Transport properties of saturated and unsaturated porous fractal materials

Inviscid, irrotational flow through fractal porous materials is studied. The key parameter is the variation of tortuosity with the filling fraction phi of fluid in the porous material. Altering the filling fraction provides a way of probing the effect of the fractal structure over all its length scales. The variation of tortuosity with phi is found to follow a power law of the form alpha approximately phi (-E) for deterministic and stochastic fractals in two and three dimensions. A phenomenological argument for the scaling of tortuosity alpha with filling fraction phi is presented and is given by alpha approximately phi(D_{w}-2/D_{f}-d_{E}), where D_{f} is the fractal dimension, D_{w} is the random walk dimension, and d_{E} is the Euclidean dimension. Numerically calculated values of the exponents show good agreement with those predicted from the phenomenological argument for both the saturated and the unsaturated model.     

A random field model for anomalous diffusion in heterogeneous porous media

Heterogeneity, as it occurs in porous media, is characterized in terms of a scaling exponent, or fractal dimension. A feature of primary interest for two-phase flow is the mixing length. This paper determines the relation between the scaling exponent for the heterogeneity and the scaling exponent which governs the mixing length. The analysis assumes a linear transport equation and uses random fields first in the characterization of the heterogeneity and second in the solution of the flow problem, in order to determine the mixing exponents. The scaling behavior changes from long-length-scale dominated to short-length-scale dominated at a critical value of the scaling exponent of the rock heterogeneity. The long-length-scale-dominated diffusion is anomalous.     

The Finite-Size Scaling Study of the Ising Model for the Fractals

The fractals are obtained by using the model of diffusion-limited aggregation (DLA) for 40 ≤ L ≤ 240. The two-dimensional Ising model is simulated on the Creutz cellular automaton for 40 ≤ L ≤ 240. The critical exponents and the fractal dimensions are computed to be β = 0.124(8), γ = 1.747(10), α = 0.081(21), δ = 14.994(11), η = 0.178(10), ν = 0.960(23) and \(d_{f}^{\beta } =1.876(8), \,d_{f}^{\gamma } =3.747(10), \,d_{f}^{\alpha } =2.081(68), \,d_{f}^{\delta } =1.940(22)\), \(d_{f}^{\eta } =2.178(10)\), \(d_{f}^{\nu } =2.960(22)\), which are consistent with the theoretical values of β = 0.125, γ = 1.75, α = 0, δ = 15, η = 0.25, ν = 1 and \(d_{f}^{\beta } =1.875, \,d_{f}^{\gamma } =3.75, \,d_{f}^{\alpha } =2, \,d_{f}^{\delta } =1.933, \,d_{f}^{\eta } =2.25, \,d_{f}^{\nu } =3\).     

Evidence of intermittent fluctuation of target fragments in ^84Kr-AgBr interactions at 1.7 A GeV

Intermittency and fractal behaviour have been studied of emission spectra of target associated fragments from ^84Kr-AgBr interactions at 1.7 A GeV in emission angle space and azimuthal angle space separately. The intermittent behaviour is observed in the two spaces separately. Prom the intermittency exponent, the anomalous fractal dimension dq is calculated and the variation of dq with the order q is investigated. It is found that the anomalous dimensions are found to increase with the order of moments q, thereby indicating the relation of multifractality to production mechanism of target associated fragments.     

Dimensionally frustrated diffusion towards fractal adsorbers

Diffusion towards a fractal adsorber is a well-researched problem with many applications. While the steady-state flux towards such adsorbers is known to be characterized by the fractal dimension (D{F}) of the surface, the more general problem of time-dependent adsorption kinetics of fractal surfaces remains poorly understood. In this Letter, we show that the time-dependent flux to fractal adsorbers (1相似文献   

Crossover from attractive to repulsive Casimir forces and vice versa

Systems described by an O(n) symmetrical varphi;{4} Hamiltonian are considered in a d-dimensional film geometry at their bulk critical points. The critical Casimir forces between the film's boundary planes B_{j}, j=1,2, are investigated as functions of film thickness L for generic symmetry-preserving boundary conditions partial differential_{n}phi=c[over composite function]_{j}phi. The L-dependent part of the reduced excess free energy per cross-sectional area takes the scaling form f_{res} approximately D(c_{1}L;{Phi/nu},c_{2}L;{Phi/nu})/L;{d-1} when d<4, where c_{i} are scaling fields associated with the variables c[over composite function]_{i} and Phi is a surface crossover exponent. Explicit two-loop renormalization group results for the function D(c_{1},c_{2}) at d=4- dimensions are presented. These show that (i) the Casimir force can have either sign, depending on c_{1} and c_{2}, and (ii) for appropriate choices of the enhancements c[over composite function]_{j}, crossovers from attraction to repulsion and vice versa occur as L increases.     

Anomalous Hall effect of facing-target sputtered ferrimagnetic Mn4N epitaxial films with perpendicular magnetic anisotropy

Epitaxial Mn$_{4}$N films with different thicknesses were fabricated by facing-target reactive sputtering and their anomalous Hall effect (AHE) is investigated systematically. The Hall resistivity shows a reversed magnetic hysteresis loop with the magnetic field. The magnitude of the anomalous Hall resistivity sharply decreases with decreasing temperature from 300 K to 150 K. The AHE scaling law in Mn$_{4}$N films is influenced by the temperature-dependent magnetization, carrier concentration and interfacial scattering. Different scaling laws are used to distinguish the various contributions of AHE mechanisms. The scaling exponent $\gamma > 2$ for the conventional scaling in Mn$_{4}$N films could be attributed to the residual resistivity $\rho_{xx0}$. The longitudinal conductivity $\sigma_{xx}$ falls into the dirty regime. The scaling of $\rho_{\rm AH}=\alpha \rho_{xx0} +b\rho_{xx}^{n}$ is used to separate out the temperature-independent $\rho_{xx0}$ from extrinsic contribution. Moreover, the relationship between $\rho_{\rm AH}$ and $\rho_{xx}$ is fitted by the proper scaling to clarify the contributions from extrinsic and intrinsic mechanisms of AHE, which demonstrates that the dominant mechanism of AHE in the Mn$_{4}$N films can be ascribed to the competition between skew scattering, side jump and the intrinsic mechanisms.     

Preferential attachment network model with aging and initial attractiveness

In this paper, we generalize the growing network model with preferential attachment for new links to simultaneously include aging and initial attractiveness of nodes. The network evolves with the addition of a new node per unit time, and each new node has m new links that with probability Π_i are connected to nodes i already present in the network. In our model, the preferential attachment probability Π_i is proportional not only to k_i + A, the sum of the old node i's degree k_i and its initial attractiveness A, but also to the aging factor ${\tau }_{i}^{-\alpha }$, where τ_i is the age of the old node i. That is, ${{\rm{\Pi }}}_{i}\propto ({k}_{i}+A){\tau }_{i}^{-\alpha }$. Based on the continuum approximation, we present a mean-field analysis that predicts the degree dynamics of the network structure. We show that depending on the aging parameter α two different network topologies can emerge. For α < 1, the network exhibits scaling behavior with a power-law degree distribution P(k) ∝ k^−γ for large k where the scaling exponent γ increases with the aging parameter α and is linearly correlated with the ratio A/m. Moreover, the average degree k(t_i, t) at time t for any node i that is added into the network at time t_i scales as $k({t}_{i},t)\propto {t}_{i}^{-\beta }$ where 1/β is a linear function of A/m. For α > 1, such scaling behavior disappears and the degree distribution is exponential.     

Anomalous diffusion and charge relaxation on comb model: exact solutions

The random walks on the comb structure are considered. It is shown that due to fingers a diffusion has an anomalous character, that is an r.m.s. displacement depends on time by a power way with exponent . The generalized diffusion equation for an anomalous case is deduced. It essentially differs from a usual diffusion equation in the continuity equation form: instead of the first time derivative, the time derivative of fractal order appears. In the second part the charge relaxation on the comb structure is studied. A non-Maxwell character is established. The reason is that the electric field has three components, but a charge may relax only along some conducting lines.     

含有广义守恒律的生长方程标度奇异性的直接标度分析

利用直接标度分析方法研究一个含有广义守恒律生长方程的标度奇异性,得到强弱耦合区域的奇异标度指数.作为其特殊情况,这个方程包含Kardar-Parisi-Zhang（KPZ）方程、 Sun-Guo-Grant（SGG）方程以及分子束外延（MBE）生长方程,并能对其进行统一的研究.研究发现, KPZ方程和SGG方程,无论在弱耦合还是在强耦合区域内都遵从自仿射Family -Vicsek正常标度规律;而MBE 方程在弱耦合区域内服从正常标度,在强耦合区域内能呈现内禀奇异标度行为.这里所得到生长方程的奇异标度性质与利用重正化群理论、数值模拟以及实验相符很好. 关键词： 标度奇异性 强耦合 弱耦合     

Heterogeneous Memorized Continuous Time Random Walks in an External Force Fields

In this paper, we study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated memorized waiting times, which involves Reimann–Liouville fractional derivative or Reimann–Liouville fractional integral. We show that the mean squared displacement of the test particle \(X_{x}\) which is dependent on its location \(x\) of the form (El-Wakil and Zahran, Chaos Solitons Fractals, 12, 1929–1935, 2001) 1 $$\begin{aligned} \langle \mathbb {X}_x^2\rangle (t)=\langle (\Delta X_x(t))^2\rangle _0\sim |x|^{-\theta }t^{\gamma }, \quad 0<\gamma <1, \quad \theta =d_w-2, \end{aligned}$$ where \(d_w>2\) is the anomalous exponent, the diffusion exponent \(\gamma \) is dependent on the model parameters. We obtain the Fokker–Planck-type dynamic equations, and their stationary solutions are of the Boltzmann–Gibbs form. These processes obey a generalized Einstein–Stokes–Smoluchowski relation and the second Einstein relation. We observe that the asymptotic behavior of waiting times and subordinations are of stretched Gaussian distributions. We also discuss the time averaged in the case of an harmonic potential, and show that the process exhibits aging and ergodicity breaking.     

Scaling behavior of jamming fluctuations upon random sequential adsorption

It is shown that the fluctuations of the jamming coverage upon Random Sequential Adsorption (RSA) ( ), decay with the lattice size according to the power-law , with ,where D is the dimension of the substrate and is the fractal dimension of the set of sites belonging to the substrate where the RSA process actually takes place. This result is in excellent agreement with the figure recently reported by Vandewalle et al. [Eur. Phys. J. B 14, 407 (2000)], namely for the RSA of needles with D = 2 and , that gives . Furthermore, our prediction is in excellent agreement with different previous numerical results. The derived relationships are also confirmed by means of extensive numerical simulations applied to the RSA of dimers on both stochastic and deterministic fractal substrates.Received: 17 October 2003, Published online: 8 December 2003PACS: 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 02.50.-r Probability theory, stochastic processes, and statistics     

Compactons in PT \mathcal{P}\mathcal{T} -symmetric generalized Korteweg-de Vries equations

This paper considers the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric extensions of the equations examined by Cooper, Shepard and Sodano. From the scaling properties of the $ \mathcal{P}\mathcal{T} $ \mathcal{P}\mathcal{T} -symmetric equations a general theorem relating the energy, momentum and velocity of any solitarywave solution of the generalized KdV equation is derived. We also discuss the stability of the compacton solution as a function of the parameters affecting the nonlinearities.     

Anomalous scaling in systems partially controlled by diffusion

We study the nature of anomalous scaling in several systems partially controlled by diffusion. We quantify the departure from Fickian scaling by means of an apparent exponent governing the scaling of long-time behavior with system size. We find that anomalous scaling should be expected whenever complex geometries, higher dimensionality, or time-dependent boundary conditions are encountered.     

Scaling in the diffusion limited aggregation model

We present a self-consistent picture of diffusion limited aggregation (DLA) growth based on the assumption that the probability density P(r,N) for the next particle to be attached within the distance r to the center of the cluster is expressible in the scale-invariant form P[r/R{dep}(N)]. It follows from this assumption that there is no multiscaling issue in DLA and there is only a single fractal dimension D for all length scales. We check our assumption self-consistently by calculating the particle-density distribution with a measured P(r/R{dep}) function on an ensemble with 1000 clusters of 5×10{7} particles each. We also show that a nontrivial multiscaling function D(x) can be obtained only when small clusters (N<10?000) are used to calculate D(x). Hence, multiscaling is a finite-size effect and is not intrinsic to DLA.     

Mott transition in a valence-bond solid insulator with a triangular lattice

We have investigated the Mott transition in a quasi-two-dimensional Mott insulator EtMe{3}P[Pd(dmit){2}]{2} with a spin-frustrated triangular-lattice in hydrostatic pressure and magnetic-field [Et and Me denote C2H5 and CH3, respectively, and Pd(dmit){2} (dmit=1,3-dithiole-2-thione-4,5-dithiolate,dithiolate) is an electron-acceptor molecule]. In the pressure-temperature (P-T) phase diagram, a valence-bond solid phase is found to neighbor the superconductor and metal phases at low temperatures. The profile of the phase diagram is common to those of Mott insulators with antiferromagnetic order. In contrast to the antiferromagnetic Mott insulators, the resistivity in the metallic phase exhibits anomalous temperature dependence, rho=rho{0}+AT(2.5).     

Shot noise in ballistic graphene

We have investigated shot noise in graphene field effect devices in the temperature range of 4.2-30 K at low frequency (f=600-850 MHz). We find that for our graphene samples with a large width over length ratio W/L, the Fano factor F reaches a maximum F ~ 1/3 at the Dirac point and that it decreases strongly with increasing charge density. For smaller W/L, the Fano factor at Dirac point is significantly lower. Our results are in good agreement with the theory describing that transport at the Dirac point in clean graphene arises from evanescent electronic states.