Analysis of shape and location effects of closely spaced metal loss defects in pressurised pipes

Metal loss due to corrosion is a serious threat to the integrity of pressurised oil and gas transmission pipes. Pipe metal loss defects are found in either single form or in groups (clusters). One of the critical situations arises when two or more defects are spaced close enough to act as a single lengthier defect with respect to the axial direction, causing pipe ruptures rather than leaks, and impacting on the pressure containing capacity of a pipe. There have been few studies conducted to determine the distance needed for defects to interact leading to a failure pressure lower than that when the defects are treated as single defects and not interacting. Despite such efforts, there is no universally agreed defect interaction rule and pipe operators around the world have various rules to pick and choose from. In this work, the effects of defect shape and location on closely spaced defects are analysed using finite element analysis. The numerical results showed that defect shapes and locations have a great influence on the peak stress and its location as well as the failure pressure of pipes containing interacting defects

Universal flow diagram for the magnetoconductance in disordered GaAs layers

The temperature driven flow lines of the diagonal and Hall magnetoconductance data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers with different thicknesses. The flow lines are quantitatively well described by a recent universal scaling theory developed for the case of duality symmetry. The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator or the QHE state at low temperatures happens along a semicircle separatrix G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at (G_{xx},G_{xy})=(1,1).Comment: 10 pages, 5 figures, submitted to Phys. Rev. Let

On String Theory Duals of Lifshitz-like Fixed Points

We present type IIB supergravity solutions which are expected to be dual to certain Lifshitz-like fixed points with anisotropic scale invariance. They are expected to describe a class of D3-D7 systems and their finite temperature generalizations are straightforward. We show that there exist solutions that interpolate between these anisotropic solutions in the IR and the standard AdS5 solutions in the UV. This predicts anisotropic RG flows from familiar isotropic fixed points to anisotropic ones. In our case, these RG flows are triggered by a non-zero theta-angle in Yang-Mills theories that linearly depends on one of the spatial coordinates. We study the perturbations around these backgrounds and discuss the possibility of instability. We also holographically compute their thermal entropies, viscosities, and entanglement entropies.Comment: 47 pages, 4 figure

Identification of Spatio-Temporal Systems Using Multi-resolution Wavelet Models

A novel modelling structure for identifying spatio-temporal systems is proposed based on multi-resolution wavelet decompositions. Two classes of spatio-temporal systems, coupled map lattices and cellular automata, are considered and the new modelling approach is applied to identify these systems. Several examples are provided to demonstrate the applicability and effectiveness of the new identification procedure

Helium bubble formation in ultrafine and nanocrystalline tungsten under different extreme conditions

We have investigated the effects of helium ion irradiation energy and sample temperature on the performance of grain boundaries as helium sinks in ultrafine grained and nanocrystalline tungsten. Irradiations were performed at displacement and non-displacement energies and at temperatures above and below that required for vacancy migration. Microstructural investigations were performed using Transmission Electron Microscopy (TEM) combined with either in-situ or ex-situ ion irradiation. Under helium irradiation at an energy which does not cause atomic displacements in tungsten (70 eV), regardless of temperature and thus vacancy migration conditions, bubbles were uniformly distributed with no preferential bubble formation on grain boundaries. At energies that can cause displacements, bubbles were observed to be preferentially formed on the grain boundaries only at high temperatures where vacancy migration occurs. Under these conditions, the decoration of grain boundaries with large facetted bubbles occurred on nanocrystalline grains with dimensions less than 60 nm. We discuss the importance of vacancy supply and the formation and migration of radiation-induced defects on the performance of grain boundaries as helium sinks and the resulting irradiation tolerance of ultrafine grained and nanocrystalline tungsten to bubble formatio

Critical magnetic fluctuations induced superconductivity and residual density of states in CeRhIn5CeRhIn_5 superconductor

We propose the multiband extension of the spin-fermion model to address the superconducting d-wave pairing due to magnetic interaction near critical point. We solve the unrestricted gap equation with a general d-wave symmetry gap and find that divergent magnetic correlation length $\xi$ leads to the very unharmonic shape of the gap function with shallow gap regions near nodes. These regions are extremely sensitive to disorder. Small impurity concentration induces substantial residual density of states. We argue that we can understand the large $N_{res}(0) = \lim_{T\to 0} C_p(T)/T$ value and its pressure dependence of the recently discovered $CeRhIn_5$ superconductor under pressure within this approach.Comment: 5 figure

Arachidonic Acid Inhibits Epithelial Na Channel Via Cytochrome P450 (CYP) Epoxygenase-dependent Metabolic Pathways

We used the patch-clamp technique to study the effect of arachidonic acid (AA) on epithelial Na channels (ENaC) in the rat cortical collecting duct (CCD). Application of 10 μM AA decreased the ENaC activity defined by NPo from 1.0 to 0.1. The dose–response curve of the AA effect on ENaC shows that 2 μM AA inhibited the ENaC activity by 50%. The effect of AA on ENaC is specific because neither 5,8,11,14-eicosatetraynoic acid (ETYA), a nonmetabolized analogue of AA, nor 11,14,17-eicosatrienoic acid mimicked the inhibitory effect of AA on ENaC. Moreover, inhibition of either cyclooxygenase (COX) with indomethacin or cytochrome P450 (CYP) ω-hydroxylation with N-methylsulfonyl-12,12-dibromododec-11-enamide (DDMS) failed to abolish the effect of AA on ENaC. In contrast, the inhibitory effect of AA on ENaC was absent in the presence of N-methylsulfonyl-6-(propargyloxyphenyl)hexanamide (MS-PPOH), an agent that inhibits CYP-epoxygenase activity. The notion that the inhibitory effect of AA is mediated by CYP-epoxygenase–dependent metabolites is also supported by the observation that application of 200 nM 11,12-epoxyeicosatrienoic acid (EET) inhibited ENaC in the CCD. In contrast, addition of 5,6-, 8,9-, or 14,15-EET failed to decrease ENaC activity. Also, application of 11,12-EET can still reduce ENaC activity in the presence of MS-PPOH, suggesting that 11,12-EET is a mediator for the AA-induced inhibition of ENaC. Furthermore, gas chromatography mass spectrometry analysis detected the presence of 11,12-EET in the CCD and CYP2C23 is expressed in the principal cells of the CCD. We conclude that AA inhibits ENaC activity in the CCD and that the effect of AA is mediated by a CYP-epoxygenase–dependent metabolite, 11,12-EET

Some No-go Theorems for String Duals of Non-relativistic Lifshitz-like Theories

We study possibilities of string theory embeddings of the gravity duals for non-relativistic Lifshitz-like theories with anisotropic scale invariance. We search classical solutions in type IIA and eleven-dimensional supergravities which are expected to be dual to (2+1)-dimensional Lifshitz-like theories. Under reasonable ansaetze, we prove that such gravity duals in the supergravities are not possible. We also discuss a possible physical reason behind this.Comment: 18 pages, Latex, flux conditions clarified (v2), brief summary of results added (v3

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.Comment: 1. This is a revised version with several new sections and an appendix that will appear in Communications in Mathematical Physics. 2. A "microscopic" approach to some of these monotonicity formulae leads to celebrated blow-up techniques and regularity theory in geometric measure theory. 3. Our unique solution of the Dirichlet problems generalizes the work of Karcher and Wood on harmonic map

Classification and nondegeneracy of SU(n+1)SU(n+1) Toda system with singular sources

We consider the following Toda system \Delta u_i + \D \sum_{j = 1}^n a_{ij}e^{u_j} = 4\pi\gamma_{i}\delta_{0} \text{in}\mathbb R^2, \int_{\mathbb R^2}e^{u_i} dx -1$,$\delta_0$is Dirac measure at 0, and the coefficients$a_{ij}$form the standard tri-diagonal Cartan matrix. In this paper, (i) we completely classify the solutions and obtain the quantization result:$$\sum_{j=1}^n a_{ij}\int_{\R^2}e^{u_j} dx = 4\pi (2+\gamma_i+\gamma_{n+1-i}), \;\;\forall\; 1\leq i \leq n.$$This generalizes the classification result by Jost and Wang for$\gamma_i=0$,$\forall \;1\leq i\leq n$. (ii) We prove that if$\gamma_i+\gamma_{i+1}+...+\gamma_j \notin \mathbb Z$for all$1\leq i\leq j\leq n$, then any solution$u_i$ is \textit{radially symmetric} w.r.t. 0. (iii) We prove that the linearized equation at any solution is \textit{non-degenerate}. These are fundamental results in order to understand the bubbling behavior of the Toda system.Comment: 28 page