Structure and fluctuations of the premelted liquid film of ice at the triple point

ABSTRACT

In this paper, we study the structure of the ice/vapour interface in the neighbourhood of the triple point for the TIP4P/2005 model. We probe the fluctuations of the ice/film and film/vapour surfaces that separate the liquid film from the coexisting bulk phases at basal, primary prismatic and secondary prismatic planes. The results are interpreted using a coupled sine Gordon plus Interface Hamiltonian model. At large length scales, the two bounding surfaces are correlated and behave as a single complex ice/vapour interface. For small length, on the contrary, the ice/film and film/vapour surfaces behave very much like independent ice/water and water/vapour interfaces. The study suggests that the basal facet of the TIP4P/2005 model is smooth, the prismatic facet is close to a roughening transition, and the secondary prismatic facet is rough. For the faceted basal face, our fluctuation analysis allows us to estimate the step free energy in good agreement with experiment. Our results allow for a quantitative characterisation of the extent to which the adsorbed quasi-liquid layer behaves as water and explains experimental observations which reveal similar activation energies for crystals grown in bulk vapour or bulk water.     

Error Bounds for Semi-Galerkin Approximations of Nonhomogeneous Incompressible Fluids

We consider spectral semi-Galerkin approximations for the strong solutions of the nonhomogeneous Navier–Stokes equations. We derive an optimal uniform in time error bound in the H¹ norm for approximations of the velocity. We also derive an error estimate for approximations of the density in some spaces L^r. P. Braz e Silva was supported for this work by FAPESP/Brazil, #02/13270-1 and is currently supported in part by CAPES/MECD-DGU Brazil/Spain, #117/06. M. Rojas-Medar is partially supported by CAPES/MECD-DGU Brazil/Spain, #117/06 and project BFM2003-06446-CO-01, Spain.     

Self-correcting networks: function, robustness, and motif distributions in biological signal processing

Statistical properties of large ensembles of networks, all designed to have the same functions of signal processing, but robust against different kinds of perturbations, are analyzed. We find that robustness against noise and random local damage plays a dominant role in determining motif distributions of networks and may underlie their classification into network superfamilies.     

Desvitrification on an oxyfluoride glass doped with Tm3+ and Yb3+ ions under Ar laser irradiation

Desvitrification in a Tm³⁺ and Yb³⁺ codoped oxyfluoride glass has been obtained by exciting with a continuous Argon laser radiation increasing the average laser power from 144 to 2900 mW. Excitation spectra inside a locally damaged zone in a 1 mol% Tm³⁺ and 2.5 mol% Yb³⁺ codoped glass have been measured under excitation in the wavelength range 750–830 nm detecting the ²F_5/2 (Yb³⁺) level. This curve is the result of the contribution of two different kinds of centers, the fluoride nanocrystals and the glassy phase of the glass ceramic sample created due to the irradiation. The weight of the contributions of each of the centers depends on the excitation wavelength, and from the analysis of the decay of the luminescence it can be concluded that approximately 80% of the Tm³⁺ ions are located in the nanocrystals and therefore less than 20% in the glassy phase.     

First example of an atropselective dehydro-Diels-Alder (ADDA) reaction

A new concept of a stereoselective synthesis of axially chiral biaryls, formed in the course of the dehydro-Diels-Alder (DDA) reaction, has been disclosed. It is based on asymmetric induction of the newly formed chirality axis by a chirality center, which is present in the two synthesized DDA reactants. Depending on the different length of the linkers joining the alkyne moieties the DDA reaction may be triggered photochemically or thermally, where only the thermal variant was stereoselective.     

THE BLOCH SPACE ON THE UNIT BALL OF A HILBERT SPACE:MAXIMALITY AND MULTIPLIERS

We prove that,as in the finite dimensional case,the space of Bloch functions on the unit ball of a Hilbert space contains,under very mild conditions,any semi-Ba...     

Convergence rate of block-coordinate maximization Burer–Monteiro method for solving large SDPs

Mathematical Programming - Semidefinite programming (SDP) with diagonal constraints arise in many optimization problems, such as Max-Cut, community detection and group synchronization. Although...     

On the asymptotic maximal density of a set avoiding solutions to linear equations modulo a prime

Given a finite family F\mathcal{F} of linear forms with integer coefficients, and a compact abelian group G, an F\mathcal{F}-free set in G is a measurable set which does not contain solutions to any equation L(x)=0 for L in F\mathcal{F}. We denote by d_F(G)d_{\mathcal{F}}(G) the supremum of μ(A) over F\mathcal{F}-free sets A⊂G, where μ is the normalized Haar measure on G. Our main result is that, for any such collection F\mathcal{F} of forms in at least three variables, the sequence d_F(\mathbb Z_p)d_{\mathcal{F}}({\mathbb {Z}}_{p}) converges to d_F(\mathbb R/\mathbb Z)d_{\mathcal{F}}({\mathbb {R}}/{\mathbb {Z}}) as p→∞ over primes. This answers an analogue for ℤ _p of a question that Ruzsa raised about sets of integers.