Adsorption of molecular gases on porous materials in the SAFT-VR approximation

A simple molecular thermodynamic approach is applied to the study of the adsorption of gases of chain molecules on solid surfaces. We use a model based on the Statistical Associating Fluid Theory for Variable Range (SAFT-VR) potentials [A. Gil-Villegas, A. Galindo, P. J. Whitehead, S. J. Mills, G. Jackson, A. N. Burgess, J. Chem. Phys. 106 (1997) 4168] that we extend by including a quasi-two-dimensional approximation to describe the adsorption properties of this type of real gases [A. Martinez, M. Castro, C. McCabe, A. Gil-Villegas, J. Chem. Phys. 126 (2007) 074707]. The model is applied to ethane, ethylene, propane, and carbon dioxide adsorbed on activated carbon and silica gel, which are porous media of significant industrial interest. We show that the adsorption isotherms obtained by means of the present SAFT-VR modeling are in fair agreement with the experimental results provided in the literatureComment: 9 pages, 12 eps figure

Optimal sampling patterns for Zernike polynomials

A pattern of interpolation nodes on the disk is studied, for which the interpolation problem is theoretically unisolvent, and which renders a minimal numerical condition for the collocation matrix when the standard basis of Zernike polynomials is used. It is shown that these nodes have an excellent performance also from several alternative points of view, providing a numerically stable surface reconstruction, starting from both the elevation and the slope data. Sampling at these nodes allows for a more precise recovery of the coefficients in the Zernike expansion of a wavefront or of an optical surface.Comment: 21 pages, 7 figures. Submitted to Appl. Math. Compu

Quadratic differentials and asymptotics of Laguerre polynomials with varying complex parameters

In this paper we study the asymptotics (as $n\to \infty$) of the sequences of Laguerre polynomials with varying complex parameters $\alpha$ depending on the degree $n$. More precisely, we assume that $\alpha_n = n A_n,$ and $\lim_n A_n=A \in \mathbb{C}$. This study has been carried out previously only for $\alpha_n\in \mathbb{R}$, but complex values of $A$ introduce an asymmetry that makes the problem more difficult. The main ingredient of the asymptotic analysis is the right choice of the contour of orthogonality, which requires the analysis of the global structure of trajectories of an associated quadratic differential on the complex plane, which may have an independent interest. While the weak asymptotics is obtained by reduction to the theorem of Gonchar--Rakhmanov--Stahl, the strong asymptotic results are derived via the non-commutative steepest descent analysis based on the Riemann-Hilbert characterization of the Laguerre polynomials.Comment: 40 pages, 11 figures. To appear in J. Math. Anal. Appl. arXiv admin note: text overlap with arXiv:math/0204248 by other authors. text overlap with arXiv:math/0204248 by other author

Equivalence between the mobility edge of electronic transport on disorderless networks and the onset of chaos via intermittency in deterministic maps

We exhibit a remarkable equivalence between the dynamics of an intermittent nonlinear map and the electronic transport properties (obtained via the scattering matrix) of a crystal defined on a double Cayley tree. This strict analogy reveals in detail the nature of the mobility edge normally studied near (not at) the metal-insulator transition in electronic systems. We provide an analytical expression for the conductance as function of system size that at the transition obeys a q-exponential form. This manifests as power-law decay or few and far between large spike oscillations according to different kinds of boundary conditions.Comment: 4 pages, 3 figures, minor changes in content, changed references, changed figur

Lindemann Criterion and the Anomalous Melting Curve of Sodium

Recent reports of the melting curve of sodium at high pressure have shown that it has a very steep descent after a maximum of around 1000K at 31 GPa. This is not due to a phase transition. According to the Lindemann criterion, this behaviour should be apparent in the evolution of the Debye temperature with pressure. In this work, we have performed an "ab-initio" analysis of the behaviour of both the Debye temperature and the elastic constants up to 102 GPa, and find a clear trend at high pressure that should cause a noticeable effect on the melting curve.Comment: 4 pages, 3 figure

Chemical order lifetimes in liquids in the energy landscape paradigm

Recent efforts to deal with the complexities of the liquid state, particularly those of glassforming systems, have focused on the "energy landscape" as a means of dealing with the collective variables problem [1]. The "basins of attraction" that constitute the landscape features in configuration space represent a distinct class of microstates of the system. So far only the microstates that are related to structural relaxation and viscosity have been considered in this paradigm. But most of the complex systems of importance in nature and industry are solutions, particularly solutions that are highly non-ideal in character. In these, a distinct class of fluctuations exists, the fluctuations in concentration. The mean square amplitudes of these fluctuations relate to the chemical activity coefficients [2], and their rise and decay times may be much longer than those of the density fluctuations - from which they may be statistically independent. Here we provide data on the character of chemical order fluctuations in viscous liquids and on their relation to the enthalpy fluctuations that determine the structural relaxation time, and hence the glass temperature Tg. Using a spectroscopically active chemical order probe, we identify a "chemical fictive temperature", Tchm, by analogy with the familiar "fictive temperature" Tf (the cooling Tg). Like Tf, Tchm must be the same as the real temperature for the system to be in complete equilibrium. It is possible for mobile multicomponent liquids to be permanently nonergodic, insofar as Tchm > Tf = T, which must be accommodated within the landscape paradigm. We note that, in appropriate systems, an increase in concentration of slow chemically ordering units in liquids can produce a crossover to fast ion conducting glass phenomenology.Comment: 15 pages, 4 figures, submitted to Natur

Topological dynamics and current-induced motion in a skyrmion lattice

We study the Thiele equation for current-induced motion in a skyrmion lattice through two soluble models of the pinning potential. Comprised by a Magnus term, a dissipative term and a pinning force, Thiele's equation resembles Newton's law but in virtue of the topological character of the first two, it differs significantly from Newtonian mechanics and because the Magnus force is dominant, unlike its mechanical counterpart, the Coriolis force, skyrmion trajectories do not necessarily have mechanical counterparts. This is important if we are to understand skykrmion dynamics and tap into its potential for data-storage technology. We identify a pinning threshold velocity for the one-dimensional potential and for a two-dimensional potential we find a pinning point and the skyrmion trajectories toward the point are spirals whose frequency (compare Kepler's second law) and amplitude decay depends only on the Gilbert constant and potential at the pinning point.Comment: 14 pages, 5 figure

Nondegenerate and almost hexagonal skyrmion lattices

We obtain the lowest energy solutions for the skymion field equations and their corresponding vortex structures. Two nondegenerate solutions emerge with their vortex swirls in opposite directions. The solutions are associated with an extremum property, which favors an array of almost hexagonal shape. We predict that a regular hexagonal lattice must have a mix of skyrmions of both swirls. Although our solutions could not keep the norm of the magnetization constant at unity, their greatest deviation from unity occurred in regions where the spins are far from planar; we show how to improve this situation.Comment: 12 pages, 5 figure

Constraints on top quark FCNC from electroweak precision measurements

We study the one-loop contributions of the effective flavor changing neutral couplings (FCNC) tcZ and tcH on the electroweak precision observables Gamma_Z, R_c, R_b, R_l, A_c and A^FB_c. Using the known experimental limits on these observables, we may place 95% CL bounds on these FCNC couplings which in turn translate into the following limits for the branching ratios: BR(t -> cZ) < 6.7 10^-2 and BR(t -> cH) < (0.09 - 2.9) 10^-3 for 114 < m_H < 170 GeV.Comment: 10 pages, 3 figures. References added. Errors corrected. Numerical results for BR have change

Monte Carlo Investigation of Ising Nanotubes and Nanostrips

Monte Carlo simulations of the magnetization temperature dependence in $D\times L$ nanotubes (periodic lateral boundary conditions) and nanostrips (free lateral boundary conditions) with $D$=8, 16, 32, 64$\ll L\longrightarrow 5000$ have been performed. The apparent critical temperature was determinated using the Binder Cumulant method (crossing of data for $D\times L$ with data for $D\times 2L)$ and it was found to be $T_{C}=0$ for small $D$ values $(D<D^{\ast})$, as it might have been expected.Comment: 13 pages, 9 figure