A Robust, Fully Adaptive Hybrid Level-Set/Front-Tracking Method for Two-Phase Flows with an Accurate Surface Tension Computation

We present a variable time step, fully adaptive in space, hybrid method for the accurate simulation of incompressible two-phase flows in the presence of surface tension in two dimensions. The method is based on the hybrid level set/front-tracking approach proposed in [H. D. Ceniceros and A. M. Roma, J. Comput. Phys., 205, 391400, 2005]. Geometric, interfacial quantities are computed from front-tracking via the immersed-boundary setting while the signed distance (level set) function, which is evaluated fast and to machine precision, is used as a fluid indicator. The surface tension force is obtained by employing the mixed Eulerian/Lagrangian representation introduced in [S. Shin, S. I. Abdel-Khalik, V. Daru and D. Juric, J. Comput. Phys., 203, 493-516, 2005] whose success for greatly reducing parasitic currents has been demonstrated. The use of our accurate fluid indicator together with effective Lagrangian marker control enhance this parasitic current reduction by several orders of magnitude. To resolve accurately and efficiently sharp gradients and salient flow features we employ dynamic, adaptive mesh refinements. This spatial adaption is used in concert with a dynamic control of the distribution of the Lagrangian nodes along the fluid interface and a variable time step, linearly implicit time integration scheme. We present numerical examples designed to test the capabilities and performance of the proposed approach as well as three applications: the long-time evolution of a fluid interface undergoing Rayleigh-Taylor instability, an example of bubble ascending dynamics, and a drop impacting on a free interface whose dynamics we compare with both existing numerical and experimental data.

Wavelets And Adaptive Grids For The Discontinuous Galerkin Method

In this paper, space adaptivity is introduced to control the error in the numerical solution of hyperbolic systems of conservation laws. The reference numerical scheme is a new version of the discontinuous Galerkin method, which uses an implicit diffusive term in the direction of the streamlines, for stability purposes. The decision whether to refine or to unrefine the grid in a certain location is taken according to the magnitude of wavelet coefficients, which are indicators of local smoothness of the numerical solution. Numerical solutions of the nonlinear Euler equations illustrate the efficiency of the method. © Springer 2005.

Novel method for measuring nanofriction by atomic force microscope

The authors describe a novel approach to the measurement of nanofriction, and demonstrate the application of the method by measurement of the coefficient of friction for diamondlike carbon (DLC) on DLC, Si on DLC, and Si on Si surfaces. The technique employs an atomic force microscope in a mode in which the tip moves only in the z (vertical) direction and the sample surface is sloped. As the tip moves vertically on the sloped surface, lateral tip slipping occurs, allowing the cantilever vertical deflection and the frictional (lateral) force to be monitored as a function of tip vertical deflection. The advantage of the approach is that cantilever calibration to obtain its spring constants is not necessary. Using this method, the authors have measured friction coefficients, for load range 0 < L M 6 mu N, of 0.047 +/- 0.002 for Si on Si, 0.0173 +/- 0.0009 for Si on DLC, and 0.0080 +/- 0.0005 for DLC on DLC. For load range 9 < L < 13 mu N, the DLC on DLC coefficient of friction increased to 0.051 +/- 0.003. (C) 2008 American Vacuum Society.

The natural force density method for the shape finding of taut structures

This work presents, with the aid of the natural approach, an extension of the force density method for the initial shape finding of cable and membrane structures, which leads to the solution of a system of linear equations. This method, here called the natural force density method, preserves the linearity which characterizes the original force density method. At the same time, it overcomes the difficulties that the original procedure presents to cope with irregular triangular finite element meshes. Furthermore, if this method is applied iteratively in the lines prescribed herewith, it leads to a viable initial configuration with a uniform, isotropic plane Cauchy stress state. This means that a minimal surface for the membrane can be achieved through a succession of equilibrated configurations. Several numerical examples illustrate the simplicity and robustness of the method. (C) 2008 Elsevier B.V. All rights reserved.

A flexible method for rapid force computation in elliptical magnets

The design of open-access elliptical cross-section magnet systems has recently come under consideration. Obtaining values for the forces generated within these unusual magnets is important to progress the designs towards feasible instruments. This paper presents a novel and flexible method for the rapid computation of forces within elliptical magnets. The method is demonstrated by the analysis of a clinical magnetic resonance imaging magnet of elliptical cross-section and open design. The analysis reveals the non-symmetric nature of the generated Maxwell forces, which are an important consideration, particularly in the design of superconducting systems.

A new wavelet-based adaptive method for solving population balance equations

A new wavelet-based adaptive framework for solving population balance equations (PBEs) is proposed in this work. The technique is general, powerful and efficient without the need for prior assumptions about the characteristics of the processes. Because there are steeply varying number densities across a size range, a new strategy is developed to select the optimal order of resolution and the collocation points based on an interpolating wavelet transform (IWT). The proposed technique has been tested for size-independent agglomeration, agglomeration with a linear summation kernel and agglomeration with a nonlinear kernel. In all cases, the predicted and analytical particle size distributions (PSDs) are in excellent agreement. Further work on the solution of the general population balance equations with nucleation, growth and agglomeration and the solution of steady-state population balance equations will be presented in this framework. (C) 2002 Elsevier Science B.V. All rights reserved.

Bid definition method for electricity markets based on an adaptive multiagent system

Electricity markets are complex environments with very particular characteristics. MASCEM is a market simulator developed to allow deep studies of the interactions between the players that take part in the electricity market negotiations. This paper presents a new proposal for the definition of MASCEM players’ strategies to negotiate in the market. The proposed methodology is multiagent based, using reinforcement learning algorithms to provide players with the capabilities to perceive the changes in the environment, while adapting their bids formulation according to their needs, using a set of different techniques that are at their disposal. Each agent has the knowledge about a different method for defining a strategy for playing in the market, the main agent chooses the best among all those, and provides it to the market player that requests, to be used in the market. This paper also presents a methodology to manage the efficiency/effectiveness balance of this method, to guarantee that the degradation of the simulator processing times takes the correct measure.

An adaptive multiscale method for density-driven instabilities

Accurate modeling of flow instabilities requires computational tools able to deal with several interacting scales, from the scale at which fingers are triggered up to the scale at which their effects need to be described. The Multiscale Finite Volume (MsFV) method offers a framework to couple fine-and coarse-scale features by solving a set of localized problems which are used both to define a coarse-scale problem and to reconstruct the fine-scale details of the flow. The MsFV method can be seen as an upscaling-downscaling technique, which is computationally more efficient than standard discretization schemes and more accurate than traditional upscaling techniques. We show that, although the method has proven accurate in modeling density-driven flow under stable conditions, the accuracy of the MsFV method deteriorates in case of unstable flow and an iterative scheme is required to control the localization error. To avoid large computational overhead due to the iterative scheme, we suggest several adaptive strategies both for flow and transport. In particular, the concentration gradient is used to identify a front region where instabilities are triggered and an accurate (iteratively improved) solution is required. Outside the front region the problem is upscaled and both flow and transport are solved only at the coarse scale. This adaptive strategy leads to very accurate solutions at roughly the same computational cost as the non-iterative MsFV method. In many circumstances, however, an accurate description of flow instabilities requires a refinement of the computational grid rather than a coarsening. For these problems, we propose a modified iterative MsFV, which can be used as downscaling method (DMsFV). Compared to other grid refinement techniques the DMsFV clearly separates the computational domain into refined and non-refined regions, which can be treated separately and matched later. This gives great flexibility to employ different physical descriptions in different regions, where different equations could be solved, offering an excellent framework to construct hybrid methods.

Identifying quantitative operation principles in metabolic pathways: a systematic method for searching feasible enzyme activity patterns leading to cellular adaptive responses

Background: Optimization methods allow designing changes in a system so that specific goals are attained. These techniques are fundamental for metabolic engineering. However, they are not directly applicable for investigating the evolution of metabolic adaptation to environmental changes. Although biological systems have evolved by natural selection and result in well-adapted systems, we can hardly expect that actual metabolic processes are at the theoretical optimum that could result from an optimization analysis. More likely, natural systems are to be found in a feasible region compatible with global physiological requirements. Results: We first present a new method for globally optimizing nonlinear models of metabolic pathways that are based on the Generalized Mass Action (GMA) representation. The optimization task is posed as a nonconvex nonlinear programming (NLP) problem that is solved by an outer- approximation algorithm. This method relies on solving iteratively reduced NLP slave subproblems and mixed-integer linear programming (MILP) master problems that provide valid upper and lower bounds, respectively, on the global solution to the original NLP. The capabilities of this method are illustrated through its application to the anaerobic fermentation pathway in Saccharomyces cerevisiae. We next introduce a method to identify the feasibility parametric regions that allow a system to meet a set of physiological constraints that can be represented in mathematical terms through algebraic equations. This technique is based on applying the outer-approximation based algorithm iteratively over a reduced search space in order to identify regions that contain feasible solutions to the problem and discard others in which no feasible solution exists. As an example, we characterize the feasible enzyme activity changes that are compatible with an appropriate adaptive response of yeast Saccharomyces cerevisiae to heat shock Conclusion: Our results show the utility of the suggested approach for investigating the evolution of adaptive responses to environmental changes. The proposed method can be used in other important applications such as the evaluation of parameter changes that are compatible with health and disease states.

An Hp-Adaptive Hierarchical Formulation for the Boundary Element Method Applied to Elasticity in Two Dimensions

This paper presents an HP-Adaptive Procedure with Hierarchical formulation for the Boundary Element Method in 2-D Elasticity problems. Firstly, H, P and HP formulations are defined. Then, the hierarchical concept, which allows a substantial reduction in the dimension of equation system, is introduced. The error estimator used is based on the residual computation over each node inside an element. Finally, the HP strategy is defined and applied to two examples.

Numerical comparison between Maxwell stress method and equivalent multipole approach for calculation of the dielectrophoretic force in octupolar cell traps

This work presents detailed numerical calculations of the dielectrophoretic force in octupolar traps designed for single-cell trapping. A trap with eight planar electrodes is studied for spherical and ellipsoidal particles using an indirect implementation of the boundary element method (BEM). Multipolar approximations of orders one to three are compared with the full Maxwell stress tensor (MST) calculation of the electrical force on spherical particles. Ellipsoidal particles are also studied, but in their case only the dipolar approximation is available for comparison with the MST solution. The results show that the full MST calculation is only required in the study of non-spherical particles.