An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 2: shells

Following the approach developed for rods in Part 1 of this paper (Pimenta et al. in Comput. Mech. 42:715-732, 2008), this work presents a fully conserving algorithm for the integration of the equations of motion in nonlinear shell dynamics. We begin with a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, allowing for an extremely simple update of the rotational variables within the scheme. The weak form is constructed via non-orthogonal projection, the time-collocation of which ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that general hyperelastic materials (and not only materials with quadratic potentials) are permitted in a totally consistent way. Spatial discretization is performed using the finite element method and the robust performance of the scheme is demonstrated by means of numerical examples.

An exact conserving algorithm for nonlinear dynamics with rotational DOFs and general hyperelasticity. Part 1: Rods

A fully conserving algorithm is developed in this paper for the integration of the equations of motion in nonlinear rod dynamics. The starting point is a re-parameterization of the rotation field in terms of the so-called Rodrigues rotation vector, which results in an extremely simple update of the rotational variables. The weak form is constructed with a non-orthogonal projection corresponding to the application of the virtual power theorem. Together with an appropriate time-collocation, it ensures exact conservation of momentum and total energy in the absence of external forces. Appealing is the fact that nonlinear hyperelastic materials (and not only materials with quadratic potentials) are permitted without any prejudice on the conservation properties. Spatial discretization is performed via the finite element method and the performance of the scheme is assessed by means of several numerical simulations.

Abrasive wear study of white cast iron with different solidification rates

The abrasive wear resistance of white cast iron was studied. The iron was solidified using two solidification rates of 1.5 and 15 degrees C/s. Mass loss was evaluated with tests of the type pin on abrasive disc using alumina of different sizes. Two matrices were tested: one predominantly austenitic and the other predominantly martensitic, containing M(3)C carbides. Samples with cooling rate of 15 degrees C/s showed higher hardness and more refined microstructure compared with those solidified at 1.5 degrees C/s. During the test, the movement of successive abrasives gave rise to the strain hardening of the austenite phase, leading to the attainment of similar levels of surface hardness, which explains why the wear rate showed no difference compared to the austenite samples with different solidification rates. For the austenitic matrix the wear rate seems to depend on the hardness of the worn surface and not on the hardness of the material without deformation. The austenitic samples showed cracking and fracture of M(3)C carbides. For the predominantly martensitic matrix, the wear rate was higher at the solidification rate of 1.5 degrees C/s, for grain size of 66 and 93 mu m. Higher abrasive sizes were found to produce greater penetration and strain hardening of austenitic matrices. However, martensitic iron produces more microcutting, increasing the wear rate of the material. The analysis of the worn surface by scanning electron microscopy indicated abrasive wear mechanisms such as: microcutting, microfatigue and microploughing. Yet, for the iron of austenitic matrix, the microploughing mechanism was more severe. (C) 2009 Elsevier B.V. All rights reserved.

An Array Recursive Least-Squares Algorithm With Generic Nonfading Regularization Matrix

We present a novel array RLS algorithm with forgetting factor that circumvents the problem of fading regularization, inherent to the standard exponentially-weighted RLS, by allowing for time-varying regularization matrices with generic structure. Simulations in finite precision show the algorithm`s superiority as compared to alternative algorithms in the context of adaptive beamforming.

A Separation Principle for the Continuous-Time LQ-Problem With Markovian Jump Parameters

In this paper, we devise a separation principle for the finite horizon quadratic optimal control problem of continuous-time Markovian jump linear systems driven by a Wiener process and with partial observations. We assume that the output variable and the jump parameters are available to the controller. It is desired to design a dynamic Markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. As in the case with no jumps, we show that an optimal controller can be obtained from two coupled Riccati differential equations, one associated to the optimal control problem when the state variable is available, and the other one associated to the optimal filtering problem. This is a separation principle for the finite horizon quadratic optimal control problem for continuous-time Markovian jump linear systems. For the case in which the matrices are all time-invariant we analyze the asymptotic behavior of the solution of the derived interconnected Riccati differential equations to the solution of the associated set of coupled algebraic Riccati equations as well as the mean square stabilizing property of this limiting solution. When there is only one mode of operation our results coincide with the traditional ones for the LQG control of continuous-time linear systems.

On the Filtering Problem for Continuous-Time Markov Jump Linear Systems with no Observation of the Markov Chain

We consider in this paper the optimal stationary dynamic linear filtering problem for continuous-time linear systems subject to Markovian jumps in the parameters (LSMJP) and additive noise (Wiener process). It is assumed that only an output of the system is available and therefore the values of the jump parameter are not accessible. It is a well known fact that in this setting the optimal nonlinear filter is infinite dimensional, which makes the linear filtering a natural numerically, treatable choice. The goal is to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the mean square estimation error. It is shown that an explicit analytical solution to this optimal filtering problem is obtained from the stationary solution associated to a certain Riccati equation. It is also shown that the problem can be formulated using a linear matrix inequalities (LMI) approach, which can be extended to consider convex polytopic uncertainties on the parameters of the possible modes of operation of the system and on the transition rate matrix of the Markov process. As far as the authors are aware of this is the first time that this stationary filtering problem (exact and robust versions) for LSMJP with no knowledge of the Markov jump parameters is considered in the literature. Finally, we illustrate the results with an example.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

In this paper we obtain the linear minimum mean square estimator (LMMSE) for discrete-time linear systems subject to state and measurement multiplicative noises and Markov jumps on the parameters. It is assumed that the Markov chain is not available. By using geometric arguments we obtain a Kalman type filter conveniently implementable in a recurrence form. The stationary case is also studied and a proof for the convergence of the error covariance matrix of the LMMSE to a stationary value under the assumption of mean square stability of the system and ergodicity of the associated Markov chain is obtained. It is shown that there exists a unique positive semi-definite solution for the stationary Riccati-like filter equation and, moreover, this solution is the limit of the error covariance matrix of the LMMSE. The advantage of this scheme is that it is very easy to implement and all calculations can be performed offline. (c) 2011 Elsevier Ltd. All rights reserved.

New Analytic Solution Related to the Richards, Philip, and Green-Ampt Equations for Infiltration

Based on physical laws of similarity, an analytic solution of the soil water potential form of the Richards equation was derived for water infiltration into a homogeneous sand. The derivation assumes a similarity between the soil water retention function and that of the soil water content profiles taken at fixed times. The new solution successfully described soil water content profiles experimentally measured for water infiltrating downward, upward, and horizontally into a homogeneous sand and agrees with that presented by Philip in 1957. The utility of this analysis is still to be verified, but it is expected to hold for soils that have a narrow pore-size distribution before wetting and that manifest a sharp increase of water content at the wetting front during infiltration. The effect of van Genuchten`s parameters alpha and n on the application of the solution to other porous media was investigated. The solution also improves and provides a more realistic description of the infiltration process than that pioneered by Green and Ampt in 1911.

Production and carbon allocation in a clonal Eucalyptus plantation with water and nutrient manipulations

We examined resource limitations on growth and carbon allocation in a fast-growing, clonal plantation of Eucalyptus grandis x urophylla in Brazil by characterizing responses to annual rainfall, and response to irrigation and fertililization for 2 years. Productivity measures included gross primary production (GPP), total belowground carbon allocation (TBCA), bole growth, and net ecosystem production (NEP). Replicate plots within a single plantation were established at the midpoint of the rotation (end of year 3), with treatments of no additional fertilization or irrigation, heavy fertilization (to remove any nutrient limitation), irrigation (to remove any water limitation), and irrigation plus fertilization. Rainfall was unusually high in the first year (1769mm) of the experiment, and control plots had high rates of GPP (6.64 kg C m(-2) year(-1)), TBCA (2.14 kg C m(-2) year(-1)), and bole growth (1.81 kg C m(-2) year). Irrigation increased each of these rates by 15-17%. The second year of the experiment had average rainfall (1210 mm), and lower rainfall decreased production in control plots by 46% (GPP), 52% (TBCA), and 40% (bole growth). Fertilization treatments had neglible effects. The response to irrigation was much greater in the drier year, with irrigated plots exceeding the production in control plots by 83% (GPP), 239% (TBCA), and 24% (bole growth). Even though the rate of irrigation ensured no water limitation to tree growth, the high rainfall year showed higher production in irrigated plots for both GPP (38% greater than in drier year) and bole growth (23% greater). Varying humidity and supplies of water led to a range in NEP of 0.8-2.7 kg C m(-2) year. This difference between control and irrigated treatments, combined with differences between drier and wetter years, indicated a strong response of these Eucalyptus trees to both water supply and atmospheric humidity during the dry season. The efficiency of converting light energy into fixed carbon ranged from a low of 0.027 mol C to a high of 0.060 mol C per mol of absorbed photosynthetically active radiation (APAR), and the efficiency of bolewood production ranged from 0.78 to 1.98 g wood per MJ of APAR. Irrigation increased the efficiency of wood production per unit of water used from 2.55 kg wood m(-3) in the rainfed plot to 3.51 kg m(-3) in irrigated plots. Detailed information on the response of C budgets to environmental conditions and resource supplies will be necessary for accurate predictions of plantation yields across years and landscapes. (V) 2007 Elsevier B.V. All rights reserved.

Evaluation of FAO Penman-Monteith and alternative methods for estimating reference evapotranspiration with missing data in Southern Ontario, Canada

Grass reference evapotranspiration (ETo) is an important agrometeorological parameter for climatological and hydrological studies, as well as for irrigation planning and management. There are several methods to estimate ETo, but their performance in different environments is diverse, since all of them have some empirical background. The FAO Penman-Monteith (FAD PM) method has been considered as a universal standard to estimate ETo for more than a decade. This method considers many parameters related to the evapotranspiration process: net radiation (Rn), air temperature (7), vapor pressure deficit (Delta e), and wind speed (U); and has presented very good results when compared to data from lysimeters Populated with short grass or alfalfa. In some conditions, the use of the FAO PM method is restricted by the lack of input variables. In these cases, when data are missing, the option is to calculate ETo by the FAD PM method using estimated input variables, as recommended by FAD Irrigation and Drainage Paper 56. Based on that, the objective of this study was to evaluate the performance of the FAO PM method to estimate ETo when Rn, Delta e, and U data are missing, in Southern Ontario, Canada. Other alternative methods were also tested for the region: Priestley-Taylor, Hargreaves, and Thornthwaite. Data from 12 locations across Southern Ontario, Canada, were used to compare ETo estimated by the FAD PM method with a complete data set and with missing data. The alternative ETo equations were also tested and calibrated for each location. When relative humidity (RH) and U data were missing, the FAD PM method was still a very good option for estimating ETo for Southern Ontario, with RMSE smaller than 0.53 mm day(-1). For these cases, U data were replaced by the normal values for the region and Delta e was estimated from temperature data. The Priestley-Taylor method was also a good option for estimating ETo when U and Delta e data were missing, mainly when calibrated locally (RMSE = 0.40 mm day(-1)). When Rn was missing, the FAD PM method was not good enough for estimating ETo, with RMSE increasing to 0.79 mm day(-1). When only T data were available, adjusted Hargreaves and modified Thornthwaite methods were better options to estimate ETo than the FAO) PM method, since RMSEs from these methods, respectively 0.79 and 0.83 mm day(-1), were significantly smaller than that obtained by FAO PM (RMSE = 1.12 mm day(-1). (C) 2009 Elsevier B.V. All rights reserved.

Modeling of transpiration reduction in van Genuchten-Mualem type soils

We derive an analytic expression for the matric flux potential (M) for van Genuchten-Mualem (VGM) type soils which can also be written in terms of a converging infinite series. Considering the first four terms of this series, the accuracy of the approximation was verified by comparing it to values of M estimated by numerical finite difference integration. Using values of the parameters for three soils from different texture classes, the proposed four-term approximation showed an almost perfect match with the numerical solution, except for effective saturations higher than 0.9. Including more terms reduced the discrepancy but also increased the complexity of the equation. The four-term equation can be used for most applications. Cases with special interest in nearly saturated soils should include more terms from the infinite series. A transpiration reduction function for use with the VGM equations is derived by combining the derived expression for M with a root water extraction model. The shape of the resulting reduction function and its dependency on the derivative of the soil hydraulic diffusivity D with respect to the soil water content theta is discussed. Positive and negative values of dD/d theta yield concave and convex or S-shaped reduction functions, respectively. On the basis of three data sets, the hydraulic properties of virtually all soils yield concave reduction curves. Such curves based solely on soil hydraulic properties do not account for the complex interactions between shoot growth, root growth, and water availability.

Changes in the genetic structure of Bacteria and microbial activity in an agricultural soil amended with tannery sludge

The application of tannery sludge to soils is a form of recycling; however, few studies have examined the impacts of this practice on soil microbial properties. We studied effects of two applications (2006 and 2007) of tannery sludge (with a low chromium content) on the structure of the bacterial community and on the microbial activity of soils. We fertilized an agricultural area in Rolandia, Parana state, Brazil with different doses of sludge based on total N content, which ranged from 0 to 1200 kg N ha(-1). Sludge remained on the soil surface for three months before being plowed. Soils were sampled seven times during the experiment. Bacterial community structure, assessed by denaturing gradient gel electrophoresis (DGGE), was modified by the application of tannery sludge. Soon after the first application, there was clear separation between the bacterial communities in different treatments, such that each dose of sludge was associated with a specific community. These differences remained until 300 days after application and also after the second sludge application, but 666 days after the beginning of the experiment no differences were found in the bacterial communities of the lowest doses and the control. The principal response curve (PRC) analysis showed that the first sludge application strongly stimulated biological activity even 300 days after application. The second application also stimulated activity, but at a lower magnitude and for a shorter time, given that 260 days after the second application there was no difference in biological activity among treatments. PRC also showed that the properties most influenced by the application of tannery sludge were enzymatic activities related to N cycling (asparaginase and urease). The redundancy analysis (RDA) showed that tannery sludge`s influence on microbial activity is mainly related to increases in inorganic N and soil pH. Results showed that changes in the structure of the bacterial community in the studied soils were directly related to changes of their biological activity. (C) 2010 Elsevier Ltd. All rights reserved.

Relating MODIS vegetation index time-series with structure, light absorption and stem production of fast-growing Eucalyptus plantations

By allowing the estimation of forest structural and biophysical characteristics at different temporal and spatial scales, remote sensing may contribute to our understanding and monitoring of planted forests. Here, we studied 9-year time-series of the Normalized Difference Vegetation Index (NDVI) from the Moderate Resolution Imaging Spectroradiometer (MODIS) on a network of 16 stands in fast-growing Eucalyptus plantations in Sao Paulo State, Brazil. We aimed to examine the relationships between NDVI time-series spanning entire rotations and stand structural characteristics (volume, dominant height, mean annual increment) in these simple forest ecosystems. Our second objective was to examine spatial and temporal variations of light use efficiency for wood production, by comparing time-series of Absorbed Photosynthetically Active Radiation (APAR) with inventory data. Relationships were calibrated between the NDVI and the fractions of intercepted diffuse and direct radiation, using hemispherical photographs taken on the studied stands at two seasons. APAR was calculated from the NDVI time-series using these relationships. Stem volume and dominant height were strongly correlated with summed NDVI values between planting date and inventory date. Stand productivity was correlated with mean NDVI values. APAR during the first 2 years of growth was variable between stands and was well correlated with stem wood production (r(2) = 0.78). In contrast, APAR during the following years was less variable and not significantly correlated with stem biomass increments. Production of wood per unit of absorbed light varied with stand age and with site index. In our study, a better site index was accompanied both by increased APAR during the first 2 years of growth and by higher light use efficiency for stem wood production during the whole rotation. Implications for simple process-based modelling are discussed. (C) 2009 Elsevier B.V. All rights reserved.

Components of Surface Charge in Tropical Soils With Contrasting Mineralogies

Study of surface electric charges of soil colloids helps in understanding the physicochemical phenomena that influence the capacity of retaining nutrients and their availability to plants. The structural charge (sigma(0), (min)), the variable charge (sigma(q, min)), and the organic matter (OM) charge (sigma(total) (OM)) of 12 tropical soils with contrasting mineralogies were evaluated based on the difference of selectivity for Cs(+) and Li(+) between the functional ionizable surfaces groups and the mineral 2:1 siloxane surface. Soils were divided into three groups: G1, soils with a predominance of kaolinite and gibbsite in the clay fraction; G2, soils with hydroxy-interlayered 2:1 minerals; and G3, soils with smectite but without hydroxy-interlayered 2:1 minerals. The Cs absorption method was efficient for detecting the charge components in tropical soils. The mineral structural charge contributed 11% and 16%, 28% and 31%, and 52% and 59% of total soil charge of A and B horizons of soils from groups G 1, G2, and G3, respectively. On the other hand, OM contributed 53% and 37%, 48% and 41%, and 21% and 20% of total charge for the same samples, respectively, In highly weathered soils of group G I and, to a lesser extent, in soils in group G2, surface charges depended mainly on their variable components, resulting from the OM (sigma(toal) (OM)), as well as from imperfections found in 1:1 minerals (sigma(q, min)). The importance of OM in determining the magnitude of electric charges in humid tropical soils is highlighted.