An extravariation model for improving confidence intervals of population size estimates from removal data

We propose a new model for estimating the size of a population from successive catches taken during a removal experiment. The data from these experiments often have excessive variation, known as overdispersion, as compared with that predicted by the multinomial model. The new model allows catchability to vary randomly among samplings, which accounts for overdispersion. When the catchability is assumed to have a beta distribution, the likelihood function, which is refered to as beta-multinomial, is derived, and hence the maximum likelihood estimates can be evaluated. Simulations show that in the presence of extravariation in the data, the confidence intervals have been substantially underestimated in previous models (Leslie-DeLury, Moran) and that the new model provides more reliable confidence intervals. The performance of these methods was also demonstrated using two real data sets: one with overdispersion, from smallmouth bass (Micropterus dolomieu), and the other without overdispersion, from rat (Rattus rattus).

Size-dependent melting of nanoparticles: Hundred years of thermodynamic model

Thermodynamic model first published in 1909, is being used extensively to understand the size-dependent melting of nanoparticles. Pawlow deduced an expression for the size-dependent melting temperature of small particles based on the thermodynamic model which was then modified and applied to different nanostructures such as nanowires, prism-shaped nanoparticles, etc. The model has also been modified to understand the melting of supported nanoparticles and superheating of embedded nanoparticles. In this article, we have reviewed the melting behaviour of nanostructures reported in the literature since 1909.

Effects of particle size distribution in the response of model granular materials in multi-ring shear

Rail track undergoes complex loading patterns under moving traffic conditions compared to roads due to its continued and discontinued multi-layered structure, including rail, sleepers, ballast layer, sub-ballast layer, and subgrade. Particle size distributions (PSDs) of ballast, subballast, and subgrade layers can be critical in cyclic plastic deformation of rail track under moving traffic on frequent track degradation of rail tracks, especially at bridge transition zones. Conventional test approaches: static shear and cyclic single-point load tests are however unable to replicate actual loading patterns of moving train. Multi-ring shear apparatus; a new type of torsional simple shear apparatus, which can reproduce moving traffic conditions, was used in this study to investigate influence of particle size distribution of rail track layers on cyclic plastic deformation. Three particle size distributions, using glass beads were examined under different loading patterns: cyclic sin-gle-point load, and cyclic moving wheel load to evaluate cyclic plastic deformation of rail track under different loading methods. The results of these tests suggest that particle size distributions of rail track structural layers have significant impacts on cyclic plastic deformation under moving train load. Further, the limitations in con-ventional test methods used in laboratories to estimate the plastic deformation of rail track materials lead to underestimate the plastic deformation of rail tracks.

Bayesian mixture model estimation of aerosol particle size distributions

In this paper, we examine approaches to estimate a Bayesian mixture model at both single and multiple time points for a sample of actual and simulated aerosol particle size distribution (PSD) data. For estimation of a mixture model at a single time point, we use Reversible Jump Markov Chain Monte Carlo (RJMCMC) to estimate mixture model parameters including the number of components which is assumed to be unknown. We compare the results of this approach to a commonly used estimation method in the aerosol physics literature. As PSD data is often measured over time, often at small time intervals, we also examine the use of an informative prior for estimation of the mixture parameters which takes into account the correlated nature of the parameters. The Bayesian mixture model offers a promising approach, providing advantages both in estimation and inference.

Shell-model calculation of defect energies in alkali halides employing crystal-independent interionic potential parameters

Shell model calculation of defect energies in alkali halides have been carried out using the ion-dependent, crystal-independent potential parameters of Sangster and Atwood (1978). Results indicate that appreciable differences exist between barrier heights for migration of cations and anions. While barrier heights for cations are generally lower than for anions in alkali halides of NaCl structure, the opposite is true in alkali halides of CsCl structure.

Improved retrieval of aerosol size-resolved properties from moderate resolution imaging spectroradiometer over India: Role of aerosol model and surface reflectance

We have compared the total as well as fine mode aerosol optical depth (tau and tau(fine)) retrieved by Moderate Resolution Imaging Spectroradiometer (MODIS) onboard Terra and Aqua (2001-2005) with the equivalent parameters derived by Aerosol Robotic Network (AERONET) at Kanpur (26.45 degrees N, 80.35 degrees E), northern India. MODIS Collection 005 (C005)-derived tau(0.55) was found to be in good agreement with the AERONET measurements. The tau(fine) and eta (tau(fine)/tau) were, however, biased low significantly in most matched cases. A new set of retrieval with the use of absorbing aerosol model (SSA similar to 0.87) with increased visible surface reflectance provided improved tau and tau(fine) at Kanpur. The new derivation of eta also compares well qualitatively with an independent set of in situ measurements of accumulation mass fraction over much of the southern India. This suggests that though MODIS land algorithm has limited information to derive size properties of aerosols over land, more accurate parameterization of aerosol and surface properties within the existing C005 algorithm may improve the accuracy of size-resolved aerosol optical properties. The results presented in this paper indicate that there is a need to reconsider the surface parameterization and assumed aerosol properties in MODIS C005 algorithm over the Indian region in order to retrieve more accurate aerosol optical and size properties, which are essential to quantify the impact of human-made aerosols on climate.

Spin-1 Kitaev model in one dimension

We study a one-dimensional version of the Kitaev model on a ring of size N, in which there is a spin S > 1/2 on each site and the Hamiltonian is J Sigma(nSnSn+1y)-S-x. The cases where S is integer and half-odd integer are qualitatively different. We show that there is a Z(2)-valued conserved quantity W-n for each bond (n, n + 1) of the system. For integer S, the Hilbert space can be decomposed into 2N sectors, of unequal sizes. The number of states in most of the sectors grows as d(N), where d depends on the sector. The largest sector contains the ground state, and for this sector, for S=1, d=(root 5+1)/2. We carry out exact diagonalization for small systems. The extrapolation of our results to large N indicates that the energy gap remains finite in this limit. In the ground-state sector, the system can be mapped to a spin-1/2 model. We develop variational wave functions to study the lowest energy states in the ground state and other sectors. The first excited state of the system is the lowest energy state of a different sector and we estimate its excitation energy. We consider a more general Hamiltonian, adding a term lambda Sigma W-n(n), and show that this has gapless excitations in the range lambda(c)(1)<=lambda <=lambda(c)(2). We use the variational wave functions to study how the ground-state energy and the defect density vary near the two critical points lambda(c)(1) and lambda(c)(2).

Fatigue crack propagation model and size effect in concrete using dimensional analysis

It is well known that fatigue in concrete causes excessive deformations and cracking leading to structural failures. Due to quasi-brittle nature of concrete and formation of a fracture process zone, the rate of fatigue crack growth depends on a number of parameters, such as, the tensile strength, fracture toughness, loading ratio and most importantly the structural size. In this work, an analytical model is proposed for estimating the fatigue crack growth in concrete by using the concepts of dimensional analysis and including the above parameters. Knowing the governed and the governing parameters of the physical problem and by using the concepts of self-similarity, a relationship is obtained between different parameters involved. It is shown that the proposed fatigue law is able to capture the size effect in plain concrete and agrees well with different experimental results. Through a sensitivity analysis, it is shown that the structural size plays a dominant role followed by loading ratio and the initial crack length in fatigue crack propagation. (C) 2010 Elsevier Ltd. All rights reserved.

Model for Predicting the Mean Drop Size in Effervescent Sprays

This paper is focused on the development of a model for predicting the mean drop size in effervescent sprays. A combinatorial approach is followed in this modeling scheme, which is based on energy and entropy principles. The model is implemented in cascade in order to take primary breakup (due to exploding gas bubbles) and secondary breakup (due to shearing action of surrounding medium) into account. The approach in this methodology is to obtain the most probable drop size distribution by maximizing the entropy while satisfying the constraints of mass and energy balance. The comparison of the model predictions with the past experimental data is presented for validation. A careful experimental study is conducted over a wide range of gas-to-liquid ratios, which shows a good agreement with the model predictions: It is observed that the model gives accurate results in bubbly and annular flow regimes. However, discrepancies are observed in the transitional slug flow regime of the atomizer.

Influence of system size on spatiotemporal dynamics of a model for plastic instability: Projecting low-dimensional and extensive chaos

This work is a continuation of our efforts to quantify the irregular scalar stress signals from the Ananthakrishna model for the Portevin-Le Chatelier instability observed under constant strain rate deformation conditions. Stress related to the spatial average of the dislocation activity is a dynamical variable that also determines the time evolution of dislocation densities. We carry out detailed investigations on the nature of spatiotemporal patterns of the model realized in the form of different types of dislocation bands seen in the entire instability domain and establish their connection to the nature of stress serrations. We then characterize the spatiotemporal dynamics of the model equations by computing the Lyapunov dimension as a function of the drive parameter. The latter scales with the system size only for low strain rates, where isolated dislocation bands are seen, and at high strain rates, where fully propagating bands are seen. At intermediate applied strain rates corresponding to the partially propagating bands, the Lyapunov dimension exhibits two distinct slopes, one for small system sizes and another for large. This feature is rationalized by demonstrating that the spatiotemporal patterns for small system sizes are altered from the partially propagating band types to isolated burst type. This in turn allows us to reconfirm that low-dimensional chaos is projected from the stress signals as long as there is a one-to-one correspondence between the bursts of dislocation bands and the stress drops. We then show that the stress signals in the regime of partially to fully propagative bands have features of extensive chaos by calculating the correlation dimension density. We also show that the correlation dimension density also depends on the system size. A number of issues related to the system size dependence of the Lyapunov dimension density and the correlation dimension density are discussed.