Radius Standard Deviation Research Articles

A Cloud Microphysics Parameterization for Shallow Cumulus Clouds Based on Lagrangian Cloud Model Simulations

Abstract Cloud microphysics parameterizations for shallow cumulus clouds are analyzed based on Lagrangian cloud model (LCM) data, focusing on autoconversion and accretion. The autoconversion and accretion rates, A and C, respectively, are calculated directly by capturing the moment of the conversion of individual Lagrangian droplets from cloud droplets to raindrops, and it results in the reproduction of the formulas of A and C for the first time. Comparison with various parameterizations reveals the closest agreement with Tripoli and Cotton, such as and , where and are the mixing ratio and the number concentration of cloud droplets, is the mixing ratio of raindrops, is the threshold volume radius, and H is the Heaviside function. Furthermore, it is found that increases linearly with the dissipation rate and the standard deviation of radius and that decreases rapidly with while disappearing at > 3.5 μm. The LCM also reveals that and increase with time during the period of autoconversion, which helps to suppress the early precipitation by reducing A with smaller and larger in the initial stage. Finally, is found to be affected by the accumulated collisional growth, which determines the drop size distribution.

The effect of different thickness alumina capping layers on the final morphology of dewet thin Ni films

Nanoparticles on a substrate have numerous applications in nanotechnology, from enhancements to solar cell efficiency to improvements in carbon nanotube growth. Producing nanoparticles in a cost effective fashion with control over size and spacing is desired, but difficult to do. This work presents a scalable method for altering the radius and pitch distributions of nickel nanoparticles. The introduction of alumina capping layers to thin nickel films during a pulsed laser-induced dewetting process has yielded reductions in the mean and standard deviation of radii and pitch for dewet nanoparticles with no noticeable difference in final morphology with increased capping layer thickness. The differences in carbon nanotube mats grown, on the uncapped sample and one of the capped samples, is also presented here, with a more dense mat being present for the capped case.

Estimation of size and number density of microbubbles based on analysis of frequency-dependent attenuation

A method of estimating the size and number density of microbubbles in suspension is proposed, which matches the theoretically calculated frequency dependent attenuation coefficient with the experimental data. Assuming that the size distribution of bubbles is given by a log-normal function, three parameters (expected value and standard deviation of radius and the number density of bubbles) of Sonazoid® in the steady flow were estimated. Bubbles are exposed to ultrasound with a center frequency of 5 MHz and mechanical indices of 0.4, 0.5, 0.7, and 1.1. The expected value and standard deviation for the size distribution were estimated to be 70–85 and 45–60% of the reference values in the case of a lower mechanical index, respectively. The number density was estimated to be 20–30 times smaller than the reference values. This fundamental examination indicates that the number density of bubbles can be qualitatively evaluated by the proposed method.

ROUGHNESS VARIATION CAUSED BY GRINDING ERRORS OF CUTTING EDGES IN SIDE MILLING

A numerical model was developed to predict the roughness profile along a line in the feed direction, in contour milling operations with cylindrical milling tools. From the model, average roughness Ra and maximum peak-to-valley roughness Rt were calculated for families of tools defined by 100,000 random combinations of radius values. Radii were selected by means of the Monte Carlo Method. Each family is defined by an average radius and a standard deviation of radius, assuming normal behavior. Histograms, roughness variation intervals, medians and modes, were calculated at different feeds. The model was validated through experimental tests. Effect of standard deviation of radius, number of teeth and tool diameter were studied. Although radius values were randomly selected according to a normal law, roughness values did not follow a normal distribution. At low standard deviations, intervals of roughness values, medians and modes vary only slightly with feed, except at very low feeds where intervals are narrow. On the contrary, at higher standard deviations, median, mode and width of roughness intervals rise as feed increases. Use of a lower number of teeth and higher tool diameter leads to narrower intervals and asymmetrical roughness frequency distributions even at high feeds, with modes near upper reference values.

In Situ and Time-Resolved SAXS Studies of Pd Nanoparticle Formation in a Template of Block Copolymer Microdomain Structures

Time-resolved small-angle X-ray scattering (SAXS) measurements were performed to study in-situ formation of palladium (Pd) nanoparticles in block copolymer microdomains. The nanoparticles were reduced in a reaction medium containing a fixed composition of polyisoprene-block-poly(2-vinylpyridine) (PI-b-P2VP), palladium acetylacetonate, Pd(acac)2, and benzyl alcohol as a solvent and a reducing agent. The polymer concentration is high enough so that it forms swollen ordered lamellae before reduction. The reduction was induced by a rapid temperature jump, and the polymer concentration was kept constant in a sealed sample cell. It was clearly elucidated that the formation of Pd nanoparticles occurred in the templates of the swollen lamellar microdomains. By fitting the theoretical scattered intensity for spherical particles to the observed SAXS profiles, we analyzed time evolution of mean radius, standard deviation of radius, and total volume of Pd nanoparticles in concentrated PI-b-P2VP solutions after T-jump...

Ray optics approximation for Gaussian random cylinders

We study light scattering by Gaussian random cylinders in the ray optics approximation. The random shape is fully described by the covariance function, which can be conveniently modelled by three statistical parameters: the standard deviation of radius and the correlation lengths of angular and axial variations. We present a Fourier-series method for generating sample Gaussian cylinders and, by studying the total curvature, develop a criterion for the validity of the ray optics approximation. We outline a ray tracing algorithm that can be adapted to almost arbitrary, mathematically star-like particles in the cylindrical geometry. We study the scattering and absorption properties of Gaussian cylinders much larger than the wavelength by systematically varying their statistical parameters.

Light scattering by Gaussian random particles: Rayleigh and Rayleigh-Gans approximations

We study absorption and scattering by Gaussian random particles in the Rayleigh and Rayleigh-Gans approximations. The random shape is characterized by the autocovariance function, usually parameterized by the standard deviation of radius and the correlation length of angular variations. As for the Rayleigh-Gans approximation, we outline a Monte Carlo algorithm that can be adjusted for almost arbitrary, mathematically star-like particles in random orientation. The algorithm is computationally constrained to particles with size parameters less than about five. We examine how the autocovariance function affects the scattering and absorption properties of Gaussian particles, and compare to the Rayleigh-Gans solution for spheres. By ensemble-averaging the volume of the Gaussian particle, we develop criteria for the validity of the Rayleigh and Rayleigh-Gans approximations. The results help us understand, in part, light scattering by small particles in planetary atmospheres and cometary comae.

Light scattering by Gaussian random particles: Ray optics approximation

We model the shapes of irregular small particles using multivariate lognormal statistics (Gaussian random shape), and compute absorption and scattering cross sections, asymmetry parameters, and scattering phase matrices in the ray optics approximation. The random shape is fully described by the autocovariance function, which can be conveniently modeled by two statistical parameters: the standard deviation of radius and the correlation length of angular variations. We present an efficient spherical harmonics method for generating sample Gaussian random particles, and outline a ray tracing algorithm that can be adapted to almost arbitrary, mathematically star-like particles. We study the scattering and absorption properties of Gaussian random particles much larger than the wavelength by systematically varying their statistical parameters and complex refractive indices. The results help us understand, in part, light scattering by solar system dust particles, and thereby constrain the physical properties of, for example, asteroid regoliths and cometary comae.