Front tracking with moving-least-squares surfaces

The representation of interfaces by means of the algebraic moving-least-squares (AMLS) technique is addressed. This technique, in which the interface is represented by an unconnected set of points, is interesting for evolving fluid interfaces since there is]to surface connectivity. The position of the surface points can thus be updated without concerns about the quality of any surface triangulation. We introduce a novel AMLS technique especially designed for evolving-interfaces applications that we denote RAMLS (for Robust AMLS). The main advantages with respect to previous AMLS techniques are: increased robustness, computational efficiency, and being free of user-tuned parameters. Further, we propose a new front-tracking method based on the Lagrangian advection of the unconnected point set that defines the RAMLS surface. We assume that a background Eulerian grid is defined with some grid spacing h. The advection of the point set makes the surface evolve in time. The point cloud can be regenerated at any time (in particular, we regenerate it each time step) by intersecting the gridlines with the evolved surface, which guarantees that the density of points on the surface is always well balanced. The intersection algorithm is essentially a ray-tracing algorithm, well-studied in computer graphics, in which a line (ray) is traced so as to detect all intersections with a surface. Also, the tracing of each gridline is independent and can thus be performed in parallel. Several tests are reported assessing first the accuracy of the proposed RAMLS technique, and then of the front-tracking method based on it. Comparison with previous Eulerian, Lagrangian and hybrid techniques encourage further development of the proposed method for fluid mechanics applications. (C) 2008 Elsevier Inc. All rights reserved.

A discontinuous-Galerkin-based immersed boundary method

A numerical method to approximate partial differential equations on meshes that do not conform to the domain boundaries is introduced. The proposed method is conceptually simple and free of user-defined parameters. Starting with a conforming finite element mesh, the key ingredient is to switch those elements intersected by the Dirichlet boundary to a discontinuous-Galerkin approximation and impose the Dirichlet boundary conditions strongly. By virtue of relaxing the continuity constraint at those elements. boundary locking is avoided and optimal-order convergence is achieved. This is shown through numerical experiments in reaction-diffusion problems. Copyright (c) 2008 John Wiley & Sons, Ltd.

An implicit technique for solving 3D low Reynolds number moving free surface flows

This paper describes the development of an implicit finite difference method for solving transient three-dimensional incompressible free surface flows. To reduce the CPU time of explicit low-Reynolds number calculations, we have combined a projection method with an implicit technique for treating the pressure on the free surface. The projection method is employed to uncouple the velocity and the pressure fields, allowing each variable to be solved separately. We employ the normal stress condition on the free surface to derive an implicit technique for calculating the pressure at the free surface. Numerical results demonstrate that this modification is essential for the construction of methods that are more stable than those provided by discretizing the free surface explicitly. In addition, we show that the proposed method can be applied to viscoelastic fluids. Numerical results include the simulation of jet buckling and extrudate swell for Reynolds numbers in the range [0.01, 0.5]. (C) 2008 Elsevier Inc. All rights reserved.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

Log-Burr XII regression models with censored data

In survival analysis applications, the failure rate function may frequently present a unimodal shape. In such case, the log-normal or log-logistic distributions are used. In this paper, we shall be concerned only with parametric forms, so a location-scale regression model based on the Burr XII distribution is proposed for modeling data with a unimodal failure rate function as an alternative to the log-logistic regression model. Assuming censored data, we consider a classic analysis, a Bayesian analysis and a jackknife estimator for the parameters of the proposed model. For different parameter settings, sample sizes and censoring percentages, various simulation studies are performed and compared to the performance of the log-logistic and log-Burr XII regression models. Besides, we use sensitivity analysis to detect influential or outlying observations, and residual analysis is used to check the assumptions in the model. Finally, we analyze a real data set under log-Buff XII regression models. (C) 2008 Published by Elsevier B.V.

Lot sizing and furnace scheduling in small foundries

A lot sizing and scheduling problem prevalent in small market-driven foundries is studied. There are two related decision levels: (I the furnace scheduling of metal alloy production, and (2) moulding machine planning which specifies the type and size of production lots. A mixed integer programming (MIP) formulation of the problem is proposed, but is impractical to solve in reasonable computing time for non-small instances. As a result, a faster relax-and-fix (RF) approach is developed that can also be used on a rolling horizon basis where only immediate-term schedules are implemented. As well as a MIP method to solve the basic RF approach, three variants of a local search method are also developed and tested using instances based on the literature. Finally, foundry-based tests with a real-order book resulted in a very substantial reduction of delivery delays and finished inventory, better use of capacity, and much faster schedule definition compared to the foundry`s own practice. (c) 2006 Elsevier Ltd. All rights reserved.

Entropy-Based Approach to Analyze and Classify Mineral Aggregates

This paper presents an automatic method to detect and classify weathered aggregates by assessing changes of colors and textures. The method allows the extraction of aggregate features from images and the automatic classification of them based on surface characteristics. The concept of entropy is used to extract features from digital images. An analysis of the use of this concept is presented and two classification approaches, based on neural networks architectures, are proposed. The classification performance of the proposed approaches is compared to the results obtained by other algorithms (commonly considered for classification purposes). The obtained results confirm that the presented method strongly supports the detection of weathered aggregates.

An unstructured CVFEM and moving interface algorithm for non-Newtonian Hele-Shaw flows in injection molding

Purpose - The purpose of this paper is to develop a novel unstructured simulation approach for injection molding processes described by the Hele-Shaw model. Design/methodology/approach - The scheme involves dual dynamic meshes with active and inactive cells determined from an initial background pointset. The quasi-static pressure solution in each timestep for this evolving unstructured mesh system is approximated using a control volume finite element method formulation coupled to a corresponding modified volume of fluid method. The flow is considered to be isothermal and non-Newtonian. Findings - Supporting numerical tests and performance studies for polystyrene described by Carreau, Cross, Ellis and Power-law fluid models are conducted. Results for the present method are shown to be comparable to those from other methods for both Newtonian fluid and polystyrene fluid injected in different mold geometries. Research limitations/implications - With respect to the methodology, the background pointset infers a mesh that is dynamically reconstructed here, and there are a number of efficiency issues and improvements that would be relevant to industrial applications. For instance, one can use the pointset to construct special bases and invoke a so-called ""meshless"" scheme using the basis. This would require some interesting strategies to deal with the dynamic point enrichment of the moving front that could benefit from the present front treatment strategy. There are also issues related to mass conservation and fill-time errors that might be addressed by introducing suitable projections. The general question of ""rate of convergence"" of these schemes requires analysis. Numerical results here suggest first-order accuracy and are consistent with the approximations made, but theoretical results are not available yet for these methods. Originality/value - This novel unstructured simulation approach involves dual meshes with active and inactive cells determined from an initial background pointset: local active dual patches are constructed ""on-the-fly"" for each ""active point"" to form a dynamic virtual mesh of active elements that evolves with the moving interface.

Clustering and diffusion in a symplectic map lattice with non-local coupling

We study a symplectic chain with a non-local form of coupling by means of a standard map lattice where the interaction strength decreases with the lattice distance as a power-law, in Such a way that one can pass continuously from a local (nearest-neighbor) to a global (mean-field) type of coupling. We investigate the formation of map clusters, or spatially coherent structures generated by the system dynamics. Such clusters are found to be related to stickiness of chaotic phase-space trajectories near periodic island remnants, and also to the behavior of the diffusion coefficient. An approximate two-dimensional map is derived to explain some of the features of this connection. (C) 2008 Elsevier Ltd. All rights reserved.

Transport control in fusion plasmas by changing electric and magnetic field spatial profiles

For magnetically confined plasmas in tokamaks, we have numerically investigated how Lagrangian chaos at the plasma edge affects the plasma confinement. Initially, we have considered the chaotic motion of particles in an equilibrium electric field with a monotonic radial profile perturbed by drift waves. We have showed that an effective transport barrier may be created at the plasma edge by modifying the electric field radial profile. In the second place, we have obtained escape patterns and magnetic footprints of chaotic magnetic field lines in the region near a tokamak wall with resonant modes due to the action of an ergodic magnetic limiter. For monotonic plasma current density profiles we have obtained distributions of field line connections to the wall and line escape channels with the same spatial pattern as the magnetic footprints on the tokamak walls. (c) 2008 Elsevier B.V. All rights reserved.

A scenario for torus T(2) destruction via a global bifurcation

We show a scenario of a two-frequeney torus breakdown, in which a global bifurcation occurs due to the collision of a quasi-periodic torus T(2) with saddle points, creating a heteroclinic saddle connection. We analyze the geometry of this torus-saddle collision by showing the local dynamics and the invariant manifolds (global dynamics) of the saddle points. Moreover, we present detailed evidences of a heteroclinic saddle-focus orbit responsible for the type-if intermittency induced by this global bifurcation. We also characterize this transition to chaos by measuring the Lyapunov exponents and the scaling laws. (C) 2007 Elsevier Ltd. All rights reserved.

Suppressing grazing chaos in impacting system by structural nonlinearity

In this note we investigate the influence of structural nonlinearity of a simple cantilever beam impacting system on its dynamic responses close to grazing incidence by a means of numerical simulation. To obtain a clear picture of this effect we considered two systems exhibiting impacting motion, where the primary stiffness is either linear (piecewise linear system) or nonlinear (piecewise nonlinear system). Two systems were studied by constructing bifurcation diagrams, basins of attractions, Lyapunov exponents and parameter plots. In our analysis we focused on the grazing transitions from no impact to impact motion. We observed that the dynamic responses of these two similar systems are qualitatively different around the grazing transitions. For the piecewise linear system, we identified on the parameter space a considerable region with chaotic behaviour, while for the piecewise nonlinear system we found just periodic attractors. We postulate that the structural nonlinearity of the cantilever impacting beam suppresses chaos near grazing. (C) 2007 Elsevier Ltd. All rights reserved.

Statistical treatment of misalignments in particle accelerators

To know how much misalignment is tolerable for a particle accelerator is an important input for the design of these machines. In particle accelerators the beam must be guided and focused using bending magnets and magnetic lenses, respectively. The alignment of the lenses along a transport line aims to ensure that the beam passes through their optical axes and represents a critical point in the assembly of the machine. There are more and more accelerators in the world, many of which are very small machines. Because the existing literature and programs are mostly targeted for large machines. in this work we describe a method suitable for small machines. This method consists in determining statistically the alignment tolerance in a set of lenses. Differently from the methods used in standard simulation codes for particle accelerators, the statistical method we propose makes it possible to evaluate particle losses as a function of the alignment accuracy of the optical elements in a transport line. Results for 100 key electrons, on the 3.5-m long conforming beam stage of the IFUSP Microtron are presented as an example of use. (C) 2010 Elsevier B.V. All rights reserved.

Continuum, Discrete, and Explicit Solvation Models for Describing the Low-Lying Absorption Spectrum of the Pterin Acid in Aqueous Environment

The absorption spectrum of the acid form of pterin in water was investigated theoretically. Different procedures using continuum, discrete, and explicit models were used to include the solvation effect on the absorption spectrum, characterized by two bands. The discrete and explicit models used Monte Carlo simulation to generate the liquid structure and time-dependent density functional theory (B3LYP/6-31G+(d)) to obtain the excitation energies. The discrete model failed to give the correct qualitative effect on the second absorption band. The continuum model, in turn, has given a correct qualitative picture and a semiquantitative description. The explicit use of 29 solvent molecules, forming a hydration shell of 6 angstrom, embedded in the electrostatic field of the remaining solvent molecules, gives absorption transitions at 3.67 and 4.59 eV in excellent agreement with the S(0)-S(1) and S(0)-S(2) absorption bands at of 3.66 and 4.59 eV, respectively, that characterize the experimental spectrum of pterin in water environment. (C) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 110: 2371-2377, 2010

CRITICAL BEHAVIOR AND THRESHOLD OF COEXISTENCE OF A PREDATOR-PREY STOCHASTIC MODEL IN A 2D LATTICE

We investigate the critical behavior of a stochastic lattice model describing a predator-prey system. By means of Monte Carlo procedure we simulate the model defined on a regular square lattice and determine the threshold of species coexistence, that is, the critical phase boundaries related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. A finite size scaling analysis is employed to determine the order parameter, order parameter fluctuations, correlation length and the critical exponents. Our numerical results for the critical exponents agree with those of the directed percolation universality class. We also check the validity of the hyperscaling relation and present the data collapse curves.