High-pressure DSC study on the hydriding and dehydriding of Mg/C nanocomposites

High-pressure DSC was applied to study the hydriding and dehydriding behavior of Mg 95 mass%–C 5 mass% composites, synthesized by ball milling with two different kinds of carbon additives (activated carbon derived from apricot stones AS and from bean pods BP) and magnesium with different particle sizes. The composites containing finer magnesium experience absorption capacity deterioration with hydriding/dehydriding cycling, but for the Mg–AS, this worsening is in lower degree compared to Mg–BP. The activated carbon derived from the AS, used for the composites preparation, has more pronounced positive effect on the hydrogen sorption characteristics of magnesium (with both finer and coarser particles), compared with the carbon derived from BP, due to its better protection of the Mg surface from oxidation and particles agglomeration during hydriding/dehydriding cycling.     

Nanodrop on a nanorough solid surface: density functional theory considerations

The density distributions and contact angles of liquid nanodrops on nanorough solid surfaces are determined on the basis of a nonlocal density functional theory. Two kinds of roughness, chemical and physical, are examined. The former considers the substrate as a sequence of two kinds of semi-infinite vertical plates of equal thicknesses but of different natures with different strengths for the liquid-solid interactions. The physical roughness involves an ordered set of pillars on a flat homogeneous surface. Both hydrophobic and hydrophilic surfaces were considered. For the chemical roughness, the contact angle which the drop makes with the flat surface increases when the strength of the liquid-solid interaction for one kind of plates decreases with respect to the fixed value of the other kind of plates. Such a behavior is in agreement with the Cassie-Baxter expression derived from macroscopic considerations. For the physical roughness on a hydrophobic surface, the contact angle which a drop makes with the plane containing the tops of the pillars increases with increasing roughness. Such a behavior is consistent with the Wenzel formula developed for macroscopic drops. For hydrophilic surfaces, as the roughness increases the contact angle first increases, in contradiction with the Wenzel formula, which predicts for hydrophilic surfaces a decrease of the contact angle with increasing roughness. However, a further increase in roughness changes nonmonotonously the contact angle, and at some roughness, the drop disappears and only a liquid film is present on the surface. It was also found that the contact angle has a periodic dependence on the volume of the drop.     

Hausdorffness for Lie algebra homology of Schwartz spaces and applications to the comparison conjecture

Let H be a real algebraic group acting equivariantly with finitely many orbits on a real algebraic manifold X and a real algebraic bundle \({\mathcal {E}}\) on X. Let \(\mathfrak {h}\) be the Lie algebra of H. Let \(\mathcal {S}(X,{\mathcal {E}})\) be the space of Schwartz sections of \({\mathcal {E}}\). We prove that \(\mathfrak {h}\mathcal {S}(X,{\mathcal {E}})\) is a closed subspace of \(\mathcal {S}(X,{\mathcal {E}})\) of finite codimension. We give an application of this result in the case when H is a real spherical subgroup of a real reductive group G. We deduce an equivalence of two old conjectures due to Casselman: the automatic continuity and the comparison conjecture for zero homology. Namely, let \(\pi \) be a Casselman–Wallach representation of G and V be the corresponding Harish–Chandra module. Then the natural morphism of coinvariants \(V_{\mathfrak {h}}\rightarrow \pi _{\mathfrak {h}}\) is an isomorphism if and only if any linear \(\mathfrak {h}\)-invariant functional on V is continuous in the topology induced from \(\pi \). The latter statement is known to hold in two important special cases: if H includes a symmetric subgroup, and if H includes the nilradical of a minimal parabolic subgroup of G.     

A combinatorial characterization of smooth LTCs and applications

The study of locally testable codes (LTCs) has benefited from a number of nontrivial constructions discovered in recent years. Yet, we still lack a good understanding of what makes a linear error correcting code locally testable and as a result we do not know what is the rate‐limit of LTCs and whether asymptotically good linear LTCs with constant query complexity exist. In this paper, we provide a combinatorial characterization of smooth locally testable codes, which are locally testable codes whose associated tester queries every bit of the tested word with equal probability. Our main contribution is a combinatorial property defined on the Tanner graph associated with the code tester (“well‐structured tester”). We show that a family of codes is smoothly locally testable if and only if it has a well‐structured tester. As a case study we show that the standard tester for the Hadamard code is “well‐structured,” giving an alternative proof of the local testability of the Hadamard code, originally proved by (Blum, Luby, Rubinfeld, J. Comput. Syst. Sci. 47 (1993) 549–595) (STOC 1990). Additional connections to the works of (Ben‐Sasson, Harsha, Raskhodnikova, SIAM J. Comput 35 (2005) 1–21) (SICOMP 2005) and of (Lachish, Newman and Shapira, Comput Complex 17 (2008) 70–93) are also discussed. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 49, 280–307, 2016     

Complexes of a bio-molecule and a C60 cage

C₆₀ is the most important fullerene cage and glycine is the simplest representative of a backbone unit of a protein. In this paper, the structures and the energies of glycine–C₆₀ complexes were calculated at the B3LYP/6-31G(d) level DFT. It was found that the binding of glycine to C₆₀ generated a slightly unstable complex via its amino nitrogen, a moderately unstable complex via its hydroxyl oxygen, and a very unstable complex via its carbonyl oxygen. This indicates that fullerene cages might be unable to form stable bindings to proteins via their amino nitrogen, hydroxyl oxygen and carbonyl oxygen active sites.     

Momentum and velocity autocorrelation functions of a diatomic molecule are not necessarily proportional to each other

We present a computation of the classical momentum and velocity correlation functions of Br2 considered as an idealized molecular wire connecting dissipated lead atoms at each end of the dimer. It is demonstrated that coupling of the diatomic relative momentum to the leads may result in momenta that are not equal to the mass-weighted velocity. These differences show up in numerical simulations of both the average value and time correlations of the bond momentum and velocity. These observations are supported by analytical predictions for the average temperature of the diatomic. They imply that the "standard recipes" for modeling the system with a generalized Langevin equation are insufficient.     

Universality limits in the bulk for varying measures

Universality limits are a central topic in the theory of random matrices. We establish universality limits in the bulk of the spectrum for varying measures, using the theory of entire functions of exponential type. In particular, we consider measures that are of the form in the region where universality is desired. Wn does not need to be analytic, nor possess more than one derivative—and then only in the region where universality is desired. We deduce universality in the bulk for a large class of weights of the form , for example, when W=e−Q where Q is convex and Q^′ satisfies a Lipschitz condition of some positive order. We also deduce universality for a class of fixed exponential weights on a real interval.