Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Direct and Inverse Scattering for Beltrami Fields

We consider an obstacle scattering problem for linear Beltrami fields. A vector field is a linear Beltrami field if the curl of the field is a constant times itself. We study the obstacles that are of Neumann type, that is, the normal component of the total field vanishes on the boundary of the obstacle. We prove the unique solvability for the corresponding exterior boundary value problem, in other words, the direct obstacle scattering model. For the inverse obstacle scattering problem, we deduce the formulas that are needed to apply the singular sources method. The numerical examples are computed for the direct scattering problem and for the inverse scattering problem.

Accurate determination of interference in pin joints Pin-to-plate interference in experimental models of interference-fit joints is significantly overestimated by direct physical measurements, but it can be accurately determined by a simple photoelastic method

Suitable pin-to-hole interference can significantly increase the fatigue life of a pin joint. In practical design, the initial stresses due to interference are high and they are proportional to the effective interference. In experimental studies on such joints, difficulties have been experienced in estimating the interference accurately from physical measurements of pin and hole diameters. A simple photoelastic method has been developed to determine the effective interference to a high degree of accuracy. This paper presents the method and reports illustrative data from a successful application thereof.

Direct evidence of redox interaction between metal ion and support oxide in Ce(0.98)Pd(0.02)O(2-delta) by a combined electrochemical and XPS study

A combined electrochemical method and X-ray photo electron spectroscopy (XPS) has been utilized to understand the Pd(2+)/CeO(2) interaction in Ce(1-x)Pd(x)O(2-delta) (x = 0.02). A constant positive potential (chronoamperometry) is applied to Ce(0.98)Pd(0.02)O(2-delta) working electrode which causes Ce(4+) to reduce to Ce(3+) to the extent of similar to 35%, while Pd remains in the +2 oxidation state. Electrochemically cycling this electrode between 0.0-1.2 V reverts back to the original state of the catalyst. This reversibility is attributed to the reversible reduction of Ce(4+) to Ce(3+) state. CeO(2) electrode with no metal component reduces to CeO(2-y) (y similar to 0.4) after applying 1.2 V which is not reversible and the original composition of CeO(2) cannot be brought back in any electrochemical condition. During the electro-catalytic oxygen evolution reaction at a constant 1.2 V for 1000 s, Ce(0.98)Pd(0.02)O(2-delta) reaches a steady state composition with Pd in the +2 states and Ce(4+) : Ce(3+) in the ratio of 0.65 : 0.35. This composition can be denoted as Ce(0.63)(4+)Ce(0.35)(4+)Pd(0.02)O(2-delta-y) (y similar to 0.17). When pure CeO(2) is put under similar electrochemical condition, it never reaches the steady state composition and reduces almost to 85%. Thus, Ce(0.98)Pd(0.02)O(2-delta) forms a stable electrode for the electro-oxidation of H(2)O to O(2) unlike CeO(2) due to the metal support interaction.

Apparatus and method for heat-run test on high-power PWM converters with low energy expenditure

Before installation, a voltage source converter is usually subjected to heat-run test to verify its thermal design and performance under load. For heat-run test, the converter needs to be operated at rated voltage and rated current for a substantial length of time. Hence, such tests consume huge amount of energy in case of high-power converters. Also, the capacities of the source and loads available in the research and development (R&D) centre or the production facility could be inadequate to conduct such tests. This paper proposes a method to conduct heat-run tests on high-power, pulse width modulated (PWM) converters with low energy consumption. The experimental set-up consists of the converter under test and another converter (of similar or higher rating), both connected in parallel on the ac side and open on the dc side. Vector-control or synchronous reference frame control is employed to control the converters such that one draws certain amount of reactive power and the other supplies the same; only the system losses are drawn from the mains. The performance of the controller is validated through simulation and experiments. Experimental results, pertaining to heat-run tests on a high-power PWM converter, are presented at power levels of 25 kVA to 150 kVA.

Elasticity, stability, and ideal strength of beta-SiC in plane-wave-based ab initio calculations

On the basis of the pseudopotential plane-wave method and the local-density-functional theory, this paper studies energetics, stress-strain relation, stability, and ideal strength of beta-SiC under various loading modes, where uniform uniaxial extension and tension and biaxial proportional extension are considered along directions [001] and [111]. The lattice constant, elastic constants, and moduli of equilibrium state are calculated and the results agree well with the experimental data. As the four SI-C bonds along directions [111], [(1) over bar 11], [11(1) over bar] and [111] are not the same under the loading along [111], internal relaxation and the corresponding internal displacements must be considered. We find that, at the beginning of loading, the effect of internal displacement through the shuffle and glide plane diminishes the difference among the four Si-C bonds lengths, but will increase the difference at the subsequent loading, which will result in a crack nucleated on the {111} shuffle plane and a subsequently cleavage fracture. Thus the corresponding theoretical strength is 50.8 GPa, which agrees well with the recent experiment value, 53.4 GPa. However, with the loading along [001], internal relaxation is not important for tetragonal symmetry. Elastic constants during the uniaxial tension along [001] are calculated. Based on the stability analysis with stiffness coefficients, we find that the spinodal and Born instabilities are triggered almost at the same strain, which agrees with the previous molecular-dynamics simulation. During biaxial proportional extension, stress and strength vary proportionally with the biaxial loading ratio at the same longitudinal strain.

Experiments on interaction between current-induced vibration and scour of submarine pipelines on sandy bottom

In order to understand the dynamic behavior of submarine pipelines exposed to current and the mechanism of the interaction between current-induced vibration and scour of pipelines on a sandy bottom, an experimental investigation is conducted with a small scale model A test model which can be tested in the flume is set up by taking into account the typical working conditions of the pipelines and by applying the similarity theory. The interactions between the shape of the scour hole and the behavior of the pipeline as well as the flow patterns of the current are detailed, and the interaction mechanism outlined. The effect of vibration of the pipeline on the development of dynamic scour at different stages is found out. The proposed experimental method and test results provide an effective means for design of marine pipelines against scouring.

Measurement Of Fracture Toughness And Interfacial Shear Strength Of Hard And Brittle Cr Coating On Ductile Steel Substrate

The fracture toughness and interfacial adhesion properties of a coating on its substrate are considered to be crucial intrinsic parameters determining performance and reliability of coating-substrate system. In this work, the fracture toughness and interfacial shear strength of a hard and brittle Cr coating on a normal medium carbon steel substrate were investigated by means of a tensile test. The normal medium carbon steel substrate electroplated with a hard and brittle Cr coating was quasi-statically stretched to induce an array of parallel cracks in the coating. An optical microscope was used to observe the cracking of the coating and the interfacial decohesion between the coating and the substrate during the loading. It was found that the cracking of the coating initiated at critical strain, and then the number of the cracks of the coating per unit axial distance increased with the increase in the tensile strain. At another critical strain, the number of the cracks of the coating became saturated, i.e. the number of cracks per unit axial distance became a constant after this critical strain. Based on the experiment result, the fracture toughness of the brittle coating can be determined using a mechanical model. Interestingly, even when the whole specimen fractured completely under an extreme strain of the substrate, the interfacial decohesion or buckling of the coating on its substrate was completely absent. The test result is different from that appeared in the literature though the identical test method and the brittle coating/ductile metal substrate system are taken. It was found that this difference can be attributed to an important mechanism that the Cr coating on the steel substrate has a good adhesion, and the ultimate interfacial shear strength between the Cr coating and the steel substrate has exceeded the maximum shear flow strength level of the steel substrate. This result also indicates that the maximum shear flow strength level of the ductile steel substrate can be only taken as a lower bound estimate on the ultimate shear strength of the interface. This estimation of the ultimate interfacial shear strength is consistent with the theoretical analysis and prediction presented in the literature.

Direct dynamical test for deterministic chaos and optimal embedding of a chaotic time-series

We propose here a local exponential divergence plot which is capable of providing an alternative means of characterizing a complex time series. The suggested plot defines a time-dependent exponent and a ''plus'' exponent. Based on their changes with the embedding dimension and delay time, a criterion for estimating simultaneously the minimal acceptable embedding dimension, the proper delay time, and the largest Lyapunov exponent has been obtained. When redefining the time-dependent exponent LAMBDA(k) curves on a series of shells, we have found that whether a linear envelope to the LAMBDA(k) curves exists can serve as a direct dynamical method of distinguishing chaos from noise.

Improved sampling techniques for the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a widely used approach for flow simulations having rarefied or nonequilibrium effects. It involves heavily to sample instantaneous values from prescribed distributions using random numbers. In this note, we briefly review the sampling techniques typically employed in the DSMC method and present two techniques to speedup related sampling processes. One technique is very efficient for sampling geometric locations of new particles and the other is useful for the Larsen-Borgnakke energy distribution.

A method to improve size estimates of walleye pollock (Theragra chalcogramma) Atka mackerel (Pleurogrammus monopterygius) consumed by pinnipeds: digestion correction factors applied to bones and otoliths recovered in scats

The lengths of otoliths and other skeletal structures recovered from the scats of pinnipeds, such as Steller sea lions (Eumetopias jubatus), correlate with body size and can be used to estimate the length of prey consumed. Unfortunately, otoliths are often found in too few scats or are too digested to usefully estimate prey size. Alternative diagnostic bones are frequently recovered, but few bone-size to prey-size correlations exist and bones are also reduced in size by various degrees owing to digestion. To prevent underestimates in prey sizes consumed techniques are required to account for the degree of digestion of alternative bones prior to estimating prey size. We developed a method (using defined criteria and photo-reference material) to assign the degree of digestion for key cranial structures of two prey species: walleye pollock (Theragra chalcogramma) and Atka mackerel (Pleurogrammus monopterygius). The method grades each structure into one of three condition categories; good, fair or poor. We also conducted feeding trials with captive Steller sea lions, feeding both fish species to determine the extent of erosion of each structure and to derive condition-specific digestion correction factors to reconstruct the original sizes of the structures consumed. In general, larger structures were relatively more digested than smaller ones. Mean size reduction varied between different types of structures (3.3−26.3%), but was not influenced by the size of the prey consumed. Results from the observations and experiments were combined to be able to reconstruct the size of prey consumed by sea lions and other pinnipeds. The proposed method has four steps: 1) measure the recovered structures and grade the extent of digestion by using defined criteria and photo-reference collection; 2) exclude structures graded in poor condition; 3) multiply measurements of structures in good and fair condition by their appropriate digestion correction factors to derive their original size; and 4) calculate the size of prey from allometric regressions relating corrected structure measurements to body lengths. This technique can be readily applied to piscivore dietary studies that use hard remains of fish.

Experiments in constituting a taste panel for canned and frozen prawn products

With a view to constituting a taste panel in the laboratory for detecting the flavor changes in canned and frozen prawn, three methods of panel selection (scalar scoring method, range and deviation method and triangular method) were tried. Out of the three, triangular method was found to be suitable for panel formation in canned and frozen prawn. Using this method a panel of six members was formed for detecting flavor changes in the two products.

Strength mobilization in clays and silts

A large database of 115 triaxial, direct simple shear, and cyclic tests on 19 clays and silts is presented and analysed to develop an empirical framework for the prediction of the mobilization of the undrained shear strength, cu, of natural clays tested from an initially isotropic state of stress. The strain at half the peak undrained strength (γM=2) is used to normalize the shear strain data between mobilized strengths of 0.2cu and 0.8cu. A power law with an exponent of 0.6 is found to describe all the normalized data within a strain factor of 1.75 when a representative sample provides a value for γM=2. Multi-linear regression analysis shows that γM=2 is a function of cu, plasticity index Ip, and initial mean effective stress p′0. Of the 97 stress-strain curves for which cu, Ip, and p′0 were available, the observed values of γM=2 fell within a factor of three of the regression; this additional uncertainty should be acknowledged if a designer wished to limit immediate foundation settlements on the basis of an undrained strength profile and the plasticity index of the clay. The influence of stress history is also discussed. The application of these stress-strain relations to serviceability design calculations is portrayed through a worked example. The implications for geotechnical decision-making and codes of practice are considered.

Dynamic characterisation and longitudinal strength of swaged joints

Swaging is a cold working process involving plastic deformation of the work piece to change its shape. A swaged joint is a connection between two components whereby a swaging tool induces plastic deformation of the components at their junction to effectively bind them together. This is commonly used when welding or other standard joining techniques are not viable. Swaged joints can be found for example, in nuclear fuel assemblies to connect the edges of thin rectangular plates to a supporting structure or frame. The aim of this work is to find a model to describe the vibrational behaviour of a swaged joint and to estimate its strength in resisting a longitudinally applied load. The finite element method and various experimental rigs were used in order to find relationships between the natural frequencies of the plate, the joint stiffness and the force required to shift the plate against the restraining action of the swage connection. It is found that a swaged joint is dynamically equivalent to a simple support with the rotation elastically restrained and a small stiffness is enough to resist an important load. © 2011 Elsevier Ltd. All rights reserved.