Structure and electronic properties of the (3×3\sqrt{3}\times \sqrt{3})R30∘R30^{\circ} SnAu2_2/Au(111) surface alloy

We have investigated the atomic and electronic structure of the ($\sqrt{3}\times \sqrt{3}$)$R30^{\circ}$ SnAu$_2$/Au(111) surface alloy. Low energy electron diffraction and scanning tunneling microscopy measurements show that the native herringbone reconstruction of bare Au(111) surface remains intact after formation of a long range ordered ($\sqrt{3}\times \sqrt{3}$)$R30^{\circ}$ SnAu$_2$2/Au(111) surface alloy. Angle-resolved photoemission and two-photon photoemission spectroscopy techniques reveal Rashba-type spin-split bands in the occupied valence band with comparable momentum space splitting as observed for the Au(111) surface state, but with a hole-like parabolic dispersion. Our experimental findings are compared with density functional theory (DFT) calculation that fully support our experimental findings. Taking advantage of the good agreement between our DFT calculations and the experimental results, we are able to extract that the occupied Sn-Au hybrid band is of (s, d)-orbital character while the unoccupied Sn-Au hybrid bands are of (p, d)-orbital character. Hence, we can conclude that the Rashba-type spin splitting of the hole-like Sn-Au hybrid surface state is caused by the significant mixing of Au d- to Sn s-states in conjunction with the strong atomic spin-orbit coupling of Au, i.e., of the substrate.Comment: Copyright: https://journals.aps.org/authors/transfer-of-copyright-agreement; All copyrights by AP

Phase-field-crystal models for condensed matter dynamics on atomic length and diffusive time scales: an overview

Here, we review the basic concepts and applications of the phase-field-crystal (PFC) method, which is one of the latest simulation methodologies in materials science for problems, where atomic- and microscales are tightly coupled. The PFC method operates on atomic length and diffusive time scales, and thus constitutes a computationally efficient alternative to molecular simulation methods. Its intense development in materials science started fairly recently following the work by Elder et al. [Phys. Rev. Lett. 88 (2002), p. 245701]. Since these initial studies, dynamical density functional theory and thermodynamic concepts have been linked to the PFC approach to serve as further theoretical fundaments for the latter. In this review, we summarize these methodological development steps as well as the most important applications of the PFC method with a special focus on the interaction of development steps taken in hard and soft matter physics, respectively. Doing so, we hope to present today's state of the art in PFC modelling as well as the potential, which might still arise from this method in physics and materials science in the nearby future.Comment: 95 pages, 48 figure

Fuzzy cellular model for on-line traffic simulation

This paper introduces a fuzzy cellular model of road traffic that was intended for on-line applications in traffic control. The presented model uses fuzzy sets theory to deal with uncertainty of both input data and simulation results. Vehicles are modelled individually, thus various classes of them can be taken into consideration. In the proposed approach, all parameters of vehicles are described by means of fuzzy numbers. The model was implemented in a simulation of vehicles queue discharge process. Changes of the queue length were analysed in this experiment and compared to the results of NaSch cellular automata model.Comment: The original publication is available at http://www.springerlink.co

Optimizing Traffic Lights in a Cellular Automaton Model for City Traffic

We study the impact of global traffic light control strategies in a recently proposed cellular automaton model for vehicular traffic in city networks. The model combines basic ideas of the Biham-Middleton-Levine model for city traffic and the Nagel-Schreckenberg model for highway traffic. The city network has a simple square lattice geometry. All streets and intersections are treated equally, i.e., there are no dominant streets. Starting from a simple synchronized strategy we show that the capacity of the network strongly depends on the cycle times of the traffic lights. Moreover we point out that the optimal time periods are determined by the geometric characteristics of the network, i.e., the distance between the intersections. In the case of synchronized traffic lights the derivation of the optimal cycle times in the network can be reduced to a simpler problem, the flow optimization of a single street with one traffic light operating as a bottleneck. In order to obtain an enhanced throughput in the model improved global strategies are tested, e.g., green wave and random switching strategies, which lead to surprising results.Comment: 13 pages, 10 figure

DDFT calibration and investigation of an anisotropic phase-field crystal model

The anisotropic phase-field crystal model recently proposed and used by Prieler et al. [J. Phys.: Condens. Matter 21, 464110 (2009)] is derived from microscopic density functional theory for anisotropic particles with fixed orientation. Further its morphology diagram is explored. In particular we investigated the influence of anisotropy and undercooling on the process of nucleation and microstructure formation from atomic to the microscale. To that end numerical simulations were performed varying those dimensionless parameters which represent anisotropy and undercooling in our anisotropic phase-field crystal (APFC) model. The results from these numerical simulations are summarized in terms of a morphology diagram of the stable state phase. These stable phases are also investigated with respect to their kinetics and characteristic morphological features.Comment: It contain 13 pages and total of 7 figure

Complex networks embedded in space: Dimension and scaling relations between mass, topological distance and Euclidean distance

Many real networks are embedded in space, where in some of them the links length decay as a power law distribution with distance. Indications that such systems can be characterized by the concept of dimension were found recently. Here, we present further support for this claim, based on extensive numerical simulations for model networks embedded on lattices of dimensions $d_e=1$ and $d_e=2$. We evaluate the dimension $d$ from the power law scaling of (a) the mass of the network with the Euclidean radius $r$ and (b) the probability of return to the origin with the distance $r$ travelled by the random walker. Both approaches yield the same dimension. For networks with $\delta < d_e$, $d$ is infinity, while for $\delta > 2d_e$, $d$ obtains the value of the embedding dimension $d_e$. In the intermediate regime of interest $d_e \leq \delta < 2 d_e$, our numerical results suggest that $d$ decreases continously from $d = \infty$ to $d_e$, with $d - d_e \sim (\delta - d_e)^{-1}$ for $\delta$ close to $d_e$. Finally, we discuss the scaling of the mass $M$ and the Euclidean distance $r$ with the topological distance $\ell$. Our results suggest that in the intermediate regime $d_e \leq \delta < 2 d_e$, $M(\ell)$ and $r(\ell)$ do not increase with $\ell$ as a power law but with a stretched exponential, $M(\ell) \sim \exp [A \ell^{\delta' (2 - \delta')}]$ and $r(\ell) \sim \exp [B \ell^{\delta' (2 - \delta')}]$, where $\delta' = \delta/d_e$. The parameters $A$ and $B$ are related to $d$ by $d = A/B$, such that $M(\ell) \sim r(\ell)^d$. For $\delta < d_e$, $M$ increases exponentially with $\ell$, as known for $\delta=0$, while $r$ is constant and independent of $\ell$. For $\delta \geq 2d_e$, we find power law scaling, $M(\ell) \sim \ell^{d_\ell}$ and $r(\ell) \sim \ell^{1/d_{min}}$, with $d_\ell \cdot d_{min} = d$.Comment: 17 pages, 11 figure

Extended Smoothed Boundary Method for Solving Partial Differential Equations with General Boundary Conditions on Complex Boundaries

In this article, we describe an approach for solving partial differential equations with general boundary conditions imposed on arbitrarily shaped boundaries. A continuous function, the domain parameter, is used to modify the original differential equations such that the equations are solved in the region where a domain parameter takes a specified value while boundary conditions are imposed on the region where the value of the domain parameter varies smoothly across a short distance. The mathematical derivations are straightforward and generically applicable to a wide variety of partial differential equations. To demonstrate the general applicability of the approach, we provide four examples herein: (1) the diffusion equation with both Neumann and Dirichlet boundary conditions; (2) the diffusion equation with both surface diffusion and reaction; (3) the mechanical equilibrium equation; and (4) the equation for phase transformation with the presence of additional boundaries. The solutions for several of these cases are validated against corresponding analytical and semi-analytical solutions. The potential of the approach is demonstrated with five applications: surface-reaction-diffusion kinetics with a complex geometry, Kirkendall-effect-induced deformation, thermal stress in a complex geometry, phase transformations affected by substrate surfaces, and a self-propelled droplet.Comment: This document is the revised version of arXiv:0912.1288v

Spin-Glass State in CuGa2O4\rm CuGa_2O_4

Magnetic susceptibility, magnetization, specific heat and positive muon spin relaxation (\musr) measurements have been used to characterize the magnetic ground-state of the spinel compound $\rm CuGa_2O_4$. We observe a spin-glass transition of the S=1/2 $\rm Cu^{2+}$ spins below $\rm T_f=2.5K$ characterized by a cusp in the susceptibility curve which suppressed when a magnetic field is applied. We show that the magnetization of $\rm CuGa_2O_4$ depends on the magnetic histo Well below $\rm T_f$, the muon signal resembles the dynamical Kubo-Toyabe expression reflecting that the spin freezing process in $\rm CuGa_2O_4$ results Gaussian distribution of the magnetic moments. By means of Monte-Carlo simulati we obtain the relevant exchange integrals between the $\rm Cu^{2+}$ spins in this compound.Comment: 6 pages, 16 figure