Critical temperature of metallic hydrogen at a pressure of 500 GPa

Phase transitions of the layered antiferromagnetic Ising model on a cubic lattice with allowance for intralayer next nearest neighbor interactions in the range of 0.0 ? r < 1.0 have been studied on the basis of the replica algorithm by the Monte Carlo method. The character of phase transitions has been analyzed on the basis of the histogram method and the Binder cumulant method. The phase diagram of the dependence of the critical temperature on the next nearest neighbor interaction has been constructed. It has been shown that a secondorder phase transition is observed in the interval of 0.0 ? r ? 0.5 and for the value r = 0.9 and a first-order phase transition is observed in the interval of 0.6 ? r < 0.8.     

Estimating the half-life of 241Pu and its uncertainty

Measuring the double isotope atomic abundance ratio as function of time of a homogenized stock of plutonium using mass spectroscopy provides a means to estimate the half-life of ²⁴¹Pu, denoted here as t_1/2,241. After a logarithmic transformation, estimating t_1/2,241 along with a justifiable associated uncertainty is reduced to the analysis of a linear relationship, as illustrated in this paper using 15 published data pairs (time, log(double isotope ratio)) of Wellum et al. (2009) that span approximately 31 years (greater than two half-lives). However, as noted by Wellum et al. (2009), the published 15 data pairs exhibit inconsistencies that indicate possible underestimation of individual experimental uncertainties. Similar inconsistencies often arise in multi-experiment comparisons of the same estimated quantity, typically because some components of uncertainty such as individual experimental biases are difficult to identify and assess. It is therefore an important and common problem. In such cases the experimental data must be supplemented with other information to make plausible uncertainty estimates. We therefore analyze the data pairs under several different assumptions regarding total experimental uncertainties and show quantitatively that the best estimate of t_1/2,241 and of its uncertainty depend on the assumptions regarding experimental uncertainties. It is unlikely in this context that the 15 data pairs and associated estimated experimental uncertainties could guide one toward a very certain choice among the reasonable sets of assumptions regarding total experimental uncertainties. Thus a definitive recommendation cannot be singled out. Fortunately, the best estimates and associated uncertainties arising from different yet tenable assumptions regarding experimental uncertainties are all in reasonably close agreement. And, one of those best estimates we provide (with approximately 95% confidence limits) is (14.329 ± 0.006[fit] ± 0.029[bias]) years, which uses similar data stratification arguments as in Wellum et al. (2009) but a completely different approach. Furthermore, this estimate of t_1/2,241 agrees closely with the value recommended in Wellum et al. (2009) of (14.325 ± 0.024) years. We conclude that the value of t_1/2,241 supported by the available data is robust, despite evidence of some non-ideal behavior, and that alternative means of estimating t_1/2,241 and its uncertainty yield reasonably similar results.     

Development of lattice inversion modified embedded atom method and its applications

The modified embedded atom method (MEAM) has been widely used in describing the physical properties of elemental crystals, alloys and compounds with multiple lattice structures. We report here the development of a reliable procedure to reduce the complexity of the MEAM formalism by removing the many-body screening function. In the proposed formulation, the interatomic pair potential is obtained by applying Chen-Möbius lattice inversion up to fifth nearest neighbors, so that the cohesive energy curve can be reproduced faithfully. The newly developed model (Lattice Inversion MEAM, LI-MEAM), which can be viewed as a direct extension of the embedded atom method (EAM), no longer requires the computation of many-body screen functions and has fewer adjustable parameters than MEAM. As an illustration, we optimized the potential parameters of body centered cubic iron (bcc-Fe). The values of the calculated physical properties agree well with experimental results. We further investigated the size-dependent melting behavior of bcc-Fe nanoparticles (NPs) with particle size ranging from 725-atom (∼25 Å) to 22899-atom (∼80 Å) using replica exchange molecular dynamics (REMD) simulations. Our simulations show advantages of LI-MEAM in modeling of the melting process and quantitatively reveals that the liquid skin melting (LSM) process of bcc-Fe NPs.     

Ferromagnetism in the Hubbard Model with a Gapless Nearly-Flat Band

We present a version of the Hubbard model with a gapless nearly-flat lowest band which exhibits ferromagnetism in two or more dimensions. The model is defined on a lattice obtained by placing a site on each edge of the hypercubic lattice, and electron hopping is assumed to be only between nearest and next nearest neighbor sites. The lattice, where all the sites are identical, is simple, and the corresponding single-electron band structure, where two cosine-type bands touch without an energy gap, is also simple. We prove that the ground state of the model is unique and ferromagnetic at half-filling of the lower band, if the lower band is nearly flat and the strength of on-site repulsion is larger than a certain value which is independent of the lattice size. This is the first example of ferromagnetism in three dimensional non-singular models with a gapless band structure.     

Peculiar scaling of self-avoiding walk contacts

The nearest neighbor contacts between the two halves of an N-site lattice self-avoiding walk offer an unusual example of scaling random geometry: for N-->infinity they are strictly finite in number but their radius of gyration R(c) is power law distributed proportional to R(-tau)(c), where tau>1 is a novel exponent characterizing universal behavior. A continuum of diverging length scales is associated with the R(c) distribution. A possibly superuniversal tau = 2 is also expected for the contacts of a self-avoiding or random walk with a confining wall.     

Comment on ‘An optimal algorithm for counting networks motifs’ [Physica A 381 (2007) 482-490]

Network motifs in a given network are small connected subnetworks that occur at significantly higher frequencies than would be expected for a random network. In their 2007 article “An optimal algorithm for counting network motifs”, Itzhack, Mogilevski, and Louzoun present an algorithm for detecting network motifs. Based on an experimental comparison with a motif detection software called FANMOD, they claim that their algorithm is “more than a thousand times faster” than any previous motif detection algorithm. We show that this claim is not correct and based on a significant flaw in the experimental setup. Once the experimental data of Itzhack et al. is corrected for this flaw, the implementation of their algorithm actually turns out to be a little slower than FANMOD for random Erd?s-Rényi graphs. For random scale-free networks, the implementation of Itzhack et al. is faster only by a factor of ∼1.5, not the orders of magnitude claimed by Itzhack et al.     

Morphology transition in cluster growth at different temperature

The cluster growth on two-dimensional square lattice at different temperature is investigated by Monte Carlo simulation, considering the binding energy of substrate, the coupling energy of nearest neighbor particles and a strain field. The simulation shows that, for 400 K ≤ T ≤ 480 K, the average branch width of the fractal cluster is independent to the temperature T, which is almost equal to the diameter of single particle. For 500 K ≤ T ≤ 680 K, however, the branch width increases gradually to 4 with temperature. With T further increases, clusters consist of large number of particles disappear, due to the strong activity of each particle. The coordination number distributions of clusters at different temperature are also studied.     

A new method for generation of synchronized capacitive sparks of low energy. Reconsideration of previously published findings

Using the spark generator of Randeberg et al., Randeberg and Eckhoff found a MIE of pre-mixed propane/air of <0.1 mJ, as opposed to the standard value 0.25 mJ. Literature studies revealed that this discrepancy was not a spark duration effect. The reason was a previously undetected subtle, but indeed significant, additional energy contribution. Therefore, the actual spark energies used by Randeberg et al. were considerably larger than the spark energies quoted by them. A main aim of the present paper is to explain the reason for this and to indicate a possible solution.     

De la microstructure du polymère à ses propriétés rhéologiques

We extend the previous work by Benallal et al. on the relationship between structure and rheological properties of linear polymer melts. The aim of this paper is to quantify the effect of the chemical structure on the viscoelastic properties. We show that these properties are governed by the monomer dimensions and the interaction energy. To cite this article: A. Allal et al., C. R. Physique 3 (2002) 1451–1458.     

Blowup and solitary wave solutions with ring profiles of two-component nonlinear Schrödinger systems

Blowup ring profiles have been investigated by finding non-vortex blowup solutions of nonlinear Schrödinger equations (NLSEs) (cf. Fibich et al. (2005) [7] and Fibich et al. (2007) [8]). However, those solutions have infinite L² norm, so one may not maintain the ring profile all the way up to the singularity. To find H¹ non-vortex blowup solutions with ring profiles, we study the blowup solutions of two-component systems of NLSEs with nonlinear coefficients β and ν_j, j=1,2. When β<0 and ν₁?ν₂>0, the two-component system can be transformed into a multi-scale system with fast and slow variables which may produce H¹ blowup solutions with non-vortex ring profiles. We use the localized energy method with symmetry reduction to construct these solutions rigorously. On the other hand, these solutions may describe steady non-vortex bright ring solitons. Various types of ring profiles including m-ring and ring-ring profiles are presented by numerical solutions.     

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice

Phase transitions and critical properties in the antiferromagnetic Heisenberg model on a layered cubic lattice with allowance for intralayer next nearest neighbor interactions have been studied using the replica Monte Carlo algorithm. The character of phase transitions has been analyzed using the histogram method and the Binder cumulant method. It has been found that a transition from the collinear to paramagnetic phase in the model under study occurs as a second order phase transition. The statistical critical exponents of the specific heat α, susceptibility γ, order parameter β, and correlation radius ν, as well as the Fisher index η, have been calculated using the finite-size scaling theory. It has been shown that the three-dimensional Heisenberg model on the layered cubic lattice with allowance for the next nearest neighbor interaction belongs to the same universality class of the critical behavior as the antiferromagnetic Heisenberg model on a layered triangular lattice.     

Continuous opinion model in small-world directed networks

In the compromise model of continuous opinions proposed by Deffuant et al., the states of two agents in a network can start to converge if they are neighbors and if their opinions are sufficiently close to each other, below a given threshold of tolerance ?. In directed networks, if agent i is a neighbor of agent j,j need not be a neighbor of i. In Watts-Strogatz networks we performed simulations to find the averaged number of final opinions 〈F〉 and their distribution as a function of ? and of the network structural disorder. In directed networks 〈F〉 exhibits a rich structure, being larger than in undirected networks for higher values of ?, and smaller for lower values of ?.     

Ab initio investigation of the surface properties of Cu(111) and Li diffusion in Cu thin film

Ab initio density-functional calculations have been performed to investigate the surface properties of Cu(111) and lithium diffusion in copper thin film. The calculation results including lattice constant, cohesive energy, work function and surface energy are in fair agreement with that derived from corresponding experiments. The various diffusion pathways such as diffusion of lithium as a substitution atom and various mechanisms are investigated with ab initio molecular dynamics. The energy barrier has been calculated corresponding to each possible pathway. Theoretically, we have identified that lithium can diffuse through copper thin film by successive nearest neighbor vacancy-atom exchanges, therefore, the nearest neighbor vacancy assisted jumping is deduced to be the most probable by comparing the different mechanisms. It is found that more free diffusion may be observed by increasing the number of copper vacancies in the thin film. It is also confirmed that the diffusion is more obvious as temperature is increased.     

On the exponential decay of correlation functions

We use the properties of subharmonic functions to prove the following results, First, for any lattice system with finite-range forces there is a gap in the spectrum of the transfer matrix, which persists in the thermodynamic limit, if the fugacityz lies in a regionE of the complex plane that contains the origin and is free of zeros of the grand partition function (with periodic boundary conditions) as the thermodynamic limit is approached. Secondly, if the transfer matrix is symmetric (for example, with nearest and next-nearest neighbor interactions in two dimensions), and if infinite-volume Ursell functions exist that are independent of the order in which the various sides of the periodicity box tend to infinity, then these Ursell functions decay exponentially with distance for all positivez inE. (For the Ising ferromagnet with two-body interactions, exponential decay holds forz inE even if the range of interaction is not restricted to one lattice spacing). Thirdly, if the interaction potential decays moreslowly than any decaying exponential, then so do all the infinite-volume Ursell functions, for almost all sufficiently small fugacities in the case of general lattice systems, and for all real magnetic fields in the case of Ising ferromagnets.     

Structure and chemical bond characteristics of LaB6

The structure and chemical bond characteristics of LaB₆ have been achieved by means of the density functional theory using the state-of-the-art full-potential linearized augmented plane wave (FPLAPW) method, which are implemented within the EXCITING code. The results show our optimized lattice constant a (4.158 Å), parameter z (0.1981) and bulk modulus B (170.4 GPa) are in good agreement with the corresponding experimental data. Electron localization function (ELF) shows the La–La bond mainly is ionic bond, La–B bond is between ionic and covalent bond while the covalent bond between the nearest neighbor B atoms (B2 and B3) is a little stronger than that between the nearer neighbor B atoms (B1 and B4).     

有限二维复式晶格电子结构的尺度效应

以二维复式晶格作为有限系统的集团模型,利用紧束缚近似,在考虑链间耦合及链端效应的情况下,计算了格点数分别为16、32、64、128时π电子在最近邻及次近邻跳跃集团的能谱和态密度.讨论了不同格点数和结构参数对态密度及带宽的影响.     

Searching for a near neighbor particle in DSMC cells using pseudo-subcells

LeBeau et al. (2003) [4] introduced the ‘virtual-subcell’ (VSC) method of finding a collision partner for a given DSMC particle in a cell; all potential collision partners in the cell are examined to find the nearest neighbor, which becomes the collision partner. Here I propose a modification of the VSC method, the ‘pseudo-subcell’ (PSC) method, whereby the search for a collision partner stops whenever a ‘near-enough’ particle is found, i.e. whenever another particle is found within the ‘pseudo-subcell’ of radius δ centered on the first particle. The radius of the pseudo-subcell is given by δ = Fd_n, where d_n is the expected distance to the nearest neighbor and F is a constant which can be adjusted to give a desired trade-off between CPU time and accuracy as measured by a small mean collision separation (MCS). For 3D orthogonal cells, of various aspect ratios, d_n/L ≈ 0.746/N^0.383 where N is the number of particles in the cell and L is the cube root of the cell volume. There is a good chance that a particle will be found in the pseudo-subcell and there is a good chance that such a particle is in fact the nearest neighbor. If no particle is found within the pseudo-subcell the closest particle becomes the collision partner.     

Radial distribution of dose within heavy charged particle tracks – Models and experimental verification using LiF:Mg,Cu,P TL detectors

A new method of experimental verification of radial dose distribution models using solid state thermoluminescent (TL) detectors LiF:Mg,Cu,P has been recently proposed. In this work the method was applied to verify the spatial distribution of energy deposition within a single ¹³¹Xe ion track. Detectors were irradiated at the Department of Physics of the University of Jyväskylä, Finland. The obtained results have been compared with theoretical data, calculated according to the Zhang et al., Cucinotta et al. and Geiss et al. radial dose distribution (RDD) models. At the lowest dose range the Zhang et al. RDD model exhibited the best agreement as compared to experimental data. In the intermediate dose range, up to 10⁴ Gy, the best agreement was found for the RDD model of Cucinotta et al. The probability of occurrence of doses higher than 10⁴ Gy within a single ¹³¹Xe ion track was found to be lower than predicted by all the studied RDD models. This may be a result of diffusion of the charge, which is then captured by TL-related trapping sites, at the distances up to dozens of nanometers from the ionization site.     

A Note on Dimer Models and McKay Quivers

We give one formulation of a procedure of Hanany and Vegh (J High Energy Phys 0710(029):35, 2007) which takes a lattice polygon as an input and produces a set of isoradial dimer models. We study the case of lattice triangles in detail and discuss the relation with coamoebas following Feng et al. (Adv Theor Math Phys 12(3):489–545, 2008).     

Spin polarization of two-dimensional electron system in parabolic potential

We analyze the ground state of the two-dimensional quantum system of electrons confined in a parabolic potential with the system size around 100 at 0 K. We map the system onto a classical system on the basis of the classical-map hypernetted-chain (CHNC) method which has been proven to work in the integral-equation-based analyses of uniform systems and apply classical Monte Carlo and molecular dynamics simulations. We find that, when we decrease the strength of confinement keeping the number of confined electrons fixed, the energy of the spin-polarized state with somewhat lower average density becomes smaller than that of the spin-unpolarized state with somewhat higher average density. This system thus undergoes the transition from the spin-unpolarized state to the spin polarized state and the corresponding critical value of rs estimated from the average density is as low as rs∼0.4 which is much smaller than the rs value for the Wigner lattice formation. When we compare the energies of spin-unpolarized and spin-polarized states for given average density, our data give the critical rs value for the transition between unpolarized and polarized states around 10 which is close to but still smaller than the known possibility of polarization at rs∼27. The advantage of our method is a direct applicability to geometrically complex systems which are difficult to analyze by integral equations and this is an example.