Adjoint Sensitivity Analysis of a Fluid-Structure Interaction Problem

A fluid-structure mathematical model usually includes parameters whose actual values are known only approximately or can vary around some reference values. The objective of the sensitivity analysis is to determine quantitatively the behavior of the responses of a fluid-structure system locally around a chosen point of the trajectory in the phase-space of parameters and dependent variables. In this work, the response considered is the total mechanical energy of the structure. The sensitivities with respect to all the parameters the fluid-structure system depends on are useful in many situations as well as for optimization purposes. We present the theoretical developments necessary for the application of the adjoint sensitivity analysis methods (ASAM) for the fully coupled governing equations of an aeroelastic system. The algorithm is general and can be applied for any kind of fluid-structure interaction problems. Illustrative numerical examples are presented for the case of typical section with two degrees of freedom. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

The <Emphasis Type=Italic>n</Emphasis>-Body Problem in Spaces of Constant Curvature. Part II: Singularities

We analyze the singularities of the equations of motion and several types of singular solutions of the n-body problem in spaces of positive constant curvature. Apart from collisions, the equations encounter noncollision singularities, which occur when two or more bodies are antipodal. This conclusion leads, on the one hand, to hybrid solution singularities for as few as three bodies, whose orbits end up in a collision-antipodal configuration in finite time; on the other hand, it produces nonsingularity collisions, characterized by finite velocities and forces at the collision instant.     

Coding of geodesics on some modular surfaces and applications to odd and even continued fractions

The connection between geodesics on the modular surface $PSL(2,\mathbb{Z})?\mathbb{H}$ and regular continued fractions, established by Series, is extended to a connection between geodesics on $\Gamma ?\mathbb{H}$ and odd and grotesque continued fractions, where $\Gamma ?{\mathbb{Z}}_{3}1{\mathbb{Z}}_3$ is the index two subgroup of $PSL(2,\mathbb{Z})$ generated by the order three elements $\left(\begin{array}{cc}\hfill 0\hfill & \hfill ?1\hfill \\ \hfill 1\hfill & \hfill 1\hfill \end{array}\right)$ and $\left(\begin{array}{cc}\hfill 0\hfill & \hfill 1\hfill \\ \hfill ?1\hfill & \hfill 1\hfill \end{array}\right)$, and having an ideal quadrilateral as fundamental domain.A similar connection between geodesics on $\Theta ?\mathbb{H}$ and even continued fractions is discussed in our framework, where $\Theta$ denotes the Theta subgroup of $PSL(2,\mathbb{Z})$ generated by $\left(\begin{array}{cc}\hfill 0\hfill & \hfill ?1\hfill \\ \hfill 1\hfill & \hfill 0\hfill \end{array}\right)$ and $\left(\begin{array}{cc}\hfill 1\hfill & \hfill 2\hfill \\ \hfill 0\hfill & \hfill 1\hfill \end{array}\right)$.     

Positron annihilation spectroscopy studies of implanted polymer membranes

Two different polymer membranes, polyethylene and Nafion, have been sequentially implanted under vacuum at room temperature with 90 keV copper ions up to 10¹⁷ ions/cm²; after each implantation step, the targets were subjected to analysis with Positron annihilation lifetime spectroscopy and coincidence Doppler broadening spectroscopy. Both membranes revealed a similar behavior regarding the high fluence superficial implantation, but with different degree of magnitude. In order to endorse the Positrons annihilation spectroscopy results, scanning electron microscopy coupled with energy‐dispersive energy has been performed on the same targets, despite its lower sensitivity.     

The Vlasov–Poisson System for Stellar Dynamics in Spaces of Constant Curvature

We obtain a natural extension of the Vlasov–Poisson system for stellar dynamics to spaces of constant Gaussian curvature \({\kappa \ne 0}\): the unit sphere \({\mathbb S^2}\), for \({\kappa > 0}\), and the unit hyperbolic sphere \({\mathbb H^2}\), for \({\kappa < 0}\). These equations can be easily generalized to higher dimensions. When the particles move on a geodesic, the system reduces to a 1-dimensional problem that is more singular than the classical analogue of the Vlasov–Poisson system. In the analysis of this reduced model, we study the well-posedness of the problem and derive Penrose-type conditions for linear stability around homogeneous solutions in the sense of Landau damping.     

SERS assessment of the cancer-specific methylation pattern of genomic DNA: towards the detection of acute myeloid leukemia in patients undergoing hematopoietic stem cell transplantation

In this label-free surface-enhanced Raman scattering (SERS) study of genomic DNA, we demonstrate that the cancer-specific DNA methylation pattern translates into specific spectral differences. Thus, DNA extracted from an acute myeloid leukemia (AML) cell line presented a decreased intensity of the 1005 cm⁻¹ band of 5-methylcytosine compared to normal DNA, in line with the well-described hypomethylation of cancer DNA. The unique methylation pattern of cancer DNA also influences the DNA adsorption geometry, resulting in higher adenine SERS intensities for cancer DNA. The possibility of detecting cancer DNA based on its SERS spectrum was validated on peripheral blood genomic DNA samples from n = 17 AML patients and n = 17 control samples, yielding an overall classification of 82% based on the 1005 cm⁻¹ band of 5-methylcytosine. By demonstrating the potential of SERS in assessing the methylation status in the case of real-life DNA samples, the study paves the way for novel methods of diagnosing cancer.

Graphical abstract

     

Electron spin resonance spectra of polymers during fluorination

ESR spectra characteristic of peroxy radicals appeared rapidly in all of eleven hydrogen-containing polymers examined when treated with dilute fluorine. These radicals presumably result from the reaction of hydrocarbon and fluorocarbon radicals, existing at undetectably low steady-state concentrations, with the oxygen impurity content of commercial fluorine. In poly(vinylidene fluoride) films of thickness 11 and 58 μm the radical contents were nearly proportional to surface area rather than volume, in agreement with earlier reports of a shallow depth of penetration. Some polymers exhibited also or exclusively a broad spectral component, varying in character with the polymer; examples are polystyrene, polyethylene, poly (vinyl chloride), poly(vinylidene chloride), polyoctafluoropentadiene, polyhexafluoropropene, and a fluorinated graphite. The broad spectral component did not react with ordinary radical scavengers such as propylene and oxygen, and is probably not due to a fluorocarbon radical but to unknown transition metal fluorides.     

Smeared and Unsmeared Chiral Vertex Operators

We prove unboundedness and boundedness of the unsmeared and smeared chiral vertex operators, respectively. We use elementary methods in bosonic Fock space, only. Possible applications to conformal two-dimensional quantum field theory, perturbation thereof, and to the perturbative construction of the sine-Gordon model by the Epstein-Glaser method are discussed. From another point of view the results of this paper can be looked at as a first step towards a Hilbert space interpretation of vertex operator algebras. Received: 16 October 1997 / Accepted: 7 July 1998