Incremental displacement-correction schemes for incompressible fluid-structure interaction

In this paper we introduce a class of incremental displacement-correction schemes for the explicit coupling of a thin-structure with an incompressible fluid. These methods enforce a specific Robin–Neumann explicit treatment of the interface coupling. We provide a general stability and convergence analysis that covers both the incremental and the non-incremental variants. Their stability properties are independent of the added-mass effect. The superior accuracy of the incremental schemes (with respect to the original non-incremental variant) is highlighted by the error estimates, and then confirmed in a benchmark by numerical experiments.     

First Nonlinear Syzygies of Ideals Associated to Graphs

Consider an ideal I ? K[x ₁,…, x _n ], with K an arbitrary field, generated by monomials of degree two. Assuming that I does not have a linear resolution, we determine the step s of the minimal graded free resolution of I where nonlinear syzygies first appear, we show that at this step of the resolution nonlinear syzygies are concentrated in degree s + 3, and we compute the corresponding graded Betti number β _{s, s+3}. The multidegrees of these nonlinear syzygies are also determined and the corresponding multigraded Betti numbers are shown to be all equal to 1.     

Speckle-based modulation transfer function measurements for comparative evaluation of CCD and CMOS detector arrays

Charge-coupled device (CCD) and complementary metal-oxide semiconductor (CMOS) matrices offer excellent features in imaging systems. For assessing the suitability of each technology according to the application, the complete characterization of the detector arrays becomes necessary. A system is optically characterized by the modulation transfer function (MTF). We have comparatively studied the results provided by the speckle method for detectors of two types: CCD and CMOS. To do so, we first analysed the precision in determining the MTF of the CCD using two apertures at the exit port of an integrating sphere: a single and a double-slit. For the single-slit, we propose a new procedure of fitting the experimental data which overcomes the drawbacks of the conventional procedure. Since it offered lower uncertainty and better reproducibility, the single-slit was used for the study with the CMOS detector. Significant differences were found between the MTF of the CCD and the CMOS detectors.     

The geometry and electronic structure of Aristolochic acid: possible implications for a frozen resonance

Molecular mutagens and carcinogens are structures which carry chemical and electronic properties that disturb and interact with the genomic machinery. Principally, a rule of thumb for carcinogens is that carcinogens are expected to introduce covalent irreversible bonding to one or several types of DNA bases, causing errors in the reading frame for the polymerases. 8‐methoxy‐6‐nitrophenanthro[3,4‐d][1,3]dioxole‐5‐carboxylic acid, better known as Aristolochic acid (AA1) is a recognized carcinogen which causes urotherial cancer and is found in certain plants. Its structure is particularly interesting given that it is closely related to phenanthrene in its polycyclic arrangement, and has four functional groups, a carboxyl‐, a nitro‐, a methoxy‐ and a dioxolane group. In this work, the structure of AA1 has been resolved at the MPWPW91 density functional theory method in combination with Aug‐cc‐pVDZ basis sets. A geometry analysis shows that in AA1 the carboxyl group's torsion is caused by steric strain from the nitro group, which elevates the molecular plane of the first phenanthrene ring with 0.1Å. The wavefunction analysis of AA1 shows that the ring deformation enhances a double π‐bond localization in the first ring, adjacent to the dioxalane group, and results in a decrease of ring aromaticity and induces a potentially frozen resonance. Intermolecular and intramolecular interactions were characterized by atoms in molecules and reduced density gradient analysis. This study brings novel information on the geometry and electronic structure of AA1, which are important for the further knowledge of its transformation in vivo and in situ. Copyright © 2013 John Wiley & Sons, Ltd.     

Microscopic study of neutron-rich dysprosium isotopes

Microscopic studies in heavy nuclei are very scarce due to large valence spaces involved. This computational problem can be avoided by means of the use of symmetry-based models. Ground-state, γ and β bands, and their B(E2) transition strengths in ^160–168Dy isotopes, are studied in the framework of the pseudo-SU(3) model which includes the preserving symmetry Q · Q term and the symmetry-breaking Nilsson and pairing terms, systematically parametrized. Additionally, three rotor-like terms are considered, whose free parameters, fixed for all members of the chain, are used to fine tune the moment of inertia of rotational bands and the band head of γ and β bands. The model succesfully describes in a systematic way rotational features in these nuclei and allows to extrapolate toward the midshell nucleus ¹⁷⁰Dy. The results presented show that it is possible to study a full chain of isotopes or isotones in the region with the present model.     

Prediction-based control of chaos and a dynamic Parrondoʼs paradox

We analyze the stabilization of an unstable periodic orbit (UPO) by periodic prediction-based control (PBC). We rigorously prove that, for 2-periodic orbits, a pulse strategy reduces the necessary control strength to stabilize the UPO. Moreover, we find that in some cases the periodic control prevents some undesirable effects induced by the PBC method. In this way, we provide an example of a dynamic Parrondo?s paradox: the switching between two undesirable dynamics results in a nicely periodic dynamic behavior.     

The Existence Of Nonhomogeneous,Viscous And Incompressible Flow In Unbounded Domains

The existence of global (in time) solution {ρu,p} (density, velocity field and pressure) of a partial differential problem modelling the behaviour of a viscous, nonhomogenous and incompressible flow has been recently obtained viscous, nonhomogenous and incompressible flow has been recently obtained by J. Simon. In his most general result, he finds a solution which satifies an initial condition in an appropriate weak sense. In this paper, we present an extension of this result to the case of arbitrary unbounded three–dimensional fluid domains.

1. Introduction.

2. The main result.

3. Some technical Lemmas.

4. Proof of Theorem 1.

4.1 The existence and properties of {ρR, U^R PR}

4.2 Some estimates for ρR,U^R and their time derivatives.

4.3 Further estimates.

4.4 The choice of a convergent sequence and conclusions.

References.     

Continuity of the Explosion Time in Stochastic Differential Equations

Abstract

Stochastic ordinary differential equations may have solutions that explode in finite time. In this article we prove the continuity of the explosion time with respect to the different parameters appearing in the equation, such as the initial datum, the drift, and the diffusion.     

An Elliptic Non Distributive Algebra

In this paper we extend the results of hyperbolic scator algebra introduced in [5], to consider an elliptic product in a subset of ${\mathbb{R}^{1 + n}}$ which recovers the field of complex numbers when only one director component is present. The product of this algebra, that we call elliptic scator algebra in ${\mathbb{E}^{1 + n}}$ , is associative and commutative provided that divisors of zero are excluded. However, as with the hyperbolic case, the elliptic product is not distributive over addition. We explore the geometry of this algebra by considering some interesting objects, such as spheres.