Bearing capacity of two interfering strip footings from lower bound finite elements limit analysis

A rigorous lower bound solution, with the usage of the finite elements limit analysis, has been obtained for finding the ultimate bearing capacity of two interfering strip footings placed on a sandy medium. Smooth as well as rough footingsoil interfaces are considered in the analysis. The failure load for an interfering footing becomes always greater than that for a single isolated footing. The effect of the interference on the failure load (i) for rough footings becomes greater than that for smooth footings, (ii) increases with an increase in phi, and (iii) becomes almost negligible beyond S/B>3. Compared with various theoretical and experimental results reported in literature, the present analysis generally provides the lowest magnitude of the collapse load. Copyright (c) 2011 John Wiley & Sons, Ltd.

Clusters of bound particles in the derivative delta-function Bose gas

In this paper we discuss a novel procedure for constructing clusters of bound particles in the case of a quantum integrable derivative delta-function Bose gas in one dimension. It is shown that clusters of bound particles can be constructed for this Bose gas for some special values of the coupling constant, by taking the quasi-momenta associated with the corresponding Bethe state to be equidistant points on a single circle in the complex momentum plane. We also establish a connection between these special values of the coupling constant and some fractions belonging to the Farey sequences in number theory. This connection leads to a classification of the clusters of bound particles associated with the derivative delta-function Bose gas and allows us to study various properties of these clusters like their size and their stability under the variation of the coupling constant. (C) 2013 Elsevier B.V. All rights reserved.

Can the viscosity in astrophysical black hole accretion disks be close to its string theory bound?

String theory and gauge/gravity duality suggest the lower bound of shear viscosity (eta) to entropy density (s) for any matter to be mu h/4 pi k(B), when h and k(B) are reduced Planck and Boltzmann constants respectively and mu <= 1. Motivated by this, we explore eta/s in black hole accretion flows, in order to understand if such exotic flows could be a natural site for the lowest eta/s. Accretion flow plays an important role in black hole physics in identifying the existence of the underlying black hole. This is a rotating shear flow with insignificant molecular viscosity, which could however have a significant turbulent viscosity, generating transport, heat and hence entropy in the flow. However, in presence of strong magnetic field, magnetic stresses can help in transporting matter independent of viscosity, via celebrated Blandford-Payne mechanism. In such cases, energy and then entropy produces via Ohmic dissipation. In,addition, certain optically thin, hot, accretion flows, of temperature greater than or similar to 10(9) K, may be favourable for nuclear burning which could generate/absorb huge energy, much higher than that in a star. We find that eta/s in accretion flows appears to be close to the lower bound suggested by theory, if they are embedded by strong magnetic field or producing nuclear energy, when the source of energy is not viscous effects. A lower bound on eta/s also leads to an upper bound on the Reynolds number of the flow.

Linearization of Drucker-Prager yield criterion for axisymmetric problems: implementation in lower-bound limit analysis

The linearization of the Drucker-Prager yield criterion associated with an axisymmetric problem has been achieved by simulating a sphere with the truncated icosahedron with 32 faces and 60 vertices. On this basis, a numerical formulation has been proposed for solving an axisymmetric stability problem with the usage of the lower-bound limit analysis, finite elements, and linear optimization. To compare the results, the linearization of the Mohr-Coulomb yield criterion, by replacing the three cones with interior polyhedron, as proposed earlier by Pastor and Turgeman for an axisymmetric problem, has also been implemented. The two formulations have been applied for determining the collapse loads for a circular footing resting on a cohesive-friction material with nonzero unit weight. The computational results are found to be quite convincing. (C) 2013 American Society of Civil Engineers.

Chromium isotope variations (delta Cr-53/52) in mantle-derived sources and their weathering products: Implications for environmental studies and the evolution of delta Cr-53/52 in the Earth's mantle over geologic time

Here we report chromium isotope compositions, expressed as delta Cr-53/ 52 in per mil (&) relative to NIST 979, measured in selected Cr-rich minerals and rocks formed by the primary magmatic as well as the secondary metamorphic and weathering processes. The main objectives of this study were: (i) to further constrain the isotope composition of the Earth's mantle Cr inventory and its possible variation during geological history, based on the analysis of globally distributed and stratigraphically constrained mantle-derived chromites; and (ii) to investigate the magnitude and systematics of Cr isotope fractionation during oxidative weathering and secondary alteration (i. e., hydration, serpentinization) of the magmatic Cr sources. Specifically, we analyzed delta Cr-53/ 52 in a set of globally distributed mantle-derived chromites (FeMgCr2O4, n = 30) collected from various locations in Europe, Asia, Africa and South America, and our results confirm that a chromite-hosted Earth's mantle Cr inventory is uniform at - 0.079 +/- 0.129& (2SD), which we named here as a ` canonical' mantle d 53/ 52 Cr signature. Furthermore our dataset of stratigraphically constrained chromites, whose crystallization ages cover most of the Earth's geological history, indicate that the bulk Cr isotope composition of the chromite-hosted mantle inventory has remained uniform, within about +/- 0.100&, since at least the Early Archean times (similar to 3500 million years ago, Ma). To investigate the systematics of Cr isotope fractionation associated with alteration processes we analyzed a number of secondary Cr-rich minerals and variably altered ultramafic rocks (i. e., serpentinized harzburgites, lherzolites) that revealed large positive delta Cr-53/ 52 anomalies that are systematically shifted to higher values with an increasing degree of alteration and serpentinization. The degree of aqueous alteration and serpentinization was quantified by the abundances of fluid-mobile (Rb, K) elements, and by the Loss On Ignition (LOI) parameter, which determines the amount of structurally bound water (OH/ H2O) present in secondary hydrated minerals like serpentine. Overall, we observed that altered ultramafic rocks that yielded the highest LOI values, and the lowest amounts of fluid mobile elements, also yielded the heaviest delta Cr-53/ 52 signatures. Therefore, we conclude that secondary alteration (i.e., hydration, serpentinization) of ultramafic rocks in near-surface oxidative environments tend to shift the bulk Cr isotope composition of the weathered products to isotopically heavier values, pointing to a dynamic redox cycling of Cr in the Earth's crustal and near-surface environments. Hence, if validated by future

ON POLYTOPAL UPPER BOUND SPHERES

Generalizing a result (the case k = 1) due to M. A. Perles, we show that any polytopal upper bound sphere of odd dimension 2k + 1 belongs to the generalized Walkup class K-k(2k + 1), i.e., all its vertex links are k-stacked spheres. This is surprising since it is far from obvious that the vertex links of polytopal upper bound spheres should have any special combinatorial structure. It has been conjectured that for d not equal 2k + 1, all (k + 1)-neighborly members of the class K-k(d) are tight. The result of this paper shows that the hypothesis d not equal 2k + 1 is essential for every value of k >= 1.

Upper bound solution for pullout capacity of vertical anchors in sand using finite elements and limit analysis

The horizontal pullout capacity of vertical anchors embedded in sand has been determined by using an upper bound theorem of the limit analysis in combination with finite elements. The numerical results are presented in nondimensional form to determine the pullout resistance for various combinations of embedment ratio of the anchor (H/B), internal friction angle (ϕ) of sand, and the anchor-soil interface friction angle (δ). The pullout resistance increases with increases in the values of embedment ratio, friction angle of sand and anchor-soil interface friction angle. As compared to earlier reported solutions in literature, the present solution provides a better upper bound on the ultimate collapse load.

REDUCING COMPUTATIONAL EFFORT IN SOLVING GEOMECHANICS PROBLEMS WITH UPPER BOUND FINITE ELEMENTS LIMIT ANALYSIS AND LINEAR OPTIMIZATION

This paper presents a simple technique for reducing the computational effort while solving any geotechnical stability problem by using the upper bound finite element limit analysis and linear optimization. In the proposed method, the problem domain is discretized into a number of different regions in which a particular order (number of sides) of the polygon is chosen to linearize the Mohr-Coulomb yield criterion. A greater order of the polygon needs to be selected only in that region wherein the rate of the plastic strains becomes higher. The computational effort required to solve the problem with this implementation reduces considerably. By using the proposed method, the bearing capacity has been computed for smooth and rough strip footings and the results are found to be quite satisfactory.

Solving Axisymmetric Stability Problems by Using Upper Bound Finite Elements, Limit Analysis, and Linear Optimization

A numerical formulation has been proposed for solving an axisymmetric stability problem in geomechanics with upper bound limit analysis, finite elements, and linear optimization. The Drucker-Prager yield criterion is linearized by simulating a sphere with a circumscribed truncated icosahedron. The analysis considers only the velocities and plastic multiplier rates, not the stresses, as the basic unknowns. The formulation is simple to implement, and it has been employed for finding the collapse loads of a circular footing placed over the surface of a cohesive-frictional material. The formulation can be used to solve any general axisymmetric geomechanics stability problem.

Effect of the Flow Rule on the Bearing Capacity of Strip Foundations on Sand by the Upper-Bound Limit Analysis and Slip Lines

The influence of the flow rule on the bearing capacity of strip foundations placed on sand was investigated using a new kinematic approach of upper-bound limit analysis. The method of stress characteristics was first used to find the mechanism of the failure and to compute the stress field by using the Mohr-Coulomb yield criterion. Once the failure mechanism had been established, the kinematics of the plastic deformation was established, based on the requirements of the upper-bound limit theorem. Both associated and nonassociated plastic flows were considered, and the bearing capacity was obtained by equating the rate of external plastic work to the rate of the internal energy dissipation for both smooth and rough base foundations. The results obtained from the analysis were compared with those available from the literature. (C) 2014 American Society of Civil Engineers.

CHLORAL HYDRATE AS A WATER CARRIER FOR THE EFFICIENT DEPROTECTION OF ACETALS, DITHIOACETALS, AND TETRAHYDROPYRANYL ETHERS IN ORGANIC SOLVENTS

The efficient deprotection of several acetals, dithioacetals, and tetrahydropyranyl (THP) ethers under ambient conditions, using chloral hydrate in hexane, is described. Excellent yields were realized for a wide range of both aliphatic and aromatic substrates. The method is characterized by mild conditions (room temperatures or below), simple workup, and the ready availability of chloral hydrate. High chemoselectivity was also observed in the deprotection, acetonides, esters, and amides being unaffected under the reaction conditions. Products were generally purified chromatographically and identified spectrally. These results constitute a novel addition to current methodology involving a widely employed deprotection tactic in organic synthesis. It seems likely that the mechanism of the reaction involves adsorption of the substrate on the surface of the sparingly soluble chloral hydrate.

Codes With Local Regeneration and Erasure Correction

Regenerating codes and codes with locality are two coding schemes that have recently been proposed, which in addition to ensuring data collection and reliability, also enable efficient node repair. In a situation where one is attempting to repair a failed node, regenerating codes seek to minimize the amount of data downloaded for node repair, while codes with locality attempt to minimize the number of helper nodes accessed. This paper presents results in two directions. In one, this paper extends the notion of codes with locality so as to permit local recovery of an erased code symbol even in the presence of multiple erasures, by employing local codes having minimum distance >2. An upper bound on the minimum distance of such codes is presented and codes that are optimal with respect to this bound are constructed. The second direction seeks to build codes that combine the advantages of both codes with locality as well as regenerating codes. These codes, termed here as codes with local regeneration, are codes with locality over a vector alphabet, in which the local codes themselves are regenerating codes. We derive an upper bound on the minimum distance of vector-alphabet codes with locality for the case when their constituent local codes have a certain uniform rank accumulation property. This property is possessed by both minimum storage regeneration (MSR) and minimum bandwidth regeneration (MBR) codes. We provide several constructions of codes with local regeneration which achieve this bound, where the local codes are either MSR or MBR codes. Also included in this paper, is an upper bound on the minimum distance of a general vector code with locality as well as the performance comparison of various code constructions of fixed block length and minimum distance.

Calculation of three-phase methane-ethane binary clathrate hydrate phase equilibrium from Monte Carlo molecular simulations

Methane and ethane are the simplest hydrocarbon molecules that can form clathrate hydrates. Previous studies have reported methods for calculating the three-phase equilibrium using Monte Carlo simulation methods in systems with a single component in the gas phase. Here we extend those methods to a binary gas mixture of methane and ethane. Methane-ethane system is an interesting one in that the pure components form sII clathrate hydrate whereas a binary mixture of the two can form the sII clathrate. The phase equilibria computed from Monte Carlo simulations show a good agreement with experimental data and are also able to predict the sI-sII structural transition in the clathrate hydrate. This is attributed to the quality of the TIP4P/Ice and TRaPPE models used in the simulations. (C) 2014 Elsevier B.V. All rights reserved.

Re-analysis of cryoEM data on HCV IRES bound to 40S subunit of human ribosome integrated with recent structural information suggests new contact regions between ribosomal proteins and HCV RNA

In this study, we combine available high resolution structural information on eukaryotic ribosomes with low resolution cryo-EM data on the Hepatitis C Viral RNA (IRES) human ribosome complex. Aided further by the prediction of RNA-protein interactions and restrained docking studies, we gain insights on their interaction at the residue level. We identified the components involved at the major and minor contact regions, and propose that there are energetically favorable local interactions between 40S ribosomal proteins and IRES domains. Domain II of the IRES interacts with ribosomal proteins S5 and S25 while the pseudoknot and the downstream domain IV region bind to ribosomal proteins S26, S28 and S5. We also provide support using UV cross-linking studies to validate our proposition of interaction between the S5 and IRES domains II and IV. We found that domain IIIe makes contact with the ribosomal protein S3a (S1e). Our model also suggests that the ribosomal protein S27 interacts with domain IIIc while S7 has a weak contact with a single base RNA bulge between junction IIIabc and IIId. The interacting residues are highly conserved among mammalian homologs while IRES RNA bases involved in contact do not show strict conservation. IRES RNA binding sites for S25 and S3a show the best conservation among related viral IRESs. The new contacts identified between ribosomal proteins and RNA are consistent with previous independent studies on RNA-binding properties of ribosomal proteins reported in literature, though information at the residue level is not available in previous studies.

Rotational spectra of propargyl alcohol dimer: A dimer bound with three different types of hydrogen bonds

Pure rotational spectra of the propargyl alcohol dimer and its three deuterium isotopologues have been observed in the 4 to 13 GHz range using a pulsed-nozzle Fourier transform microwave spectrometer. For the parent dimer, a total of 51 transitions could be observed and fitted within experimental uncertainty. For two mono-substituted and one bi-substituted deuterium isotopologues, a total of 14, 17, and 19 transitions were observed, respectively. The observed rotational constants for the parent dimer A = 2321.8335(4) MHz, B = 1150.4774(2) MHz, and C = 1124.8898(2) MHz] are close to those of the most stable structure predicted by ab initio calculations. Spectra of the three deuterated isotopologues and Kraitchman analysis positively confirm this structure. Geometrical parameters and ``Atoms in Molecules'' analysis on the observed structure reveal that the two propargyl alcohol units in the dimer are bound by three different types of hydrogen bonds: O-H center dot center dot center dot O, O-H center dot center dot center dot pi, and C-H center dot center dot center dot pi. To the best of our knowledge, propargyl alcohol seems to be the smallest molecule forming a homodimer with three different points of contact. (C) 2014 AIP Publishing LLC.