Application of a sensitivity equation method to the <Emphasis Type="Italic">k</Emphasis>–<Emphasis Type="Italic">ε</Emphasis> model of turbulence

In this paper, we present some examples of sensitivity analysis for flows modeled by the standard k–ε model of turbulence with wall functions. The flow and continuous sensitivity equations are solved using an adaptive finite element method. Our examples emphasize a number of applications of sensitivity analysis: identification of the most significant parameters, analysis of the flow model, assessing the influence of closure coefficients, calculation of nearby flows, and uncertainty analysis. The sensitivity parameters considered are closure coefficients of the turbulence model and constants appearing in the wall functions.     

Viscosity and Surface Tension of Saturated <Emphasis Type="Italic">n</Emphasis>-Pentane

Light scattering by thermally excited capillary waves on liquid surfaces or interfaces can be used for the investigation of viscoelastic properties of fluids. In this work, the simultaneous determination of surface tension and liquid kinematic viscosity of n-pentane by surface light scattering (SLS) on a gas–liquid interface was carried out. The experiments are based on a heterodyne detection scheme and signal analysis by photon correlation spectroscopy (PCS). Measurements were performed under saturation conditions over a wide temperature range from about 233 to 363 K. For the whole temperature range the total uncertainty of the liquid kinematic viscosity and surface tension is estimated to be better than 1.0 and 1.2, respectively. The results obtained corroborate the reliability of the SLS technique for the determination of thermophysical properties.     

A note on <Emphasis Type="Italic">T</Emphasis>-stress determination using dislocation arrays

In general, numerical determination of T-stresses requires careful handling, because of their location in the vicinity of singular points. Discretization methods, such as common finite element methods, may not lead to accurate results. However, the well known technique of using dislocation arrays for determination of stress intensity factors may also be used for determination of T-stresses. Except for a few simple cases, this technique leads to a Fredholm equation, that can be solved very accurately. The general method is described and the technique is demonstrated by examples.     

An adaptive strategy for <Emphasis Type="Italic">hp</Emphasis>-FEM based on testing for analyticity

We present an hp-adaptive strategy that is based on estimating the decay of the expansion coefficients when a function is expanded in L ²-orthogonal polynomials on a triangle or a tetrahedron. We justify this approach by showing that the decay of the coefficients is exponential if and only if the function is analytic. Numerical examples illustrate the performance of this approach, and we compare it with two other hp-adaptive strategies.     

The <Emphasis Type="Italic">α–β</Emphasis> Transition of Nitrogen

It is well-known that, aside from its triple point, nitrogen exhibits a solid-to-solid transition at about 35 K that is of some interest as a secondary reference temperature. During the recently published highly accurate measurements of the triple point of nitrogen (Metrologia 43, 435 (2006)), an extensive study was made also of the solid α–β transition of nitrogen, using both the continuous heating method and the pulse-heating method. This transition is of significantly lower quality than the triple point of nitrogen. A very high thermal resistance and a large time constant characterize the transition. Therefore, even the determination of the self-heating of the thermometer requires a very long time. A value of T ₉₀ = 35.620 K with an expanded uncertainty U = 8 mK for the coverage factor k = 2 was found, differing by +6 mK from the published CCT-recommended value. The reproducibility of the value was better than ± 5 mK. In addition to the temperature value found for the transition, a comparison is made with previous measurements on this point, and an overview is given of the available information about it.     

Study of gel grown mixed crystals of Ba<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>Ca<Subscript>(1−<Emphasis Type="Italic">x</Emphasis>)</Subscript>(IO<Subscript>3</Subscript>)<Subscript>4</Subscript>

The growth of mixed crystals of Ba _x Ca_1−x (IO₃)₄ were carried out with simple gel method. The effect of various parameters such as pH of gel solution, gel concentration, gel setting time, concentration of reactants on the growth was studied. Crystals having different morphologies and habits were obtained. The grown crystals were characterized by XRD, FT-IR, EDAX, TGA, DTA and DSC.     

Streamlined life cycle assessment of residue utilization options in <Emphasis Type="Italic">Tongkat Ali </Emphasis>(<Emphasis Type="Italic">Eurycoma longifolia</Emphasis>) water extract manufacturing process

Life cycle assessment (LCA) is often used to compare alternative process options in terms of their overall impact on the environment to easily identify the most environmentally friendly alternative. In this work, a streamlined LCA study was conducted to assess three different residue utilization schemes for Tongkat Ali (Eurycoma longifolia) extract production. The case study was firstly simulated using a batch process simulation software. The results of mass and energy balances obtained from the simulation software were then subjected to life cycle analysis. By evaluating the different schemes for using the fibrous residue from the extraction process, the potential for environmental process improvement was identified. Overall, use of the residue as process fuel was found to be the most environmentally friendly option. It produces the least emissions and reduces resource usage per unit of product than the other options evaluated.     

Skew <Emphasis Type="Italic">t</Emphasis> distributions via the sinh-arcsinh transformation

A version of the sinh-arcsinh transformation is used to generate a skew extension of Student’s t distribution which provides an alternative to previously proposed skew t distributions. The basic properties of the resulting sinh-arcsinhed t family of distributions are presented, many of them effectively having the same level of complexity as their Student t counterparts. Quantile-based measures, which come to the fore due to the non-existence of moments, are readily available. The parameters of the distribution have clear interpretations. Limiting distributions as shape parameters tend to their extreme values are especially appealing. The family’s simplest sub-class is closely related to a sub-class of the L _U family. Likelihood based inference is considered and applied in the analysis of heavy-tailed and skew data on fibre glass strengths. Comparisons are made throughout with two of the most popular existing competitors to this distribution: it scores very well relative to them on a number of tractability grounds.     

An <Emphasis Type="Italic">rp</Emphasis>-adaptive finite element method for the deformation theory of plasticity

In this paper, we present an rp-discretization strategy for physically non-linear problems based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally, whereas the r-method moves nodes and edges of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic–plastic interface in order to take into account the loss of regularity which arises along the curve of the plastic front. Numerical examples will demonstrate that this approach leads to an exponential rate of convergence and highly accurate results.     

Thermal-Conductivity Measurements of Polymers by a Modified 3<Emphasis Type="Italic">ω</Emphasis> Technique

A modified 3ω technique is designed for measurement of the thermal conductivity of polymers. In this study, samples are prepared by pressing a platinum (Pt) hot wire into melt polymers, and a LabVIEW-based virtual lock-in amplifier is employed to collect the third harmonic of the voltage across the hot wire, which has proved to overcome the disadvantages of the commercial lock-in amplifier, such as inaccuracy at low frequency, lack of flexibility/scalability, and high cost. Three kinds of commercial polymers are measured at room temperature, and the results are checked against data from the literature, which demonstrates that the modified technique can be used with high accuracy and good reproducibility.     

Periodic Sequences with Maximal Linear Complexity and Large <Emphasis Type="Italic">k</Emphasis>-Error Linear Complexity

The linear complexity and the k-error linear complexity are important concepts for the theory of stream ciphers in cryptology. Keystreams that are suitable for stream ciphers must have large values of these complexity measures. We study periodic sequences over an arbitrary finite field _q and establish conditions under which there are many periodic sequences over _q with period N, maximal linear complexity N, and k-error linear complexity close to N. The existence of many such sequences thwarts attacks against the keystreams by exhaustive search.     

A note on the derivation of the <Emphasis Type="Italic">J</Emphasis>-integral from potential energy

In a recent work Z.-H. Jin and C. T. Sun (2004) presented a derivation of the J-integral from the potential energy of a system, which is thought to circumvent previous cumbersome or flawed derivations. Two items in this work call for discussion; one is related to the effect of a singularity upon different types of contour integrals and the other to the strain energy difference term.     

Dielectric properties of Na<Subscript>1-<Emphasis Type="Italic">x</Emphasis></Subscript>K<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>NbO<Subscript>3</Subscript> in orthorhombic phase

Pellets of ceramic Na_1−xK_xNbO₃ (x = 0, 0.2 and 0.5), were prepared by conventional solid-state reaction method. Prepared samples were characterized using XRD and SEM. The frequency and temperature variation of dielectric constant, loss tangent and dielectric conductivity of prepared samples were measured in the frequency range from 10 KHz-1 MHz, and in the temperature range from 50–250°C for x = 0.2 and 0.5, and between 50 and 480°C for x = 0 compositions. It was observed that the dielectric constant and loss tangent decrease, and conductivity increases with increasing frequency. Near the transition temperature the material shows anomalous behaviour for the observed properties, and the peaks of dielectric constant and loss tangent were observed shifting towards lower temperature with increasing frequency.     

Growth features of ammonium hydrogen<Emphasis Type="Italic">d</Emphasis>-tartrate single crystals

Ammonium hydrogend-tartrate (d-AHT) single crystals were grown in silica gel. The growth features of these crystals with variation of parameters like specific gravity of the gel, gel pH, acid concentrations, concentration of the feed solution and gel age were studied in detail.     

Investigation into nonlinear vibrations of composite plates using the <Emphasis Type="Italic">R</Emphasis>-function theory

We have developed an effective approach to the solution of problems on geometrically nonlinear vibrations of orthotropic multilayer plates of irregular shapes in a classical statement based on the use of the R-function theory, Ritz variational method and Bubnov-Galerkin method. Using the proposed method, problems of vibrations of both multilayer rectangular plates and plates of complex geometries have been solved. The effect of the domain geometry and boundary conditions on the amplitude-frequency characteristics has been investigated. __________ Translated from Problemy Prochnosti, No. 5, pp. 101–113, September–October, 2007.     

Interfacial crack-tip constraints and <Emphasis Type="Italic">J</Emphasis>-integral for bi-materials with plastic hardening mismatch

This paper investigates interfacial crack tip stress fields and the J-integral for bi-materials with plastic hardening mismatch via detailed elastic-plastic finite element analyses. For small scale yielding, the modified boundary layer formulation with the elastic T-stress is employed. For fully plastic yielding, plane strain single-edge- cracked specimens under pure bending are considered. Interfacial crack tip stress fields are explained by modified Prandtl slip-line fields. It is found that, for bi-materials consisting of two elastic-plastic materials, increasing plastic hardening mismatch increases both crack-tip stress constraint in the lower hardening material and the J-contribution there. The implication of asymmetric J-integral in bi-materials is also discussed.     

Solution of generalized density evolution equation via a family of <Emphasis Type="Italic">δ</Emphasis> sequences

The traditional probability density evolution equations of stochastic systems are usually in high dimensions. It is very hard to obtain the solutions. Recently the development of a family of generalized density evolution equation (GDEE) provides a new possibility of tackling nonlinear stochastic systems. In the present paper, a numerical method different from the finite difference method is developed for the solution of the GDEE. In the proposed method, the formal solution is firstly obtained through the method of characteristics. Then the solution is approximated by introducing the asymptotic sequences of the Dirac δ function combined with the smart selection of representative point sets in the random parameters space. The implementation procedure of the proposed method is elaborated. Some details of the computation including the selection of the parameters are discussed. The rationality and effectiveness of the proposed method is verified by some examples. Some features of the numerical results are observed.     

Evaluation of the ISO <Emphasis Type="Italic">J</Emphasis> initiation procedure using the EURO fracture toughness data set

The multiple specimen J _0.2/BL initiation fracture toughness test procedure from the ISO standard, ISO 12135:2002, is evaluated using the EURO fracture toughness data set. This standard is also compared with the ASTM standard, ASTM E 1820, multiple specimen J _Ic procedure. The EURO round robin data set was generated to evaluate the transition fracture toughness methods for steels. However, many of the tests resulted in ductile fracture behavior giving final J versus ductile crack extension points. This is the information that is measured in a multiple specimen J initiation fracture toughness test. The data set has more than 300 individual points of J versus crack extension with four different specimen sizes. It may be the largest data set of that type produced for one material. Therefore, its use to determine J initiation values can provide an important evaluation of the standard procedures. The results showed that a J _0.2/BL value could be determined from the ISO standard for three of the four specimen sizes, the smallest size did not meet the specimen size requirement on J. The construction line slopes in this method are very steep compared with the ASTM construction line slopes. This resulted in low J initiation values, about a factor of two lower than the one from the ASTM method. Of the various criteria imposed to determine a valid J _0.2/BL value, the one limiting the maximum J value was the most questionable. It had an effect of eliminating small specimen data that was identical to acceptable large specimen data.     

Change-point diagnostics in competing risks models: Two posterior predictive <Emphasis Type="Italic">p</Emphasis>-value approaches

This paper presents a Bayesian diagnostic procedure for examining change-point assumption in the competing risks model framework. It considers the family of distributions arising from the cause-specific model as reported by Chiang (Introduction to stochastic processes in biostatistics. Wiley, New York, 1968) upon which change-points are added to accommodate possible distributional heterogeneity. Model departure, due to misspecification of change-points associated with either the overall survival distribution or cause-specific probabilities, is quantified in terms of a sequence of cumulative-sum statistics between each pair of adjacent change-points assumed. When assessing the asymptotic behavior of each sequence of cumulative-sum statistics using its posterior predictive p-values, see Rubin (Ann Stat 12:1151–1172, 1984) and partial posterior predictive p-values as reported by Bayarri and Berger (J Am Stat Assoc 95:1127–1142, 2000), we show that both types of p-values attain their greatest departure from 0.5 at the change-point that is missed in the assumed model, from which a diagnostic procedure is formalized. Statistical power of these two types of p-values is discussed.