Probabilistic Growth Model Research Articles

Hailstorm Detection by Satellite Microwave Radiometers

Passive microwave measurements from satellites have been used to identify the signature of hail in intense thunderstorms. The scattering signal of hailstones is typically observed as a strong depression of upwelling brightness temperatures from the cloud to the satellite. Although the relation between scattering signal and hail diameter is often assumed linear, in this work a logistic model is used which seems to well approximate the complexity of the radiation extinction process by varying the hail cross-section. A novel probability-based method for hail detection originally conceived for AMSU-B/MHS and now extended to ATMS, GMI, and SSMIS, is presented. The measurements of AMSU-B/MHS were analyzed during selected hailstorms over Europe, South America and the US to quantify the extinction of radiation due to the hailstones and large ice aggregates. To this aim, a probabilistic growth model has been developed. The validation analysis based on 12-year surface hail observations over the US (NOAA official reports) collocated with AMSU-B overpasses have demonstrated the high performance of the hail detection method in distinguishing between moderate and severe hailstorms, fitting the seasonality of hail patterns. The flexibility of the method allowed its experimental application to other microwave radiometers equipped with MHS-like frequency channels revealing a high level of portability.

Effect of storage temperature on the lag time of Geobacillus stearothermophilus individual spores

The lag times (λ) of Geobacillus stearothermophilus single spores were studied at different storage temperatures ranging from 45 to 59 °C using the Bioscreen C method. A significant variability of λ was observed among individual spores at all temperatures tested. The storage temperature affected both the position and the spread of the λ distributions. The minimum mean value of λ (i.e. 10.87 h) was observed at 55 °C, while moving away from this temperature resulted in an increase for both the mean and standard deviation of λ. A Cardinal Model with Inflection (CMI) was fitted to the reverse mean λ, and the estimated values for the cardinal parameters Tmin, Tmax, Topt and the optimum mean λ of G. stearothermophilus were found to be 38.1, 64.2, 53.6 °C and 10.3 h, respectively. To interpret the observations, a probabilistic growth model for G. stearothermophilus individual spores, taking into account λ variability, was developed. The model describes the growth of a population, initially consisting of N0 spores, over time as the sum of cells in each of the N0 imminent subpopulations originating from a single spore. Growth simulations for different initial contamination levels showed that for low N0 the number of cells in the population at any time is highly variable. An increase in N0 to levels exceeding 100 spores results in a significant decrease of the above variability and a shorter λ of the population. Considering that the number of G. stearothermophilus surviving spores in the final product is usually very low, the data provided in this work can be used to evaluate the probability distribution of the time-to-spoilage and enable decision-making based on the “acceptable level of risk”.

Model for the growth of the world airline network

We propose a probabilistic growth model for transport networks which employs a balance between popularity of nodes and the physical distance between nodes. By comparing the degree of each node in the model network and the World Airline Network (WAN), we observe that the difference between the two is minimized for [Formula: see text]. Interestingly, this is the value obtained for the node–node correlation function in the WAN. This suggests that our model explains quite well the growth of airline networks.

Extension to infinite dimensions of a stochastic second-order model associated with shape splines

Motivated by the development of a probabilistic model for growth of biological shapes in the context of large deformations by diffeomorphisms, we present a stochastic perturbation of the Hamiltonian equations of geodesics on shape spaces. We study the finite-dimensional case of groups of points for which we prove that the strong solutions of the stochastic system exist for all time. We extend the model to the space of parameterized curves and surfaces and we develop a convenient analytical setting to prove a strong convergence result from the finite-dimensional to the infinite-dimensional case. We then present some enhancements of the model.

A probabilistic growth model for partition polygons and related structures

A two-parameter, probabilistic growth model for partition polygon clusters is introduced and exact results obtained relating to the area moments and the area probability distribution. In particular, the scaling behaviour in the presence of asymmetry between growth along the two principal axes is discussed. Variants of the model are also examined, including the extension to rooted stack polygons. An interesting application relates to characterizing the asymptotic behaviour of the cumulative customer waiting time distribution in a particular discrete-time queue.

Isotropic growth on a grid

Isotropic growth from a single point on a two-dimensional square grid should generate an increasing sequence of discretized discs. We present a simple probabilistic model for growth on a grid, and discuss a class of parameterizations of the model (called kernels) which was conjectured [S. Thompson and A. Rosenfeld, Discrete stochastic growth models for two-dimensional shapes. In Shape in Picture—Mathematical Descriptions of Shape in Grey level Images, Y. L. O. A. Toet, D. H. Foster and P. Meer (eds), 301–318, Springer-Verlag, Heidelberg (1993)] to produce isotropic growth. We disprove this conjecture, but we claim that these kernels produce growth that can be decomposed into isotropic and nonisotropic other probabilistic growth processes on grids, and describe qualitative and quantitative properties of the models. We also consider a deterministic growth model based on the diffusion equation, and show empirically that discretization of this model leads to a steady state configuration that appears to be polygonal.

Infrared Properties of Thin Pt/Al2O3 Granular Metal-Insulator Composite Films

ABSTRACTThe reflection of mid- and near-infrared radiation (400-15000 cm−1 by thin Pt/Al2O3 cermet films was measured using a Fourier transform spectrometer. The data were compared with predictions of three models for the effective optical constants of heterogeneous materials: Maxwell-Garnett, Bruggeman, and a simplified version of a probabilistic growth model due to Sheng. Sheng's model provides the best description of the data over the complete range of metallic volume fraction. This result is expected based on the most likely topology of the films and is in agreement with other work on similar systems at higher frequencies.

Optical response of composite plasma polymer/metal films in the effective medium approach

A chlorotrifluoroethylene monomer and gold were used as starting materials for the deposition of composite films by simultaneous plasma polymerization and magnetron sputtering in an rf glow discharge. Thin layers composed of a plasma polymer with embedded small gold grains (10–120 nm in diameter) and characterized by gold volume fractions up to 0.5 evoked an optical resonance in the visible region of light. Spectral dependence (0.35–2.0 μm) of the optical constants n(λ) and k(gl) calculated from the transmission and reflection data was compared with the characteristics predicted by four models of an effective medium: the Maxwell-Garnett, the Bruggeman self-consistent, the coated sphere and the probabilistic growth model. Additional film characteristics were estimated from the position of the resulting effective dielectric function in the complex plane with respect to the Wiener limits. The optical properties of the layers are discussed in light of the film microstructure.

Optical response of Cermet composite films in the microstructural transition region

Measurements of the intrinsic optical constants $n$ and $k$ have been made on Au-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$ Cermet thin films with metal-fill fractions above and below the percolation threshold. The simple Maxwell-Garnett effective-medium theory, which is successful at low-metal-fill fractions, is shown to be inadequate in the description of the system near this threshold, where the microstructure of the composite undergoes a radical change. A modified effective-medium theory, based on a probabilistic growth model recently introduced by Sheng [Phys. Rev. Lett. 45, 60 (1980)], is found to predict the optical response in the transition region with few adjustable parameters.