The electrical conductivity of binary disordered systems,percolation clusters,fractals and related models

We review theoretical and experimental studies of the AC dielectric response of inhomogeneous materials, modelled as bond percolation networks, with a binary (conductor-dielectric) distribution of bond conductances. We first summarize the key results of percolation theory, concerning mostly geometrical and static (DC) transport properties, with emphasis on the scaling properties of the critical region around the percolation threshold. The frequency-dependent (AC) response of a general binary model is then studied by means of various approaches, including the effective-medium approximation, a scaling theory of the critical region, numerical computations using the transfer-matrix algorithm, and several exactly solvable deterministic fractal models. Transient regimes, related to singularities in the complex-frequency plane, are also investigated. Theoretical predictions are made more explicit in two specific cases, namely R-C and RL-C networks, and compared with a broad variety of experimental results, concerning, for example, granular composites, thin films, powders, microemulsions, cermets, porous ceramics and the viscoelastic properties of gels.     

Fano resonance sensing based on coupled sub-wavelength dielectric grating and periodic photonic crystal

Based on the diffraction effect of sub-wavelength dielectric grating and the optical property of periodic photonic crystal, a hybrid structure of sub-wavelength grating all-dielectric multilayer thin film containing periodic photonic crystal is proposed. The transmission property of the structure is simulated by finite element method (FEM). The result shows that the discrete state generated by the sub-wavelength waveguide grating will be coupled with the continuous state generated by the photonic crystal cavity and the Fano resonance can be formed. The Fano resonance sensing model based on structural parameters and resonance wavelength are established, the influence of structural parameters on the Fano resonance spectral curve is quantitatively analyzed by numerical simulations, and the dynamic detection of the refractive index of samples is realized. The above structure can realize the optical refractive index sensing with high figure of merit (FOM) value and provide an effective theoretical reference for the formation of Fano resonance in the all-dielectric hybrid structure.     

The Influence of the Magnetic Impurity Content on the Pore Size Distribution Determination via the DDIF Technique

The pore size distribution of porous media can be determined in a completely non-invasive manner using a new nuclear magnetic resonance (NMR) technique which monitors the magnetization decay due to diffusion in internal fields (DDIF). However, using of the DDIF technique is restricted to the low-phase encoding limit when only the relaxation mode and the first-order diffusion mode are excited. In the present work the fulfillment of such a limit is verified for a progressive increase of the magnetic impurity content of the porous media. If the higher order diffusion modes are excited they lead both to a stronger attenuation of the echo signal and to the appearance of ripples in the DDIF spectra which cannot be related to a pore size distribution. The samples used in this study are porous ceramics prepared using the replication technique and the magnetic impurity is iron (III) oxide which is introduced in an increasing concentration inside the porous matrix. All NMR experiments were done on water filling such porous ceramics using a low-field instrument operating at a proton resonance frequency of 20 MHz. The average pore dimension obtained with the DDIF technique in the weak encoding limit indicates a satisfactory agreement with that observed in optical microscopy images.     

二维孔隙裂隙双重介质逾渗规律研究

在孔隙介质逾渗理论的基础上，将另外一个非常重要的渗透通道——裂隙引入到介质的逾渗研究中，提出了更为普遍的孔隙裂隙双重介质的逾渗研究方法.通过对二维平面孔隙裂隙双重介质的数值计算，得到了孔隙裂隙双重介质三个重要参数：孔隙率，裂隙分形维数、裂隙数量分布初值与逾渗概率的关系，给出了孔隙裂隙双重介质逾渗阈值的数学表达式，揭示了孔隙裂隙双重介质的逾渗规律. 关键词： 孔隙 裂隙 双重介质 逾渗 逾渗阈值     

Irreversibility and spontaneous appearance of coherent behavior in reversible systems

There is empirical evidence that long time numerical simulations of conservative and reversible partial differential equations evolve, as a general rule (exceptions are the integrable models), towards an equilibrium state that is mainly a coherent structure plus small fluctuations inherent in the conservative and reversible character of the original system. The fluctuations account for the energy difference between the initial configuration and the one of the coherent structure. If the energy is not small enough, then the intrinsic fluctuations may destroy the coherent structure. Thus we arrive to the conclusion that a transition arises from a non-coherent state to a coherent structure as we decrease the initial energy below a critical value. This phenomenon has been successfully observed in various numerical simulations. In this article, we stress that this general behavior is also observed in reversible and conservative cellular automata as in the Q2R model. We point out that this conservative and reversible cellular automata is ab initio deterministic and therefore all our numerical computations are not affected by an approximation of any kind.     

Two—phase flow in correlated pore—throat random porous media

We have constructed a porous media model in which there are percolation clusters with varying percolation probability P and correlated site-bonds. Taking into account both the pore and the throat geometry, the viscous fingering (VF) in porous media has been investigated by using the standard over-relaxed Gauss-Seidel scheme. The simulation results show that the VF structure varies with the correlation parameter ε, the viscosity ratio M and the percolation probability P. The smaller the correlation parameter ε, the greater the deviation of the normalized size distribution of the invaded throat N_inv(r) from the truncated Rayleigh distribution. For a larger viscosity ratio M, the VF pattern looks like a diffusion-limited-aggregation structure in percolation clusters. The fractal dimension D increases with the increase of the percolation probability P and the correlation parameter ε. The velocity distribution f(α) of VF in percolation clusters is of a parabola-like curve. The tail of the distribution (large α) is longer for a larger correlation parameter ε. For a smaller ε, the distribution is very sharp. The sweep efficiency E decreases along with the decrease of the correlation parameter ε and the increase of the network size L_nz. E has a minimum as L_nz increases up to the maximum no matter what the values of P, M and ε. The E～ L_nz curve has a frozen zone and an active zone. The geometry and the topology of the porous media have strong effects on the displacement processes and the structure of VF.     

Visualization of transport: NMR microscopy experiments with model objects for porous media with pore sizes down to 50 microm

Hydrodynamic flow and electric currents through model porous media were investigated. The transport rates through the individual pathways of the pore network are determined by the local width of the pore channels and by the driving mechanism. The model objects represent quasi two-dimensional random site percolation clusters. The calculated design was realized by milling the structure in polystyrene sheets. Velocity maps of stationary flow and current density maps of stationary currents through the cluster were acquired by magnetic resonance imaging methods. The findings were compared to the results of numerical simulations based on the same structure. Since the difference in the transport patterns of the different driving mechanisms are expected to be more pronounced in smaller pore spaces, ultra deep X-ray lithography has been used for the fabrication of downsized model objects with a spatial resolution of better than 50 microm and an aspect ratio as large as 20. First results obtained with these objects are reported.     

Time-of-flight imaging method to observe signatures of antiferromagnetically ordered states of fermionic atoms in an optical lattice

We propose a simple method to detect the antiferromagnetic (AF) state of fermionic atoms in an optical lattice by combining a time-of-flight (TOF) imaging method and a Feshbach resonance. In this scheme, the nontrivial dynamics of fermionic atoms during the imaging process works as a probe with respect to the breaking of the translational symmetry in the AF state. Precise numerical simulations demonstrate that the characteristic oscillatory dynamics induced by the scattering process that transfers an AF ordering vector appears in TOF images, which can be easily observed experimentally.     

Propagation and trapping of excitations on percolation clusters

A study is presented of migration of optical or magnetic excitations on percolation clusters which terminates upon reaching a trapping site. The theory is based on the extension of results from the theory of random walks to systems without translational invariance, together with the use of scaling concepts. For the case of an excitation which resides on one type of atom in a randomly mixed crystal near the percolation threshold, new power laws for the time and concentration dependences of the mean number of sites visited at timet of the kinetics of arrival at traps are obtained. Some of these results are also tested for the first time by numerical simulations.     

Controllable switching behavior of optical Tamm state based on nematic liquid crystal

The controllable behavior of optical Tamm state (OTS) is investigated in a heterostructure with nematic liquid crystal (NLC). By changing the external fields (electric field and temperature), the orientation of NLC’s molecules can be modified. It offers us an effective way to control the optical properties of the optical Tamm state. We obtain the critical condition for the appearance of the optical Tamm state. Our theoretical analysis and numerical simulations show that through choosing appropriate parameters we can not only change the frequency position of the optical Tamm state, but also realize the disappearance of the OTS.     

Light propagation in porous ceramics: porosity and optical property studies using tunable diode laser spectroscopy

By integrating gas in scattering media absorption spectroscopy and frequency domain photon migration a new method is developed for the study of optical porosity and optical properties of porous media, in our case ceramics. The optical porosity is defined as the ratio of the path length through the gas-filled pores and the physical path length through the whole medium. The effective refractive index of the porous ceramics is also retrieved based on the optical porosity, which is then used to evaluate the reduced scattering coefficients of the porous ceramics. The combined method provides a new way to study light propagation in porous media. A modified Looyenga model is proposed to study the relationship between the physical porosity and the effective refractive index of the porous medium, which also connects the optical and physical porosities, and provides the possibility to use the present method for porosimetry analysis.     

Transition to spatiotemporal chaos in a two-dimensional hydrodynamic system

We study the transition to spatiotemporal chaos in a two-dimensional hydrodynamic experiment where liquid columns take place in the gravity induced instability of a liquid film. The film is formed below a plane grid which is used as a porous media and is continuously supplied with a controlled flow rate. This system can be either ordered (on a hexagonal structure) or disordered depending on the flow rate. We observe, for the first time in an initially structured state, a subcritical transition to spatiotemporal disorder which arises through spatiotemporal intermittency. Statistics of numbers, creations, and fusions of columns are investigated. We exhibit a critical behavior close to the directed percolation one.     

Bistability between different localized structures in nonlinear optics

We report the observation of different localized structures coexisting for the same parameter values in an extended system. The experimental findings are carried out in a nonlinear optical interferometer and are fully confirmed by numerical simulations. The existence of each kind of localized structure is put in relation to a corresponding delocalized pattern observed. A quantitative evaluation of the range of pump parameter allowing bistability between localized structures is given. The phenomenon reported results to be robust in parameter space.     

多孔未极化Pb(Zr0.95Ti0.05)O3铁电陶瓷单轴压缩力学响应与相变

通过添加造孔剂的方法制备了四种不同孔隙率未极化PZT95/5铁电陶瓷. 采用非接触式的数字散斑相关性分析(digital image correltation, DIC)全场应变光学测量技术, 对多孔未极化PZT95/5 铁电陶瓷开展了单轴压缩实验研究, 讨论了孔隙率对未极化PZT95/5铁电陶瓷的力学响应与畴变、相变行为的影响. 多孔未极化PZT95/5铁电陶瓷的单轴压缩应力-应变关系呈现出类似于泡沫或蜂窝材料的三阶段变形特征, 其变形机理主要归因于畴变和相变的共同作用, 与微孔洞塌缩过程无关. 多孔未极化PZT95/5铁电陶瓷的弹性模量、压缩强度都随着孔隙率的增加而明显降低, 而孔隙率对断裂应变的影响较小. 预制的微孔洞没有改善未极化PZT95/5铁电陶瓷材料的韧性, 这是因为单轴压缩下未极化PZT95/5铁电陶瓷的断裂机理是轴向劈裂破坏, 微孔洞对劈裂裂纹传播没有起到阻碍和分叉作用. 准静态单轴压缩下多孔未极化PZT95/5铁电陶瓷畴变和相变开始的临界应力都随着孔隙率的增大而呈线性衰减, 但相变开始的临界体积应变却不依赖孔隙率.     

Quantum Monte Carlo calculations of symmetric nuclear matter

We present an accurate numerical study of the equation of state of nuclear matter based on realistic nucleon-nucleon interactions by means of auxiliary field diffusion Monte Carlo (AFDMC) calculations. The AFDMC method samples the spin and isospin degrees of freedom allowing for quantum simulations of large nucleonic systems and represents an important step forward towards a quantitative understanding of problems in nuclear structure and astrophysics.     

Uniqueness of reconstruction of multiphase morphologies from two-point correlation functions

The restoration of the spatial structure of heterogeneous media, such as composites, porous materials, microemulsions, ceramics, or polymer blends from two-point correlation functions, is a problem of relevance to several areas of science. In this contribution we revisit the question of the uniqueness of the restoration problem. We present numerical evidence that periodic, piecewise uniform structures with smooth boundaries are completely specified by their two-point correlation functions, up to a translation and, in some cases, inversion. We discuss the physical relevance of the results.     

Two-component spatial optical solitons in a four-state ladder system via electromagnetically induced transparency

We propose a scheme to generate two-component spatial optical solitons in a lifetime broadened four state atomic system with a ladder configuration via electromagnetically induced transparency. We show that, different from the schemes using passive optical media such as photorefractives and planar waveguides, the two-component spatial optical solitons in the present coherent resonant system can be produced with very low light intensity. The stability of the two-component spatial optical solitons and their interaction are also investigated by numerical simulations.     

Computer simulations of two-phase flow with surface tension in the percolation cluster

Percolation clusters with varying occupation probability were constructed. Viscous fingering (VF) in the percolation cluster, based on the assumption that throat radii are Rayleigh distributed, is investigated by means of a successive over-relaxation technique. The fractal dimension and the sweep efficiency of VF in the percolation cluster when surface tension is considered are larger than when surface tension is neglected. The fractal dimension of VF will increase as the percolation probability increases or the viscous ratio decreases. VF's fractal dimension of porous media in the limit viscous ratio → ∞ is found to be identical with the DLA. The topology and the geometry of the porous medium have a strong effect on the displacement processes and the structure of the VF.     

Photon BLOCH oscillations in porous silicon optical superlattices

We report the first observation of oscillations of the electromagnetic field in an optical superlattice based on porous silicon. These oscillations are an optical equivalent of well-known electronic Bloch oscillations in crystals. Elementary cells of our structure are composed by microcavities whose coupling gives rise to the extended collective modes forming optical minigaps and minibands. By varying thicknesses of the cavities along the structure axis, we have created an effective electric field for photons. A very high quality factor of the confined optical state of the Wannier-Stark ladder may allow lasing in porous silicon-based superlattices.