Mappings of empty space-times leaving the curvature tensor invariant

It is shown that if in some local coordinate system the componentsR ⁱ _jkl of the curvature tensor of an empty space-time are known, then, provided the space-time is not of Petrov typeN with hypersurface orthogonal geodesic rays, the components of the metric tensor are uniquely determined up to a trivial constant scaling factor. The Petrov type-N empty space-times with hypersurface orthogonal geodesic rays are investigated. The most general mappings leaving the curvature tensorR ⁱ _jkl invariant are found for each class of these space-times.     

The parallel complexity of growth models

This paper investigates the parallel complexity of several nonequilibrium growth models.Invasion percolation, Eden growth, ballistic deposition, andsolid-on-solid growth are all seemingly highly sequential processes that yield self-similar or self-affine random clusters. Nonetheless, we present fast parallel randomized algorithms for generating these clusters. The running times of the algorithms scale asO(log² N), whereN is the system size, and the number of processors required scales as a polynomial inN. The algorithms are based on fast parallel procedures for finding minimum-weight paths; they illuminate the close connection between growth models and self-avoiding paths in random environments. In addition to their potential practical value, our algorithms serve to classify these growth models as less complex than other growth models, such asdiffusion-limited aggregation, for which fast parallel algorithms probably do not exist.     

Kinetic-growth self-avoiding walks on small-world networks

Kinetically-grown self-avoiding walks have been studied on Watts-Strogatz small-world networks, rewired from a two-dimensional square lattice. The maximum length L of this kind of walks is limited in regular lattices by an attrition effect, which gives finite values for its mean value 〈L 〉. For random networks, this mean attrition length 〈L 〉 scales as a power of the network size, and diverges in the thermodynamic limit (system size N ↦∞). For small-world networks, we find a behavior that interpolates between those corresponding to regular lattices and randon networks, for rewiring probability p ranging from 0 to 1. For p < 1, the mean self-intersection and attrition length of kinetically-grown walks are finite. For p = 1, 〈L 〉 grows with system size as N^1/2, diverging in the thermodynamic limit. In this limit and close to p = 1, the mean attrition length diverges as (1-p)^-4. Results of approximate probabilistic calculations agree well with those derived from numerical simulations.     

A mean spherical model with coulomb interactions. II. Correlations at a free surface

Studies of the mean spherical model with Coulomb interactions are continued, by considering a system on ad-dimensional lattice which is periodic ind–1 dimensions and has a free surface in the remaining dimension. It is shown explicitly that correlations along the free surface decay asy ^–d ind dimensions and show that the surface properties of this model are those expected for a charged system in its plasma phase.     

Non-crystalline structures in the growth of silver nanoclusters

The growth of nanometer-size free Ag clusters is studied by Molecular Dynamics simulations. The morphology transition from the icosahedron at the magic size of N = 55 atoms to the Marks truncated decahedron at N = 75 is analyzed in details, in order to single out kinetic trapping and entropic effects. At very low T, the cluster is kinetically trapped in an icosahedral structure. At intermediate T the transition takes place sharply at N≃ 65. At higher T, the transition is smeared out and finally, around 550 K no transition is found because the 75 decahedron is melted. Received 28 November 2000     

¯N interaction from meson-exchange and quark-gluon dynamics

We investigate the ˉN interaction at low energies using a meson exchange model supplemented with a short-distance contribution from one-gluon exchange. The model is developed in close analogy to the meson-exchange KN interaction of the Jülich group utilizing SU(4) symmetry constraints. The main ingredients of the interaction are provided by vector meson (ρ , ω exchange and higher-order box diagrams involving ˉ^* N , ˉΔ , and ˉ^*Δ intermediate states. The short-range part is assumed to receive additional contributions from genuine quark-gluon processes. The predicted cross-sections for ˉN for excess energies up to 150MeV are of the same order of magnitude as those for KN but with average values of around 20mb, roughly a factor two larger than for the latter system. It is found that the ω -exchange plays a very important role. Its interference pattern with the ρ -exchange, which is basically fixed by the assumed SU(4) symmetry, clearly determines the qualitative features of the ˉN interaction --very similiar to what happens also for the KN system.     

Eigenfunction structure and scaling of two interacting particles in the one-dimensional Anderson model

The localization properties of eigenfunctions for two interacting particles in theone-dimensional Anderson model are studied for system sizes up to N = 5000 sitescorresponding to a Hilbert space of dimension ≈10⁷ using the Green function Arnoldi method. Theeigenfunction structure is illustrated in position, momentum and energy representation,the latter corresponding to an expansion in non-interacting product eigenfunctions.Different types of localization lengths are computed for parameter ranges in system size,disorder and interaction strengths inaccessible until now. We confirm that one-parameterscaling theory can be successfully applied provided that the condition of N being significantlylarger than the one-particle localization length L₁ is verified.The enhancement effect of the two-particle localization length L₂ behaving asL₂ ~ L₂¹ is clearly confirmed for a certain quite large intervalof optimal interactions strengths. Further new results for the interaction dependence in avery large interval, an energy value outside the band center, and different interactionranges are obtained.     

57Fe Mössbauer effect study of well-crystallized goethite (α-FeOOH)

Well-crystallized, natural goethite has been investigated as a function of temperature. The saturation magnetic hyperfine field was found to be 507 kOe and the Néel temperatureT _N=(400±2) K. The antiferromagnetic structure is stable in external fields of up to 6O kOe and the spin direction is at right angles with respect to the EFG's principal axis. AtT/T _N<0.5, the reduced hyperfine field varies asT ² and in the range 0.80<T/T _N<0.97 asT ^1/3. From the temperature dependence of the isomer shift, the Debije temperature was found to be 440 K from which a relative Mössbauer fraction of 0.96 against hematite was evaluated.     

Neutron scattering from equilibrium-swollen networks

Small-angle neutron scattering measurements were performed on end-linked poly (dimethylsiloxane) (PDMS) networks swollen to equilibrium with d-benzene. Comparison was made with equivalent concentration PDMS solutions. Equilibrium-swollen networks consistently displayed a linear scattering regime at low q followed by a good-solvent-like scaling regime at high q in agreement with the predictions of the Gel Tensile Blob (GTB) model. Data are fit using the unified function modified for the GTB model (3-parameter fit). Equilibrium-swollen networks display a base structural size, the gel tensile-blob size, ξ, that was found to be independent of the molecular weight between crosslinks for the series of molecular weights studied, consistent with the predictions of the model. The length of the extended tensile structure, L, can be larger than the length of the fully extended network strand. The predicted scaling relationship for L, L ∼ Q^1/2N_avg, where N_avg = (1/fN_c²+1/4N_e² , Q is the equilibrium swelling ratio, N_c is the molecular weight between crosslinks, N_e is the entanglement molecular weight and f is the crosslink functionality is in agreement with experimental results for the networks studied.     

Multiplicity of metastable retrieval phases in networks of multistate neurons

It is demonstrated that networks of multistate neurons storing an ensemble of multistate patterns exhibit a multiplicity of metastable retrieval phases. These phases are described by solutions of fixed-point equations with characteristic retrieval errors. They emerge if the gain of the neural input-output relation is varied. The number of these phases increases asQ ² with the numberQ of gray levels available to each neuron. Implications for the optimal gain function and basins of attraction are briefly discussed. Again, networks endowed with pseudoinverse couplings are found to perform better than networks with Hebbian couplings: at moderate loading levels phases with retrieval errors are destabilized, whereas the error-free phase remains stable up to the theoretically possible maximum, if the gain parameter is properly chosen.     

Analysis of groove NRD waveguide bend using the coupled-mode theory

In this paper, the propagation characteristics of the dominant mode in GNRD guide bend are analysed employing the coupled-mode theory. The curves of bending loss vs. The groove depth or width, radius of curvature and frequency are given, which caused by the mode conversion of the operatingLSM ₁₁ ^x mode to the parasiticLSE ₁₁ ^x mode. It is found that the groove depth has a great influence upon the bending loss than the other parameters. According to the theoretical results, appropriate sizes of groove and radius of curvature should be chosen in designing a GNRD bend structure.     

On coordination and continuous hawk-dove games on small-world networks

It is argued that small-world networks are more suitable than ordinary graphs in modelling the diffusion of a concept (e.g. a technology, a disease, a tradition, ...). The coordination game with two strategies is studied on small-world networks, and it is shown that the time needed for a concept to dominate almost all of the network is of order , where N is the number of vertices. This result is different from regular graphs and from a result obtained by Young. The reason for the difference is explained. Continuous hawk-dove game is defined and a corresponding dynamical system is derived. Its steady state and stability are studied. Replicator dynamics for continuous hawk-dove game is derived without the concept of population. The resulting finite difference equation is studied. Finally continuous hawk-dove is simulated on small-world networks using Nash updating rule. The system is 2-cyclic for all the studied range. Received 8 July 2000 and Received in final form 23 July 2000     

Leptodermous expansion of nuclear ground state energies and the anomaly in the nuclear curvature energy

The leptodermous expansion of the total ground state energy of a nucleus into volume, surface, curvature and gauss curvature contributions has been studied starting from a semi-classical energy density formalism of extended Thomas Fermi type. A numerical procedure was used to obtain the surface energy and curvature energy contributions from surface moments of energy density profilesH(r) for a sequence of nuclei withN=Z and neglecting the coulomb interaction for the three Skyrme forces. A transition to the liquid drop model type expansion in increasing powers ofA ^−1/3 is then made, taking into account the dependence of the central density and the surface structure on the mass of the nucleus. It is found that there is no inconsistency between the curvature contribution to the total energy in the leptodermous expansion and theA ^−1/3 term contribution in the liquid drop model expansion. It has been shown that the earlier apparent anomaly between the above two methods arises due to the use of semi-infinite approximation and the mass dependence of the central density and the surface structure of finite nuclei.     

The travelling salesman problem on randomly diluted lattices: Results for small-size systems

If one places N cities randomly on a lattice of size L, we find that and vary with the city concentration p=N/L ², where is the average optimal travel distance per city in the Euclidean metric and is the same in the Manhattan metric. We have studied such optimum tours for visiting all the cities using a branch and bound algorithm, giving the exact optimized tours for small system sizes () and near-optimal tours for bigger system sizes (). Extrapolating the results for , we find that for p=1, and and with as . Although the problem is trivial for p=1, for it certainly reduces to the standard travelling salesman problem on continuum which is NP-hard. We did not observe any irregular behaviour at any intermediate point. The crossover from the triviality to the NP-hard problem presumably occurs at p=1. Received 15 April 2000     

Stability and diffusion of surface clusters

Using kinetic Monte Carlo simulations and a bond-counting ansatz, thermal stability and diffusion of an adatom island on a crystal surface are studied. At low temperatures, the diffusion constant D is found to decrease for a wide range of island sizes like , where is close to one, N being the number of adatoms in the cluster. By heating up the surface, the system undergoes a phase transition above which the island disappears. Characteristics of that transition are discussed. Received 20 January 1999     

Evolution of the N = 20 and N = 28 shell closures in neutron-rich nuclei

The isospin dependence of shell closure phenomena is studied for light neutron-rich nuclei within a microscopic self-consistent approach using the Gogny force. Introducing configuration mixing, ³²Mg is found to be dynamically deformed, although the N = 20 spherical shell closure persists at the mean-field level for all N = 20 isotones. In contrast, the N = 28 spherical shell closure is found to disappear for N - Z≥ 10 whereas deformed shell closures are preserved and lead to shape coexistence in ⁴⁴ S. Configuration mixing shows that the ground state of this nucleus is triaxially deformed. The first 2⁺ excitation energy E_x = 1.46 MeV and the reduced transition probability B(E2;0⁺ _gs→ 2⁺ ₁)= 420 e ² fm ⁴ obtained with our approach are in good agreement with experimental data. Received: 26 July 2000 / Accepted: 30 August 2000     

N2微空心阴极放电特性及其阴极溅射的PIC/MC模拟

采用两维PIC/MCC模型模拟了氮气微空心阴极放电以及轰击离子 (N₂⁺,N⁺) 的钛阴极溅射. 主要计算了氮气微空心阴极放电离子 (N₂⁺,N⁺) 及溅射原子Ti的行为分布, 并研究了溅射Ti 原子的热化过程. 结果表明: 在模拟条件下, 空心阴极效应是负辉区叠加的电子震荡; 在对应条件下, 微空心较传统空心放电两种离子 (N₂⁺,N⁺) 密度均大两个量级, 两种离子的平均能量的分布及大小几乎相同; 在放电空间N⁺的密度约为N₂⁺的1/6, 最大能量约大2倍; 在不同参数 (P, T, V)下, 轰击阴极内表面的氮离子(N₂⁺,N⁺)的密度近似均匀, 其平均能量几乎相等; 从阴极溅射出的Ti原子的初始平均能量约6.8 eV, 离开阴极约0.15 mm处几乎完全被热化. 模拟结果为N₂微空心阴极放电等离子体特性的认识提供了参考依据. 关键词： 微空心阴极放电 PIC/MC模拟 2等离子体')" href="#">N₂等离子体     

Hydrogen-like recombination X-ray lasers using ps pulse drivers

We propose a scheme for producing high gain recombination X-ray lasers on hydrogen-like Balmer transitions by irradiating fibre targets with a 2 ps Chirped Pulse Amplification CPA beam of a Nd-glass laser facility. Very high gain coefficients for H-like C, N, O, F, Na Balmer transitions are predicted. The optimum electron density and temperature for maximum gain operation scale approximately asN _e 4 × 10¹³ Z ⁷ cm^–3 and T_e 7 × 10^–3 Z ⁴ eV, respectively, at the time when maximum lasing gain appears. Significant improvement in gain performance of recombination X-ray lasers is predicted by using CPA ps pulse drivers.     

The statistical error of green's function Monte Carlo

The statistical error in the ground state energy as calculated by Green's Function Monte Carlo (GFMC) is analyzed and a simple approximate formula is derived which relates the error to the number of steps of the random walk, the variational energy of the trial function, and the time step of the random walk. Using this formula it is argued that as the thermodynamic limit is approached withN identical molecules, the computer time needed to reach a given error per molecule increases asN ^h where 0.5 <b < 1.5 and as the nuclear chargeZ of a system is increased the computer time necessary to reach a given error grows asZ ^5.5. Thus GFMC simulations will be most useful for calculating the properties of lowZ elements. The implications for choosing the optimal trial function from a series of trial functions is also discussed.