Locally activated Monte Carlo method for long-time-scale simulations

We present a technique for the structural optimization of atom models to study long time relaxation processes involving different time scales. The method takes advantage of the benefits of both the kinetic Monte Carlo (KMC) and the technimolecular dynamics simulation techniques. In contrast to ordinary KMC, our method allows for an estimation of a true lower limit for the time scale of a relaxation process. The scheme is fairly general in that neither the typical pathways nor the typical metastable states need to be known prior to the simulation. It is independent of the lattice type and the potential which describes the atomic interactions. It is adopted to study systems with structural and/or chemical inhomogeneity which makes it particularly useful for studying growth and diffusion processes in a variety of physical systems, including crystalline bulk, amorphous systems, surfaces with adsorbates, fluids, and interfaces. As a simple illustration we apply the locally activated Monte Carlo to study hydrogen diffusion in diamond.Peer reviewe

Properties of small carbon clusters inside the C60 fullerene

We present the results of an atomic-scale simulation of the confinement of small carbon clusters inside icosahedral C60 fullerene. We carefully investigate the incorporation of various clusters into C60 including chains, rings, and double ring configurations, and have analyzed both the energetics and the resulting geometries. The calculations have been performed employing the density-functional-based tight-binding methodology within the self-consistent charge representation. We find that certain carbon cluster configurations that are unstable as free molecules become stabilized inside C60. By adding single atoms into random positions inside the fullerene shell we establish an upper limit for the filling of C60 with carbon. When the number of atoms inside the fullerene exceeds ten we observe bonding to the surrounding shell and, hence, a gradual transition of the fullerene towards an sp3 rich but locally disordered carbon system.Peer reviewe

Simulations of diamond nucleation in carbon fullerene cores

Recent experiments have shown that heavy ion or electron irradiation induces the nucleation of diamond crystallites inside concentric nested carbon fullerenes, i.e., bucky onions. This suggests that the fullerene acts as a nanoscopic pressure shell. In this paper we study the formation of tetrahedrally bonded carbon inside a prototype icosahedral two-shell fullerene by means of atomic-scale computer simulations. After the simulated irradiation, we can identify regions in which almost all carbon atoms become sp3 bonded. Additionally, we observe a counteracting tendency for the carbon atoms to form shell-like substructures. To shift the balance between these two processes towards diamond nucleation strongly nonequilibrium conditions are required.Peer reviewe

Quantum Reed-Solomon Codes

After a brief introduction to both quantum computation and quantum error correction, we show how to construct quantum error-correcting codes based on classical BCH codes. With these codes, decoding can exploit additional information about the position of errors. This error model - the quantum erasure channel - is discussed. Finally, parameters of quantum BCH codes are provided.Comment: Summary only (2 pages), for the full version see: Proceedings Applied Algebra, Algebraic Algorithms and Error-Correcting Codes (AAECC-13), Lecture Notes in Computer Science 1719, Springer, 199

Tree-based Coarsening and Partitioning of Complex Networks

Many applications produce massive complex networks whose analysis would benefit from parallel processing. Parallel algorithms, in turn, often require a suitable network partition. For solving optimization tasks such as graph partitioning on large networks, multilevel methods are preferred in practice. Yet, complex networks pose challenges to established multilevel algorithms, in particular to their coarsening phase. One way to specify a (recursive) coarsening of a graph is to rate its edges and then contract the edges as prioritized by the rating. In this paper we (i) define weights for the edges of a network that express the edges' importance for connectivity, (ii) compute a minimum weight spanning tree $T^m$ with respect to these weights, and (iii) rate the network edges based on the conductance values of $T^m$'s fundamental cuts. To this end, we also (iv) develop the first optimal linear-time algorithm to compute the conductance values of \emph{all} fundamental cuts of a given spanning tree. We integrate the new edge rating into a leading multilevel graph partitioner and equip the latter with a new greedy postprocessing for optimizing the maximum communication volume (MCV). Experiments on bipartitioning frequently used benchmark networks show that the postprocessing already reduces MCV by 11.3%. Our new edge rating further reduces MCV by 10.3% compared to the previously best rating with the postprocessing in place for both ratings. In total, with a modest increase in running time, our new approach reduces the MCV of complex network partitions by 20.4%

Two flavor chiral phase transition from nonperturbative flow equations

We employ nonperturbative flow equations to compute the equation of state for two flavor QCD within an effective quark meson model. This yields the temperature and quark mass dependence of quantities like the chiral condensate or the pion mass. A precision estimate of the universal critical equation of state for the three-dimensional O(4) Heisenberg model is presented. We explicitly connect the O(4) universal behavior near the critical temperature and zero quark mass with the physics at zero temperature and a realistic pion mass. For realistic quark masses the pion correlation length near T_c turns out to be smaller than its zero temperature value.Comment: 49 pages including 15 figures, LaTeX, uses epsf.sty and rotate.st

Optimal Traffic Networks

Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a combination of topological and metric quantities. It is characterized by a strongly heterogeneous traffic, non-trivial correlations between distance and traffic and a broadly distributed centrality. A clear spatial hierarchical organization, with local hubs distributing traffic in smaller regions, emerges as a result of the optimization. Varying the parameters of the cost function, different classes of trees are recovered, including in particular the minimum spanning tree and the shortest path tree. These results suggest that a variational approach represents an alternative and possibly very meaningful path to the study of the structure of complex weighted networks.Comment: 4 pages, 4 figures, final revised versio

Heisenberg frustrated magnets: a nonperturbative approach

Frustrated magnets are a notorious example where the usual perturbative methods are in conflict. Using a nonperturbative Wilson-like approach, we get a coherent picture of the physics of Heisenberg frustrated magnets everywhere between $d=2$ and $d=4$. We recover all known perturbative results in a single framework and find the transition to be weakly first order in $d=3$. We compute effective exponents in good agreement with numerical and experimental data.Comment: 5 pages, Revtex, technical details available at http://www.lpthe.jussieu.fr/~tissie

Exact Flow Equations and the U(1)-Problem

The effective action of a SU(N)-gauge theory coupled to fermions is evaluated at a large infrared cut-off scale k within the path integral approach. The gauge field measure includes topologically non-trivial configurations (instantons). Due to the explicit infrared regularisation there are no gauge field zero modes. The Dirac operator of instanton configurations shows a zero mode even after the infrared regularisation, which leads to U_A(1)-violating terms in the effective action. These terms are calculated in the limit of large scales k.Comment: 22 pages, latex, no figures, with stylistic changes and some arguments streamlined, typos corrected, References added, to appear in Phys. Rev.

Growth of (110) Diamond using pure Dicarbon

We use a density-functional based tight-binding method to study diamond growth steps by depositing dicarbon species onto a hydrogen-free diamond (110) surface. Subsequent C_2 molecules are deposited on an initially clean surface, in the vicinity of a growing adsorbate cluster, and finally, near vacancies just before completion of a full new monolayer. The preferred growth stages arise from C_2n clusters in near ideal lattice positions forming zigzag chains running along the [-110] direction parallel to the surface. The adsorption energies are consistently exothermic by 8--10 eV per C_2, depending on the size of the cluster. The deposition barriers for these processes are in the range of 0.0--0.6 eV. For deposition sites above C_2n clusters the adsorption energies are smaller by 3 eV, but diffusion to more stable positions is feasible. We also perform simulations of the diffusion of C_2 molecules on the surface in the vicinity of existing adsorbate clusters using an augmented Lagrangian penalty method. We find migration barriers in excess of 3 eV on the clean surface, and 0.6--1.0 eV on top of graphene-like adsorbates. The barrier heights and pathways indicate that the growth from gaseous dicarbons proceeds either by direct adsorption onto clean sites or after migration on top of the existing C_2n chains.Comment: 8 Pages, 7 figure