Dynamics of forest fire under rotational constraint

A rotationally constrained forest fire model is studied on square and triangular lattices of size 400×400. The critical probabilityp _c for onset of fire propagation is determined. The scaling relationsMt ^d _r, R_gt^v andMR _g ^d _f are analysed at fire propagation probabilityp=p _c whereM is the number of burnt trees,R _g the radius of gyration andd _f the fractal dimension of the cluster of burnt trees at timet. Numerical estimates ofd _t, v andd _f have been obtained.     

Effect of Surface Roughness, Type and Size of Model Aggregates on the Bond Strength of Aggregate/Mortar Interface

The paper reports on a two-stage study of the interface between three types of model cylindrical aggregates (sandstone, limestone and granite) and two types of mortar matrix (plain and 20% Silica Fume mortar). In the first stage, the surface roughness (R _a) of the aggregates and the interfacial bond strength using push-out specimens have been experimentally determined. In the second, aggregate push-out geometry has been modelled using two different approaches. In the first approach, the surface roughness is ignored and the cylindrical aggregates are assumed to have an ideally smooth surface with a constant radius, r ₀ over the aggregate length, L. In the second approach, the surface roughness of the aggregates is included so that the radius, r varies along the length of the cored rock aggregate. Hence, the influence of the surface roughness of the aggregates on the interfacial bond strength is obtained. It is found that the surface roughness plays a significant role in determining the interfacial bond strength, in particular of smaller size aggregates. The effect, however, diminishes as the aggregate size increases, regardless of the aggregate and mortar type.     

Wetting and Phase Separation in Polymer Blend Films: Identification of Four Thickness Regimes with Distinct Morphological Pathways

Using forward recoil spectrometry and atomic force microscopy, the phase evolution of a critical blend thin film of deuterated poly(methyl methacrylate) (dPMMA) and poly(styrene-ran-acrylonitrile) (SAN) is found to depend on film thickness. Four regimes are identified as film thickness l ₀ decreases from semi-infinite to below the radius of gyration, R _g. In the semi-infinite limit or regime IV (l ₀ R _g), surface directed spinodal decomposition is observed and found to agree with cell dynamic simulations. In regime III (10 R _g < l ₀ < 150 R _g), three stages of evolution are observed. During the early stage, wetting dominates and produces a dPMMA-rich/SAN-rich/dPMMA-rich structure. During the intermediate stage, the surface phase flows back into the middle layer inducing lateral phase coarsening. During the late stage, capillary fluctuations rupture the middle layer by spinodal dewetting, resulting in a final morphology with SAN-rich droplets encapsulated by dPMMA-rich wetting layers. Although regime II (R _g < l ₀ < 10 R _g) films also exhibit a tri-layer early stage, correlated holes in the middle layer spontaneously grow suggesting that this layer is too thin to support fully developed capillary fluctuations. Three stages of roughening are observed with a final morphology similar to regime III. In regime I (l ₀ < R _g), films roughen almost immediately after annealing in contrast to the other regimes. Initially, the surface roughness increases logarithmically with time before reaching a constant value of 2 R _g. The final average droplet height, 29.5 nm, is in good agreement with a simple interfacial energy model. Whereas the final morphology for regimes I, II and III are identical, the pathways by which films roughen are distinct suggesting that erroneous conclusions can be made by simply analyzing the final morphology.     

Some fractal properties of the percolating backbone in two dimensions

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that the fractal dimensionality of the backbone isd _f ^BB =1.61±0.01, the chemical dimensionality isd _t=1.40±0.01, and the fractal dimension of the minimum pathd _min=1.15 ± 0.02 for the two-dimensional triangular lattice.     

Application of SAXS to the study of particle-size-dependent thermal conductivity in silica nanofluids

Knowledge of the size and distribution of nanoparticles in solution is critical to understanding the observed enhancements in thermal conductivity and heat transfer of nanofluids. We have applied small-angle X-ray scattering (SAXS) to the characterization of SiO₂ nanoparticles (10–30 nm) uniformly dispersed in a water-based fluid using the Advanced Photon Source at Argonne National Laboratory. Size distributions for the suspended nanoparticles were derived by fitting experimental data to an established model. Thermal conductivity of the SiO₂ nanofluids was also measured, and the relation between the average particle size and the thermal conductivity enhancement was established. The experimental data contradict models based on fluid interfacial layers or Brownian motion but support the concept of thermal resistance at the liquid–particle interface.     

Application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media

We consider the application of fractal concepts to polymer statistics and to anomalous transport in randomly porous media. It is found that answers to interesting physics questions can be expressed in terms of several new fractal dimensions (in addition to the fractal dimensiond _f ): (1)d _f ^BB , the fractal dimension of the backbone, arises in connection with electric current flow, (2)d _red, the fractal dimension of the singly connected bonds in the backbone, arises in connection with its equivalence to the thermal scaling power, (3)d _E, the fractal dimension of the of the elastic backbone, (4)d _u, the fractal dimension of the unscreened perimeter, arises in connection with the viscosity singularity at the gelation threshold, (5)d _min the fractal dimension of the minimum path (or chemical distance) between two sites, arises in co-nnection with the Aharony-Stauffer conjecture, (6)dw, the fractal dimension of a random walk, (7)d _G, the fractal dimension of growth sites that arise as a random walk creates a cluster. Relations among these fractal dimensions are discussed, some of which can be proved and others of which are conjectures whose validity has been established only in certain limiting cases.Supported in part at the Center for Polymer Studies by grants from ONR and NSF.     

2D aggregate sizing by combining laser-induced incandescence (LII) and elastic light scattering (ELS)

The combination of laser-induced incandescence and elastic light scattering has been further developed to allow for a quantitative two-dimensional determination of characteristic properties of soot aggregates, namely radius of gyration R _g and number N _p of primary particles per aggregate. In demonstrating the principle of the method, we have in a first approach approximated the particle ensemble as monodisperse and used a structure factor with an exponential cut-off function. Nonetheless, experiments performed on a laminar premixed ethene flame demonstrate basically good agreement with observations from literature and data from electron microscopy on thermophoretically obtained samples.     

Morphology Development in Multi‐Component Polymer Blends: I Composition Effect on Phase Morphology in PP/PET Polymer Blends

The relationship of the phase morphology of polypropylene/polyethylene‐terephthalate (PP/PET) blends and their corresponding compatibilized blends with composition was investigated using digital image analysis. A diameter, d _g , was defined and calculated to discuss the phase morphology of this polymer blend system. A figure‐estimation method was introduced to determine the width of the distribution of d _g . Based on the method, it is proven that the distribution of d _g obeys a log‐normal distribution and consequently, the distribution width, σ was calculated. Further, a fractal dimension, D _f , was introduced to describe the distribution of main sizes of the particles of the dispersed phase. The results showed that, while d _g increased with the concentration of the dispersed phase, σ and D _f show different dependence relations on composition;σ increases monotonously but D _f shows a maximum at a PET content of 30%, indicating that, even though the whole size distribution is much broader, the distribution of the main body of size becomes more uniform when the content of PET is less than 30%.     

Motion in the complex plane of the poles of the quantum-mechanical partial amplitude for a bond

Details are given of the analytic features of this amplitudef _g(l, k) in the g plane for a very large class of potentials that satisfy conditions (1). It is shown that there is a region (l, k²) around the point g = 0 that is free from singularities inf _g(l, k), so the Mittag-Leffler method can be applied to findf _g(l, k) and hence also the total amplitude T_g(k, t) for any g to any specified degree of accuracy with reference to the information contained in the coefficients of a finite number of terms of the series given by perturbation methods forf _g(l, k).This paper was read in substance on 8th April 1963 at Uzhgood University [1] and on 29 June 1963 at the All-Union Symposium on the Theory of Elementary Particles at Novosibirsk.     

A thermal conductivity model for nanofluids including effect of the temperature-dependent interfacial layer

The interfacial layer of nanoparticles has been recently shown to have an effect on the thermal conductivity of nanofluids. There is, however, still no thermal conductivity model that includes the effects of temperature and nanoparticle size variations on the thickness and consequently on the thermal conductivity of the interfacial layer. In the present work, the stationary model developed by Leong et al. (J Nanopart Res 8:245–254, 2006) is initially modified to include the thermal dispersion effect due to the Brownian motion of nanoparticles. This model is called the ‘Leong et al.’s dynamic model’. However, the Leong et al.’s dynamic model over-predicts the thermal conductivity of nanofluids in the case of the flowing fluid. This suggests that the enhancement in the thermal conductivity of the flowing nanofluids due to the increase in temperature does not come from the thermal dispersion effect. It is more likely that the enhancement in heat transfer of the flowing nanofluids comes from the temperature-dependent interfacial layer effect. Therefore, the Leong et al.’s stationary model is again modified to include the effect of temperature variation on the thermal conductivity of the interfacial layer for different sizes of nanoparticles. This present model is then evaluated and compared with the other thermal conductivity models for the turbulent convective heat transfer in nanofluids along a uniformly heated tube. The results show that the present model is more general than the other models in the sense that it can predict both the temperature and the volume fraction dependence of the thermal conductivity of nanofluids for both non-flowing and flowing fluids. Also, it is found to be more accurate than the other models due to the inclusion of the effect of the temperature-dependent interfacial layer. In conclusion, the present model can accurately predict the changes in thermal conductivity of nanofluids due to the changes in volume fraction and temperature for various nanoparticle sizes.     

Depletion of ideal polymer chains near a spherical colloid particle beyond the Dirichlet boundary conditions

We reconsider the depletion interaction of an ideal polymer chain, characterized by the gyration radius R_G and bond length a , and an impenetrable spherical colloid particle of radius R . Forbidding the polymer-colloid penetration explicitly (by the use of Mayer functions) without any other requirement we derive and solve analytically an integral equation for the chain partition function of a long ideal polymer chain for the spherical geometry. We find that the correction to the solution of the Dirichlet problem depends on the ratios R/R _G and R/a . The correction vanishes for the continuous chain model (i.e. in the limit R/R _G → 0 and R/a → ∞ but stays finite (even for an infinite chain) for the discrete chain model. The correction can become substantial in the case of nano-colloids (the so-called protein limit).     

Influence of the particle size distribution on the thermal conductivity of nanofluids

In a previous study, we have obtained an equation to predict the thermal conductivity of nanofluids containing nanoparticles with conductive interface. The model is maximal particle packing dependent. In this study, the maximal packing is obtained as a function of the particle size distribution, which is the Gamma distribution. The thermal conductivity enhancement depends on the averaged particle size. Discussion concerning the influence of the suspension pH on the particle packing is made. The proposed model is evaluated using number of sets from the published experimental data to the thermal conductivity enhancement for different nanofluids.     

Phase behavior of a suspension of hard spherocylinders plus ideal polymer chains

We study isotropic-isotropic and isotropic-nematic phase transitions of fluid mixtures containing hard spherocylinders (HSC) and added non-adsorbing ideal polymer chains using scaled particle theory (SPT). First, we investigate isotropic-nematic (I -N phase coexistence using SPT in the absence of polymer. We compare the results obtained using a Gaussian form of the orientational distribution function (ODF) to minimize the free energy versus minimizing numerically. We find that formal numerical minimization gives results that are much closer to computer simulation results. In order to describe mixtures of HSC plus ideal chains we studied the depletion of ideal chains around a HSC. We analyze the density profiles of ideal chains near a hard cylinder and find the depletion thickness δ is a function of the ratio of the polymer's radius of gyration R_g and the cylinder radius R_c. Our results are compared with a common approximation in which the depletion thickness is taken equal to the radius of gyration of the polymer chain. We incorporate the correct depletion thickness into SPT and find that for R _g/R _c < 1.56 using ideal chains gives phase transitions at smaller polymer concentrations, whereas for R _g/R _c > 1.56 , which is a common experimental situation, the phase transitions are found at larger polymer concentrations with respect to δ = R _g . The differences are significant, especially for R _g ≫ R _c , so we can conclude it is essential to take into account the properties of ideal polymer chains and the resulting depletion near a cylinder. Finally, we present phase diagrams for rod-polymer mixtures which could be realized under experimental conditions.     

栅极调制纳米线的场增强因子计算

利用悬浮球模型和镜像电荷法计算了栅极调制纳米线的顶端表面电场,给出了场发射增强因子表达式β=1/2（3.5+L/r₀+W）,式中L与r₀分别是纳米线长度与顶端表面曲率半径,W是由栅孔半径R、阴极与栅极间距d以及纳米线自身几何参数所决定的函数．结果表明,纳米线长径比对场增强因子的影响很显著;当阴极与栅极间距较近时,场增强因子随d的增加而减小 关键词： 栅极调制纳米线 场增强因子 悬浮球     

Height-height correlations for surface growth on percolation networks

The height-height correlations of the surface growth for equilibrium and nonequilibrium restricted solid-on-solid (RSOS) model were investigated on randomly diluted lattices, i.e., on infinite percolation networks. It was found that the correlation function calculated over the chemical distances reflected the dynamics better than that calculated over the geometrical distances. For the equilibrium growth on a critical percolation network, the correlation function for the evolution time t?1 yielded a power-law behavior with the power ζ^′, associated with the roughness exponent ζ via the relation ζ=ζ^′d_f/d_l, with d_f and d_l being, respectively, the fractal dimension and the chemical dimension of the substrate. For the nonequilibrium growth, on the other hand, the correlation functions did not yield power-law behaviors for the concentration of diluted sites x less than or equal to the critical concentration x_c.     

On the hydrodynamic behavior of colloidal aggregates

The hydrodynamic radiusR _H and the radius of gyrationR _G are calculated for a model of a colloidal aggregate, which assumes a spherically symmetric density distribution of the colloidal particles as is the fractal dimension.Dedicated to K. Dransfeld on the occasion of his 60th birthday     

Structural properties and scaling of the radius of gyration of two-dimensional star-branched polymers grown by diffusion

We built up star-branched polymers, whose morphology is fully determined by diffusion, with p=1,3,6 and 12 branches with a total of 30,000 monomer units. We investigated their structural properties by calculating the monomer-monomer correlation functions. A detailed finite size scaling analysis of the radius of gyration was also performed to determine the exponent and the corrections to scaling. From these results we calculated the fractal dimension of the branched aggregates and obtained: d_f=1.222(7), for the linear chain, d_f=1.2305(8), d_f=1.247(8) and d_f=1.261(8) for the three, six and twelve branches polymer, respectively.     

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.     

带栅极纳米线冷阴极的场增强因子研究

场增强因子是体现场发射冷阴极器件性能优劣的重要参数.利用静电场理论给出了一种带栅极(normal-gated)纳米线冷阴极的场增强因子表示式β=k₁{N²·(L-d₁)²+［1/k₁+(L-d₁)］²}^1/2，且进一步分析了几何参数对场增强因子的影响.结果表明，纳米线突出栅孔的部分(L-d₁)与栅孔半径越大，则场增强因子越大；而纳米线半径越小，则场增强因子越大；当L远大于d₁时满足β∝L/r₀.其中N=N₁(k₁r₀)/N₀(k₁r₀)，N₀(k₁r₀)和N₁(k₁r₀)分别代表零阶和一阶Neumann函数，k₁=0.8936/R，R为栅孔半径，L为纳米线长度，r₀为纳米线半径，d₁表示阴极与栅极间距.