Vorticity moments in four numerical simulations of the 3D Navier-Stokes equations

The issue of intermittency in numerical solutions of the 3D Navier-Stokes equations on a periodic box 0, L](3) is addressed through four sets of numerical simulations that calculate a new set of variables defined by D-m(t) = (pi(-1)(0) Omega(m))(alpha m) for 1 <= m <= infinity where alpha(m) = 2m/(4m - 3) and Omega(m)(t)](2m) = L-3 integral(v) vertical bar omega vertical bar(2m) dV with pi(0) = vL(-2). All four simulations unexpectedly show that the D-m are ordered for m = 1,..., 9 such that Dm+1 < D-m. Moreover, the D-m squeeze together such that Dm+1/D-m NE arrow 1 as m increases. The values of D-1 lie far above the values of the rest of the D-m, giving rise to a suggestion that a depletion of nonlinearity is occurring which could be the cause of Navier-Stokes regularity. The first simulation is of very anisotropic decaying turbulence; the second and third are of decaying isotropic turbulence from random initial conditions and forced isotropic turbulence at fixed Grashof number respectively; the fourth is of very-high-Reynolds-number forced, stationary, isotropic turbulence at up to resolutions of 4096(3).

A FRAMEWORK FOR THE ERROR ANALYSIS OF DISCONTINUOUS FINITE ELEMENT METHODS FOR ELLIPTIC OPTIMAL CONTROL PROBLEMS AND APPLICATIONS TO C-0 IP METHODS

In this article, an abstract framework for the error analysis of discontinuous Galerkin methods for control constrained optimal control problems is developed. The analysis establishes the best approximation result from a priori analysis point of view and delivers a reliable and efficient a posteriori error estimator. The results are applicable to a variety of problems just under the minimal regularity possessed by the well-posedness of the problem. Subsequently, the applications of C-0 interior penalty methods for a boundary control problem as well as a distributed control problem governed by the biharmonic equation subject to simply supported boundary conditions are discussed through the abstract analysis. Numerical experiments illustrate the theoretical findings.

Isolated singularities of polyharmonic operator in even dimension

We consider the equation Delta(2)u = g(x, u) >= 0 in the sense of distribution in Omega' = Omega\textbackslash {0} where u and -Delta u >= 0. Then it is known that u solves Delta(2)u = g(x, u) + alpha delta(0) - beta Delta delta(0), for some nonnegative constants alpha and beta. In this paper, we study the existence of singular solutions to Delta(2)u = a(x) f (u) + alpha delta(0) - beta Delta delta(0) in a domain Omega subset of R-4, a is a nonnegative measurable function in some Lebesgue space. If Delta(2)u = a(x) f (u) in Omega', then we find the growth of the nonlinearity f that determines alpha and beta to be 0. In case when alpha = beta = 0, we will establish regularity results when f (t) <= Ce-gamma t, for some C, gamma > 0. This paper extends the work of Soranzo (1997) where the author finds the barrier function in higher dimensions (N >= 5) with a specific weight function a(x) = |x|(sigma). Later, we discuss its analogous generalization for the polyharmonic operator.

A C-0 Interior Penalty Method for a Fourth-order Variational Inequality of the Second Kind

In this article, we propose a C-0 interior penalty ((CIP)-I-0) method for the frictional plate contact problem and derive both a priori and a posteriori error estimates. We derive an abstract error estimate in the energy norm without additional regularity assumption on the exact solution. The a priori error estimate is of optimal order whenever the solution is regular. Further, we derive a reliable and efficient a posteriori error estimator. Numerical experiments are presented to illustrate the theoretical results. (c) 2015Wiley Periodicals, Inc.

COMPLEX GEODESICS, THEIR BOUNDARY REGULARITY, AND A HARDY-LITTLEWOOD-TYPE LEMMA

We begin by giving an example of a smoothly bounded convex domain that has complex geodesics that do not extend continuously up to partial derivative D. This example suggests that continuity at the boundary of the complex geodesics of a convex domain Omega (sic) C-n, n >= 2, is affected by the extent to which partial derivative Omega curves or bends at each boundary point. We provide a sufficient condition to this effect (on C-1-smoothly bounded convex domains), which admits domains having boundary points at which the boundary is infinitely flat. Along the way, we establish a Hardy-Littlewood-type lemma that might be of independent interest.

The degree of predictability of earthquakes in several regions of China: statistical analysis of historical data

The stress release model, a stochastic version of the elastic-rebound theory, is applied to the historical earthquake data from three strong earthquake-prone regions of China, including North China, Southwest China, and the Taiwan seismic regions. The results show that the seismicity along a plate boundary (Taiwan) is more active than in intraplate regions (North and Southwest China). The degree of predictability or regularity of seismic events in these seismic regions, based on both the Akaike information criterion (AIC) and fitted sensitivity parameters, follows the order Taiwan, Southwest China, and North China, which is further identified by numerical simulations. (c) 2004 Elsevier Ltd. All rights reserved.

Laser Guiding in the Randomicity of Discrete Surface Strengthening by Arc Discharge

Several discharge areas by laser-guided discharge (LGD) were compared with those by common arc discharge. The randomicity of discharge areas by common arc discharge was controlled by laser guiding on two scales: large scale (the spacing of the discharge areas) and small scale (the inside of the discharge area). The position of the discharge area overlapped completely with a laser focus; therefore, the distribution and surface shape of the discharge areas were controlled. The stochastic movement of anode spot in the discharge area was controlled by laser guiding. As such, the repetitive melting and solidifying of microstructures in the discharge area was constrained. The tempered microstruc- tures in the discharge area were voided, the utilization efficiency of input energy was improved, and the strengthened depth of the discharge areas was increased. The regularity of cross-sectional shape of the discharge area was also improved. The hardness of microstructures in both discharge areas is greater than that of the base material. The highest level of hardness of microstructures in both discharge areas measures above 1000 HV. In summary, the hardness ofmicrostructures in the discharge area by LGD is larger and more discrete than that by common arc discharge.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.

Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach

Constitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.

The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.

Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.

In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.

In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.

Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.

Epigenetic inheritance in plants.

The function of plant genomes depends on chromatin marks such as the methylation of DNA and the post-translational modification of histones. Techniques for studying model plants such as Arabidopsis thaliana have enabled researchers to begin to uncover the pathways that establish and maintain chromatin modifications, and genomic studies are allowing the mapping of modifications such as DNA methylation on a genome-wide scale. Small RNAs seem to be important in determining the distribution of chromatin modifications, and RNA might also underlie the complex epigenetic interactions that occur between homologous sequences. Plants use these epigenetic silencing mechanisms extensively to control development and parent-of-origin imprinted gene expression.

Can the occurrence of rare insertion/deletion polymorphisms in human mtDNA be verified from phylogeny?

Due to its specific characteristics, such as maternal inheritance and absence of recombination, each mtDNA belongs to certain monophyletic clade in the rooted mtDNA tree (haplogroup) according to the mutations it harbors. Rare mutation (excluding parallel mutation) occurring at multiple times in different haplogroups could thus be a potential reading error according to the mtDNA phylogeny. This experience has been widely used in double-checking the credibility of the rare mutations in human mtDNA sequences. However, no test has been performed so far for the feasibility of applying this strategy to the rare insertion/deletion (indel) events in mtDNA sequences. In this study, we attempted to relate the rare indels in mtDNAs to their haplogroup status in a total of 2352 individuals from 50 populations in China. Our results show that the insertion of A at position 16259 is restricted to a subclade of haplogroup C and can be verified. The other indel polymorphisms, which occur in the repeat of the deleted or inserted nucleotide(s), may not be distinguished from phantom mutations from a phylogenetic point of view. Independently and multiply sequencing the fragment with the indel is the best and the most reliable way for confirmation.

Irregular morphine administration affects the retention but not acquisition of conditioned place preference in rats

Drug addiction is increasingly viewed as the expression of abnormal associative learning following repeated exposures to the drugs of abuse Previous I studies have demonstrated that the patterns of repetition such as frequency and spacing are important to many kinds of learning and memory retention We hypothesized that drug repetition pattern might affect the reward-related learning although the total doses of the drug were the same. In the present study, we tested morphine-induced place preference following either regular or irregular pattern of morphine pairing in rats Regular morphine group received morphine administration daily at a regular time with the same dose Irregular morphine groups received morphine administration either at the same time but irregular doses, irregular time but same dose, or irregular time and irregular doses. We found that rats, who received irregular morphine pairing, exhibited similar acquisition of peace preference but different preference retentions compared with regular morphine-treated rats after the same total dose of morphine Rats, who received morphine administration at the same time but irregular doses and at irregular time and irregular doses, showed rapid disruption of place preference than the regular morphine group. Rats, who received morphine at irregular time but the same dose, showed similar retention of place preference to regular morphine group Our results suggest that the pattern of drug pairing plays an important role in the retention of reward-related memory This study may provide new evidence to broaden our understanding of the development and maintenance of drug craving (C) 2009 Elsevier B V. All rights reserved

Robust estimation of local genetic ancestry in admixed populations using a nonparametric Bayesian approach.

We present a new haplotype-based approach for inferring local genetic ancestry of individuals in an admixed population. Most existing approaches for local ancestry estimation ignore the latent genetic relatedness between ancestral populations and treat them as independent. In this article, we exploit such information by building an inheritance model that describes both the ancestral populations and the admixed population jointly in a unified framework. Based on an assumption that the common hypothetical founder haplotypes give rise to both the ancestral and the admixed population haplotypes, we employ an infinite hidden Markov model to characterize each ancestral population and further extend it to generate the admixed population. Through an effective utilization of the population structural information under a principled nonparametric Bayesian framework, the resulting model is significantly less sensitive to the choice and the amount of training data for ancestral populations than state-of-the-art algorithms. We also improve the robustness under deviation from common modeling assumptions by incorporating population-specific scale parameters that allow variable recombination rates in different populations. Our method is applicable to an admixed population from an arbitrary number of ancestral populations and also performs competitively in terms of spurious ancestry proportions under a general multiway admixture assumption. We validate the proposed method by simulation under various admixing scenarios and present empirical analysis results from a worldwide-distributed dataset from the Human Genome Diversity Project.

Microsatellites assessment of Chinese sturgeon (Acipenser sinensis Gray) genetic variability

Four microsatellites were used to examine the genetic variability of the spawning stocks of Chinese sturgeon, Acipenser sinensis, from the Yangtze River sampled over a 3-year period (1999-2001). Within 60 individuals, a total of 28 alleles were detected over four polymorphic microsatellite loci. The number of alleles per locus ranged from 4 to 15, with an average allele number of 7. The number of genotypes per locus ranged from 6 to 41. The genetic diversity of four microsatellite loci varied from 0.34 to 0.67, with an average value of 0.54. For the four microsatellite loci, the deviation from the Hardy-Weinberg equilibrium was mainly due to null alleles. The mean number of alleles per locus and the mean heterozygosity were lower than the average values known for anadromous fishes. Fish were clustered according to their microsatellite characteristics using an unsupervised 'Artificial Neural Networks' method entitled 'Self-organizing Map'. The results revealed no significant genetic differentiation considering genetic distance among samples collected during different years. Lack of heterogeneity among different annual groups of spawning stocks was explained by the complex age structure (from 8 to 27 years for males and 12 to 35 years for females) of Chinese sturgeon, leading to formulate an hypothesis about the maintenance of genetic diversity and stability in long-lived animals.

Genetic diversity among different clones of the gynogenetic silver crucian carp, Carassius auratus gibelio, revealed by transferrin and isozyme markers

Genetic diversity among four clones (A, D, E, F) of gynogenetic silver crucian carp was studied using transferrin and isozymes in the blood as markers. Of the five proteins investigated, three (transferrin, esterase and superoxide dismutase) indicated polymorphism and eight polymorphic loci were detected. These loci were probably encoded by codominant alleles and their inheritance patterns were analyzed. Intraclonal homogeneity and interclonal heterogeneity were observed in these clones, which allowed us to infer the clonal nature and evolutionary relationship between them. Clonal diversity in this population of silver crucian carp in China was also compared with data reported from gynogenetic crucian carp in Germany.