Symmetry Groups and Non-Planar Collisionless Action-Minimizing Solutions of the Three-Body Problem in Three-Dimensional Space

Periodic and quasi-periodic solutions of the n-body problem can be found as minimizers of the Lagrangian action functional restricted to suitable spaces of symmetric paths. The main purpose of this paper is to develop a systematic approach to the equivariant minimization for the three-body problem in three-dimensional space. First we give a finite complete list of symmetry groups fitting to the minimization of the action, with the property that any other symmetry group can be reduced to be isomorphic to one of these representatives. A second step is to prove that the resulting (local and global) symmetric action-minimizers are always collisionless (when they are not already bound to collisions). Furthermore, we prove some results which address the question of whether minimizers are planar or non-planar; as a consequence of our theory we will give general criteria for a symmetry group to yield planar or homographic minimizers (either homographic or not, as in the Chenciner-Montgomery eight solution). On the other hand we will provide a rigorous proof of the existence of some interesting one-parameter families of periodic and quasi-periodic non-planar orbits. These include the choreographic Marchal's P₁₂ family with equal masses – together with a less-symmetric choreographic family (which anyway probably coincides with the P₁₂ family).     

Uniaxial Modeling of Multivariant Shape-Memory Materials with Internal Sublooping using Dissipation Functions

Models for the macroscopic behavior of Shape Memory Materials can be conveniently constructed within the Ziegler–Green–Naghdi framework where all the constitutive information is encoded in two ingredients: the free energy and the dissipation function. In a previous work, we have proposed various expressions for the basic functions suitable to model pseudoelasticity with complete transformations cycles. In this work we consider additional effects due to Martensite reorientation and to transformation reversal prior to transformation completion. The new constitutive model allows for the modeling of a variety of effects including: shape memory associated with thermally induced transformation, internal pseudoelastic subloops and the determination of limit cycles associated with repetitive stress cycling.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

Coherent Structures Formation During Wake-Boundary Layer Interaction on a LP Turbine Blade

Particle Image Velocimetry (PIV) measurements have been analyzed in order to characterize the dynamics of coherent structures (eddies and streaks) within the suction side boundary layer of a low pressure turbine cascade perturbed by impinging wakes. To this end, the instantaneous flow fields at low Reynolds number and elevated free-stream turbulence intensity level (simulating the real condition of the blade row within the engine) were investigated in two orthogonal planes (a blade-to-blade and a wall-parallel plane). Proper Orthogonal Decomposition (POD) has been employed to filter the instantaneous flow maps allowing a better visualization of the structures involved in the transition process of the boundary layer. For the unsteady case properly selected POD modes have been also used to sort the instantaneous PIV images in the wake passage period. This procedure allows computing phase-averaged data and visualizing structures size and intensity in the different parts of the boundary layer during the different wake passage phases. The contributions to the whole shear stress due to the largest spanwise oriented scales at the leading and trailing boundaries of the wake-jet structures and those associated with streaky structures observed in the bulk of the wake are discussed. Instantaneous images in the wall-parallel plane are filtered with POD and they allow us to further highlight the occurrence of low and high speed traveling streaks (Klebanoff mode). The periodic advection along the suction side of the high turbulent content regions carried by the wakes anticipates both formation and sinuous instability of the streaks inside the boundary layer as compared with the steady case. The dynamics driving the breakdown of the streaks and the consequent formation of nuclei with high wall-normal vorticity have been found to be almost the same in the steady and the unsteady cases. Auto-correlation of the instantaneous images are also presented in order to highlight analogies and differences in the size and spacing of streaks in the two cases. These results are also compared with the available literature concerning simplified geometries (i.e flat plate) operating under steady inflow.     

Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces

In this paper we compute Stokes matrices and monodromy of the quantum cohomology of projective spaces. This problem can be formulated in a “classical” framework, as the problem of computation of Stokes matrices and monodromy of differential equations with regular and irregular singularities. We prove that the Stokes' matrix of the quantum cohomology coincides with the Gram matrix in the theory of derived categories of coherent sheaves. We also study the monodromy group of the quantum cohomology and we show that it is related to hyperbolic triangular groups. Received: 24 October 1998 / Accepted: 27 April 1999     

Modular engineering of H-bonded supramolecular polymers for reversible functionalization of carbon nanotubes

A H-bond-driven, noncovalent, reversible solubilization/functionalization of multiwalled carbon nanotubes (MWCNTs) in apolar organic solvents (CHCl(3), CH(2)Cl(2), and toluene) has been accomplished through a dynamic combination of self-assembly and self-organization processes leading to the formation of supramolecular polymers, which enfold around the outer wall of the MWCNTs. To this end, a library of phenylacetylene molecular scaffolds with complementary recognition sites at their extremities has been synthesized. They exhibit triple parallel H-bonds between the NH-N-NH (DAD) functions of 2,6-di(acetylamino)pyridine and the CO-NH-CO (ADA) imidic groups of uracil derivatives. These residues are placed at 180° relative to each other (linear systems) or at 60°/120° (angular modules), in order to tune their ability of wrapping around MWCNTs. Molecular Dynamics (MD) simulations showed that the formation of the hybrid assembly MWCNT?[X?Y](n) (where X = 1a or 1b -DAD- and Y = 2, 3, or 4 -ADA-) is attributed to π-π and CH-π interactions between the graphitic walls of the carbon materials and the oligophenyleneethynylene polymer backbones along with its alkyl groups, respectively. Addition of polar or protic solvents, such as DMSO or MeOH, causes the disruption of the H-bonds with partial detachment of the polymer from the CNTs, followed by precipitation. Taking advantage of the chromophoric and luminescence properties of the molecular subunits, the solubilization/precipitation processes have been monitored by UV-vis absorption and luminescence spectroscopies. All hybrid MWCNTs-polymer materials have been also structurally characterized via thermogravimetric analysis (TGA), transmission electron microscopy (TEM), atomic force microscopy (AFM), scanning tunneling microscopy (STM), and X-ray photoelectron spectroscopy (XPS).     

Cannabidiol as Self-Assembly Inducer for Anticancer Drug-Based Nanoparticles

Cannabidiol (CBD) is a biologically active compound present in the plants of the Cannabis family, used as anticonvulsant, anti-inflammatory, anti-anxiety, and more recently, anticancer drug. In this work, its use as a new self-assembly inducer in the formation of nanoparticles is validated. The target conjugates are characterized by the presence of different anticancer drugs (namely N-desacetyl thiocolchicine, podophyllotoxin, and paclitaxel) connected to CBD through a linker able to improve drug release. These nanoparticles are formed via solvent displacement method, resulting in monodisperse and stable structures having hydrodynamic diameters ranging from 160 to 400 nm. Their biological activity is evaluated on three human tumor cell lines (MSTO-211H, HT-29, and HepG2), obtaining GI₅₀ values in the low micromolar range. Further biological assays were carried out on MSTO-211H cells for the most effective NP 8B, confirming the involvement of paclitaxel in cytotoxicity and cell death mechanism     

Rationality in families of threefolds

We prove that in a family of projective threefolds defined over an algebraically closed field, the locus of rational fibers is a countable union of closed subsets of the locus of separably rationally connected fibers. When the ground field has characteristic zero, this implies that the locus of rational fibers in a smooth family of projective threefolds is the union of at most countably many closed subfamilies.