Adsorption of rare-gas atoms on Cu(111) and Pb(111) surfaces by van der Waals-corrected Density Functional Theory

The DFT/vdW-WF method, recently developed to include the Van der Waals interactions in Density Functional Theory (DFT) using the Maximally Localized Wannier functions, is applied to the study of the adsorption of rare-gas atoms (Ne, Ar, Kr, and Xe) on the Cu(111) and Pb(111) surfaces, at three high-symmetry sites. We evaluate the equilibrium binding energies and distances, and the induced work-function changes and dipole moments. We find that, for Ne, Ar, and Kr on the Cu(111) surface the different adsorption configurations are characterized by very similar binding energies, while the favored adsorption site for Xe on Cu(111) is on top of a Cu atom, in agreement with previous theoretical calculations and experimental findings, and in common with other close-packed metal surfaces. Instead, the favored site is always the hollow one on the Pb(111) surface, which therefore represents an interesting system where the investigation of high-coordination sites is possible. Moreover, the Pb(111) substrate is subject, upon rare-gas adsorption, to a significantly smaller change in the work function (and to a correspondingly smaller induced dipole moment) than Cu(111). The role of the chosen reference DFT functional and of different Van der Waals corrections, and their dependence on different rare-gas adatoms, are also discussed

Variational Monte Carlo for spin-orbit interacting systems

Recently, a diffusion Monte Carlo algorithm was applied to the study of spin dependent interactions in condensed matter. Following some of the ideas presented therein, and applied to a Hamiltonian containing a Rashba-like interaction, a general variational Monte Carlo approach is here introduced that treats in an efficient and very accurate way the spin degrees of freedom in atoms when spin orbit effects are included in the Hamiltonian describing the electronic structure. We illustrate the algorithm on the evaluation of the spin-orbit splittings of isolated carbon and lead atoms. In the case of the carbon atom, we investigate the differences between the inclusion of spin-orbit in its realistic and effective spherically symmetrized forms. The method exhibits a very good accuracy in describing the small energy splittings, opening the way for a systematic quantum Monte Carlo studies of spin-orbit effects in atomic systems.Comment: 7 pages, 0 figure

Gauge approach to the specific heat in the normal state of cuprates

Many experimental features of the electronic specific heat and entropy of high Tc cuprates in the normal state, including the nontrivial temperature dependence of the specific heat coefficient and negative intercept of the extrapolated entropy to T=0 for underdoped cuprates, are reproduced using the spin-charge gauge approach to the t-J model. The entropy turns out to be basically due to fermionic excitations, but with a temperature dependence of the specific heat coefficient controlled by fluctuations of a gauge field coupling them to gapful bosonic excitations. In particular the negative intercept of the extrapolated entropy at T=0 in the pseudogap ``phase'' is attributed to the scalar component of the gauge field, which implements the local no-double occupancy constraint.Comment: 5 pages, 5 figure

Critical sets of nonlinear Sturm-Liouville operators of Ambrosetti-Prodi type

The critical set C of the operator F:H^2_D([0,pi]) -> L^2([0,pi]) defined by F(u)=-u''+f(u) is studied. Here X:=H^2_D([0,pi]) stands for the set of functions that satisfy the Dirichlet boundary conditions and whose derivatives are in L^2([0,pi]). For generic nonlinearities f, C=\cup C_k decomposes into manifolds of codimension 1 in X. If f''0, the set C_j is shown to be non-empty if, and only if, -j^2 (the j-th eigenvalue of u -> u'') is in the range of f'. The critical components C_k are (topological) hyperplanes.Comment: 6 pages, no figure

Quasi-periodic solutions of completely resonant forced wave equations

We prove existence of quasi-periodic solutions with two frequencies of completely resonant, periodically forced nonlinear wave equations with periodic spatial boundary conditions. We consider both the cases the forcing frequency is: (Case A) a rational number and (Case B) an irrational number.Comment: 25 pages, 1 figur

The Conformal Willmore Functional: a Perturbative Approach

The conformal Willmore functional (which is conformal invariant in general Riemannian manifold $(M,g)$) is studied with a perturbative method: the Lyapunov-Schmidt reduction. Existence of critical points is shown in ambient manifolds $(\mathbb{R}^3, g_\epsilon)$ -where $g_\epsilon$ is a metric close and asymptotic to the euclidean one. With the same technique a non existence result is proved in general Riemannian manifolds $(M,g)$ of dimension three.Comment: 34 pages; Journal of Geometric Analysis, on line first 23 September 201

Familial hypercholesterolemia in cardiac rehabilitation: a new field of interest

Familial hypercholesterolemia (FH) is a frequently undiagnosed genetic disease characterized by substantial elevations of low-density lipoprotein cholesterol (LDL-C). The prevalence of heterozygous FH (HeFH) in the general population is 1:500 inhabitants, while the prevalence of homozygous FH (HoFH) is 1:1,000,000. If FH is not identified and aggressively treated at an early age, affected individuals have a 20-fold increased lifetime risk of coronary heart disease compared with the general population. This narrative review provide a concise overview of recommendations for diagnosis and treatment of adults and children with FH, and discuss the utility of considering FH as a comorbidity at the entry of cardiac rehabilitation programme

Percolation-to-hopping crossover in conductor-insulator composites

Here, we show that the conductivity of conductor-insulator composites in which electrons can tunnel from each conducting particle to all others may display both percolation and tunneling (i.e. hopping) regimes depending on few characteristics of the composite. Specifically, we find that the relevant parameters that give rise to one regime or the other are $D/\xi$ (where $D$ is the size of the conducting particles and $\xi$ is the tunneling length) and the specific composite microstructure. For large values of $D/\xi$, percolation arises when the composite microstructure can be modeled as a regular lattice that is fractionally occupied by conducting particle, while the tunneling regime is always obtained for equilibrium distributions of conducting particles in a continuum insulating matrix. As $D/\xi$ decreases the percolating behavior of the conductivity of lattice-like composites gradually crosses over to the tunneling-like regime characterizing particle dispersions in the continuum. For $D/\xi$ values lower than $D/\xi\simeq 5$ the conductivity has tunneling-like behavior independent of the specific microstructure of the composite.Comment: 8 pages, 5 figure

Geometric Aspects of Ambrosetti-Prodi operators with Lipschitz nonlinearities

For Dirichlet boundary conditions on a bounded domain, what happens to the critical set of the Ambrosetti-Prodi operator if the nonlinearity is only a Lipschitz map? It turns out that many properties which hold in the smooth case are preserved, despite of the fact that the operator is not even differentiable at some points. In particular, a global Lyapunov-Schmidt decomposition of great convenience for numerical inversion is still available

Trajectory and smooth attractors for Cahn-Hilliard equations with inertial term

The paper is devoted to a modification of the classical Cahn-Hilliard equation proposed by some physicists. This modification is obtained by adding the second time derivative of the order parameter multiplied by an inertial coefficient which is usually small in comparison to the other physical constants. The main feature of this equation is the fact that even a globally bounded nonlinearity is "supercritical" in the case of two and three space dimensions. Thus the standard methods used for studying semilinear hyperbolic equations are not very effective in the present case. Nevertheless, we have recently proven the global existence and dissipativity of strong solutions in the 2D case (with a cubic controlled growth nonlinearity) and for the 3D case with small inertial coefficient and arbitrary growth rate of the nonlinearity. The present contribution studies the long-time behavior of rather weak (energy) solutions of that equation and it is a natural complement of the results of our previous papers. Namely, we prove here that the attractors for energy and strong solutions coincide for both the cases mentioned above. Thus, the energy solutions are asymptotically smooth. In addition, we show that the non-smooth part of any energy solution decays exponentially in time and deduce that the (smooth) exponential attractor for the strong solutions constructed previously is simultaneously the exponential attractor for the energy solutions as well