Critical lattice size limit for synchronized chaotic state in one- and two-dimensional diffusively coupled map lattices

We consider diffusively coupled map lattices with P neighbors (where P is arbitrary) and study the stability of the synchronized state. We show that there exists a critical lattice size beyond which the synchronized state is unstable. This generalizes earlier results for nearest neighbor coupling. We confirm the analytical results by performing numerical simulations on coupled map lattices with logistic map at each node. The above analysis is also extended to two-dimensional P-neighbor diffusively coupled map lattices.

Free vibration and wave propagation analysis of uniform and tapered rotating beams using spectrally formulated finite elements

This paper presents a formulation of an approximate spectral element for uniform and tapered rotating Euler-Bernoulli beams. The formulation takes into account the varying centrifugal force, mass and bending stiffness. The dynamic stiffness matrix is constructed using the weak form of the governing differential equation in the frequency domain, where two different interpolating functions for the transverse displacement are used for the element formulation. Both free vibration and wave propagation analysis is performed using the formulated elements. The studies show that the formulated element predicts results, that compare well with the solution available in the literature, at a fraction of the computational effort. In addition, for wave propagation analysis, the element shows superior convergence. (C) 2007 Elsevier Ltd. All rights reserved.

Genetic programming metamodel for rotating beams

This paper investigates the use of Genetic Programming (GP) to create an approximate model for the non-linear relationship between flexural stiffness, length, mass per unit length and rotation speed associated with rotating beams and their natural frequencies. GP, a relatively new form of artificial intelligence, is derived from the Darwinian concept of evolution and genetics and it creates computer programs to solve problems by manipulating their tree structures. GP predicts the size and structural complexity of the empirical model by minimizing the mean square error at the specified points of input-output relationship dataset. This dataset is generated using a finite element model. The validity of the GP-generated model is tested by comparing the natural frequencies at training and at additional input data points. It is found that by using a non-dimensional stiffness, it is possible to get simple and accurate function approximation for the natural frequency. This function approximation model is then used to study the relationships between natural frequency and various influencing parameters for uniform and tapered beams. The relations obtained with GP model agree well with FEM results and can be used for preliminary design and structural optimization studies.

Simulation of Dust Loaded V-I Characteristics of a Commercial Thermal Power Plant Precipitator

A new approach based on finite difference method, is proposed for the simulation of electrical conditions in a dc energized wire-duct electrostatic precipitator with and without dust loading. Simulated voltage-curren characteristics with and without dust loading were compared with the measured characteristics for analyzing the performance of a precipitator. The simple finite difference method gives sufficiently accurate results with reduced mesh size. The results for dust free simulation were validated with published experimental data. Further measurements were conducted at a thermal power plant in India and the results compares well with the measured ones.

Fractional damping: Stochastic origin and finite approximations

Fractional-order derivatives appear in various engineering applications including models for viscoelastic damping. Damping behavior of materials, if modeled using linear, constant coefficient differential equations, cannot include the long memory that fractional-order derivatives require. However, sufficiently great rnicrostructural disorder can lead, statistically, to macroscopic behavior well approximated by fractional order derivatives. The idea has appeared in the physics literature, but may interest an engineering audience. This idea in turn leads to an infinite-dimensional system without memory; a routine Galerkin projection on that infinite-dimensional system leads to a finite dimensional system of ordinary differential equations (ODEs) (integer order) that matches the fractional-order behavior over user-specifiable, but finite, frequency ranges. For extreme frequencies (small or large), the approximation is poor. This is unavoidable, and users interested in such extremes or in the fundamental aspects of true fractional derivatives must take note of it. However, mismatch in extreme frequencies outside the range of interest for a particular model of a real material may have little engineering impact.

Linear time algorithms for Abelian group isomorphism and related problems

We consider the problem of determining if two finite groups are isomorphic. The groups are assumed to be represented by their multiplication tables. We present an O(n) algorithm that determines if two Abelian groups with n elements each are isomorphic. This improves upon the previous upper bound of O(n log n) [Narayan Vikas, An O(n) algorithm for Abelian p-group isomorphism and an O(n log n) algorithm for Abelian group isomorphism, J. Comput. System Sci. 53 (1996) 1-9] known for this problem. We solve a more general problem of computing the orders of all the elements of any group (not necessarily Abelian) of size n in O(n) time. Our algorithm for isomorphism testing of Abelian groups follows from this result. We use the property that our order finding algorithm works for any group to design a simple O(n) algorithm for testing whether a group of size n, described by its multiplication table, is nilpotent. We also give an O(n) algorithm for determining if a group of size n, described by its multiplication table, is Abelian. (C) 2007 Elsevier Inc. All rights reserved.

Generalized survival in step fluctuations

The properties of the generalized survival probability, that is, the probability of not crossing an arbitrary location R during relaxation, have been investigated experimentally (via scanning tunneling microscope observations) and numerically. The results confirm that the generalized survival probability decays exponentially with a time constant tau(s)(R). The distance dependence of the time constant is shown to be tau(s)(R)=tau(s0)exp[-R/w(T)], where w(2)(T) is the material-dependent mean-squared width of the step fluctuations. The result reveals the dependence on the physical parameters of the system inherent in the prior prediction of the time constant scaling with R/L-alpha, with L the system size and alpha the roughness exponent. The survival behavior is also analyzed using a contrasting concept, the generalized inside survival S-in(t,R), which involves fluctuations to an arbitrary location R further from the average. Numerical simulations of the inside survival probability also show an exponential time dependence, and the extracted time constant empirically shows (R/w)(lambda) behavior, with lambda varying over 0.6 to 0.8 as the sampling conditions are changed. The experimental data show similar behavior, and can be well fit with lambda=1.0 for T=300 K, and 0.5 scaling effect due to the true correlation time is relevant in the parameter space of the experimental observations.

Modelling of solute transport in a mild heterogeneous porous medium using stochastic finite element method: Effects of random source conditions

Randomness in the source condition other than the heterogeneity in the system parameters can also be a major source of uncertainty in the concentration field. Hence, a more general form of the problem formulation is necessary to consider randomness in both source condition and system parameters. When the source varies with time, the unsteady problem, can be solved using the unit response function. In the case of random system parameters, the response function becomes a random function and depends on the randomness in the system parameters. In the present study, the source is modelled as a random discrete process with either a fixed interval or a random interval (the Poisson process). In this study, an attempt is made to assess the relative effects of various types of source uncertainties on the probabilistic behaviour of the concentration in a porous medium while the system parameters are also modelled as random fields. Analytical expressions of mean and covariance of concentration due to random discrete source are derived in terms of mean and covariance of unit response function. The probabilistic behaviour of the random response function is obtained by using a perturbation-based stochastic finite element method (SFEM), which performs well for mild heterogeneity. The proposed method is applied for analysing both the 1-D as well as the 3-D solute transport problems. The results obtained with SFEM are compared with the Monte Carlo simulation for 1-D problems.

New rational interpolation functions for finite element analysis of rotating beams

A rotating beam finite element in which the interpolating shape functions are obtained by satisfying the governing static homogenous differential equation of Euler–Bernoulli rotating beams is developed in this work. The shape functions turn out to be rational functions which also depend on rotation speed and element position along the beam and account for the centrifugal stiffening effect. These rational functions yield the Hermite cubic when rotation speed becomes zero. The new element is applied for static and dynamic analysis of rotating beams. In the static case, a cantilever beam having a tip load is considered, with a radially varying axial force. It is found that this new element gives a very good approximation of the tip deflection to the analytical series solution value, as compared to the classical finite element given by the Hermite cubic shape functions. In the dynamic analysis, the new element is applied for uniform, and tapered rotating beams with cantilever and hinged boundary conditions to determine the natural frequencies, and the results compare very well with the published results given in the literature.

The effects of manganese content and mould size on abrasion and slurry erosion behaviour of chromium-manganese iron systems investigated by positron lifetime spectroscopy

Abrasion and slurry erosion behaviour of chromium-manganese iron samples with chromium (Cr) in the range similar to 16-19% and manganese (Mn) at 5 and 10% levels have been characterized for hardness followed by microstructural examination using optical and scanning electron microscopy. Positron lifetime studies have been conducted to understand the defects/microporosity influence on the microstructure. The samples were heat treated and characterized to understand the structural transformations in the matrix. The data reveals that hardness decreased with increase in Mn content from 5 to 10% in the first instance and then increase in the section size in the other case, irrespective of the sample conditions. The abrasion and slurry erosion losses show increase with increase in the section size as well as with increase in Mn content. The positron results show that as hardness increases from as-cast to heat treated sample, the positron trapping rate and hence defect concentration showed opposite trend as expected. So a good correlation between defects concentration and the hardness has been observed. These findings also corroborate well with the microstructural features obtained from optical and scanning electron microscopy. (C) 2009 Elsevier B. V. All rights reserved.

Aerosol size distribution and its connection to cloud droplet number concentration

In order to predict the current state and future development of Earth s climate, detailed information on atmospheric aerosols and aerosol-cloud-interactions is required. Furthermore, these interactions need to be expressed in such a way that they can be represented in large-scale climate models. The largest uncertainties in the estimate of radiative forcing on the present day climate are related to the direct and indirect effects of aerosol. In this work aerosol properties were studied at Pallas and Utö in Finland, and at Mount Waliguan in Western China. Approximately two years of data from each site were analyzed. In addition to this, data from two intensive measurement campaigns at Pallas were used. The measurements at Mount Waliguan were the first long term aerosol particle number concentration and size distribution measurements conducted in this region. They revealed that the number concentration of aerosol particles at Mount Waliguan were much higher than those measured at similar altitudes in other parts of the world. The particles were concentrated in the Aitken size range indicating that they were produced within a couple of days prior to reaching the site, rather than being transported over thousands of kilometers. Aerosol partitioning between cloud droplets and cloud interstitial particles was studied at Pallas during the two measurement campaigns, First Pallas Cloud Experiment (First PaCE) and Second Pallas Cloud Experiment (Second PaCE). The method of using two differential mobility particle sizers (DMPS) to calculate the number concentration of activated particles was found to agree well with direct measurements of cloud droplet. Several parameters important in cloud droplet activation were found to depend strongly on the air mass history. The effects of these parameters partially cancelled out each other. Aerosol number-to-volume concentration ratio was studied at all three sites using data sets with long time-series. The ratio was found to vary more than in earlier studies, but less than either aerosol particle number concentration or volume concentration alone. Both air mass dependency and seasonal pattern were found at Pallas and Utö, but only seasonal pattern at Mount Waliguan. The number-to-volume concentration ratio was found to follow the seasonal temperature pattern well at all three sites. A new parameterization for partitioning between cloud droplets and cloud interstitial particles was developed. The parameterization uses aerosol particle number-to-volume concentration ratio and aerosol particle volume concentration as the only information on the aerosol number and size distribution. The new parameterization is computationally more efficient than the more detailed parameterizations currently in use, but the accuracy of the new parameterization was slightly lower. The new parameterization was also compared to directly observed cloud droplet number concentration data, and a good agreement was found.

Fracture process zone size and true fracture energy of concrete using acoustic emission

Acoustic emission (AE) energy, instead of amplitude, associated with each of the event is used to estimate the fracture process zone (FPZ) size. A steep increase in the cumulative AE energy of the events with respect to time is correlated with the formation of FPZ. Based on the AE energy released during these events and the locations of the events, FPZ size is obtained. The size-independent fracture energy is computed using the expressions given in the boundary effect model by least squares method since over-determined system of equations are obtained when data from several specimens are used. Instead of least squares method a different method is suggested in which the transition ligament length, measured from the plot of histograms of AE events plotted over the un-cracked ligament, is used directly to obtain size-independent fracture energy. The fracture energy thus calculated seems to be size-independent.