandgap of alloys.     

Long term coarsening of γ′ precipitates in a Ni-base superalloy

The mechanical properties of a Ni-based superalloy strongly depend on the distribution and size of the precipitate particle γ′ phase: Ni₃(Al, Ti). Such particles grow during the initial heat treatment and it is very important to predict the kinetic growth owing to their technological application at high temperatures. In this work, we performed analysis of particle coarsening in IN-713C during long ageing times at constant temperature, given an initial size and volume fraction distribution of the γ′ precipitate phase, and the evaluation of two different heat treatments through the microstructure analysis and γ′ morphology. We found that for short ageing times, t < 2500 h, the coarsening can be approximated by a linear volumetric growth as predicted by Lifshitz, Slyozov and Wagner (LSW) theory. For a time greater than 2500 h the growth rate of γ′ precipitate shows an asymptotic behaviour in both heat treatments. This revised version was published online in November 2006 with corrections to the Cover Date.     

Kinetics of reactive diffusion between Ta and Cu–9.3Sn–0.3Ti alloy

Tantalum is used as a diffusion barrier in the superconducting Nb₃Sn composite-wire manufactured by the bronze method. In order to examine the consumption behavior of the Ta barrier during annealing in the bronze method, the kinetics of the reactive diffusion between Ta and a bronze was experimentally observed using sandwich diffusion couples composed of Ta and a Cu–9.3Sn–0.3Ti alloy. The (Cu–Sn–Ti)/Ta/(Cu–Sn–Ti) diffusion couples were isothermally annealed at temperatures of T = 973–1053 K for various times up to t = 1462 h. Owing to annealing, Ta₉Sn is formed as a uniform layer at the initial (Cu–Sn–Ti)/Ta interface in the diffusion couple, and gradually grows mainly toward Ta. The mean thickness of the Ta₉Sn layer is proportional to a power function of the annealing time. However, the exponent of the power function is equal to unity at t < t _c but smaller than 0.5 at t > t _c. Thus, the transition of the rate-controlling process for the growth of Ta₉Sn occurs at t = t _c. The critical annealing time t _c takes values of 1.83 × 10⁶, 4.63 × 10⁵, and 5.98 × 10⁵ s at T = 973, 1023, and 1053 K, respectively. The growth of Ta₉Sn is controlled by the interface reaction at the migrating Ta₉Sn/Ta interface in the early stages with t < t _c but by the volume and boundary diffusion across the Ta₉Sn layer in the late stages with t > t _c. Due to the transition of the rate-controlling process, the growth rate is always much smaller for Ta₉Sn than for Nb₃Sn. As a result, Ta works as an effective barrier against the diffusion of Sn from the bronze to the Cu stabilizer in the superconducting Nb₃Sn composite-wire.     

Power generation of the touching Cu/Bi-Te/Cu composites under the periodically alternating temperature gradients

The thermo-emf ΔV of the touching p- and n-type Cu/Bi-Te/Cu composites with different thicknesses of t _Bi-Te and t _Cu was measured as a function of time by alternating the temperature difference ΔT at periods of T = 20, 60, 120, 240 and ∞ sec, where t _Bi-Te was varied from 0.1 to 2.0 mm and t _Cu from 0 to 4.0 mm. As a result, ΔV changes significantly with t _Bi-Te, t _Cu and T. The effective thermo-emf ΔV _eff increases significantly with an increase of 1/T and exhibited a local maximum at 1/T = 1/240 s⁻¹. The resultant | α | and the effective temperature difference ΔT _eff were increased significantly by optimizing t _Bi-Te and t _Cu at 1/T = 1/240 s⁻¹. The power generation ΔW _eff (= ΔV _eff²/4R _calc) estimated using the measured ΔV _eff and calculated R _calc also exhibited a local maximum at 1/240 s⁻¹ for an optimum combination of t _Bi-Te = 0.1 mm and t _Cu = 2.0 mm, so that the maxima ΔW _eff at 1/T = 1/240 s⁻¹ for the p- and n-type composites were 2.28 and 2.92 times higher than those obtained at 1/T = 0 s⁻¹. This significant increase in ΔW _eff is owing to both the increase in ΔT _eff and the increase in ZT due to the increase in |α|. The power generation was thus found to be enhanced significantly by imposing the alternating temperature gradients on touching Cu/Bi-Te/Cu composites.     

Some aspects related to stability of a moving interface separating two fluids flowing in a porous medium

Summary In this paper a theoretical analysis regarding the stability of a moving interface seperating two incompressible and immiscible fluids flowing through a porous medium is performed. An approximate analytical solution for determining the evolution in time of the shape of a moving interface, assuming that its shape at the initial momentt=0 is known, has been obtained. The lengths of the two zones of flow, i.e. ahead and behind the moving interface, were considered of finite extent in which case the appropriate boundary conditions as well as those required at the interface have been formulated.With 1 Figure     

Long binary narrow-sense BCH codes are normal

Let C be the binary narrow-sense BCH code of length n = (2 ^m − l)/h, where m is the order of 2 modulo n. Using characters of finite fields and a theorem of Weil, and results of Vladut-Skorobogatov and Lang-Weil we prove that the code C is normal in the non-primitive case h > 1 if 2^m ≥ 4(2th)^{4t + 2}, and in the primitive case h = 1 if m ≥ m ₀ where the constant m ₀ depends only on t.     

Formation of nanoscale tungsten oxide structures and colouration characteristics

In this work, pH dependent evolution of tungsten oxide (WO₃) nanostructures is being reported along with physical characteristics. The synthesis was carried out via an inexpensive solvothermal cum chemical reduction route, with sodium tungstate (Na₂WO₄) and cetyl trimethyl ammonium bromide (C₁₉H₄₂NBr) as main reactants. The X-ray diffraction, together with transmission electron microscopic studies have revealed formation of regular polyhedral nanocrystalline structures and fractals as one goes from higher pH (= 5·5) to lower pH (= 2) values. The average crystallite size, as calculated through Williamson–Hall plots, was varied within 2·8–6·8 nm for different pH samples. Fourier transform infrared spectroscopy reveals in-plane bending vibration δ (W–OH), observable at ∼1630 cm^− 1 and strong stretching ν (W–O–W) located at ∼814 cm^− 1. Raman spectroscopy has divulged WO₃ Raman active optical phonon modes positioned at ∼717 and 805 cm^− 1. The thermochromic and photochromic properties of the nanoscale WO₃ sample prepared at pH = 5·5, are also highlighted.     

Effect of the thickness of Bi–Te compound and Cu electrode on the resultant Seebeck coefficient in touching Cu/Bi–Te/Cu composites

The resultant Seebeck coefficient α of the touching p- and n-type Cu/Bi–Te/Cu composites with different thicknesses of t _Bi–Te and t _Cu was measured as a function of t, where t _Bi–Te was varied from 0.1 to 2.0 mm, t _Cu from 0.3 to 4.0 mm and t is the lapse time after imposing the voltage. The temperature difference ΔT is produced by imposing a constant voltage of 1.70 V on two Peltier modules connected in series. The resultant α of composites was calculated from the relation α = ΔV/ΔT, where ΔV and ΔT were measured with two probes placed on both end coppers. ΔV decreases abruptly with an increase of t below t = 5 min, while above t = 7 min, it tends to saturate to a constant value. The resultant α and saturated ΔV vary significantly with changes in t _Cu and t _Bi–Te. When a composite has a combination of t _Cu = 1.0 mm and t _Bi–Te=0.1 mm, the generating powers ΔW (=(ΔV)²/4R) estimated using the saturated ΔV and calculated electrical resistance R for the p- and n-type composites have great local maximum values which are 4–5 times as large as those obtained for the conventional combination of t _Bi-Te = 2.0 mm and t _Cu = 0.3 mm. It is surprising that the generating power ΔW is enhanced significantly by sandwiching a very thin Bi–Te material between two thick coppers, unlike the conventional composition of thermoelectric modules. On the other hand, when a composite has a combination of t _Bi–Te = 0.1 mm and t _Cu = 0.3 mm, the resultant α of the p- and n-type composites exhibited great values of 711 and −755 μV/K, respectively, so that the maximum resultant ZT of the p- and n-type composites reached extremely large values of 8.81 and 5.99 at 298 K. However, the resultant ZT decreases rapidly with an increase of t _Cu or t _Bi–Te. The resultant ZT is thus found to be enhanced significantly not only in superlattice systems but also in macroscopic composites. The present enhancement in ZT is attributed to the large barrier thermo-emf generated in the Bi–Te region shallower than 50 μm from the boundary.     

Coarsening of Co-rich precipitates in a Cu–Co–Fe ternary alloy

The effect of coherency on coarsening of fcc Co–Fe precipitates in a Cu–1.47 wt.%Co–0.56 wt.%Fe (Co : Fe = 7:3 in atomic ratio) alloy aged at 873–973 K has been studied by measuring both the precipitate size by transmission electron microscopy and the solute concentration in the Cu matrix by electrical resistivity measurements. The precipitate phase consists of 7 parts of Co and 3 parts of Fe in atomic ratio, irrespective of the precipitate size. The precipitates smaller than about 8 nm in radius are coherent with the Cu-matrix. When the average precipitate radius is over 18 nm, all the precipitates become semi-coherent. The coarsening rates are not affected by the coherency of the precipitates. The precipitate/matrix interface energy γ has been derived, independently of the diffusivities of solute atoms using a coarsening model developed by Kuehmann and Voorhees for ternary systems. The precipitates are coherent or semi-coherent with the matrix, the experimentally obtained value of γ is 0.2 J/m². This value lies between the reported values of γ  = 0.15 J/m² for Co precipitates and γ = 0.25 J/m² for γ-Fe precipitates.     

New TeO2/NbSi Detectors for Rare Event Search

The present limitation for experiments looking for rare events, such as neutrinoless double beta decay (0ν β β) and direct WIMPs detection, is the radioactive background and in particular its discrimination. When the search is based on the bolometric technique, near-surface events constitute a serious problem, due to full volume sensitivity of the detector; in fact for a 0ν β β experiment they may cause signals close to the Q-value while for a dark matter (DM) experiment, which exploits ionization signal for particle identification, they may originate an incomplete charge collection simulating a nuclear recoil. We will describe a technique for the active suppression of the surface background which uses NbSi thin film thermometers acting as out-of-equilibrium phonon sensor. After very promising results obtained on germanium and sapphire bolometers, here we present some results on a small TeO₂ one equipped with two NbSi films; in fact TeO₂ is an interesting material for the search for 0ν β β of ¹³⁰Te. In particular we show that we are able to identify α surface events on TeO₂ by pulse shape analysis with a good separation between bulk and surface events.      

Kernel estimation of the regression function with random sampling times

Summary LetZ = (X, Y)= {Z(t)} _t∈ℛ be a stationary continuous-time process taking values in ℛ. By means of the corresponding discrete-time process {X(t _i ),Y(t _i )} _i=1 ⁿ , sampled at random instants {t _i }, a nonparametric kernel estimator of the regression function,m(x)=E(Y|X=x), is studied. Under mixing dependence conditions, the Mean Integrated Square Error (MISE) is derived and asymptotic normality is proven. In addition, we compare our results with those obtained under a classical approach for evenly-spaced observations. Finally, similar issues arising in the recursive case are considered. This work was awarded the Ramiro Melendreras price, offered to young researchers by the Spanish Statistical Society.     

Introduction of Wall Corrections to a Model of Turbulence of thek-ε type for the calculation of flows in boundary layer

A model for the calculation of wall turbulence is suggested. The model is based on the hypothesis about the presence of damping introduced by the wall into all turbulent interactions. The obtained model of thek-ε-〈t’ ² 〉-ε _t type includes one correction function for thek-ε model and one function for the 〈t’²〉-ε model, which coincide at Pr = 1, and reproduces adequately all main characteristics of the boundary layer.