Radar polarimetry of Saturn's rings: Modeling ring particles as fractal aggregates built of small ice monomers

We analyze ground-based radar polarimetric observations of Saturn's rings at a wavelength of 12.6 cm by employing the model of a vertically and horizontally plane-parallel homogeneous slab composed of clumpy particles in the form of fractal aggregates of small ice monomers. Our model takes full account of the effects of polarization, multiple scattering, and coherent backscattering. Using efficient superposition T-matrix and vector radiative transfer codes, we perform computations of the backscattering circular polarization ratio for fractal aggregates generated with a cluster–cluster aggregation model and having the following characteristics: monomer refractive index m=1.78+i0.003; monomer packing density p=0.2; fractal dimensions D_f=2.5 and 3; and overall fractal radii R in the range 4?R?10 cm. In order to obtain physically realistic values of single-scattering properties of the aggregates we perform averaging over an ensemble of clusters generated for the same values of fractal parameters but having different geometrical configurations of the monomers. We conclude that in the framework of the above morphological model of Saturn's rings and the specific cluster–cluster aggregation procedure, it may be problematic to obtain a satisfactory and realistic agreement between theoretical computations and the observed values of the radar circular polarization ratio.     

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.     

Effects of Monomer Size Distribution on the fractal dimensionality of diffusion-limited aggregates

Computer simulations of diffusion-limited aggregation (DLA) for monomers to investigate the effects of size and of lognormal distribution on the fractal dimensionality of the aggregates were conducted on a two-dimensional lattice. The results show the DLA clusters posses multifractal characteristics. For clusters consisting of monodisperse monomers, the bifurcation point on the graph of the pair correlation function (PCF) for each cluster is located right at the monomers size under investigation The textural dimension (D_f1) has a stable value of about 1.65, whereas the structural dimension (D_f2) decreased with increase in monomer size. For the cases with monomers in log-normal distributions, the textural dimension is around 1.67; however, the structural dimension decreases with increasing polydispersity of monomer size.     

A new example of the diffusion-limited aggregation: Ni-Cu film patterns

The mechanism of the growth of the dendrites in the Ni-Cu films is studied by comparing them with the aggregates obtained by Monte Carlo (MC) simulations according to the diffusion-limited aggregation (DLA) model. The films were grown by electrodeposition. The structural analysis of the films carried out using the x-ray diffraction showed that the films have a face-centered cubic structure. Scanning electron microscope (SEM) was used for morphological observations and the film compositions were determined by energy dispersive x-ray spectroscopy. The observed SEM images are compared with the patterns obtained by MC simulations according to DLA model in which the sticking probability, P between the particles is used as a parameter. For all samples between the least and the densest aggregates in the films, the critical exponents of the density-density correlation functions, α were within the interval 0.160 ± 0.005-0.124 ± 0.006, and the fractal dimensions, D_f, varies from 1.825 ± 0.006 to 1.809 ± 0.008 according to the method of two-point correlation function. These values are also verified by the mass-radius method. The pattern with α and D_f within these intervals was obtained by MC simulations to DLA model while the sticking probability, P was within the interval from 0.35 to 0.40 obtained by varying P (1-0.001). The results showed that the DLA model in this binary system is a possible mechanism for the formation of the ramified pattern of Ni-Cu within the Ni-rich base part of the Ni-Cu films due to the diffusive characteristics of Cu.     

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.     

Dynamic hysteresis of magnetic aggregates with non-integer dimension

We investigate the dynamic hysteresis of nanoscale magnetic aggregates by employing Monte Carlo simulation, based on Ising model in non-integer dimensional space. The diffusion-limited aggregation (DLA) model with adjustable sticking probability is used to generate magnetic aggregates with different fractal dimension D. It is revealed that the exponential scaling law A(H₀, ω)∼H₀^α·ω^β, where A is the hysteresis area, H₀ and ω the amplitude and frequency of external magnetic field, applies to both the low-ω and high-ω regimes, while exponents α and β decrease with increasing D in the low-ω regime and keep invariant in the high-ω regime. A mean-field approach is developed to explain the simulated results.     

On Different Approaches to Estimate the Mass Fractal Dimension of Coal Aggregates

Several methods to measure the structures of coal aggregates are compared. Loose and compact coal aggregates were generated through flocculation of ultrafine coal particles (mean volume diameter of 12 μm) under specific shearing conditions. Aggregate structure in terms of mass fractal dimension, D_f, was determined using various methods; namely 2D and 3D image analysis, interpretation of intensity patterns from small angle light scattering, changes in aggregation state through light obscuration, and settling behavior. In this study, the measured values of D_f ranged from 1.84–2.19 for coal aggregates with more open structures, and around 2.27–2.66 for the compact ones. All of these approaches could distinguish structural differences between aggregates, albeit with variation in D_f values estimated by the different techniques. The discrepancy in the absolute values for fractal dimension is due to the different physical properties measured by each approach, depending on the assumptions used to infer D_f from measurable parameters. In addition, image analysis and settling techniques are based on the examination of individual aggregates, such that a large number of data points are required to yield statistically representative estimations. Light scattering and obscuration measure the aggregates collectively to give average D_f values of the particulate systems; consequently ignoring any structural variation between the aggregates, and leaving possible small contaminations undetected (e.g. by dust particles or air bubbles). Appropriate utilization of a particular method is thus largely determined by system properties and required data quality.     

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.     

Dimension of fractal growth patterns as a dynamical exponent

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension D of DLA can be estimated, 1.69相似文献   

Magnetic spectra of Fe-based nanocrystalline wires with axial or transverse domains

The circular permeability μ′=μ′−jμ″ of two Fe-based soft magnetic wires with axial and transverse domains, has been determined from the measurements of impedance Z=R+jX as functions of frequency (f=10-10⁵ Hz) and AC current amplitude (I=0.1-100 mA). From the magnetic spectra of μ′−f and μ″−f for a few circular fields (H_φ=0.4, 1.2, 4, 12, 40 A/m), we found that the sample with axial domain structure exhibits a relaxational feature, while for the one with transverse domain resonance-like spectra were observed when the circular field H_φ≥4 A/m. These results have been discussed in terms of domain structure and circular magnetization processes.     

Doppler spectroscopy of arbitrarily polarized light in rubidium

We present an experimental and theoretical study of the transmission of an arbitrarily polarized laser beam for a Doppler broadened rubidium vapor cell. As the polarization of the probe beam was varied from linear to circular, the transmission for the transitions F_g = 3 → F_e = 2, 3, 4 of the D₂ line of ⁸⁵Rb atoms was measured and compared with calculated results. In the calculation, the time-dependent absorption coefficient, calculated numerically from the density-matrix equation, was averaged over the velocity distribution and various transit time crossing the laser beam. The final transmission was obtained by considering the Gaussian profile of the laser beam. We found good agreement between experimental and calculated results.     

Surface characterization and microstructure of ITO thin films at different annealing temperatures

In this study, the electron beam evaporation method is used to generate an indium tin oxide (ITO) thin film on a glass substrate at room temperature. The surface characteristics of this ITO thin film are then investigated by means of an AFM (atomic force microscopy) method. The influence of postgrowth thermal annealing on the microstructure and surface morphology of ITO thin films are also examined. The results demonstrate that the film annealed at higher annealing temperature (300 °C) has higher surface roughness, which is due to the aggregation of the native grains into larger clusters upon annealing. The fractal analysis reveals that the value of fractal dimension D_f falls within the range 2.16-2.20 depending upon the annealing temperatures and is calculated by the height-height correlation function.     

Sooting tendencies of nonvolatile aromatic hydrocarbons

We have measured sooting tendencies of 72 nonvolatile aromatic hydrocarbons, only five of which have been previously reported in the literature. The tested compounds include long-chain alkylbenzenes up to tridecylbenzene, methyl-substituted benzenes, naphthalenes, biaryls, and polycyclic aromatic hydrocarbons (PAH) with up to four rings. Sooting tendency was defined as the maximum soot concentration f_v,max in a methane/air coflow nonpremixed flame with 5-80 ppm of the aromatic added to the fuel. The f_v,max were converted into Yield Sooting Indices (YSI’s) by the equation YSI = C^∗f_v,max + D, where C and D are constants chosen so that YSI-2-heptanone = 17 and YSI-phenanthrene = 191. The aromatics were dissolved in 2-heptanone and added to the fuel mixture with a syringe pump. Soot concentrations were measured with laser-induced incandescence (LII). The burner and fuel lines were heated; time-resolved soot measurements verified that all of the test compounds were quantitatively transmitted to the flame without losses to the walls. The uncertainties in the results range from ±3 to ±10%.     

The influence of a demagnetizing field on hysteresis losses in a dense assembly of superparamagnetic nanoparticles

The electrodynamic method is used to measure the hysteresis losses of a dense assembly of magnetite nanoparticles with an average diameter D=25 nm in the frequency range f=10–150 kHz and for magnetic field amplitudes H₀=100–300 Oe. It is found that the specific loss power is determined by a demagnetizing factor of a whole sample. It diminishes approximately 4.5 times when the sample aspect ratio decreases from L/d=11.4 to L/d≈1, where L and d are the sample length and diameter, respectively. For H₀≤300 Oe the maximal specific loss power 120 W/g is obtained for the sample with L/d=11.4 at f=120 kHz. For comparison, the assembly specific absorption rate has been determined also by means of direct measurement of the temperature difference between the inner and outer surfaces of a flat cuvette containing magnetic nanoparticles. For both methods of measurement close values for the specific absorption rate are obtained for samples with similar demagnetizing factors.     

Novel device to measure critical point "Onset" of capillary wave and interpretation of Faraday instability wave by numerical analysis

A capillary wave was created on a surface by vibrating from the bottom of a container. When the amplitude of the container vibration approached the critical point, called the onset state, the surface broke up and bursted into very small drops on the air. The numerical analysis was used to determine the amplitude of the onset. The onset point was found to be 0.349 μm at f = 500 kHz. The critical amplitude h_cr was determined by using a multi-Fourier horn nozzle (MFHN) device. The onset point was measured to be 0.37 μm using a laser Doppler vibrometer (LDV) with the MFHN at f = 486 kHz. These drops indicate that particle size distributions of 10.8 μm and 7.0 μm were produced by the MFHN at f = 289 kHz and f = 486 kHz, respectively. These results agreed with those obtained using Kelvin’s equation, which predicted D = 0.34λ.     

各向异性扩散DLA集团的豪斯道夫维数与标度性质

讨论了DLA集团的各向异性扩散效应.计算机模拟证实了具有各向异性扩散规则的DLA集团有严格的菱形结构.导出了一个粒子的各向异性扩散的新方程，计算了各向异性扩散DLA集团的豪斯道夫维数，结果表明，有效外半角β_eff=min(β_ix,β_iy).讨论了各向异性扩散DLA集团的广义维数，使用修改的楔模型得到了广义维数D_q的表达式. 关键词：     

The multiphoton ionization spectrum of jet-cooled pyrimidine in the 3p Rydberg and B1 (π,n) states

Resonance-enhanced multiphoton ionization (REMPI) has been applied to study the n → 3p Rydberg transition of pyrimidine (jet-cooled sample and mass resolved spectrum). Only the one component, the 3p_z(B₂), appears in the (2 + 1) REMPI and the active vibrations are ν_6a = 622, ν₁ = 946, and ν_9a = 1116 cm⁻¹. The symmetry of the state was determined by polarization measurements (linear, circular polarization). The first (π^∗,n) ³B₁ triplet state appears as a one-photon resonance in the three-photon ionization process.     

Synthesis of LECBD grown cluster assembled SeO2 thin films

Cluster assembled selenium oxide (SeO₂) thin films, as a function of oxygen flow pressure (OFP) have been synthesized by a low energy cluster beam deposition (LECBD) technique. The OFP dependent surface morphology leading to well separated nanoclusters (size ranging from 50 to 200 nm) and fractal features are confirmed from transmission electron microscopic (TEM) measurements. A diffusion limited aggregation (DLA) mediated fractal growth with dimension as 1.71 ± 0.01 has been observed for high OFP (60 mbar). Structural analysis by glancing angle X-ray diffraction (GXRD) and selected area diffraction (SAD) studies identify the presence of tetragonal phase SeO₂ in the deposit. Micro-Raman studies indicate the shifts in bending and stretching vibrational phonon modes in cluster assembled SeO₂ as compared to their bulk counter part due to the phonon confinement effect.     

Anomalous spectral behavior of vectorial apertured ultrashort pulsed beams beyond the paraxial approximation

Based on the vectorial Rayleigh diffraction integrals, the analytical expression for the spectral intensity of a vectorial nonparaxial ultrashort pulsed Gaussian beam diffracted at a circular hard-aperture is derived. The effect of f-parameter (f = 1/k₀w₀) on the spectral anomalies near phase singularities of the vectorial nonparaxial ultrashort pulsed beams is studied. It is shown that the spectral switch near the phase singularity of diffracted vectorial nonparaxial ultrashort pulsed beam still exists beyond paraxial regime, but disappears when the f-parameter is larger than a certain value.     

Monte Carlo simulation of aggregate morphology for simultaneous coagulation and sintering

A model for simulation of the three-dimensional morphology of nano-structured aggregates formed by concurrent coagulation and sintering is presented. Diffusion controlled cluster–cluster aggregation is assumed to be the prevailing coagulation mechanism which is implemented using a Monte–Carlo algorithm. Sintering is modeled as a successive overlapping of spherical primary particles, which are allowed to grow as to preserve overall mass. Simulations are characterized by individual ratios of characteristic collision to fusion time. A number of resulting aggregate-structures is displayed and reveals structure formation by coagulation and sintering for different values of . These aggregates are described qualitatively and quantitatively by their mass fractal dimension D_f and radius of gyration. The fractal dimension increases from 1.86 for pure aggregation to 2.75 for equal characteristic time scales. As sintering turns out to be more and more relevant, increasingly compact aggregates start to form and the radius of gyration decreases significantly. The simulation results clearly reveal a strong dependence of the fractal dimension on the kinetics of the concurrent coagulation and sintering processes. Considering appropriate values of D_f in aerosol process simulations may therefore be important in many cases.