Front roughening in three-dimensional imbibition

We investigate the structure and dynamics of the interface between two immiscible liquids in a three-dimensional disordered porous medium. We apply a phase-field model that includes explicitly disorder and discuss both spontaneous and forced imbibition. The structure of the interface is dominated by a length scale ξ_× which arises from liquid conservation. We further show that disorder in the capillary and permeability act on different length scales and give rise to different scalings and structures of the interface properties. We conclude with a range of applications.     

Limited resolution in complex network community detection with Potts model approach

According to Fortunato and Barthélemy, modularity-based community detection algorithms have a resolution threshold such that small communities in a large network are invisible. Here we generalize their work and show that the q-state Potts community detection method introduced by Reichardt and Bornholdt also has a resolution threshold. The model contains a parameter by which this threshold can be tuned, but no a priori principle is known to select the proper value. Single global optimization criteria do not seem capable for detecting all communities if their size distribution is broad.     

Incremental unknowns preconditioning for solving the Helmholtz equation

An efficient preconditioner is developed for solving the Helmholtz problem in both high and low frequency (wavenumber) regimes. The preconditioner is based on hierarchical unknowns on nested grids, known as incremental unknowns (IU). The motivation for the IU preconditioner is provided by an eigenvalue analysis of a simplified Helmholtz problem. The performance of our preconditioner is tested on the iterative solution of two‐dimensional electromagnetic scattering problems. When compared with other well‐known methods, our technique is shown to often provide a better numerical efficacy and, most importantly, to be more robust. Moreover, for the best performance, the number of IU levels used in the preconditioner should be designed for the coarsest grid to have roughly two points per linear wavelength. This result is consistent with the conventional sampling criteria for wave phenomena in contrast with existing IU applications for solving the Laplace/Poisson problem, where the coarsest grid comprises just one interior point. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

第三类Painlevé方程(δ=0或γ=0)解的渐近性态

对带有一般实参数第三类Painlevé方程,已有γ<0,δ>0时,解的有界性以及振荡渐近解的表达形式的结论.在本文中,我们给出当δ=0或γ=0时其振荡渐近解的表达形式.     

Separation of Variables in the Kovalevskaya–Goryachev–Chaplygin Gyrostat

We construct separation variables for the Kovalevskaya–Goryachev–Chaplygin gyrostat for arbitrary values of the parameters. We show that different separation variables can be constructed for the same integrable system if different integrals of motion are chosen.     

Numerical analysis for stochastic age-dependent population equations with Poisson jumps

In this paper, stochastic age-dependent population equations with Poisson jumps are considered. In general, most of stochastic age-dependent population equations with jumps do not have explicit solutions, thus numerical approximation schemes are invaluable tools for exploring their properties. The main purpose of this paper is to develop a numerical Euler scheme and show the convergence of the numerical approximation solution to the true solution.     

Anomalous electric-field effect and glassy behaviour in granular aluminium thin films: electron glass?

We present a study of non-equilibrium phenomena observed in the electrical conductance of insulating granular aluminium thin films. An anomalous field effect and its slow relaxation are studied in some detail. The phenomenology is very similar to the one already observed in indium oxide. The origin of the phenomena is discussed. In granular systems, the present experiments can naturally be interpreted along two different lines. One relies on a slow polarisation in the dielectric surrounding the metallic islands. The other one relies on a purely electronic mechanism: the formation of an electron Coulomb glass in the granular metal. More selective experiments and/or quantitative predictions about the Coulomb glass properties are still needed to definitely distinguish between the two scenarios.     

A model for the interaction of near-infrared laser pulses with metal powders in selective laser sintering

A thermal model of the interaction of pulsed near-infrared laser radiation from a Nd:YAG laser was made, taking the measured powder properties such as reflectance, optical penetration depth and thermal conductivity into account. It allows an estimation of the evolution of two different temperatures: the average temperature of the powder (taken over the grains in a volume given by the laser beam diameter and the optical penetration depth) and the temperature distinction within a single grain. It showed that in pulsed mode consolidation can be achieved at much lower average power as the surface of the powder particles are molten but their cores remain at nearly room temperature. This leads to a much lower average temperature and therefore a dramatic decrease in residual thermal stresses in the finished piece. The results of the model were experimentally tested and confirmed. Received: 26 July 2001 / Accepted: 23 November 2001 / Published online: 23 January 2002     

Effect of anions on the phase stability of γ-FeOOH nanoparticles and the magnetic properties of gamma-ferric oxide derived from lepidocrocite

The effect of anions such as Cl⁻, SO₄²⁻, and HPO₄²⁻ on the phase stability of FeOOH (α or γ) during precipitation is investigated. Oxidation of Fe(OH)₂·xH₂O from FeCl₂ solution with high Cl⁻ concentration ([Cl⁻]/[Fe]=R_Cl≥8) or (NH₄)₂Fe(SO₄)₂ (FAS) with [HPO₄²⁻]/[Fe]=R_P≥0.02 yields phase-pure γ-FeOOH. In the medium ranges of R_Cl and R_P, mixed phases of α-FeOOH and γ-FeOOH are obtained. Replacement of OH⁻ by Cl⁻ with the bridging cations or strongly bonded HPO₄²⁻ ions in the matrix of the intermediate phase (Fe_x²⁺Fe_y³⁺(OH)_2x+2y−nz·xH₂O(A)_zⁿ⁻, where A is anions such as Cl⁻, SO₄²⁻, HPO₄²⁻, etc.), promoted the lower density γ-FeOOH. However, the particles are less developed and have poor crystallinity as evidenced from transmission electron microscope and thermogravimetry-differential thermal analysis of the precipitates. Whereas, monophasic, uniformly sized, nano-lath shaped particles with high aspect ratio >10 are obtained when morphology-controlling cation additives such as Pt⁴⁺, Pd²⁺ or Rh³⁺ are present in FeCl₂ (R_Cl≥8) solution. Preferential adsorption of additives on (0k0) and (h00) planes limits the growth in the perpendicular directions leading to high aspect ratios. The effect of these additives are suppressed by the phosphate ion, a strong complexing ligand, giving rise to fibrous aggregate with the length of individual particles as small as 10-30 nm. While most of the Cl⁻ ion is removed from the final precipitates on washing, phosphate remained as HPO₄²⁻ as evidenced from IR absorption spectra. Maghemite obtained by dehydroxylating γ-FeOOH contains randomly distributed micropores bringing in the relaxation effects of spins on the surface atoms as deciphered from Mössbauer spectroscopy. This leads to the low σ_s (44-48 emu/g) and H_c (120-130 Oe) for γ-Fe₂O_3−δ particles. Whereas nearly pore-free single crystalline particles obtained by reduction followed by reoxidation has high value of σ_s (73 emu/g) and H_c (320 Oe), which decreases to 30 emu/g and 75 Oe, respectively, for nanoparticles obtained from phosphate stabilized lepidocrocite. The mobility of iron ions and counter mobility of vacancies during the topotactic transformation of γ-FeOOH to magnetite to γ-Fe₂O_3−δ renders the particles pore-free.     

Nondensely defined evolution impulsive differential inclusions with nonlocal conditions

In this paper, we shall establish sufficient conditions for the existence of integral solutions for some nondensely defined evolution impulsive differential inclusions in Banach spaces with nonlocal conditions.