A finite element method for the Saint-Venant torsion and bending problems for prismatic beams

In this work, we present a finite element formulation for the Saint-Venant torsion and bending problems for prismatic beams. The torsion problem formulation is based on the warping function, and can handle multiply-connected regions (including thin-walled structures), compound and anisotropic bars. Similarly, the bending formulation, which is based on linearized elasticity theory, can handle multiply-connected domains including thin-walled sections. The torsional rigidity and shear centers can be found as special cases of these formulations. Numerical results are presented to show the good coarse-mesh accuracy of both the formulations for both the displacement and stress fields. The stiffness matrices and load vectors (which are similar to those for a variable body force in a conventional structural mechanics problem) in both formulations involve only domain integrals, which makes them simple to implement and computationally efficient. (C) 2014 Elsevier Ltd. All rights reserved.

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.

Infection of human amniotic and endothelial cells by Japanese encephalitis virus: Increased expression of HLA-F

Productive infection of human amniotic and endothelial cell lines with Japanese encephalitis virus (JEV) was established leading to the induction of NF kappa B and HLA-F, a non-classical MHC molecule. Induction of the HLA-F gene and protein in JEV-infected cells was shown to be NF kappa B dependent since it was blocked by inhibitors of NF kappa B activation. ShRNA targeting lentivirus-mediated stable knockdown of the p65 subunit of NF kappa B inhibited JEV-mediated induction of HLA-F both in the amniotic cell line, AV-3 as well as the human brain microendothelial cell line, HBMEC. The induction of HLA-F by treatment of AV-3 with TNF-alpha was also inhibited by ShRNA mediated knockdown of NF kappa B. TNF-alpha treatment of HEK293T cells that were transfected with reporter plasmids under the control of HLA-F enhancer A elements resulted in significant transactivation of the luciferase reporter gene. NF kappa B-mediated induction of HLA-F following JEV infection and TNF-alpha exposure is being suggested for the first time. (C) 2014 Elsevier Inc. All rights reserved.

Optimal error estimate using mesh equidistribution technique for singularly perturbed system of reaction-diffusion boundary-value problems

In this article, we study the problem of determining an appropriate grading of meshes for a system of coupled singularly perturbed reaction-diffusion problems having diffusion parameters with different magnitudes. The central difference scheme is used to discretize the problem on adaptively generated mesh where the mesh equation is derived using an equidistribution principle. An a priori monitor function is obtained from the error estimate. A suitable a posteriori analogue of this monitor function is also derived for the mesh construction which will lead to an optimal second-order parameter uniform convergence. We present the results of numerical experiments for linear and semilinear reaction-diffusion systems to support the effectiveness of our preferred monitor function obtained from theoretical analysis. (C) 2014 Elsevier Inc. All rights reserved.

An interior penalty method for distributed optimal control problems governed by the biharmonic operator

In this paper, a C-0 interior penalty method has been proposed and analyzed for distributed optimal control problems governed by the biharmonic operator. The state and adjoint variables are discretized using continuous piecewise quadratic finite elements while the control variable is discretized using piecewise constant approximations. A priori and a posteriori error estimates are derived for the state, adjoint and control variables under minimal regularity assumptions. Numerical results justify the theoretical results obtained. The a posteriori error estimators are useful in adaptive finite element approximation and the numerical results indicate that the sharp error estimators work efficiently in guiding the mesh refinement. (C) 2014 Elsevier Ltd. All rights reserved.

Hydrodynamic instability and shear layer effect on the response of an acoustically excited laminar premixed flame

Combustion instabilities can cause serious problems which limit the operating envelope of low-emission lean premixed combustion systems. Predicting the onset of combustion instability requires a description of the unsteady heat release driving the instability, i.e., the heat release response transfer function of the system. This study focuses on the analysis of fully coupled two-way interactions between a disturbance field and a laminar premixed flame that incorporates gas expansion effects by solving the conservation equations of a compressible fluid. Results of the minimum and maximum flame front deflections are presented to underline the impact of the hydrodynamic instability on the flame and the shear layer effect on the initial flame front wrinkling which is increased at decreasing gas expansion. These phenomena influence the magnitude of the burning area and burning area rate response of the flame at lower frequency excitation more drastically than reduced-order model (ROM) predictions even for low temperature ratios. It is shown that the general trend of the flame response magnitudes can be well captured at higher frequency excitation, where stretch effects are dominant. The phase response is influenced by the DL mechanism, which cannot be captured by the ROM, and by the resulting discrepancy in the flame pocket formation and annihilation process at the flame tip. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved,

A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems

A finite difference method for a time-dependent singularly perturbed convection-diffusion-reaction problem involving two small parameters in one space dimension is considered. We use the classical implicit Euler method for time discretization and upwind scheme on the Shishkin-Bakhvalov mesh for spatial discretization. The method is analysed for convergence and is shown to be uniform with respect to both the perturbation parameters. The use of the Shishkin-Bakhvalov mesh gives first-order convergence unlike the Shishkin mesh where convergence is deteriorated due to the presence of a logarithmic factor. Numerical results are presented to validate the theoretical estimates obtained.

Changes in the expression of DNA double strand break repair genes in primordial follicles from immature and aged rats

Oocytes present at birth undergo a progressive process of apoptosis in humans and other mammals as they age. Accepted opinion is that no fresh oocytes are produced other than those present at the time of birth. Studies have shown that DNA repair genes in oocytes of mice and women decline with age, and lack of these genes show higher DNA breaks and increased oocyte death rates. In contrast to the ethical problems associated with monitoring the changes in DNA double-strand breaks in oocytes from young and old humans, it is relatively easy to carry out such a study using a rodent model. In this study, the mRNA levels of DNA repair genes are compared with protein products of some of the genes in the primordial follicles isolated from immature (18-20 days) and aged (400-450 days) female rats. Results revealed a significant decline in mRNA levels of BRAC1 (P < 0.01), RAD51 (P < 0.05), ERCC2 (P < 0.05), and H2AX (P < 0.01) of DNA repair genes and phospho-protein levels of BRAC1 (P < 0.01) and H2AX (P < 0.05) in primordial follicles of aged rats. Impaired DNA repair is confirmed as a mechanism of oocyte ageing. (C) 2014 Reproductive Healthcare Ltd. Published by Elsevier Ltd. All rights reserved.

Comparison of a priori and a posteriori meshes for singularly perturbed nonlinear parameterized problems

This paper deals with the adaptive mesh generation for singularly perturbed nonlinear parameterized problems with a comparative research study on them. We propose an a posteriori error estimate for singularly perturbed parameterized problems by moving mesh methods with fixed number of mesh points. The well known a priori meshes are compared with the proposed one. The comparison results show that the proposed numerical method is highly effective for the generation of layer adapted a posteriori meshes. A numerical experiment of the error behavior on different meshes is carried out to highlight the comparison of the approximated solutions. (C) 2015 Elsevier B.V. All rights reserved.

Minimization Problems Based on Relative alpha-Entropy I: Forward Projection

Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative alpha-entropies (denoted I-alpha), arise as redundancies under mismatched compression when cumulants of compressed lengths are considered instead of expected compressed lengths. These parametric relative entropies are a generalization of the usual relative entropy (Kullback-Leibler divergence). Just like relative entropy, these relative alpha-entropies behave like squared Euclidean distance and satisfy the Pythagorean property. Minimizers of these relative alpha-entropies on closed and convex sets are shown to exist. Such minimizations generalize the maximum Renyi or Tsallis entropy principle. The minimizing probability distribution (termed forward I-alpha-projection) for a linear family is shown to obey a power-law. Other results in connection with statistical inference, namely subspace transitivity and iterated projections, are also established. In a companion paper, a related minimization problem of interest in robust statistics that leads to a reverse I-alpha-projection is studied.

Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted I-alpha) were studied. Such minimizers were called forward I-alpha-projections. Here, a complementary class of minimization problems leading to the so-called reverse I-alpha-projections are studied. Reverse I-alpha-projections, particularly on log-convex or power-law families, are of interest in robust estimation problems (alpha > 1) and in constrained compression settings (alpha < 1). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse I-alpha-projection into a forward I-alpha-projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

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.

Unique Covering Problems with Geometric Sets

The Exact Cover problem takes a universe U of n elements, a family F of m subsets of U and a positive integer k, and decides whether there exists a subfamily(set cover) F' of size at most k such that each element is covered by exactly one set. The Unique Cover problem also takes the same input and decides whether there is a subfamily F' subset of F such that at least k of the elements F' covers are covered uniquely(by exactly one set). Both these problems are known to be NP-complete. In the parameterized setting, when parameterized by k, Exact Cover is W1]-hard. While Unique Cover is FPT under the same parameter, it is known to not admit a polynomial kernel under standard complexity-theoretic assumptions. In this paper, we investigate these two problems under the assumption that every set satisfies a given geometric property Pi. Specifically, we consider the universe to be a set of n points in a real space R-d, d being a positive integer. When d = 2 we consider the problem when. requires all sets to be unit squares or lines. When d > 2, we consider the problem where. requires all sets to be hyperplanes in R-d. These special versions of the problems are also known to be NP-complete. When parameterizing by k, the Unique Cover problem has a polynomial size kernel for all the above geometric versions. The Exact Cover problem turns out to be W1]-hard for squares, but FPT for lines and hyperplanes. Further, we also consider the Unique Set Cover problem, which takes the same input and decides whether there is a set cover which covers at least k elements uniquely. To the best of our knowledge, this is a new problem, and we show that it is NP-complete (even for the case of lines). In fact, the problem turns out to be W1]-hard in the abstract setting, when parameterized by k. However, when we restrict ourselves to the lines and hyperplanes versions, we obtain FPT algorithms.