Numerical transformation methods: a constructive approach

Within group invariance theory we consider a constructive approach in order to define numerical transformation methods. These are initial-value methods for the solution of boundary value problems governed by ordinary differential equations. Here we consider the class of free boundary value problems governed by the most general second-order equation in normal form. For this class of problems the main theorem is concerned with the definition of an iterative transformation method. The definition of a noniterative method, applicable to a subclass of the original class of problems, follows as a corollary. Therefore, the proposed constructive approach allows us to establish a unifying framework for noniterative and iterative transformation methods.     

Chirality and correlations in graphene

Graphene is described at low energy by a massless Dirac equation whose eigenstates have definite chirality. We show that the tendency of Coulomb interactions in lightly doped graphene to favor states with larger net chirality leads to suppressed spin and charge susceptibilities. Our conclusions are based on an evaluation of graphene's exchange and random-phase-approximation correlation energies. The suppression is a consequence of the quasiparticle chirality switch which enhances quasiparticle velocities near the Dirac point.     

Hydrogen–hydrogen bonding: The current density perspective

Current density plots of closed‐shell intermolecular H? H interactions characterized by a bond critical point (BCP) show two vortices separated by a saddle, a pattern which allows for a clear definition of a pair current strength. This H? H current strength turns out to be roughly related to the potential energy density at the BCP and then to the dissociation energy. The same pattern is also recognizable, at least for an azimuthal orientation of a field perpendicular to the H? H line, for the intramolecular interactions previously investigated to propose the H? H bonding. In the case of the H atoms of the bay region of polycyclic aromatic hydrocarbons, the current of the H? H delocalized diatropic vortex gives a quantitative indication of stabilization; however, on rotation of the field and the subsequent onset of a bay‐delocalized paratropic vortex (a typical signature of antiaromaticity), the diatropic vortex can be reshaped or it can even disappear, consistently with its smallness, and thus showing the effect of other more relevant interactions. © 2015 Wiley Periodicals, Inc.     

Quasi-periodic water waves

We present the result and the ideas of the recent paper (Berti and Montalto, Quasi-periodic standing wave solutions of gravity-capillary water waves, http://arxiv.org/abs/1602.02411, 2016) concerning the existence of Cantor families of small-amplitude time quasi-periodic standing wave solutions (i.e. periodic and even in the space variable x) of a 2-dimensional ocean, with infinite depth, in irrotational regime, under the action of gravity and surface tension at the free boundary. These quasi-periodic solutions are linearly stable.     

Adlayers of dimannoside thiols on gold: surface chemical analysis

Carbohydrate films on gold based on dimannoside thiols (DMT) were prepared, and a complementary surface chemical analysis was performed in detail by X-ray photoelectron spectroscopy (XPS), time-of-flight secondary ion mass spectrometry (ToF-SIMS), near-edge X-ray absorption fine structure (NEXAFS), FT-IR, and contact angle measurements in order to verify formation of ω-carbohydrate-functionalized alkylthiol films. XPS (C 1s, O 1s, and S 2p) reveals information on carbohydrate specific alkoxy (C-O) and acetal moieties (O-C-O) as well as thiolate species attached to gold. Angle-resolved synchrotron XPS was used for chemical speciation at ultimate surface sensitivity. Angle-resolved XPS analysis suggests the presence of an excess top layer composed of unbound sulfur components combined with alkyl moieties. Further support for DMT attachment on Au is given by ToF-SIMS and FT-IR analysis. Carbon and oxygen K-edge NEXAFS spectra were interpreted by applying the building block model supported by comparison to data of 1-undecanethiol, poly(vinyl alcohol), and polyoxymethylene. No linear dichroism effect was observed in the angle-resolved C K-edge NEXAFS.     

Amphiphilic antioxidants from "cashew nut shell liquid" (CNSL) waste

Hydrogenated cardanol and cardols, contained in industrial grade cardanol oil and obtained by distillation of the raw "cashew nut shell liquid" (CNSL), are easily transformed into efficient 4-thiaflavane antioxidants bearing a long alkyl chain on A ring and a catechol group on B ring.