Self-organized Criticality in an Earthquake Model on Random Network

A simplified Olami-Feder-Christensen model on a random network has been studied. We propose a new toppling rule — when there is an unstable site toppling, the energy of the site is redistributed to its nearest neighbors randomly not averagely. The simulation results indicate that the model displays self-organized criticality when the system is conservative, and the avalanche size probability distribution of the system obeys finite size scaling. When the system is nonconservative, the model does not display scaling behavior. Simulation results of our model with different nearest neighbors q is also compared, which indicates that the spatial topology does not alter the critical behavior of the system.     

Large scale structures, symmetry, and universality in sandpiles

We introduce a sandpile model where, at each unstable site, all grains are transferred randomly to downstream neighbors. The model is local and conservative, but not Abelian. This does not appear to change the universality class for the avalanches in the self-organized critical state. It does, however, introduce long-range spatial correlations within the metastable states. For the transverse direction d(perpendicular)>0, we find a fractal network of occupied sites, whose density vanishes as a power law with distance into the sandpile.     

Electron cooling of high-Z ion beams parallel to a guidemagnetic field

The cooling of high-Z ion beams through collisions with electrons whose temperature parallel to a guide magnetic field is considerably lower than their perpendicular temperature is considered. For initial electron temperatures, magnetic fields, and charged-particle densities, electrons tend to be trapped in the vicinity of their nearest ion neighbor. This results in an energy exchange with the ions that is qualitatively different from conventional models, where electron cooling is described in terms of small angle collisions or within the linearized dielectric response theory. Such models are justified for situations where the potential energy of interactions is small compared to the relevant kinetic energy; e.g. for light ions. For the case of high-Z ions, however, it is the trapping process itself that drives the cooling. Using a variety of parameterizations of the electron shielding of the ions, it is found that resulting steady-state ion temperature parallel to the magnetic field is less than a factor of ten higher than the original parallel electron temperature. The e-folding times of approach to the equilibrium temperature have been found to be on the order of a few milliseconds for Z in the range of 20 and above. This result is encouraging with respect to the production of ultracold beams or even a crystalline heavy-ion state     

A colloidal model system with tunable disorder: Solid-fluid transition and discontinuities in the limit of zero disorder

We study a colloidal model system where disorder can be continuously tuned from no disorder --corresponding to a system that can crystallize-- to large disorder where geometrical frustration occurs. The model system consists of colloidal particles with screened electrostatic repulsion. They can only move on single lines which are parallel and equidistant to each other. We introduce disorder by modulating the particle line density. The system exhibits a solid-to-fluid transition which we study by the structure factor and the temporal evolution of the mean-square distance of nearest neighbors on neighboring lines. A determining feature is the occurrence of discontinuities when disorder is tuned to zero. We observe that the peak height of the pair correlation function in the solid phase does not extrapolate to the value of the perfect crystal. Similarly, the mean interaction energy and the screening length at which the solid-fluid transition occurs seem to be discontinuous when the limit of zero disorder is approached.     

Nonadiabatic effects in the lattice dynamics of compressed rare-gas crystals

Electron-ion contributions to the energy of rare-gas crystals are discussed from first principles in the framework of the Tolpygo model and its variants. The frequencies of phonons in a neon crystal at pressures p ≠ 0 are calculated in terms of models that go beyond the scope of the adiabatic approximation. Analysis of the contributions from different interactions to the lattice dynamics of the crystals demonstrates that the phonon frequencies calculated in the framework of the simplest model (allowing only for the nearest neighbors) and the most complex model (with the inclusion of the nearest neighbors, next-nearest neighbors, nonadiabatic effects, etc.) for small wave vectors are close to each other. The difference between the phonon frequencies calculated within the above models is most pronounced at the Brillouin zone boundary. Under strong compression, the phonon spectrum along the Δ direction is distorted and the longitudinal mode is softened as a result of the electron-phonon interaction. The contribution from terms of higher orders in the overlap integral S at p ≠ 0 to the phonon frequencies is more significant than that obtained in the band-structure calculations of the neon crystal.     

混合自旋(S=1,1/2)模型具有再次近邻反铁磁相互作用晶格基态

本文发展文献[1]的方法到两种不同自旋的原子(S_a=1,S_b=1/2)构成的晶格中,计算了简单立方晶格在具有再次近邻反铁磁相互作用下在外磁场中的基态自旋结构、能量和相界。从文中给出的相图可知:这种晶格有两种反铁磁自旋结构,有四种亚铁磁自旋结构。 关键词：     

Atomic displacements due to interstitial hydrogen in Cu and Pd

The density functional theory (DFT) is used to study the atomic interactions in transition metal-based interstitial alloys. The strain field is calculated in the discrete lattice model using Kanzaki method. The total energy and hence atomic forces between interstitial hydrogen and transition metal hosts are calculated using DFT. The norm-conserving pseudopotentials for H, Cu and Pd are generated self-consistently. The dynamical matrices are evaluated considering interaction up to first nearest neighbors whereas impurity-induced forces are calculated with M₃₂H shell (where M = Cu and Pd). The atomic displacements produced by interstitial hydrogen at the octahedral site in Cu and Pd show displacements of 7.36% and 4.3% of the first nearest neighbors respectively. Both Cu and Pd lattices show lattice expansion due to the presence of hydrogen and the obtained average lattice expansion ΔV/V = 0.177 for Cu and 0.145 for Pd.      

Work functions and surface double layer potentials of monovalent metals from a network model

The model described in this paper uses an electronic wave function which is defined to be nonzero only along the lines connecting first nearest neighbors in the metallic lattice. The electrons are assumed to move freely along the lines between nearest neighbors. No electron-electron or electron-nucleus force is included in the model calculations (except for forces arising from the Pauli exclusion principle). The work function is defined as the amount of energy required to move an electron from a point slightly inside the crystal to a point slightly outside. The contribution of the electronic double layer is included in the calculation of the work function as well as the dependence of the double layer potential on the surface geometry. Surface states, where the electron is localized in the neighborhood of the face of the crystal, are found to have energies sufficiently above the Fermi level to eliminate the possibility that they make any contribution to the double layer potential for the case of the (100) crystal plane. Consequently, surface states have been ignored in all the calculations. The surface double layer is assumed to be caused by the presence of a finite potential barrier at the surface of the crystal. Bulk electronic wave functions can penetrate this barrier and decay exponentially outside the crystal. The only parameters required by the model are the nearest neighbor distance for the lattice and the height of the potential barrier at the surface. The former quantity is fixed by the lattice structure (body centered cubic for the alkali metals) and by the density, while the latter quantity can be adjusted to give the best agreement between the model calculations and experiment. For the alkali metals, lithium through sodium, the best value of the barrier height is about 50% of the sum of the ionization potential energy, the heat of vaporization, and the calculated Fermi level for the corresponding metal. In addition, the value of the double layer potential for sodium agrees very well with a more sophisticated calculation by Bardeen and is reasonably close to the experimental measurement.     

Charge states of substitutional S in Si

We study the electronic structure of the various charge states of a substitutional S impurity in Si in the tight-binding approximation. We take into account the changes in the diagonal elements of the host Hamiltonian on the impurity site and on its nearest neighbors and the changes in the off-diagonal elements between the impurity site and its nearest neighbors. Good agreement is found with experimental results and with more a priori calculations.     

How to introduce temperature to the 1D Sznajd model

We investigate the possibility of introducing temperature to the one dimensional Sznajd model and propose a natural extension of the original model by including other types of interactions. We characterise different kinds of equilibria into which the extended system can evolve. We determine the consequences of fulfilling the detailed balance condition and we prove that in some cases it is equivalent to microscopic reversibility. We found the equivalence of the model to the standard (inflow) model with interactions up to next nearest neighbors. It is shown that under some constraints there exists a Hamiltonian compatible with the dynamics and its form resembles that of the 1D ANNNI model. It appears however, that the standard approach of constructing temperature from the Hamiltonian fails. In this situation we propose a simple definition of the temperature-like quantity that measures the size of fluctuations in the system at equilibrium. The complete list of zero-temperature degenerated cases as well as the list of ground states of the derived Hamiltonian are provided.     

Anyons in an exactly solved model and beyond

A spin-1/2 system on a honeycomb lattice is studied. The interactions between nearest neighbors are of XX, YY or ZZ type, depending on the direction of the link; different types of interactions may differ in strength. The model is solved exactly by a reduction to free fermions in a static Z₂ gauge field. A phase diagram in the parameter space is obtained. One of the phases has an energy gap and carries excitations that are Abelian anyons. The other phase is gapless, but acquires a gap in the presence of magnetic field. In the latter case excitations are non-Abelian anyons whose braiding rules coincide with those of conformal blocks for the Ising model. We also consider a general theory of free fermions with a gapped spectrum, which is characterized by a spectral Chern number ν. The Abelian and non-Abelian phases of the original model correspond to ν = 0 and ν = ±1, respectively. The anyonic properties of excitation depend on ν mod 16, whereas ν itself governs edge thermal transport. The paper also provides mathematical background on anyons as well as an elementary theory of Chern number for quasidiagonal matrices.     

Ferrimagnetic ground state of a phenylene polymer with organic radicals

A ferrimagnetic polymer with m-phenylene skeleton as coupling unit is studied with the Hubbard model in the self-consistent mean-field theory. The ferrimagnetic ground state with a total spin S = 1 per unit cell is obtained and originates from the antiferromagnetic correlations between the nearest neighbors. If the on-site electron-electron repulsions at the radical sites and at the phenylene ring sites are different, the gap in energy band structure may disappear and the ferrimagnetic ground state becomes unstable. The charge density and spin density can transfer between the radical sites and the phenylene ring sites due to the competition between the hopping integral and the on-site repulsion at different sites. Received 15 July 2002 Published online 31 December 2002     

Lattice relaxation for normal muonium in diamond

The effects of symmetric lattice relaxation around the tetrahedral (T) and the hexagonal (H) interstitial sites are calculated for normal muonium (Mu) in diamond using the non-semiempirical method of Partial Retention of Diatomic Differential Overlap (PRDDO). We use clusters containing 3 and 4 host atom shells around the T and the H sites (C₂₀H₃₂ and C₃₀H₄₀). The only significant relaxations are the outward displacement of the 6 nearest neighbors (NN) to the H site and, when the muon is at the T site, the simultaneous outward displacement of the first and second NN to the T site. In the case of diamond, the effects of these relaxations on the energy profiles and spin densities are small.     

Interface free energy and critical line for the ising model with nearest and next-nearest-neighbor interactions

A method due to Müller-Hartmann and Zittartz is used to calculate the free energy of a diagonal interface in an Ising model on a square lattice with interactions between nearest and next-nearest neighbors. Instead of solving the full bulk problem, one only takes into account a simple subset of interface configurations. The subset, which is somewhat different from that considered by Müller-Hartmann and Zittartz, is chosen in such a way that exact results for the interface free energy are reproduced if the system has only nearest or only next-nearest-neighbor interactions. When the critical line of ferromagnetic transitions is obtained by demanding that the interface free energy as a function of both couplings vanish, a surprisingly accurate approximation is obtained.     

Frustrated antiferromagnetic spin 1 Heisenberg model with single ion anisotropy on a simple cubic lattice

We study the effects of frustration between nearest, next-nearest neighbor and next-next-nearest neighbors (NNN) of the quantum S=1 anisotropic antiferromagnetic Heisenberg model on a simple cubic lattice with single ion anisotropy using the bond operator technique. We calculate the phase diagram at zero temperature and the gap as a function of temperature in the disordered paramagnetic phase.     

Load-redistribution strategy based on time-varying load against cascading failure of complex network

Cascading failure can cause great damage to complex networks, so it is of great significance to improve the network robustness against cascading failure. Many previous existing works on load-redistribution strategies require global information, which is not suitable for large scale networks, and some strategies based on local information assume that the load of a node is always its initial load before the network is attacked, and the load of the failure node is redistributed to its neighbors according to their initial load or initial residual capacity. This paper proposes a new load-redistribution strategy based on local information considering an ever-changing load. It redistributes the loads of the failure node to its nearest neighbors according to their current residual capacity, which makes full use of the residual capacity of the network. Experiments are conducted on two typical networks and two real networks, and the experimental results show that the new load-redistribution strategy can reduce the size of cascading failure efficiently.     

Si中掺Er的原子构型与电子特性

采用定域密度泛函-离散变分方法(LDF-DVM)计算了Si中掺Er的原子构型与电子特性，并计算了O共掺杂对Si中掺Er体系的原子构型与电子特性的影响.结果表明，在没有O共掺杂时，Er处于四面体间隙位置时能量最低，此时Er的5d轨道在Si的导带中引入浅的共振态.处于替代位置的Er形成能略高，Er的5d轨道在Si的导带顶附近引入了受主态.当有O存在时，体系的形成能降低，能量最低的构型是Er处于六角形间隙位置，周围有6个O，此时Er的5d轨道在Si的导带下约为0.3eV处引入杂质态.从而解释了Si中掺Er体系在 关键词：     

Ising自旋S=1,具有次近邻相互作用的面心立方格子的反铁磁体在外场下的基态能量

本文用文献[4]中提出的方法,变S=1的Ising体系成一个粒子数不守恒的费密体系,严格地求得了具有最近邻及次近邻相互作用的反铁磁Ising晶格在任意外场下的基态能量,得到了零温的相图。 关键词：     

各向异性扩散问题Kershaw格式的守恒保正修复算法

针对各向异性扩散方程Kershaw格式的数值解在正交网格及扭曲网格上计算出负的现象,给出一种守恒的保正修复算法（CENZ）,该算法对简单遇负置零（ENZ）方法进行改进,使修复后的数值解不仅具有非负性,而且保持法向通量的局部守恒性.数值算例表明,该方法不受计算网格类型和扩散系数各向异性比的限制,可用于对任意违背单调性（或保正性）的有限体积格式数值解的修复.     

Influence of the structural properties on the pseudocritical magnetic behavior of single-wall ferromagnetic nanotubes

In this work we address the influence of the crystalline structure, concretely when the system under study is formed by square or hexagonal unit cells, upon the magnetic properties and pseudocritical behavior of single-wall ferromagnetic nanotubes. We focus not only on the effect of the geometrical shape of the unit cell but also on their dimensions. The model employed is based on the Monte Carlo method, the Metropolis dynamics and a nearest neighbors classical Heisenberg Hamiltonian. Magnetization per magnetic site, magnetic susceptibility, speci?c heat and magnetic energy were computed. These properties were computed varying the system size, unit cell dimension and temperature. The dependence of the nearest neighbor exchange integral on the nanotubes geometrical characteristics is also discussed. Results revealed a strong influence of the system topology on the magnetic properties caused by the difference in the coordination number between square and hexagonal unit cell. Moreover, the nanotubes diameter influence on magnetic properties is only observed at very low values, when the distance between atoms is less than it, presented by the 2D sheet. On the other hand, it was concluded that the surface-related finite-size effects do not influence the magnetic nanotubes properties, contrary to the case of other nano-systems as thin films and nanoparticles among others.