Deterministic phase transitions and self-organization in logistic cellular automata.

We present a simple extension in which a single parameter tunes the dynamics of cellular automata (CA) by consequently expanding their discrete state space into a Cantor set. Such an implementation serves as a potent platform for further investigation of several emergent phenomena, including deterministic phase transitions, pattern formation, autocatalysis, and self-organization. We first apply this approach to Conway's Game of Life and observe sudden changes in the asymptotic dynamics of the system accompanied by the emergence of complex propagators. Incorporation of the new state space with system features is used to explain the transitions and formulate the tuning parameter range where the propagators adaptively survive by investigating their autocatalytic local interactions. Similar behavior is present when the same recipe is applied to Rule 90, an outer totalistic elementary one-dimensional cellular automaton. In addition, the latter case shows that deterministic transitions between classes of CA can be achieved by tuning a single parameter continuously.

Hall conductance in graphene with point defects.

We investigate the Hall conductance of graphene with point defects within the Kubo formalism, which allows us to calculate the Hall conductance without constraining the Fermi energy to lie in a gap. For pure graphene, which we model using a tight-binding Hamiltonian, we recover both the usual and the anomalous integer quantum Hall effects depending on the proximity to the Dirac points. We investigate the effect of point defects on Hall conduction by considering a dilute but regular array of point defects incorporated into the graphene lattice. We extend our calculations to include next nearest neighbor hopping, which breaks the bipartite symmetry of the lattice. We find that impurity atoms which are weakly coupled to the rest of the lattice result in gradual disappearance of the high conductance value plateaus. For such impurities, especially for vacancies which are decoupled from the lattice, strong modification of the Hall conductance occurs near the E = 0 eV line, as impurity states are highly localized. In contrast, if the impurities are strongly coupled, they create additional Hall conductance plateaus at the extremum values of the spectrum, signifying separate impurity bands. Hall conductance values within the original spectrum are not strongly modified.

The integer quantum Hall effect of a square lattice with an array of point defects.

The electronic properties of a square lattice under an applied perpendicular magnetic field in the presence of impurities or vacancies are investigated by the tight-binding method including up to second nearest neighbor interactions. These imperfections result in new gaps and bands in the Hofstadter butterfly even when the second order interactions break the bipartite symmetry. In addition, the whole spectrum of the Hall conduction is obtained by the Kubo formula for the corresponding cases. The results are in accordance with the Thouless-Kohmoto-Nightingale-den Nijs integers when the Fermi energy lies in an energy gap. We find that the states due to the vacancies or impurities with small hopping constants are highly localized and do not contribute to the Hall conduction. However, the impurities with high hopping constants result in new Hall plateaus with constant conduction of σ(xy) =± e(2)/h, since high hopping constants increase the probability of an electron contributing to the conduction.

Ab initio study of neutral (TiO2)n clusters and their interactions with water and transition metal atoms.

We have systematically investigated the growth behavior and stability of small stoichiometric (TiO(2))(n) (n = 1-10) clusters as well as their structural, electronic and magnetic properties by using the first-principles plane wave pseudopotential method within density functional theory. In order to find out the ground state geometries, a large number of initial cluster structures for each n has been searched via total energy calculations. Generally, the ground state structures for the case of n = 1-9 clusters have at least one monovalent O atom, which only binds to a single Ti atom. However, the most stable structure of the n = 10 cluster does not have any monovalent O atom. On the other hand, Ti atoms are at least fourfold coordinated for the ground state structures for n ≥ 4 clusters. Our calculations have revealed that clusters prefer to form three-dimensional structures. Furthermore, all these stoichiometric clusters have nonmagnetic ground state. The formation energy and the highest occupied molecular orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) gap for the most stable structure of (TiO(2))(n) clusters for each n have also been calculated. The formation energy and hence the stability increases as the cluster size grows. In addition, the interactions between the ground state structure of the (TiO(2))(n) cluster and a single water molecule have been studied. The binding energy (E(b)) of the H(2)O molecule exhibits an oscillatory behavior with the size of the clusters. A single water molecule preferably binds to the cluster Ti atom through its oxygen atom, resulting an average binding energy of 1.1 eV. We have also reported the interaction of the selected clusters (n = 3, 4, 10) with multiple water molecules. We have found that additional water molecules lead to a decrease in the binding energy of these molecules to the (TiO(2))(n) clusters. Finally, the adsorption of transition metal (TM) atoms (V, Co and Pt) on the n = 10 cluster has been investigated for possible functionalization. All these elements interact strongly with this cluster, and a permanent magnetic moment is induced upon adsorption of Co and V atoms. We have observed gap localized TM states leading to significant HOMO-LUMO gap narrowing, which is essential to achieve visible light response for the efficient use of TiO(2) based materials. In this way, electronic and optical as well as magnetic properties of TiO(2) materials can be modulated by using the appropriate adsorbate atoms.

Characterization of platinum nitride from first-principles calculations.

We have performed a systematic study of the ground state properties of the zinc-blende, rock-salt, tetragonal, cuprite, fluorite and pyrite phases of platinum nitride by using the plane wave pseudopotential calculations within the density functional theory. The equilibrium structural parameters and bulk moduli are computed within both the local density approximation (LDA) and generalized gradient approximation (GGA). The comparison of the equation of state (EOS) calculated within the LDA for the pyrite structure with the experimental results demonstrates an excellent agreement, hence the use of the LDA rather than the GGA is essential. Complete sets of elastic moduli are presented for cubic forms. The analysis of the results reveal that the pyrite phase with PtN(2) stoichiometry leads to the formation of a hard material with the shear modulus G = 206 GPa. The electronic structure of pyrite PtN(2) is given, which shows a narrow indirect gap. The vibrational properties of platinum nitride are investigated in detail from lattice dynamical calculations. The calculations show that fluorite and pyrite structures are dynamically stable as well. However, the calculated vibrational modes of pyrite PtN(2) do not show complete agreement with experimental Raman frequencies.

Tunable adsorption on carbon nanotubes.

We investigated the adsorption of a single atom, hydrogen and aluminum, on single-wall carbon nanotubes from first principles. The adsorption is exothermic, and the associated binding energy varies inversely as the radius of the zigzag tube. We found that the adsorption of a single atom and related properties can be modified continuously and reversibly by the external radial deformation. The binding energy on the high curvature site of the deformed tube increases with increasing radial deformation. The effects of curvature and radial deformation depend on the chirality of the tube.

Elasticity of iron at the temperature of the Earth's inner core.

Seismological body-wave and free-oscillation studies of the Earth's solid inner core have revealed that compressional waves traverse the inner core faster along near-polar paths than in the equatorial plane. Studies have also documented local deviations from this first-order pattern of anisotropy on length scales ranging from 1 to 1,000 km (refs 3, 4). These observations, together with reports of the differential rotation of the inner core, have generated considerable interest in the physical state and dynamics of the inner core, and in the structure and elasticity of its main constituent, iron, at appropriate conditions of pressure and temperature. Here we report first-principles calculations of the structure and elasticity of dense hexagonal close-packed (h.c.p.) iron at high temperatures. We find that the axial ratio c/a of h.c.p. iron increases substantially with increasing temperature, reaching a value of nearly 1.7 at a temperature of 5,700 K, where aggregate bulk and shear moduli match those of the inner core. As a consequence of the increasing c/a ratio, we have found that the single-crystal longitudinal anisotropy of h.c.p. iron at high temperature has the opposite sense from that at low temperature. By combining our results with a simple model of polycrystalline texture in the inner core, in which basal planes are partially aligned with the rotation axis, we can account for seismological observations of inner-core anisotropy.

Giant anharmonicity and nonlinear electron-phonon coupling in MgB2: a combined first-principles calculation and neutron scattering study.

First-principles calculations of the electronic band structure and lattice dynamics for the new superconductor MgB (2) are carried out and found to be in excellent agreement with our inelastic neutron scattering measurements. The numerical results reveal that the E(2g) in-plane boron phonons near the zone center are very anharmonic and strongly coupled to the planar B sigma bands near the Fermi level. This giant anharmonicity and nonlinear electron-phonon coupling is key to quantitatively explaining the observed high T(c) and boron isotope effect in MgB (2).