An asymptotic solution for the main problem

In this paper, an analytical solution of the main problem, a satellite only perturbed by the J2 harmonic, is derived with the aid of perturbation theory and by using DROMO variables. The solution, which is valid for circular and elliptic orbits with generic eccentricity and inclination, describes the instantaneous time variation of all orbital elements, that is, the actual values of the osculating elements

Asymptotic Solution for the Two Body Problem with Radial Perturbing Acceleration

In this article, an approximate analytical solution for the two body problem perturbed by a radial, low acceleration is obtained, using a regularized formulation of the orbital motion and the method of multiple scales. The results reveal that the physics of the problem evolve in two fundamental scales of the true anomaly. The first one drives the oscillations of the orbital parameters along each orbit. The second one is responsible of the long-term variations in the amplitude and mean values of these oscillations. A good agreement is found with high precision numerical solutions.

Asymptotic optimality of RESTART estimators in highly dependable systems

Abstract We consider a wide class of models that includes the highly reliable Markovian systems (HRMS) often used to represent the evolution of multi-component systems in reliability settings. Repair times and component lifetimes are random variables that follow a general distribution, and the repair service adopts a priority repair rule based on system failure risk. Since crude simulation has proved to be inefficient for highly-dependable systems, the RESTART method is used for the estimation of steady-state unavailability and other reliability measures. In this method, a number of simulation retrials are performed when the process enters regions of the state space where the chance of occurrence of a rare event (e.g., a system failure) is higher. The main difficulty involved in applying this method is finding a suitable function, called the importance function, to define the regions. In this paper we introduce an importance function which, for unbalanced systems, represents a great improvement over the importance function used in previous papers. We also demonstrate the asymptotic optimality of RESTART estimators in these models. Several examples are presented to show the effectiveness of the new approach, and probabilities up to the order of 10-42 are accurately estimated with little computational effort.

Forced Response of Mistuned Bladed Disks: Quantitative Validation of the Asymptotic Description

The effect of small mistuning in the forced response of a bladed disk is analyzed using a recently introduced methodology: the asymptotic mistuning model. The asymptotic mistuning model is an extremely reduced, simplified model that is derived directly from the full formulation of the mistuned bladed disk using a consistent perturbative procedure based on the relative smallness of the mistuning distortion. A detailed description of the derivation of the asymptotic mistuning model for a realistic bladed disk configuration is presented. The asymptotic mistuning model results for several different mistuning patterns and forcing conditions are compared with those from a high-resolution finite element model. The asymptotic mistuning model produces quantitatively accurate results, and, probably more relevant, it gives precise information about the factors (tuned modes and components of the mistuning pattern) that actually play a role in the vibrational forced response of mistuned bladed disks.

Asymptotic and computational analysis of mistuning effects on the dynamics of bladed disks

Es bien conocido que las pequeñas imperfecciones existentes en los álabes de un rótor de turbomaquinaria (conocidas como “mistuning”) pueden causar un aumento considerable de la amplitud de vibración de la respuesta forzada y, por el contrario, tienen típicamente un efecto beneficioso en el flameo del rótor. Para entender estos efectos se pueden llevar a cabo estudios numéricos del problema aeroelástico completo. Sin embargo, el cálculo de “mistuning” usando modelos de alta resolución es una tarea difícil de realizar, ya que los modelos necesarios para describir de manera precisa el componente de turbomáquina (por ejemplo rotor) tienen, necesariamente, un número muy elevado de grados de libertad, y, además, es necesario hacer un estudio estadístico para poder explorar apropiadamente las distribuciones posibles de “mistuning”, que tienen una naturaleza aleatoria. Diferentes modelos de orden reducido han sido desarrollados en los últimos años para superar este inconveniente. Uno de estos modelos, llamado “Asymptotic Mistuning Model (AMM)”, se deriva de la formulación completa usando técnicas de perturbaciones que se basan en que el “mistuning” es pequeño. El AMM retiene sólo los modos relevantes para describir el efecto del mistuning, y permite identificar los mecanismos clave involucrados en la amplificación de la respuesta forzada y en la estabilización del flameo. En este trabajo, el AMM se usa para estudiar el efecto del “mistuning” de la estructura y de la amortiguación sobre la amplitud de la respuesta forzada. Los resultados obtenidos son validados usando modelos simplificados del rotor y también otros de alta definición. Además, en el marco del proyecto europeo FP7 "Flutter-Free Turbomachinery Blades (FUTURE)", el AMM se aplica para diseñar distribuciones de “mistuning” intencional: (i) una que anula y (ii) otra que reduce a la mitad la amplitud del flameo de un rotor inestable; y las distribuciones obtenidas se validan experimentalmente. Por último, la capacidad de AMM para predecir el comportamiento de flameo de rotores con “mistuning” se comprueba usando resultados de CFD detallados. Abstract It is well known that the small imperfections of the individual blades in a turbomachinery rotor (known as “mistuning”) can cause a substantial increase of the forced response vibration amplitude, and it also typically results in an improvement of the flutter vibration characteristics of the rotor. The understanding of these phenomena can be attempted just by performing numerical simulations of the complete aeroelastic problem. However, the computation of mistuning cases using high fidelity models is a formidable task, because a detailed model of the whole rotor has to be considered, and a statistical study has to be carried out in order to properly explore the effect of the random mistuning distributions. Many reduced order models have been developed in recent years to overcome this barrier. One of these models, called the Asymptotic Mistuning Model (AMM), is systematically derived from the complete bladed disk formulation using a consistent perturbative procedure that exploits the smallness of mistuning to simplify the problem. The AMM retains only the essential system modes that are involved in the mistuning effect, and it allows to identify the key mechanisms of the amplification of the forced response amplitude and the flutter stabilization. In this work, AMM methodolgy is used to study the effect of structural and damping mistuning on the forced response vibration amplitude. The obtained results are verified using a one degree of freedom model of a rotor, and also high fidelity models of the complete rotor. The AMM is also applied, in the frame of the European FP7 project “Flutter-Free Turbomachinery Blades (FUTURE)”, to design two intentional mistuning patterns: (i) one to complete stabilize an unstable rotor, and (ii) other to approximately reduce by half its flutter amplitude. The designed patterns are validated experimentally. Finally, the ability of AMM to predict the flutter behavior of mistuned rotors is checked against numerical, high fidelity CFD results.

Orientation-dependent and sequence-specific expansions of CTG/CAG trinucleotide repeats in Saccharomyces cerevisiae

A quantitative and selective genetic assay was developed to monitor expansions of trinucleotide repeats (TNRs) in yeast. A promoter containing 25 repeats allows expression of a URA3 reporter gene and yields sensitivity to the drug 5-fluoroorotic acid. Expansion of the TNR to 30 or more repeats turns off URA3 and provides drug resistance. When integrated at either of two chromosomal loci, expansion rates were 1 × 10−5 to 4 × 10−5 per generation if CTG repeats were replicated on the lagging daughter strand. PCR analysis indicated that 5–28 additional repeats were present in 95% of the expanded alleles. No significant changes in CTG expansion rates occurred in strains deficient in the mismatch repair gene MSH2 or the recombination gene RAD52. The frequent nature of CTG expansions suggests that the threshold number for this repeat is below 25 in this system. In contrast, expansions of the complementary repeat CAG occurred at 500- to 1,000-fold lower rates, similar to a randomized (C,A,G) control sequence. When the reporter plasmid was inverted within the chromosome, switching the leading and lagging strands of replication, frequent expansions were observed only when CTG repeats resided on the lagging daughter strand. Among the rare CAG expansions, the largest gain in tract size was 38 repeats. The control repeats CTA and TAG showed no detectable rate of expansions. The orientation-dependence and sequence-specificity data support the model that expansions of CTG and CAG tracts result from aberrant DNA replication via hairpin-containing Okazaki fragments.

Synpolydactyly phenotypes correlate with size of expansions in HOXD13 polyalanine tract

Synpolydactyly (SPD) is a dominantly inherited congenital limb malformation. Typical cases have 3/4 finger and 4/5 toe syndactyly, with a duplicated digit in the syndactylous web, but incomplete penetrance and variable expressivity are common. The condition has recently been shown to be caused by expansions of an imperfect trinucleotide repeat sequence encoding a 15-residue polyalanine tract in HOXD13. We have studied 16 new and 4 previously published SPD families, with between 7 and 14 extra residues in the tract, to analyze the molecular basis for the observed variation in phenotype. Although there is no evidence of change in expansion size within families, even over six generations, there is a highly significant increase in the penetrance and severity of phenotype with increasing expansion size, affecting both hands (P = 0.012) and feet (P < 0.00005). Affected individuals from a family with a 14-alanine expansion, the largest so far reported, all have a strikingly similar and unusually severe limb phenotype, involving the first digits and distal carpals. Affected males from this family also have hypospadias, not previously described in SPD, but consistent with HOXD13 expression in the developing genital tubercle. The remarkable correlation between phenotype and expansion size suggests that expansion of the tract leads to a specific gain of function in the mutant HOXD13 protein, and has interesting implications for the role of polyalanine tracts in the control of transcription.

The asymptotic distribution of canonical correlations and vectors in higher-order cointegrated models

The study of the large-sample distribution of the canonical correlations and variates in cointegrated models is extended from the first-order autoregression model to autoregression of any (finite) order. The cointegrated process considered here is nonstationary in some dimensions and stationary in some other directions, but the first difference (the “error-correction form”) is stationary. The asymptotic distribution of the canonical correlations between the first differences and the predictor variables as well as the corresponding canonical variables is obtained under the assumption that the process is Gaussian. The method of analysis is similar to that used for the first-order process.

Evolution of vertebrate steroid receptors from an ancestral estrogen receptor by ligand exploitation and serial genome expansions

The evolution of novelty in tightly integrated biological systems, such as hormones and their receptors, seems to challenge the theory of natural selection: it has not been clear how a new function for any one part (such as a ligand) can be selected for unless the other members of the system (e.g., a receptor) are already present. Here I show—based on identification and phylogenetic analysis of steroid receptors in basal vertebrates and reconstruction of the sequences and functional attributes of ancestral proteins—that the first steroid receptor was an estrogen receptor, followed by a progesterone receptor. Genome mapping and phylogenetic analyses indicate that the full complement of mammalian steroid receptors evolved from these ancient receptors by two large-scale genome expansions, one before the advent of jawed vertebrates and one after. Specific regulation of physiological processes by androgens and corticoids are relatively recent innovations that emerged after these duplications. These findings support a model of ligand exploitation in which the terminal ligand in a biosynthetic pathway is the first for which a receptor evolves; selection for this hormone also selects for the synthesis of intermediates despite the absence of receptors, and duplicated receptors then evolve affinity for these substances. In this way, novel hormone-receptor pairs are created, and an integrated system of increasing complexity elaborated. This model suggests that ligands for some “orphan” receptors may be found among intermediates in the synthesis of ligands for phylogenetically related receptors.

One-sided asymptotic inferences for a proportion.

Two-sided asymptotic confidence intervals for an unknown proportion p have been the subject of a great deal of literature. Surprisingly, there are very few papers devoted, like this article, to the case of one tail, despite its great importance in practice and the fact that its behavior is usually different from that of the case with two tails. This paper evaluates 47 methods and concludes that (1) the optimal method is the classic Wilson method with a correction for continuity and (2) a simpler option, almost as good as the first, is the new adjusted Wald method (Wald's classic method applied to the data increased in the values proposed by Borkowf: adding a single imaginary failure or success).

Nonequilibrium expansions of air with coupled chemical reactions

Caption title.

Asymptotic properties of stationary sequences.

Bibliography: p. 146.

Asymptotic bifurcation results for quasilinear elliptic operators

We develop results for bifurcation from the principal eigenvalue for certain operators based on the p-Laplacian and containing a superlinear nonlinearity with a critical Sobolev exponent. The main result concerns an asymptotic estimate of the rate at which the solution branch departs from the eigenspace. The method can also be applied for nonpotential operators.