Directed Nonabelian Sandpile Models on Trees

We define two general classes of nonabelian sandpile models on directed trees (or arborescences), as models of nonequilibrium statistical physics. Unlike usual applications of the well-known abelian sandpile model, these models have the property that sand grains can enter only through specified reservoirs. In the Trickle-down sandpile model, sand grains are allowed to move one at a time. For this model, we show that the stationary distribution is of product form. In the Landslide sandpile model, all the grains at a vertex topple at once, and here we prove formulas for all eigenvalues, their multiplicities, and the rate of convergence to stationarity. The proofs use wreath products and the representation theory of monoids.

Design of a Portable Compliant Device for Estimating the Failure-Load of Mesoscale Cemented Sand Specimens

In this paper, we present the design and development of a portable, hand-operated composite compliant mechanism for estimating the failure-load of cm-sized stiff objects whose stiffness is of the order of 10 s of kN/m. The motivation for the design comes from the need to estimate the failure-load of mesoscale cemented sand specimens in situ, which is not possible with traditional devices used for large specimens or very small specimens. The composite compliant device, developed in this work, consists of two compliant mechanisms: a force-amplifying compliant mechanism (FaCM) to amplify sufficiently the force exerted by hand in order to break the specimen and a displacement-amplifying compliant mechanism (DaCM) to enable measurement of the force using a proximity sensor. The two mechanisms are designed using the selection-maps technique to amplify the force up to 100N by about a factor of 3 and measure the force with a resolution of 15 mN. The composite device, made using a FaCM, a DaCM, and a Hall effect-based proximity sensor, was tested on mesoscale cemented sand specimens that were 10mm in diameter and 20mm in length. The results are compared with those of a large commercial instrument. Through the experiments, it was observed that the failure-load of the cemented sand specimens varied from 0.95N to 24.33 N, depending on the percentage of cementation and curing period. The estimation of the failure-load using the compliant device was found to be within 1.7% of the measurements obtained using the commercial instrument and thus validating the design. The details of the design, prototyping, specimen preparation, testing, and the results comprise the paper.

Evaluation of Precipitation Retrievals From Orbital Data Products of TRMM Over a Subtropical Basin in India

The spatial error structure of daily precipitation derived from the latest version 7 (v7) tropical rainfall measuring mission (TRMM) level 2 data products are studied through comparison with the Asian precipitation highly resolved observational data integration toward evaluation of the water resources (APHRODITE) data over a subtropical region of the Indian subcontinent for the seasonal rainfall over 6 years from June 2002 to September 2007. The data products examined include v7 data from the TRMM radiometer Microwave Imager (TMI) and radar precipitation radar (PR), namely, 2A12, 2A25, and 2B31 (combined data from PR and TMI). The spatial distribution of uncertainty from these data products were quantified based on performance metrics derived from the contingency table. For the seasonal daily precipitation over a subtropical basin in India, the data product of 2A12 showed greater skill in detecting and quantifying the volume of rainfall when compared with the 2A25 and 2B31 data products. Error characterization using various error models revealed that random errors from multiplicative error models were homoscedastic and that they better represented rainfall estimates from 2A12 algorithm. Error decomposition techniques performed to disentangle systematic and random errors verify that the multiplicative error model representing rainfall from 2A12 algorithm successfully estimated a greater percentage of systematic error than 2A25 or 2B31 algorithms. Results verify that although the radiometer derived 2A12 rainfall data is known to suffer from many sources of uncertainties, spatial analysis over the case study region of India testifies that the 2A12 rainfall estimates are in a very good agreement with the reference estimates for the data period considered.

Susceptibility Of strength development by lime in gypsiferous soil-A micro mechanistic study

The role of gypsum on the strength of lime treated soils after a long period of interaction is not well understood yet. The present study is performed to scrutinize the physical and strength behavior of lime treated soil with varying gypsum content. Lime and gypsum contents varying from 0 to 6% are considered in the present study for curing periods up to 28 days. To understand the long-term effects, the work has been extended up to 365 days, particularly with the use of 6% lime content and varying gypsum contents. Atterberg's limits turned out to be marginally affected by cation exchange. Unconfined compressive strength behavior of lime treated soil varies considerably with gypsum content and curing period. However, trivial alteration in strength is observed in the soil treated with lower lime content (up to 4%) and gypsum content up to 6%. On the contrary, strength of soil-6% lime mixture with addition of varying gypsum content shows acceleration in early strength at 14 days curing period. However, the strength at 28 days of curing declines but regains afterwards for 90 days. The trend at longer curing period for 180 and 365 days is, however, not unique but varies with gypsum contents. An attempt has been made to explain these changes on the basis of the form of gypsum, formation and conversion of reacted compounds (CASHH, CASH, MI and Ettringite). The proposed explanations were supported by detailed characterization through thermal analysis, XRD, SEM and EDAX studies of soil-lime-gypsum mixtures. (C) 2015 Elsevier B.V. All rights reserved.

Bearing capacity of a circular foundation on layered sand-clay media

The bearing capacity of a circular footing lying over fully cohesive strata, with an overlaying sand layer, is computed using the axisymmetric lower bound limit analysis with finite elements and linear optimization. The effects of the thickness and the internal friction angle of the sand are examined for different combinations of c(u)/(gamma b) and q, where c(u)=the undrained shear strength of the cohesive strata, gamma=the unit weight of either layer, b=the footing radius, and q=the surcharge pressure. The results are given in the form of a ratio (eta) of the bearing capacity with an overlaying sand layer to that for a footing lying directly over clayey strata. An overlaying medium dense to dense sand layer considerably improves the bearing capacity. The improvement continuously increases with decreases in c(u)/(gamma b) and increases in phi and q/(gamma b). A certain optimum thickness of the sand layer exists beyond which no further improvement occurs. This optimum thickness increases with an increase in 0 and q and with a decrease in c(u)/(gamma b). Failure patterns are also drawn to examine the inclusion of the sand layer. (C) 2015 The Japanese Geotechnical Society. Production and hosting by Elsevier B.V. All rights reserved.

Mechanism of improvement in the strength and volume change behavior of lime stabilized soil

An attempt has been made to bring out the influence on strength and volume change behavior of fabric changes and new cementitious compound formation in a soil upon addition of various lime contents and with curing periods. The effects of changes in fabric of treatment with various lime contents (0, 2,4 and 6%) and with curing periods (0, 7, 14 and 28 days) have been evaluated by one-dimensional consolidation tests, in terms of void ratio changes and compressibility. The strength of soil treated with different lime contents with curing periods up to 28 days, and with the optimum lime content of 6% up to one year has been determined by unconfined compression tests. Comparison of effects of lime on the strength and volume change behavior of the soil brings out that the formation of flocculated fabric and cation exchange significantly reduces the compressibility of soil but marginally increases the strength. Cementation of soil particles and filling with cementitious compounds of the voids of flocculated fabric in the soil marginally reduces the compressibility but significantly increases the strength. Thus, the mechanism of volume change behavior of soil treated with lower lime content at short curing periods is distinctly different from that of the soil treated with optimum lime content at longer curing periods. This is consistent with the increase in the permeability caused by the addition from 2 to 4% lime and the decrease following the addition of 6% lime. Changes consistent with mechanical behavior have been determined by scanning electron microscope, X-ray diffraction and thermal analyses, energy dispersive X-ray spectrometer and pH value in microstructure, mineralogy, chemical composition and alkalinity, respectively. (C) 2015 Published by Elsevier B.V.

Determinantal point processes in the plane from products of random matrices

We show that the density of eigenvalues for three classes of random matrix ensembles is determinantal. First we derive the density of eigenvalues of product of k independent n x n matrices with i.i.d. complex Gaussian entries with a few of matrices being inverted. In second example we calculate the same for (compatible) product of rectangular matrices with i.i.d. Gaussian entries and in last example we calculate for product of independent truncated unitary random matrices. We derive exact expressions for limiting expected empirical spectral distributions of above mentioned ensembles.

Uplift Resistance of Interfering Pipelines Buried in Sand

The vertical uplift resistance of interfering pipelines buried in sands has been computed using the lower-bound limit analysis in conjunction with finite elements and nonlinear optimization. The soil mass is assumed to follow the Mohr-Coulomb failure criterion and an associated flow rule. It is specified that all the pipes fail simultaneously at the same magnitude of the failure load. For different clear spacing (S) between the pipes, the magnitude of the efficiency factor (xi(gamma)) is determined. Because of pipes' interference, with a reduction in the spacing between the pipelines, the magnitude of xi(gamma) is found to decrease continuously. The results were found to compare quite well with the available data from literature for horizontal strip anchors. (C) 2015 American Society of Civil Engineers.

A PRACTICAL PROCEDURE TO ESTIMATE THE BEARING CAPACITY OF FOOTINGS ON SAND-APPLICATION TO 87 CASE STUDIES

Following the recent work of the authors in development and numerical verification of a new kinematic approach of the limit analysis for surface footings on non-associative materials, a practical procedure is proposed to utilize the theory. It is known that both the peak friction angle and dilation angle depend on the sand density as well as the stress level, which was not the concern of the former work. In the current work, a practical procedure is established to provide a better estimate of the bearing capacity of surface footings on sand which is often non-associative. This practical procedure is based on the results obtained theoretically and requires the density index and the critical state friction angle of the sand. The proposed practical procedure is a simple iterative computational procedure which relates the density index of the sand, stress level, dilation angle, peak friction angle and eventually the bearing capacity. The procedure is described and verified among available footing load test data.

Effect of particle size of sand and surface asperities of reinforcement on their interface shear behaviour

This paper investigates the effect of particle size of sand and the surface asperities of reinforcing material on their interlocking mechanism and its influence on the interfacial shear strength under direct sliding condition. Three sands of different sizes with similar morphological characteristics and four different types of reinforcing materials with different surface features were used in this study. Interface direct shear tests on these materials were performed in a specially developed symmetric loading interface direct shear test setup. Morphological characteristics of sand particles were determined from digital image analysis and the surface roughness of the reinforcing materials was measured using an analytical expression developed for this purpose. Interface direct shear tests at three different normal stresses were carried out by shearing the sand on the reinforcing material fixed to a smooth surface. Test results revealed that the peak interfacial friction and dilation angles are hugely dependent upon the interlocking between the sand particles and the asperities of reinforcing material, which in turn depends on the relative size of sand particles and asperities. Asperity ratio (AS/D-50) of interlocking materials, which is defined as the ratio of asperity spacing of the reinforcing material and the mean particle size of sand was found to govern the interfacial shear strength with highest interfacial strength measured when the asperity ratio was equal to one, which represents the closest fitting of sand particles into the asperities. It was also understood that the surface roughness of the reinforcing material influences the shear strength to an extent, the influence being more pronounced in coarser particles. Shear bands in the interface shear tests were analysed through image segmentation technique and it was observed that the ratio of shear band thickness (t) to the median particle size (D-50) was maximum when the AS/D-50 was equal to one. (C) 2015 Elsevier Ltd. All rights reserved.

The Liquefaction and Displacement of Highly Saturated Sand under Water Pressure Oscillation

In order to investigate the characteristics of water wave induced liquefaction in highly saturated sand in vertical direction, a one-dimensional model of highly saturated sand to water pressure oscillation is presented based oil the two-phase continuous media theory. The development of the effective stresses and the liquefaction thickness are analyzed. It is shown that water pressure oscillating loading affects liquefaction severely and the developing rate of liquefaction increases with the decreasing of the sand strength or the increasing of the loading strength. It is shown also that there is obvious phase lag in the sand Column. If the sand permeability is non-uniform, the pore pressure and the strain rise sharply at which the smallest permeability occurs. This solution may explain Why the fracture occurs in the sand column in some conditions.

Saltation in wind blown sand

The Boltzmann equation of the sand particle velocity distribution function in wind-blown sand two-phase flow is established based on the motion equation of single particle in air. And then, the generalized balance law of particle property in single phase granular flow is extended to gas-particle two-phase flow. The velocity distribution function of particle phase is expanded into an infinite series by means of Grad's method and the Gauss distribution is used to replace Maxwell distribution. In the case of truncation at the third-order terms, a closed third-order moment dynamical equation system is constructed. The theory is further simplified according to the measurement results obtained by stroboscopic photography in wind tunnel tests.

Industry perceptions of barriers to commercialization of regenerative medicine products in the UK.

AIMS: Regenerative medicine is an emerging field with the potential to provide widespread improvement in healthcare and patient wellbeing via the delivery of therapies that can restore, regenerate or repair damaged tissue. As an industry, it could significantly contribute to economic growth if products are successfully commercialized. However, to date, relatively few products have reached the market owing to a variety of barriers, including a lack of funding and regulatory hurdles. The present study analyzes industry perceptions of the barriers to commercialization that currently impede the success of the regenerative medicine industry in the UK. MATERIALS & METHODS: The analysis is based on 20 interviews with leading industrialists in the field. RESULTS: The study revealed that scientific research in regenerative medicine is thriving in the UK. Unfortunately, lack of access to capital, regulatory hurdles, lack of clinical evidence leading to problems with reimbursement, as well as the culture of the NHS do not provide a good environment for the commercialization of regenerative medicine products. CONCLUSION: Policy interventions, including increased translational government funding, a change in NHS and NICE organization and policies, and regulatory clarity, would likely improve the general outcomes for the regenerative medicine industry in the UK.

Numerical Simulation of Particle Separation in An Oil-Sand Separator

The gathering systems of crude oil are greatly endangered by the fine sand and soil in oil. Up to now , how to separate sand from the viscid oil is still a technical problem for oil production home or abroad. Recently , Institute of Mechanics in Chinese Academy of Sciences has developed a new type of oil-sand separator , which has been applied successfully in oil field in situ. In this paper, the numerical method of vortex-stream function is used to predict the liquid-solid separating course and the efficiency for this oil-sand separator. Results show that the viscosity and particle diameter have much influence on the particle motion. The calculating separating efficiency is compared with that of experiment and indicates that this method can be used to model the complex two-phase flow in the separator.