Lower bounds on Ricci flow invariant curvatures and geometric applications

We consider Ricci flow invariant cones C in the space of curvature operators lying between the cones ``nonnegative Ricci curvature'' and ``nonnegative curvature operator''. Assuming some mild control on the scalar curvature of the Ricci flow, we show that if a solution to the Ricci flow has its curvature operator which satisfies R + epsilon I is an element of C at the initial time, then it satisfies R + epsilon I is an element of C on some time interval depending only on the scalar curvature control. This allows us to link Gromov-Hausdorff convergence and Ricci flow convergence when the limit is smooth and R + I is an element of C along the sequence of initial conditions. Another application is a stability result for manifolds whose curvature operator is almost in C. Finally, we study the case where C is contained in the cone of operators whose sectional curvature is nonnegative. This allows us to weaken the assumptions of the previously mentioned applications. In particular, we construct a Ricci flow for a class of (not too) singular Alexandrov spaces.

Lower-Bound Axisymmetric Formulation for Geomechanics Problems Using Nonlinear Optimization

A lower-bound limit analysis formulation, by using two-dimensional finite elements, the three-dimensional Mohr-Coulomb yield criterion, and nonlinear optimization, has been given to deal with an axisymmetric geomechanics stability problem. The optimization was performed using an interior point method based on the logarithmic barrier function. The yield surface was smoothened (1) by removing the tip singularity at the apex of the pyramid in the meridian plane and (2) by eliminating the stress discontinuities at the corners of the yield hexagon in the pi-plane. The circumferential stress (sigma(theta)) need not be assumed. With the proposed methodology, for a circular footing, the bearing-capacity factors N-c, N-q, and N-gamma for different values of phi have been computed. For phi = 0, the variation of N-c with changes in the factor m, which accounts for a linear increase of cohesion with depth, has been evaluated. Failure patterns for a few cases have also been drawn. The results from the formulation provide a good match with the solutions available from the literature. (C) 2014 American Society of Civil Engineers.

Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis

The ultimate bearing capacity of a circular footing, placed over rock mass, is evaluated by using the lower bound theorem of the limit analysis in conjunction with finite elements and nonlinear optimization. The generalized Hoek-Brown (HB) failure criterion, but by keeping a constant value of the exponent, alpha = 0.5, was used. The failure criterion was smoothened both in the meridian and pi planes. The nonlinear optimization was carried out by employing an interior point method based on the logarithmic barrier function. The results for the obtained bearing capacity were presented in a non-dimensional form for different values of GSI, m(i), sigma(ci)/(gamma b) and q/sigma(ci). Failure patterns were also examined for a few cases. For validating the results, computations were also performed for a strip footing as well. The results obtained from the analysis compare well with the data reported in literature. Since the equilibrium conditions are precisely satisfied only at the centroids of the elements, not everywhere in the domain, the obtained lower bound solution will be approximate not true. (C) 2015 Elsevier Ltd. All rights reserved.

Lower Bound Axisymmetric Limit Analysis Using Drucker-Prager Yield Cone and Simulation with Mohr-Coulomb Pyramid

This paper presents a lower bound limit analysis approach for solving an axisymmetric stability problem by using the Drucker-Prager (D-P) yield cone in conjunction with finite elements and nonlinear optimization. In principal stress space, the tip of the yield cone has been smoothened by applying the hyperbolic approximation. The nonlinear optimization has been performed by employing an interior point method based on the logarithmic barrier function. A new proposal has also been given to simulate the D-P yield cone with the Mohr-Coulomb hexagonal yield pyramid. For the sake of illustration, bearing capacity factors N-c, N-q and N-gamma have been computed, as a function of phi, both for smooth and rough circular foundations. The results obtained from the analysis compare quite well with the solutions reported from literature.

Lower Bounds for Sums of Powers of Low Degree Univariates

We consider the problem of representing a univariate polynomial f(x) as a sum of powers of low degree polynomials. We prove a lower bound of Omega(root d/t) for writing an explicit univariate degree-d polynomial f(x) as a sum of powers of degree-t polynomials.

Bearing capacity factors for a conical footing using lower- and upper-bound finite elements limit analysis

Bearing capacity factors, N-c, N-q, and N-gamma, for a conical footing are determined by using the lower and upper bound axisymmetric formulation of the limit analysis in combination with finite elements and optimization. These factors are obtained in a bound form for a wide range of the values of cone apex angle (beta) and phi with delta = 0, 0.5 phi, and phi. The bearing capacity factors for a perfectly rough (delta = phi) conical footing generally increase with a decrease in beta. On the contrary, for delta = 0 degrees, the factors N-c and N-q reduce gradually with a decrease in beta. For delta = 0 degrees, the factor N-gamma for phi >= 35 degrees becomes a minimum for beta approximate to 90 degrees. For delta = 0 degrees, N-gamma for phi <= 30 degrees, as in the case of delta = phi, generally reduces with an increase in beta. The failure and nodal velocity patterns are also examined. The results compare well with different numerical solutions and centrifuge tests' data available from the literature.

An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas

We show here a 2(Omega(root d.log N)) size lower bound for homogeneous depth four arithmetic formulas. That is, we give an explicit family of polynomials of degree d on N variables (with N = d(3) in our case) with 0, 1-coefficients such that for any representation of a polynomial f in this family of the form f = Sigma(i) Pi(j) Q(ij), where the Q(ij)'s are homogeneous polynomials (recall that a polynomial is said to be homogeneous if all its monomials have the same degree), it must hold that Sigma(i,j) (Number of monomials of Q(ij)) >= 2(Omega(root d.log N)). The above mentioned family, which we refer to as the Nisan-Wigderson design-based family of polynomials, is in the complexity class VNP. Our work builds on the recent lower bound results 1], 2], 3], 4], 5] and yields an improved quantitative bound as compared to the quasi-polynomial lower bound of 6] and the N-Omega(log log (N)) lower bound in the independent work of 7].

Reply to Discussion on ``Bearing capacity of circular footings over rock mass by using axisymmetric quasi lower bound finite element limit analysis'' Comput. Geotech. 70 (2015) 138-149]

A discussion has been provided for the comments raised by the discusser (Clausen, 2015)1] on the article recently published by the authors (Chakraborty and Kumar, 2015). The effect of exponent alpha for values of GSI approximately smaller than 30 becomes more critical. On the other hand, for greater values of GSI, the results obtained by the authors earlier remain primarily independent of alpha and can be easily used. (C) 2015 Elsevier Ltd. All rights reserved.

Two-Dimensional Flood Simulation of the Lower Yellow River from Huayuankou to Jiahetan

黄河下游花园口至夹河滩河段系典型的游荡型河段.在该河段,黄河大堤内范围宽广,一般洪水频率年份,水流主要限制在主槽内,因此大堤内分布有不少居民点以及纵横交错的保护居民点的生产堤和不少高于地面的灌溉渠堤和公路,使洪水行洪范围受到了很大的限制.当洪峰流量很大时,洪水将造成生产堤溃决,极大地危害滩区居民的生活.因此,设计模拟模型计算网格时需要考虑大堤、生产堤、明显高于地面的道路等阻水建筑物的影响,使这些堤及公路成为计算格网的边.不规则四边形网格能够很好地拟合黄河这种复杂的计算域.数值模拟时采用有限体积法,为确保通量的单向性,文中使用Osher格式计算通量.通过对1982年洪水的模拟,模拟结果表明了模型的合理性.

80 C 147 U.S. Aeroplane carrier "Saratoga" and H.M.S. "Despatch" in lower chambers, Miraflores Locks - Panama Canal - 2/7/28

Leonard Carpenter Panama Canal Collection. Photographs: Views of Panama and the Canal. [Box 1] from the Special Collections & Area Studies Department, George A. Smathers Libraries, University of Florida.

PICES-GLOBEC International Program on Climate Change and Carrying Capacity: Report of the 1999 MONITOR and REX Workshops, and the 2000 MODEL Workshop on Lower Trophic Level Modelling

Table of Contents [pdf, 0.11 Mb] Executive Summary [pdf, 0.07 Mb] MODEL Task Team Workshop Report Final Report of the International Workshop to Develop a Prototype Lower Trophic Level Ecosystem Model for Comparison of Different Marine Ecosystems in the North Pacific [pdf, 11.64 Mb] Report of the 1999 MONITOR Task Team Workshop [pdf, 0.32 Mb] Report of the 1999 REX Task Team Workshop Herring and Euphausiid population dynamics Douglas E. Hay and Bruce McCarter Spatial, temporal and life-stage variation in herring diets in British Columbia [pdf, 0.10 Mb] Augustus J. Paul and J. M. Paul Over winter changes in herring from Prince William Sound, Alaska [pdf, 0.08 Mb] N. G. Chupisheva Qualitative texture characteristic of herring (Clupea pallasi pallasi) pre-larvae developed from the natural and artificial spawning-grounds in Severnaya Bay (Peter the Great Bay) [pdf, 0.07 Mb] Gordon A. McFarlane, Richard J. Beamish and Jake SchweigertPacific herring: Common factors have opposite impacts in adjacent ecosystems [pdf, 0.15 Mb] Tokimasa Kobayashi, Keizou Yabuki, Masayoshi Sasaki and Jun-Ichi Kodama Long-term fluctuation of the catch of Pacific herring in Northern Japan [pdf, 0.39 Mb] Jacqueline M. O’Connell Holocene fish remains from Saanich Inlet, British Columbia, Canada [pdf, 0.40 Mb] Elsa R. Ivshina and Irina Y. Bragina On relationship between crustacean zooplankton (Euphausiidae and Copepods) and Sakhalin-Hokkaido herring (Tatar Strait, Sea of Japan) [pdf, 0.14 Mb] Stein Kaartvbeedt Fish predation on krill and krill antipredator behaviour [pdf, 0.08 Mb] Nikolai I. Naumenko Euphausiids and western Bering Sea herring feeding [pdf, 0.07 Mb] David M. Checkley, Jr. Interactions Between Fish and Euphausiids and Potential Relations to Climate and Recruitment [pdf, 0.08 Mb] Vladimir I. Radchenko and Elena P. Dulepova Shall we expect the Korf-Karaginsky herring migrations into the offshore western Bering Sea? [pdf, 0.75 Mb] Young Shil Kang Euphausiids in the Korean waters and its relationship with major fish resources [pdf, 0.29 Mb] William T. Peterson, Leah Feinberg and Julie Keister Ecological Zonation of euphausiids off central Oregon [pdf, 0.11 Mb] Scott M. Rumsey Environmentally forced variability in larval development and stage-structure: Implications for the recruitment of Euphausia pacifica (Hansen) in the Southern California Bight [pdf, 3.26 Mb] Scott M. Rumsey Inverse modelling of developmental parameters in Euphausia pacifica: The relative importance of spawning history and environmental forcing to larval stage-frequency distributions [pdf, 98.79 Mb] Michio J. Kishi, Hitoshi Motono & Kohji Asahi An ecosystem model with zooplankton vertical migration focused on Oyashio region [pdf, 33.32 Mb] PICES-GLOBEC Implementation Panel on Climate Change and Carrying Capacity Program Executive Committee and Task Team List [pdf, 0.05 Mb] (Document pdf contains 142 pages)