Ideal, Defective, and Gold--Promoted Rutile TiO2(110) Surfaces: Structures, Energies, Dynamics, and Thermodynamics from PBE+U

Extensive first principles calculations are carried out to investigate gold-promoted TiO2(110) surfaces in terms of structure optimizations, electronic structure analyses, ab initio thermodynamics calculations of surface phase diagrams, and ab initio molecular dynamics simulations. All computations rely on density functional theory in the generalized gradient approximation (PBE) and account for on-site Coulomb interactions via inclusion of a Hubbard correction, PBE+U, where U is computed from linear response theory. This approach is validated by investigating the interaction between TiO2(110) surfaces and typical probe species (H, H2O, CO). Relaxed structures and binding energies are compared to both data from the literature and plain PBE results. The main focus of the study is on the properties of gold-promoted titania surfaces and their interactions with CO. Both PBE+U and PBE optimized structures of Au adatoms adsorbed on stoichiometric and reduced TiO2 surfaces are computed, along with their electronic structure. The charge rearrangement induced by the adsorbates at the metal/oxide contact are also analyzed and discussed. By performing PBE+U ab initio molecular dynamics simulations, it is demonstrated that the diffusion of Au adatoms on the stoichiometric surface is highly anisotropic. The metal atoms migrate either along the top of the bridging oxygen rows, or around the area between these rows, from one bridging position to the next along the [001] direction. Approximate ab initio thermodynamics predicts that under O-rich conditions, structures obtained by substituting a Ti5c atom with an Au atom are thermodynamically stable over a wide range of temperatures and pressures.Comment: 20 pages, 12 figures, accepted for publication in Phys. Rev.

Quantum Fluctuations Driven Orientational Disordering: A Finite-Size Scaling Study

The orientational ordering transition is investigated in the quantum generalization of the anisotropic-planar-rotor model in the low temperature regime. The phase diagram of the model is first analyzed within the mean-field approximation. This predicts at $T=0$ a phase transition from the ordered to the disordered state when the strength of quantum fluctuations, characterized by the rotational constant $\Theta$, exceeds a critical value $\Theta_{\rm c}^{MF}$. As a function of temperature, mean-field theory predicts a range of values of $\Theta$ where the system develops long-range order upon cooling, but enters again into a disordered state at sufficiently low temperatures (reentrance). The model is further studied by means of path integral Monte Carlo simulations in combination with finite-size scaling techniques, concentrating on the region of parameter space where reentrance is predicted to occur. The phase diagram determined from the simulations does not seem to exhibit reentrant behavior; at intermediate temperatures a pronounced increase of short-range order is observed rather than a genuine long-range order.Comment: 27 pages, 8 figures, RevTe

Varying Coefficient Tensor Models for Brain Imaging

We revisit a multidimensional varying-coefficient model (VCM), by allowing regressor coefficients to vary smoothly in more than one dimension, thereby extending the VCM of Hastie and Tibshirani. The motivating example is 3-dimensional, involving a special type of nuclear magnetic resonance measurement technique that is being used to estimate the diffusion tensor at each point in the human brain. We aim to improve the current state of the art, which is to apply a multiple regression model for each voxel separately using information from six or more volume images. We present a model, based on P-spline tensor products, to introduce spatial smoothness of the estimated diffusion tensor. Since the regression design matrix is space-invariant, a 4-dimensional tensor product model results, allowing more efficient computation with penalized array regression

Space-Varying Coefficient Models for Brain Imaging

The methodological development and the application in this paper originate from diffusion tensor imaging (DTI), a powerful nuclear magnetic resonance technique enabling diagnosis and monitoring of several diseases as well as reconstruction of neural pathways. We reformulate the current analysis framework of separate voxelwise regressions as a 3d space-varying coefficient model (VCM) for the entire set of DTI images recorded on a 3d grid of voxels. Hence by allowing to borrow strength from spatially adjacent voxels, to smooth noisy observations, and to estimate diffusion tensors at any location within the brain, the three-step cascade of standard data processing is overcome simultaneously. We conceptualize two VCM variants based on B-spline basis functions: a full tensor product approach and a sequential approximation, rendering the VCM numerically and computationally feasible even for the huge dimension of the joint model in a realistic setup. A simulation study shows that both approaches outperform the standard method of voxelwise regressions with subsequent regularization. Due to major efficacy, we apply the sequential method to a clinical DTI data set and demonstrate the inherent ability of increasing the rigid grid resolution by evaluating the incorporated basis functions at intermediate points. In conclusion, the suggested fitting methods clearly improve the current state-of-the-art, but ameloriation of local adaptivity remains desirable

Pattern formation without heating in an evaporative convection experiment

We present an evaporation experiment in a single fluid layer. When latent heat associated to the evaporation is large enough, the heat flow through the free surface of the layer generates temperature gradients that can destabilize the conductive motionless state giving rise to convective cellular structures without any external heating. The sequence of convective patterns obtained here without heating, is similar to that obtained in B\'enard-Marangoni convection. This work present the sequence of spatial bifurcations as a function of the layer depth. The transition between square to hexagonal pattern, known from non-evaporative experiments, is obtained here with a similar change in wavelength.Comment: Submitted to Europhysics Letter

Composition, structure, and stability of the rutile TiO_2(110) surface: oxygen depletion, hydroxylation, hydrogen migration and water adsorption

A comprehensive phase diagram of lowest-energy structures and compositions of the rutile TiO_2(110) surface in equilibrium with a surrounding gas phase at finite temperatures and pressures has been determined using density functional theory in combination with a thermodynamic formalism. The exchange of oxygen, hydrogen, and water molecules with the gas phase is considered. Particular attention is given to the convergence of all calculations with respect to lateral system size and slab thickness. In addition, the reliability of semilocal density functionals to describing the energetics of the reduced surfaces is critically evaluated. For ambient conditions the surface is found to be fully covered by molecularly adsorbed water. At low coverages, in the limit of single, isolated water molecules, molecular and dissociative adsorption become energetically degenerate. Oxygen vacancies form in strongly reducing, oxygen-poor environments. However, already at slightly more moderate conditions it is shown that removing full TiO_2 units from the surface is thermodynamically preferred. In agreement with recent experimental observations it is furthermore confirmed that even under extremely hydrogen-rich environments the surface cannot be fully hydroxylated, but only a maximum coverage with hydrogen of about 0.6-0.7 monolayer can be reached. Finally, calculations of migration paths strongly suggest that hydrogen prefers to diffuse into the bulk over desorbing from the surface into the gas phase.Comment: 17 pages, 11 figures, to appear in PR

Structurally Parameterized d-Scattered Set

In $d$-Scattered Set we are given an (edge-weighted) graph and are asked to select at least $k$ vertices, so that the distance between any pair is at least $d$, thus generalizing Independent Set. We provide upper and lower bounds on the complexity of this problem with respect to various standard graph parameters. In particular, we show the following: - For any $d\ge2$, an $O^*(d^{\textrm{tw}})$-time algorithm, where $\textrm{tw}$ is the treewidth of the input graph. - A tight SETH-based lower bound matching this algorithm's performance. These generalize known results for Independent Set. - $d$-Scattered Set is W[1]-hard parameterized by vertex cover (for edge-weighted graphs), or feedback vertex set (for unweighted graphs), even if $k$ is an additional parameter. - A single-exponential algorithm parameterized by vertex cover for unweighted graphs, complementing the above-mentioned hardness. - A $2^{O(\textrm{td}^2)}$-time algorithm parameterized by tree-depth ($\textrm{td}$), as well as a matching ETH-based lower bound, both for unweighted graphs. We complement these mostly negative results by providing an FPT approximation scheme parameterized by treewidth. In particular, we give an algorithm which, for any error parameter $\epsilon > 0$, runs in time $O^*((\textrm{tw}/\epsilon)^{O(\textrm{tw})})$ and returns a $d/(1+\epsilon)$-scattered set of size $k$, if a $d$-scattered set of the same size exists