Tunable uptake of poly(ethylene oxide) by graphite-oxide-based materials

We investigate the role of structure and chemical composition on the uptake of poly(ethylene oxide) by a series of graphite oxides (GOs) and thermally reduced GOs, leading to the formation of polymer-intercalated GO and polymer-adsorbed graphene nanostructures. To this end, a series of poly(ethylene oxide) (PEO) - GO hybrid materials exhibiting a variable degree of GO oxidation and exfoliation has been investigated in detail using a combination of techniques including X-ray photoelectron spectroscopy, X-ray diffraction, thermogravimetry, scanning-electron microscopy, and nitrogen adsorption. Intercalation of the polymer phase into well-defined GO galleries is found to correlate well with both the degree of GO oxidation and with the presence of hydroxyl groups. The latter feature is an essential prerequisite to optimize polymer uptake owing to the predominance of hydrogen-bonding interactions between intercalant and host. Unlike the bulk polymer, these intercalation compounds show neither crystallisation nor glass-transition associated with the polymer phase. Exfoliation and reduction of GO result in high-surface-area graphene layers exhibiting the highest polymer uptake in these GO-based materials. In this case, PEO undergoes surface adsorption, where we observe the recovery of glass and melting transitions associated with the polymer phase albeit at significantly lower temperatures than the bulk

A refined hydrogen bond potential for flexible protein models

One of the major disadvantages of coarse-grained hydrogen bond potentials, for their use in protein folding simulations, is the appearance of abnormal structures when these potentials are used in flexible chain models, and no other geometrical restrictions or energetic contributions are defined into the system.We have efficiently overcome this problem, for chains of adequate size in a relevant temperature range, with a refined coarse-grained hydrogen bond potential. With it, we have been able to obtain nativelike alpha-helices and beta-sheets in peptidic systems, and successfully reproduced the competition between the populations of these secondary structure elements by the effect of temperature and concentration changes. In this manuscript we detail the design of the interaction potential and thoroughly examine its applicability in energetic and structural terms, considering factors such as chain length, concentration, and temperature

A remark on an overdetermined problem in Riemannian Geometry

Let $(M,g)$ be a Riemannian manifold with a distinguished point $O$ and assume that the geodesic distance $d$ from $O$ is an isoparametric function. Let $\Omega\subset M$ be a bounded domain, with $O \in \Omega$, and consider the problem $\Delta_p u = -1$ in $\Omega$ with $u=0$ on $\partial \Omega$, where $\Delta_p$ is the $p$-Laplacian of $g$. We prove that if the normal derivative $\partial_{\nu}u$ of $u$ along the boundary of $\Omega$ is a function of $d$ satisfying suitable conditions, then $\Omega$ must be a geodesic ball. In particular, our result applies to open balls of $\mathbb{R}^n$ equipped with a rotationally symmetric metric of the form $g=dt^2+\rho^2(t)\,g_S$, where $g_S$ is the standard metric of the sphere.Comment: 8 pages. This paper has been written for possible publication in a special volume dedicated to the conference "Geometric Properties for Parabolic and Elliptic PDE's. 4th Italian-Japanese Workshop", organized in Palinuro in May 201

Nonrelativistic hydrogen type stability problems on nonparabolic 3-manifolds

We extend classical Euclidean stability theorems corresponding to the nonrelativistic Hamiltonians of ions with one electron to the setting of non parabolic Riemannian 3-manifolds.Comment: 20 pages; to appear in Annales Henri Poincar

Green's function for the Hodge Laplacian on some classes of Riemannian and Lorentzian symmetric spaces

We compute the Green's function for the Hodge Laplacian on the symmetric spaces M\times\Sigma, where M is a simply connected n-dimensional Riemannian or Lorentzian manifold of constant curvature and \Sigma is a simply connected Riemannian surface of constant curvature. Our approach is based on a generalization to the case of differential forms of the method of spherical means and on the use of Riesz distributions on manifolds. The radial part of the Green's function is governed by a fourth order analogue of the Heun equation.Comment: 18 page

An ISS Small-Gain Theorem for General Networks

We provide a generalized version of the nonlinear small-gain theorem for the case of more than two coupled input-to-state stable (ISS) systems. For this result the interconnection gains are described in a nonlinear gain matrix and the small-gain condition requires bounds on the image of this gain matrix. The condition may be interpreted as a nonlinear generalization of the requirement that the spectral radius of the gain matrix is less than one. We give some interpretations of the condition in special cases covering two subsystems, linear gains, linear systems and an associated artificial dynamical system.Comment: 26 pages, 3 figures, submitted to Mathematics of Control, Signals, and Systems (MCSS

New superintegrable models with position-dependent mass from Bertrand's Theorem on curved spaces

A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of Hamiltonian systems defined on certain 3-dimensional (Riemannian) spaces. These two systems are shown to be either the Kepler or the oscillator potentials on the corresponding Bertrand spaces, and both of them are maximally superintegrable. Afterwards, the relationship between such Bertrand Hamiltonians and position-dependent mass systems is explicitly established. These results are illustrated through the example of a superintegrable (nonlinear) oscillator on a Bertrand-Darboux space, whose quantization and physical features are also briefly addressed.Comment: 13 pages; based in the contribution to the 28th International Colloquium on Group Theoretical Methods in Physics, Northumbria University (U.K.), 26-30th July 201

The structure of fluid trifluoromethane and methylfluoride

We present hard X-ray and neutron diffraction measurements on the polar fluorocarbons HCF3 and H3CF under supercritical conditions and for a range of molecular densities spanning about a factor of ten. The Levesque-Weiss-Reatto inversion scheme has been used to deduce the site-site potentials underlying the measured partial pair distribution functions. The orientational correlations between adjacent fluorocarbon molecules -- which are characterized by quite large dipole moments but no tendency to form hydrogen bonds -- are small compared to a highly polar system like fluid hydrogen chloride. In fact, the orientational correlations in HCF3 and H3CF are found to be nearly as small as those of fluid CF4, a fluorocarbon with no dipole moment.Comment: 11 pages, 9 figure