基于分形多孔介质三维网络模型的非混溶两相流驱替数值模拟

提出了一个描述多孔介质孔隙尺寸分布的三维分形网络模型,利用该模型对多孔介质中的非混溶两相流驱替进行了数值模拟,研究了孔隙尺寸分布分维D_f和两相流黏滞比M对驱替前沿指进型的影响,结果表明指进型容量维数D_h随着孔隙尺寸分布分维D_f以及黏滞比M的增大而减少,并通过曲线拟合得到了它们之间的定量关系. 关键词： 多孔介质 三维网络 黏滞指进 非混溶两相流     

The effective thermal conductivity of porous media based on statistical self-similarity

A fractal model is presented based on the thermal-electrical analogy technique and statistical self-similarity of fractal saturated porous media. A dimensionless effective thermal conductivity of saturated fractal porous media is studied by the relationship between the dimensionless effective thermal conductivity and the geometrical parameters of porous media with no empirical constant. Through this study, it is shown that the dimensionless effective thermal conductivity decreases with the increase of porosity (?) and pore area fractal dimension (Df) when ks/kg>1. The opposite trends is observed when ks/kg<1. In addition, the dimensionless effective thermal conductivity decreases with increasing tortuous fractal dimension (Dt). The model predictions are compared with existing experimental data and the results show that they are in good agreement with existing experimental data.     

Exploration of fractal nature of WO3 nanowire aggregates

The morphology of WO₃ aggregates formed by irregular nanoparticles (D∼40 nm) and nanowires of different aspect ratios (2, 4, 6, and 10 μm nominal lengths) dispersed in commonly used polar solvents without dispersant agents is investigated using a small-angle light scattering technique and by means of fractal theory. Nanoparticles form compact spherical aggregates (D_f∼2.6), whereas 2 μm nanowires with low aspect ratio (L/D∼10) follow a slow cluster-cluster aggregation mechanism with no discernable change in fractal dimension (D_f=2.1) monitored in an extended period of 6 months, despite a notable growth in size (R_g=2.3-3.1 μm). For higher aspect ratio nanowires, scattered intensity profiles, which migrate towards the Porod regime, qualitatively obey the Lorenz-Mie theory predictions. The 10 μm nanowires with very high aspect ratio (L/D∼250) are observed to form stable dispersions in a time span of 6 days. Analytical methods based on spherical primary particle formulations predict D_f=1.9, 1.7, and 1.4 for 4, 6, and 10 μm nanowires, respectively.     

Fractal representation of the Debye theory for studying the heat capacity of macro-and nanostructures

The traditional theory of Debye heat capacity with a single free parameter (characteristic temperature θ_D) is extended to fractal spaces taking into account two more “latent” parameters contained in it, viz., the phonon spectrum dimension d _f and dimension d determining the geometry of the skeleton of the structure under investigation. In the classical version of the Debye theory, d _f = d = 3. In the case under investigation, these parameters can assume arbitrary (including fractional) values, which is typical of materials such as polymers, colloid aggregates, and various porous structures and nanostructures, as well as materials with a complex chemical composition. The application of a fractal approach makes it possible to substantially extend the class of materials with a heat capacity described by the continual Debye approximation.     

Dynamic cracking resistance of metallic materials during rapid propagation of a self-similar crack

A model is proposed to determine the dynamic cracking resistance K _ID of metals and alloys for the case of a rapidly moving fractal or self-affine crack. The values of this characteristic correlate with the fractal dimension D _f of the future contour of a crack surface profile. K _ID is lower or higher than K _IC depending on the fractal dimension.     

A Particle Resistance Model for Flow through Porous Media

A particle model for resistance of flow in isotropic porous media is developed based on the fractal geometry theory and on the drag force flowing around sphere. The proposed model is expressed as a function of porosity, fluid property, particle size, fluid velocity （or Reynolds number） and fractal characters D f of particles in porous media. The model predictions are in good agreement with the experimental data. The validity of the proposed model is thus verified.     

Pore size distribution in porous glass: fractal dimension obtained by calorimetry

By differential Scanning Calorimetry (DSC), at low heating rate and using a technique of fractionation, we have measured the equilibrium DSC signal (heat flow) J _q ⁰ of two families of porous glass saturated with water. The shape of the DSC peak obtained by these techniques is dependent on the sizes distribution of the pores. For porous glass with large pore size distribution, obtained by sol-gel technology, we show that in the domain of ice melting, the heat flow J_q is related to the melting temperature depression of the solvent, ΔT _m , by the scaling law: J _q ⁰∼ΔT _m ^{- (1 + D)}. We suggest that the exponent D is of the order of the fractal dimension of the backbone of the pore network and we discuss the influence of the variation of the melting enthalpy with the temperature on the value of this exponent. Similar D values were obtained from small angle neutron scattering and electronic energy transfer measurements on similar porous glass. The proposed scaling law is explained if one assumes that the pore size distribution is self similar. In porous glass obtained from mesomorphic copolymers, the pore size distribution is very sharp and therefore this law is not observed. One concludes that DSC, at low heating rate ( q? 2^°C/min) is the most rapid and less expensive method for determining the pore distribution and the fractal exponent of a porous material. Received 23 July 1999 and Received in final form 16 February 2001     

Turbulent diffusion for the radial twist map

An analytical tool is given to study the statistical properties of the radial twist map, X_n+1 = X_n + α(Y_n+1) and Y_n+1 = Y_n + Af (X_n), with arbitrary rotation number α(Y) and arbitrary periodic force f(X). The case for which f(X) = sin 2 πX and with arbitrary α is treated in the region of large A. The turbulent diffusion coefficient D for the chaotic orbit relaxes as $\text{t}{}^{\mathrm{<mtext>?</mtext><mtext>1</mtext><mtext>2</mtext>}}$ to $\text{A}{}^2\text{4}$, except for the case of the standard map, where the eventual value of D is different from $\text{A}{}^2\text{4}$.     

Study of the centrally produced ωρ0 and ωω systems inpp interactions at 300 GeV/c

We have performed a search for vector-vector final states centrally produced in proton proton interactions at 300 GeV/c using the CERN Ω spectrometer. Evidence is found for ωρ⁰ production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s and for ωω production in the reactionpp→p _f (2π⁺2π^?2π⁰)p _s . However no evidence is found for ωø production in the reactionpp→p _f (K ⁺ K ^?π⁺π^?π⁰)p _s .     

Numerical simulations of single and multiple scattering by fractal ice clusters

We consider the scattering model in the form of a vertically and horizontally homogeneous particulate slab of an arbitrary optical thickness composed of widely separated fractal aggregates built of small spherical ice monomers. The aggregates are generated by applying three different approaches, including simulated cluster-cluster aggregation (CCA) and diffusion-limited aggregation (DLA) procedures. Having in mind radar remote-sensing applications, we report and analyze the results of computations of the backscattering circular polarization ratio obtained using efficient superposition T-matrix and vector radiative-transfer codes. The computations have been performed at a wavelength of 12.6 cm for fractal aggregates with the following characteristics: monomer refractive index m=1.78+i0.003, monomer radius r=1 cm, monomer packing density p=0.2, overall aggregate radii R in the range 4≤R≤10 cm and fractal dimensions D_f=2.5 and 3.We show that for aggregates generated with simulated CCA and DLA procedures, the respective values of the backscattering circular polarization ratio differ weakly for D_f=2.5, but the differences can increase somewhat for D_f=3, especially in case of an optically semi-infinite medium. For aggregates with a spheroidal overall shape, the dependence of the circular polarization ratio on the cluster morphology can be quite significant and increases with increasing the aspect ratio of the circumscribing spheroid.     

Characterization of Porous Materials by Magnetic Relaxometry in the Earth’s Field

In this paper, it is shown how free induction decay signals recorded in the Earth’s magnetic field from water protons confined in porous media can be used to derive transversal relaxation times (T ₂) and their distributions. After T ₂ determination of six sintered glass samples with various pore sizes, the common theoretical model can be fitted to the data set. The T ₂ distribution of water protons in a bimodal porous system is analyzed and compared to mercury porosimetry results. The implications for the calculation of pore sizes and pore size distributions of porous media by this method are discussed.     

Tortuosity for streamlines in porous media

An analysis of tortuosity for streamlines in porous media is presented by coupling the circle and square models. It is assumed that some particles in porous media do not overlap and that fluid in porous media is incompressible. The relationship between tortuosity and porosity is attained with different configurations by using a statistical method. In addition, the tortuosity fractal dimension is expressed as a function of porosity. Those correlations do not include any empirical constant. The percolation threshold and tortuosity fractal dimension threshold of porous media are also presented as: c = 0.32, D T c = 1.07. The predicted correlations of the tortuosity and the porosity agree well with the existing experimental and simulated results.     

Scalar Glueball: Analysis of the (IJ PC = 00++)-wave

Basing on the previously performed K-matrix analysis of experimental data, we investigate, in the framework of the propagator matrix (D-matrix) technique, the 1100–1900 MeV mass region, where overlapping resonances f ₀(1300), f ₀(1500), f ₀ (1530 ± ₂₅₀ ⁹⁰ ), and f ₀(1780) are located. Necessary elements of the D-matrix technique are developed. The D-matrix analysis confirms previous K-matrix results: in the region 900–1900 MeV five scalar/isoscalar states are located. Four of them are members of the two qq?-nonets, while one state is an extra for the qq? systematics, being a good candidate for the lightest scalar glueball. The D-matrix analysis shows that this extra state, a candidate for the lightest scalar glueball, is dispersed, due to a mixing with qq?- states, over three resonances: f ₀(1300), f ₀(1500), and f ₀ (1530 ± ₂₅₀ ⁹⁰ ). The broad resonance f ₀ (1530 ± ₂₅₀ ⁹⁰ ) is a descendant of the lightest glueball carrying about 50% of the gluonium component, the rest of the gluonium is shared between f ₀(1300) and f ₀(1500). The broad resonance is formed by accumulating a large part of the neighbouring resonance widths that elaborates some type of a trap for the adjoining states.     

A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Study of longitudinal distributions in the fragmentation regions,using the quark-parton model,in K−p interactions at 70 GeV/c

The study of π^±, π⁰, K⁰ and Λ production in the fragmentation regions (|x|0.2) of K^?p interactions at 70 GeV/c shows that the x-dependence of each invariant cross section is well described by the power law (1?|x|)ⁿ suggested by the dimensional counting rule. Furthermore, pion production is found, both in K^? and proton fragmentation regions, to be very similar to their production in $\text{ν(}\text{ν}\text{)}\text{p}$ interactions as expected from quark-parton models. The quark and diquark fragmentation functions D_u^π, D_uu^π and D_ud^π are extracted from our data.     

Joint densities for random walks in the plane

We point out the existence of computationally convenient techniques for calculating the joint probability density for the position of a Pearson random walk after n steps. A new Fourier-Bessel function expansion for p_n(r, θ) is developed for this purpose which does not require radial symmetry, but does require that p_n(r, θ) = 0 when r exceeds some maximum radius, R.     

Assessment of the link between quantitative biexponential diffusion-weighted imaging and contrast-enhanced MRI in the liver

PurposeTo investigate if intravoxel incoherent motion (IVIM) modeled diffusion-weighted imaging (DWI) can be linked to contrast-enhanced (CE-)MRI in liver parenchyma and liver lesions.MethodsTwenty-five patients underwent IVIM-DWI followed by multiphase CE-MRI using Gd-EOB-DTPA (n = 20) or Gd-DOTA (n = 5) concluded with IVIM-DWI. Diffusion (D_slow), microperfusion (D_fast), its fraction (f_fast), wash-in-rate (R_early) and late-enhancement-rate (R_late) of Gd-EOB-DTPA were calculated voxel-wise for the liver. Parenchyma and lesions were segmented. Pre-contrast IVIM was compared 1) between low, medium and high R_early for parenchyma 2) to post-contrast IVIM substantiated with simulations 3) between low and high R_late per lesion type.ResultsD_fast and f_fast increased (P < 0.001) with 25.6% and 33.8% between low and high R_early of Gd-EOB-DTPA. D_slow decreased (− 15.0%; P < 0.001) with increasing R_early. Gd-DOTA demonstrated similar observations. f_fast (+ 10%; P < 0.001) and D_fast (+ 6.6%; P < 0.001) increased after Gd-EOB-DTPA, while decreasing after Gd-DOTA (− 4.2% and − 5.7%, P < 0.001) and were confirmed by simulations. For focal nodular hyperplasia lesions (n = 5) D_fast and f_fast increased (P < 0.001) with increasing R_late, whereas for hepatocellular carcinoma (n = 4) and adenoma (n = 7) no differences were found.ConclusionMicroperfusion measured by IVIM reflects perfusion in a way resembling CE-MRI. Also IVIM separated intra- and extracellular MR contrast media. This underlines the potential of IVIM in quantitative liver imaging.     

Two-photon spectroscopy of ytterbium

Two-photon laser spectra of the Yb vapor have been obtained. Transitions to highly excited 4f¹⁴ 6sns¹S₀ and 4f¹⁴ 6snd ¹D₂ states are seen in direct two-photon excitation. Hybrid resonances involving 4f¹⁴ 6s6p ¹P⁰₁ and 4f¹⁴ 5d6s ³D₂ intermediate states lead to transitions to 4f¹⁴ 6sns¹S₀, 4f¹⁴ 6snp ³P⁰_2,1 and 4f¹⁴ 6snd ¹D₂ levels.     

The relationship between current and channel diameter of 30 cm long laboratory sparks

In this study the dependence of channel diameter of 30 cm long sparks on discharge current is analyzed using a photographic technique. The results show the radial channel intensity variation follows a Gaussian distribution. The channel diameter (D), defined as the width of the intensity profile at 10% level, increases with the increasing peak current (I_p) up to 3 kA. The relationship between the two parameters can be represented by the equation, D = 8.36 ln(I_p) + 1.598, where D is in mm and I_p is in kA. The experimental results agree reasonably well with the available theory.     

Uniform boundedness of conditional gauge and Schrödinger equations

We prove that for a bounded domainD ?R ⁿ withC ² boundary and \(q \in K_n^{loc} (n \geqq 3) if E^x \exp \int\limits_0^{\tau _D } {q(x_t )dt} \mathop \ddag \limits_--- \infty \) inD, then $$\mathop {\sup }\limits_{\mathop {x \in D}\limits_{z \in \partial D} } E_z^x \exp \int\limits_0^{\tau _D } {q(x_t )dt}< + \infty $$ ({x _t : Brownian motion}) The important corollary of this result is that if the Schrödinger equation Δ/2u+qu=0 has a strictly positive solution onD, then for anyD ₀ ? ?D, there exists a constantC=C(n,q,D,D ₀) such that for anyf εL ¹(?D, σ), (σ: area measure on ?D) we have $$\mathop {\sup |}\limits_{x \in D_0 } u_f (x)| \mathop< \limits_ = C\int\limits_{\partial D} {|f(y)|\sigma (dy)} $$ whereu _f is the solution of the Schrödinger equation corresponding to the boundary valuef. To prove the main result we set up the following estimate inequalities on the Poisson kernelK(x,z) corresponding to the Laplace operator: $$C_1 \frac{{d(x,\partial D)}}{{|x - z|^n }}\mathop< \limits_ = K(x,z)\mathop< \limits_ = C_2 \frac{{d(x,\partial D)}}{{|x - z|^n }},x \in D,z \in \partial D$$ whereC ₁ andC ₂ are constants depending onn andD.