Finding safety in partially controllable chaotic systems

Many discrete-time dynamical systems have a region Q from which all or almost all trajectories leave, or at least they leave in the presence of perturbations that we call disturbances. We partially control systems so that despite disturbances the trajectories of a dynamical system stay in the region Q at least for some initial points in Q. The disturbances can be thought of as either noise or as purposeful, hostile efforts of an enemy to drive the trajectory out of the region. Our goal is to keep trajectories inside Q despite the disturbances and our partial control of chaos method succeeds.Surprisingly this goal can be achieved with a control whose maximum allowable size is smaller than the maximum allowed disturbance. A fundamental step towards this goal is to compute a set called the safe set that had, until now, been found only in certain very special situations.This paper provides a general algorithm for computing safe sets. The algorithm is able to compute the safe sets for a specified region in phase space, the maximum disturbance value, and the maximum allowed control. We call it the Sculpting Algorithm. Its operation is analogous to removing material while sculpting a statue. The algorithm sculpts the safe sets. Our Sculpting Algorithm is independent of the dimension and is fast for one- and two-dimensional dynamical systems. As examples, we apply the algorithm to two paradigmatic nonlinear dynamical systems, namely, the Hénon map and the Duffing oscillator.     

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re _c  = 10⁴), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re _c  = 10⁴), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re _c  = 4 × 10⁴, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For Re _c = 4.85 × 10⁴, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.     

Thermal analysis of thin layer boilover

A mathematical model is developed to simulate the thin layer boilover phenomenon. This model takes into account convective currents as well as conduction and radiation absorption through the fuel layer and is resolved numerically employing a scheme of Runge–Kutta, combined with the numerical method of lines. Solutions of the model showed a good agreement with the experimental data, both from this work and by other authors, demonstrating the importance of the convective currents. The model provided velocities of these currents, of the same order of magnitude as the values reported in the technical literature. Thickness of the remaining fuel and the interface temperature are correctly calculated by the model, allowing the prediction of the time required for the boilover to start.     

Direct determination of 1-naphthoxylactic acid in biological fluids by non-protected fluid room temperature phosphorimetry

A selective and sensitive room-temperature phosphorimetric method for the direct determination of 1-naphthoxylactic acid (NA) in biological fluids is described. It is based on obtaining a phosphorescence signal from NA using TlNO₃ as a heavy atom perturber and Na₂SO₃ as a deoxygenator without a protective medium. This technique is named non-protected room-temperature phosphorescence (NP-RTP), which allows to determine analytes in complex matrices without the need for tedious prior separation. Optimization of the operational conditions resulted in a detection limit for NA of 9.6 ng/mL according to the error propagation theory. The repeatability and standard deviation were also determined. This method was successfully applied to the determination of NA in urine and human serum.     

A ruthenium(II) complex with p‐cymene and (S)‐2‐(anilinomethyl)pyrrolidine

The title compound, [(S)‐2‐(anilino­methyl)­pyrrolidine‐N,N′]‐chloro(η⁶‐para‐cymene)­ruthenium(II) chloride, [RuCl‐(C₁₀H₁₄)(C₁₁H₁₆N₂)]Cl, has been synthesized by the reaction of [RuCl₂(p‐cymene)]₂ (p‐cymene is para‐iso­propyl­toluene) with (S)‐2‐(anilinomethyl)­pyrrolidine in triethyl­amine/2‐propanol. The Ru atom is in a pseudo‐tetrahedral environment coordinated by a chloride ligand, the aromatic hydro­carbon is linked in a η⁶ manner and the amine is linked via its two N atoms. The chloride anion is involved in hydrogen bonding with the di­amine moieties through N—H?Cl interactions, with N?Cl distances of 3.273 (4) and 3.352 (4) Å.     

Influence of the Curing Temperature in the Mechanical and Thermal Properties of Nanosilica Filled Epoxy Resin Coating

0.5–3 wt% nanosilica was added to an epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) and cured at 25, 40 or 60 °C using isophoronediamine (IPDA) as hardener. Aggregates of nanosilica were properly dispersed into the DGEBA-IPDA resin and agglomerates formation was avoided. Addition of nanosilica increased the storage modulus E′ and the area and height of the tan δ curve of DGEBA-IPDA resin cured at 25 °C, but no significant differences were found by curing at higher temperature. Gel time measurements and the results obtained by applying the Kamal model to isotherm DSC curing of DGEBA-IPDA-nanosilica revealed that nanosilica catalysed the curing reaction between DGEBA and IPDA, in less extent by increasing the curing temperature.     

Study of the Impact Resistance of Physically and Dynamically Vulcanized Mixtures of PP/EPDM

Physically and dynamically vulcanized (TPV) mixtures of polypropylene (PP) and ethylene propylene diene terpolymer (EPDM) are prepared by extrusion in order to improve the impact resistance of PP. To enhance the chemical compatibility and provide better interaction between the PP and EPDM in the physical mixtures, both polymers are modified with maleic anhydride (MAH) in solution using xylene as solvent and dicumyl peroxide (DCP) as initiator. The qualitative and quantitative determination of the degree of grafting is study by Fourier Transform Infrared Spectroscopy (FTIR) and varying the amount of DCP and/or amount of MAH in order to determine the optimum amounts to obtain the highest degree of grafting. The effect of the relation of PP/EPDM, the amount of reinforcement filler and mix rate are studied for modified polymer mixtures (PP-g-MAH/EPDM-g-MAH). For the TPV of PP/EPDM the effects of amount and triallylisocyanurate (TAC) as coupling agent in presence of different amounts of DCP are studied. The physical mixtures of modified polymers prepared with a PP/EPDM ratio of 80/20 and the TPVs blends prepared with a PP/EPDM ratio of 70/30 and containing 15% filler at 60 rpm show the highest impact resistance. The impact resistance, melt flow index and hardness of the different mixtures are measured to determine their possible applications to prepare front panels and bumpers for automobiles by injection molding.     

Level-set techniques for microwave medical imaging

Microwave tomographic imaging is showing significant promise as a new technique for the early detection of breast cancer. Its physical basis is the contrast between the dielectric properties of the healthy breast tissue and the malignant tumors at microwave frequencies. We propose and analyze a novel shape-reconstruction technique for the early detection of breast cancer from microwave data which is based on a level-set technique. The advantages of this method compared to more traditional pixel-based approaches are well-defined boundaries and the incorporation of an intrinsic regularization in form of a-priori assumptions about the general anatomical structure of breast that reduces the dimensionality of the inverse problem and thereby stabilizes the reconstruction. Our goal is not only to detect the tumors but to simultaneously determine their approximate locations, sizes and permittivity values. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)