An Iterative Procedure for Solving Nonsmooth Generalized Equation

2000 Mathematics Subject Classification: 47H04, 65K10.

Steffensen Methods for Solving Generalized Equations

2000 Mathematics Subject Classification: 65G99, 65K10, 47H04.

Assessing the above-ground biomass of a complex tropical rainforest using a canopy crane

Current estimates of the total biomass in tropical rainforests vary considerably; this is due in large part to the different approaches that are used to calculate biomass. In this study we have used a canopy crane to measure the tree architectures in a 1 ha plot of complex mesophyll vine forest at Cape Tribulation, Australia. Methods were developed to measure and calculate the crown and stem biomass of six major species of tree and palm (Alstonia scholaris (Apocynaceae), Cleistanthus myrianthus (Euphorbiaceae), Endiandra microneura (Lauraceae), Myristica insipida (Myristicaceae), Acmena graveolens (Myrtaceae), Normanbya normanbyi (Arecaceae)) using the unique access provided by the crane. This has allowed the first non-destructive biomass estimate to be carried out for a forest of this type. Allometric equations which relate tree biomass to the measured variable 'diameter at breast height' were developed for the six species, and a general equation was also developed for trees on the plot. The general equation was similar in form to equations developed for tropical rainforests in Brazil and New Guinea. The species equations were applied at the level of families, the generalized equation was applied to the remaining species which allowed the biomass of a total of 680 trees to be calculated. This has provided a current estimate of 270 t ha-1 above-ground biomass at the Australian Canopy Crane site; a value comparable to lowland rainforests in Panama and French Guiana. Using the same tree database seven alternative allometric equations (literature equations for tropical rainforests) were used to calculate the site biomass, the range was large (252-446 t ha-1) with only three equations providing estimates within 34 t ha-1 (12.5%) of the site value. Our use of multiple species-specific allometric equations has provided a site estimate only slightly larger (1%) than that obtained using allometric equations developed specifically for tropical wet rainforests. We have demonstrated that it is possible to non-destructively measure the biomass in a complex forest using an on-site canopy crane. In conjunction the development of crown maps and a detailed tree architecture database allows changes in forest structure to be followed quantitatively. © 2007 Ecological Society of Australia.

Desenvolvimento de equações para estimativa do VO2PICO pelo teste de 9 minutos

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On the development of advanced techniques for mixed-elastohydrodynamic lubrification modelling of journal and sliding bearing systems.

The present thesis is focused on the development of a thorough mathematical modelling and computational solution framework aimed at the numerical simulation of journal and sliding bearing systems operating under a wide range of lubrication regimes (mixed, elastohydrodynamic and full film lubrication regimes) and working conditions (static, quasi-static and transient conditions). The fluid flow effects have been considered in terms of the Isothermal Generalized Equation of the Mechanics of the Viscous Thin Films (Reynolds equation), along with the massconserving p-Ø Elrod-Adams cavitation model that accordingly ensures the so-called JFO complementary boundary conditions for fluid film rupture. The variation of the lubricant rheological properties due to the viscous-pressure (Barus and Roelands equations), viscous-shear-thinning (Eyring and Carreau-Yasuda equations) and density-pressure (Dowson-Higginson equation) relationships have also been taken into account in the overall modelling. Generic models have been derived for the aforementioned bearing components in order to enable their applications in general multibody dynamic systems (MDS), and by including the effects of angular misalignments, superficial geometric defects (form/waviness deviations, EHL deformations, etc.) and axial motion. The bearing exibility (conformal EHL) has been incorporated by means of FEM model reduction (or condensation) techniques. The macroscopic in fluence of the mixedlubrication phenomena have been included into the modelling by the stochastic Patir and Cheng average ow model and the Greenwood-Williamson/Greenwood-Tripp formulations for rough contacts. Furthermore, a deterministic mixed-lubrication model with inter-asperity cavitation has also been proposed for full-scale simulations in the microscopic (roughness) level. According to the extensive mathematical modelling background established, three significant contributions have been accomplished. Firstly, a general numerical solution for the Reynolds lubrication equation with the mass-conserving p - Ø cavitation model has been developed based on the hybridtype Element-Based Finite Volume Method (EbFVM). This new solution scheme allows solving lubrication problems with complex geometries to be discretized by unstructured grids. The numerical method was validated in agreement with several example cases from the literature, and further used in numerical experiments to explore its exibility in coping with irregular meshes for reducing the number of nodes required in the solution of textured sliding bearings. Secondly, novel robust partitioned techniques, namely: Fixed Point Gauss-Seidel Method (PGMF), Point Gauss-Seidel Method with Aitken Acceleration (PGMA) and Interface Quasi-Newton Method with Inverse Jacobian from Least-Squares approximation (IQN-ILS), commonly adopted for solving uid-structure interaction problems have been introduced in the context of tribological simulations, particularly for the coupled calculation of dynamic conformal EHL contacts. The performance of such partitioned methods was evaluated according to simulations of dynamically loaded connecting-rod big-end bearings of both heavy-duty and high-speed engines. Finally, the proposed deterministic mixed-lubrication modelling was applied to investigate the in fluence of the cylinder liner wear after a 100h dynamometer engine test on the hydrodynamic pressure generation and friction of Twin-Land Oil Control Rings.

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.

Fluidization characteristics of moist food particles

Changes in fluidization behaviour of green peas particulates with change in moisture content during drying were investigated using a fluidized bed dryer. All drying experiments were conducted at 50 + 2 0C and 13 + 2 % RH using a heat pump dehumidifier system. Fluidization experiments were undertaken for the bedheights of 100, 80, 60 and 40 mm and at 10 moisture content levels. Fluidization behaviour was best fitted to the linear model of Umf = A + B m. A generalized model was also formulated using the height variation. Also generalized equation and Ergun equation was used to compare minimum fluidization velocity. Copyright ©2006 The Berkeley Electronic Press. All rights reserved.

Time scale analysis for fluidizedbedmeltgranulation III: binder solidification rate

In series I and II of this study ([Chua et al., 2010a] and [Chua et al., 2010b]), we discussed the time scale of granule–granule collision, droplet–granule collision and droplet spreading in Fluidized Bed Melt Granulation (FBMG). In this third one, we consider the rate at which binder solidifies. Simple analytical solution, based on classical formulation for conduction across a semi-infinite slab, was used to obtain a generalized equation for binder solidification time. A multi-physics simulation package (Comsol) was used to predict the binder solidification time for various operating conditions usually considered in FBMG. The simulation results were validated with experimental temperature data obtained with a high speed infrared camera during solidification of ‘macroscopic’ (mm scale) droplets. For the range of microscopic droplet size and operating conditions considered for a FBMG process, the binder solidification time was found to fall approximately between 10-3 and 10-1 s. This is the slowest compared to the other three major FBMG microscopic events discussed in this series (granule–granule collision, granule–droplet collision and droplet spreading).

Uniform Convergence of the Newton Method for Aubin Continuous Maps

* This work was supported by National Science Foundation grant DMS 9404431.

Acceleration of Convergence in Dontchev’s Iterative Method for Solving Variational Inclusions

2000 Mathematics Subject Classification: 47H04, 65K10.

Modeling height-diameter relationship in pinus pinaster ait. in the forest intervention zone of Lomba, NE-Portugal

In this work, the relationship between diameter at breast height (d) and total height (h) of individual-tree was modeled with the aim to establish provisory height-diameter (h-d) equations for maritime pine (Pinus pinaster Ait.) stands in the Lomba ZIF, Northeast Portugal. Using data collected locally, several local and generalized h-d equations from the literature were tested and adaptations were also considered. Model fitting was conducted by using usual nonlinear least squares (nls) methods. The best local and generalized models selected, were also tested as mixed models applying a first-order conditional expectation (FOCE) approximation procedure and maximum likelihood methods to estimate fixed and random effects. For the calibration of the mixed models and in order to be consistent with the fitting procedure, the FOCE method was also used to test different sampling designs. The results showed that the local h-d equations with two parameters performed better than the analogous models with three parameters. However a unique set of parameter values for the local model can not be used to all maritime pine stands in Lomba ZIF and thus, a generalized model including covariates from the stand, in addition to d, was necessary to obtain an adequate predictive performance. No evident superiority of the generalized mixed model in comparison to the generalized model with nonlinear least squares parameters estimates was observed. On the other hand, in the case of the local model, the predictive performance greatly improved when random effects were included. The results showed that the mixed model based in the local h-d equation selected is a viable alternative for estimating h if variables from the stand are not available. Moreover, it was observed that it is possible to obtain an adequate calibrated response using only 2 to 5 additional h-d measurements in quantile (or random) trees from the distribution of d in the plot (stand). Balancing sampling effort, accuracy and straightforwardness in practical applications, the generalized model from nls fit is recommended. Examples of applications of the selected generalized equation to the forest management are presented, namely how to use it to complete missing information from forest inventory and also showing how such an equation can be incorporated in a stand-level decision support system that aims to optimize the forest management for the maximization of wood volume production in Lomba ZIF maritime pine stands.

A numerical analysis of generalized Boussinesq-type equation using continuos/discontinuous FEM

An improved class of Boussinesq systems of an arbitrary order using a wave surface elevation and velocity potential formulation is derived. Dissipative effects and wave generation due to a time-dependent varying seabed are included. Thus, high-order source functions are considered. For the reduction of the system order and maintenance of some dispersive characteristics of the higher-order models, an extra O(mu 2n+2) term (n ??? N) is included in the velocity potential expansion. We introduce a nonlocal continuous/discontinuous Galerkin FEM with inner penalty terms to calculate the numerical solutions of the improved fourth-order models. The discretization of the spatial variables is made using continuous P2 Lagrange elements. A predictor-corrector scheme with an initialization given by an explicit RungeKutta method is also used for the time-variable integration. Moreover, a CFL-type condition is deduced for the linear problem with a constant bathymetry. To demonstrate the applicability of the model, we considered several test cases. Improved stability is achieved.

Local thermodynamics and the generalized Gibbs-Duhem equation in systems with long-range interactions

The local thermodynamics of a system with long-range interactions in d dimensions is studied using the mean-field approximation. Long-range interactions are introduced through pair interaction potentials that decay as a power law in the interparticle distance. We compute the local entropy, Helmholtz free energy, and grand potential per particle in the microcanonical, canonical, and grand canonical ensembles, respectively. From the local entropy per particle we obtain the local equation of state of the system by using the condition of local thermodynamic equilibrium. This local equation of state has the form of the ideal gas equation of state, but with the density depending on the potential characterizing long-range interactions. By volume integration of the relation between the different thermodynamic potentials at the local level, we find the corresponding equation satisfied by the potentials at the global level. It is shown that the potential energy enters as a thermodynamic variable that modifies the global thermodynamic potentials. As a result, we find a generalized Gibbs-Duhem equation that relates the potential energy to the temperature, pressure, and chemical potential. For the marginal case where the power of the decaying interaction potential is equal to the dimension of the space, the usual Gibbs-Duhem equation is recovered. As examples of the application of this equation, we consider spatially uniform interaction potentials and the self-gravitating gas. We also point out a close relationship with the thermodynamics of small systems.

On the Hamilton-Jacobi equation in the framework of generalized functions

In this work we study, in the framework of Colombeau`s generalized functions, the Hamilton-Jacobi equation with a given initial condition. We have obtained theorems on existence of solutions and in some cases uniqueness. Our technique is adapted from the classical method of characteristics with a wide use of generalized functions. We were led also to obtain some general results on invertibility and also on ordinary differential equations of such generalized functions. (C) 2011 Elsevier Inc. All rights reserved.

Generalized solutions of a nonlinear parabolic equation with generalized functions as initial data

In [H. Brezis, A. Friedman, Nonlinear parabolic equations involving measures as initial conditions, J. Math. Pure Appl. (9) (1983) 73-97.] Brezis and Friedman prove that certain nonlinear parabolic equations, with the delta-measure as initial data, have no solution. However in [J.F. Colombeau, M. Langlais, Generalized solutions of nonlinear parabolic equations with distributions as initial conditions, J. Math. Anal. Appl (1990) 186-196.] Colombeau and Langlais prove that these equations have a unique solution even if the delta-measure is substituted by any Colombeau generalized function of compact support. Here we generalize Colombeau and Langlais` result proving that we may take any generalized function as the initial data. Our approach relies on recent algebraic and topological developments of the theory of Colombeau generalized functions and results from [J. Aragona, Colombeau generalized functions on quasi-regular sets, Publ. Math. Debrecen (2006) 371-399.]. (C) 2009 Elsevier Ltd. All rights reserved.