Ergodicity of a Single Particle Confined in a Nanopore

We analyze the dynamics of a gas particle moving through a nanopore of adjustable width with particular emphasis on ergodicity. We give a measure of the portion of phase space that is characterized by quasiperiodic trajectories which break ergodicity. The interactions between particle and wall atoms are mediated by a Lennard-Jones potential, so that an analytical treatment of the dynamics is not feasible, but making the system more physically realistic. In view of recent studies, which proved non-ergodicity for systems with scatterers interacting via smooth potentials, we find that the non-ergodic component of the phase space for energy levels typical of experiments, is surprisingly small, i.e. we conclude that the ergodic hypothesis is a reasonable approximation even for a single particle trapped in a nanopore. Due to the numerical scope of this work, our focus will be the onset of ergodic behavior which is evident on time scales accessible to simulations and experimental observations rather than ergodicity in the infinite time limit.     

On the integrability of Degasperis–Procesi equation: Control of the Sobolev norms and Birkhoff resonances

We consider the dispersive Degasperis–Procesi equation $u_t?u_{xxt}?\mathtt{c}{u}_{xxx}+4\mathtt{c}{u}_x?u{u}_{xxx}?3u_x{u}_{xx}+4u{u}_x=0$ with $\mathtt{c}\in \mathbb{R}?\{0\}$. In [15] the authors proved that this equation possesses infinitely many conserved quantities. We prove that there are infinitely many of such constants of motion which control the Sobolev norms and which are analytic in a neighborhood of the origin of the Sobolev space $H^s$ with $s\ge 2$, both on $\mathbb{R}$ and $\mathbb{T}$. By the analysis of these conserved quantities we deduce a result of global well-posedness for solutions with small initial data and we show that, on the circle, the formal Birkhoff normal form of the Degasperis–Procesi at any order is action-preserving.     

Fractional powers of the noncommutative Fourier's law by the S‐spectrum approach

Let e_?, for ? = 1,2,3, be orthogonal unit vectors in and let be a bounded open set with smooth boundary ?Ω. Denoting by a point in Ω, the heat equation, for nonhomogeneous materials, is obtained replacing the Fourier law, given by the following: into the conservation of energy law, here a, b, are given functions. With the S‐spectrum approach to fractional diffusion processes we determine, in a suitable way, the fractional powers of T. Then, roughly speaking, we replace the fractional powers of T into the conservation of energy law to obtain the fractional evolution equation. This method is important for nonhomogeneous materials where the Fourier law is not simply the negative gradient. In this paper, we determine under which conditions on the coefficients a, b, the fractional powers of T exist in the sense of the S‐spectrum approach. More in general, this theory allows to compute the fractional powers of vector operators that arise in different fields of science and technology. This paper is devoted to researchers working in fractional diffusion and fractional evolution problems, partial differential equations, and noncommutative operator theory.     

Controlling the propagation of broadband light pulses by Electromagnetically Induced Transparency

We present an experimental and theoretical investigation, performed on hot sodium atoms in a ladder scheme, showing the control of the absorption and of the propagation velocity of a probe light pulse with a spectral bandwidth as large as 1.8 GHz. The predictions of the theoretical model compare favorably with the experimental results.     

Ambivalent role of metal chlorides in ring opening reactions of 2H-azirines: synthesis of imidazoles,pyrroles and pyrrolinones

2H-Azirines were found to react with imines, enaminones and enaminoesters in the presence of metal salts. Imidazoles, pyrroles and new pyrrolinones derivatives are isolated in good overall yields. The role of metal salts was investigated as they can act as Lewis acids or electron donors. Mechanisms are proposed suggesting that imidazoles arise from addition of azirine to imines via radical or ionic mechanism; pyrroles and pyrrolinones are obtained from azirines with enamino derivatives when the salt acts as a Lewis acid. In the latter case the properties of the metallic compound influence the reaction regioselectivity.     

The statistical significance of selected sense–antisense peptide interactions

Sense and antisense peptides, encoded by sense and corresponding antisense DNA strands, are capable of specific interactions that could be a driving force to mediate protein–protein or protein–peptide binding associations. The complementary residue hypothesis suggests that these interactions are founded upon the sum of pairwise interactions between amino acids encoded by corresponding sense and antisense codons. Despite many successful experimental results obtained with the hypothesis, however, the physicochemical basis for these interactions is poorly understood. We examined the potential of the hypothesis for general identification of protein–protein interaction sites, and the possible role of the hypothesis in determining folding in a broad set of protein structures. In addition, we performed a structural study to investigate the binding of a complementary peptide to IL‐1F2. Our results suggest that complementary residue pairs are no more frequent or conserved than average in protein–protein interfaces, and are statistically under‐represented amongst contacting residue pairs in folded protein structures. Although our structural results matched experimental observations of binding between the peptide and IL‐1F2, complementary residue interactions do not appear to be dominant in the bound structure. Overall, our data do not allow us to conclude that the complementary residue hypothesis accounts for specific sense–antisense peptide interactions. © 2012 Wiley Periodicals, Inc.     

Characterization of nanochannel delivery membrane systems for the sustained release of resveratrol and atorvastatin: new perspectives on promoting heart health

Novel drug delivery systems capable of continuous sustained release of therapeutics have been studied extensively for use in the prevention and management of chronic diseases. The use of these systems holds promise as a means to achieve higher patient compliance while improving therapeutic index and reducing systemic toxicity. In this work, an implantable nanochannel drug delivery system (nDS) is characterized and evaluated for the long-term sustained release of atorvastatin (ATS) and trans-resveratrol (t-RES), compounds with a proven role in managing atherogenic dyslipidemia and promoting cardioprotection. The primary mediators of drug release in the nDS are nanofluidic membranes with hundreds of thousands of nanochannels (up to 100,000/mm²) that attain zero-order release kinetics by exploiting nanoconfinement and molecule-to-surface interactions that dominate diffusive transport at the nanoscale. These membranes were characterized using gas flow analysis, acetone diffusion, and scanning and transmission electron microscopy (SEM, TEM). The surface properties of the dielectric materials lining the nanochannels, SiO₂ and low-stress silicon nitride, were further investigated using surface charge analysis. Continuous, sustained in vitro release for both ATS and t-RES was established for durations exceeding 1 month. Finally, the influence of the membranes on cell viability was assessed using human microvascular endothelial cells. Morphology changes and adhesion to the surface were analyzed using SEM, while an MTT proliferation assay was used to determine the cell viability. The nanochannel delivery approach, here demonstrated in vitro, not only possesses all requirements for large-scale high-yield industrial fabrication, but also presents the key components for a rapid clinical translation as an implantable delivery system for the sustained administration of cardioprotectants.     

HRMAS NMR spectroscopy combined with chemometrics as an alternative analytical tool to control cigarette authenticity

In this paper, we present for the first time the use of high-resolution magic angle spinning nuclear magnetic resonance (HRMAS NMR) spectroscopy combined with chemometrics as an alternative tool for the characterization of tobacco products from different commercial international brands as well as for the identification of counterfeits. Although cigarette filling is a very complex chemical mixture, we were able to discriminate between dark, bright, and additive-free cigarette blends belonging to six different filter-cigarette brands, commercially available, using an approach for which no extraction procedure is required. Second, we focused our study on a specific worldwide-distributed brand for which established counterfeits were available. We discriminated those from their genuine counterparts with 100 % accuracy using unsupervised multivariate statistical analysis. The counterfeits that we analyzed showed a higher amount of nicotine and solanesol and a lower content of sugars, all endogenous tobacco leaf metabolites. This preliminary study demonstrates the great potential of HRMAS NMR spectroscopy to help in controlling cigarette authenticity.