Holographic recording in [Sb(Po-3)(3)](n)-Sb2O3 glassy films by photoinduced volume and refraction index changes

Glassy films of 0.2[Sb(PO3)(3)]-0,8Sb(2)O(3) with 0.8 mum-thickness were deposited on quartz substrates by electron beam evaporation. A contraction in the film thickness (photoinduced decrease in volume) and photobleaching effect associated with a decrease of up to 25% in the index of refraction has been observed in the films after irradiation near the bandgap (3.89 eV), using the 350.7 nm (3.54 eV) Kr+ ion laser line with 2.5 W/cm(2) for 30 min. A loss of 30% in the phosphorus concentration was measured by wavelength dispersive X-ray microanalysis in the film after laser irradiation with 5.0 W/cm(2) for 1.0 h. These photoinduced changes in the samples are dependent on the power density and intensity profile of the laser beam. Using a Lloyd's mirror setup for continuous wave holography it was possible to record holographic gratings with period from 500 nm up to 20 mum and depth profile of similar to50 nm in the films after laser irradiation with 5.0 W/cm(2) for 1 h. Real-time diffraction efficiency measurements have shown that ultraviolet irradiation induces first a refractive index grating formation, and after this, the photocon traction effect takes place generating an irreversible relief grating. Diffraction efficiency up to 10% was achieved for the recorded gratings. 3D-refraction index measurements and atomic force microscopy images are presented. (C) 2004 Elsevier B.V. All rights reserved.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.

A sixth-order finite volume method for the 1D biharmonic operator: application to intramedullary nail simulation

A new very high-order finite volume method to solve problems with harmonic and biharmonic operators for one- dimensional geometries is proposed. The main ingredient is polynomial reconstruction based on local interpolations of mean values providing accurate approximations of the solution up to the sixth-order accuracy. First developed with the harmonic operator, an extension for the biharmonic operator is obtained, which allows designing a very high-order finite volume scheme where the solution is obtained by solving a matrix-free problem. An application in elasticity coupling the two operators is presented. We consider a beam subject to a combination of tensile and bending loads, where the main goal is the stress critical point determination for an intramedullary nail.

Numerical analysis of finite volume schemes for population balance equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Comparative study of human erythrocytes by digital holographic microscopy, confocal microscopy, and impedance volume analyzer.

Red blood cell (RBC) parameters such as morphology, volume, refractive index, and hemoglobin content are of great importance for diagnostic purposes. Existing approaches require complicated calibration procedures and robust cell perturbation. As a result, reference values for normal RBC differ depending on the method used. We present a way for measuring parameters of intact individual RBCs by using digital holographic microscopy (DHM), a new interferometric and label-free technique with nanometric axial sensitivity. The results are compared with values achieved by conventional techniques for RBC of the same donor and previously published figures. A DHM equipped with a laser diode (lambda = 663 nm) was used to record holograms in an off-axis geometry. Measurements of both RBC refractive indices and volumes were achieved via monitoring the quantitative phase map of RBC by means of a sequential perfusion of two isotonic solutions with different refractive indices obtained by the use of Nycodenz (decoupling procedure). Volume of RBCs labeled by membrane dye Dil was analyzed by confocal microscopy. The mean cell volume (MCV), red blood cell distribution width (RDW), and mean cell hemoglobin concentration (MCHC) were also measured with an impedance volume analyzer. DHM yielded RBC refractive index n = 1.418 +/- 0.012, volume 83 +/- 14 fl, MCH = 29.9 pg, and MCHC 362 +/- 40 g/l. Erythrocyte MCV, MCH, and MCHC achieved by an impedance volume analyzer were 82 fl, 28.6 pg, and 349 g/l, respectively. Confocal microscopy yielded 91 +/- 17 fl for RBC volume. In conclusion, DHM in combination with a decoupling procedure allows measuring noninvasively volume, refractive index, and hemoglobin content of single-living RBCs with a high accuracy.

Analysis of a finite volume element method for the Stokes problem

In this paper we propose a stabilized conforming finite volume element method for the Stokes equations. On stating the convergence of the method, optimal a priori error estimates in different norms are obtained by establishing the adequate connection between the finite volume and stabilized finite element formulations. A superconvergence result is also derived by using a postprocessing projection method. In particular, the stabilization of the continuous lowest equal order pair finite volume element discretization is achieved by enriching the velocity space with local functions that do not necessarily vanish on the element boundaries. Finally, some numerical experiments that confirm the predicted behavior of the method are provided.

Hybrid Multiscale Finite Volume method for two-phase flow in porous media

We present a novel hybrid (or multiphysics) algorithm, which couples pore-scale and Darcy descriptions of two-phase flow in porous media. The flow at the pore-scale is described by the Navier?Stokes equations, and the Volume of Fluid (VOF) method is used to model the evolution of the fluid?fluid interface. An extension of the Multiscale Finite Volume (MsFV) method is employed to construct the Darcy-scale problem. First, a set of local interpolators for pressure and velocity is constructed by solving the Navier?Stokes equations; then, a coarse mass-conservation problem is constructed by averaging the pore-scale velocity over the cells of a coarse grid, which act as control volumes; finally, a conservative pore-scale velocity field is reconstructed and used to advect the fluid?fluid interface. The method relies on the localization assumptions used to compute the interpolators (which are quite straightforward extensions of the standard MsFV) and on the postulate that the coarse-scale fluxes are proportional to the coarse-pressure differences. By numerical simulations of two-phase problems, we demonstrate that these assumptions provide hybrid solutions that are in good agreement with reference pore-scale solutions and are able to model the transition from stable to unstable flow regimes. Our hybrid method can naturally take advantage of several adaptive strategies and allows considering pore-scale fluxes only in some regions, while Darcy fluxes are used in the rest of the domain. Moreover, since the method relies on the assumption that the relationship between coarse-scale fluxes and pressure differences is local, it can be used as a numerical tool to investigate the limits of validity of Darcy's law and to understand the link between pore-scale quantities and their corresponding Darcy-scale variables.

An iterative Multiscale Finite-Volume algorithm converging to the exact solution

The multiscale finite volume (MsFV) method has been developed to efficiently solve large heterogeneous problems (elliptic or parabolic); it is usually employed for pressure equations and delivers conservative flux fields to be used in transport problems. The method essentially relies on the hypothesis that the (fine-scale) problem can be reasonably described by a set of local solutions coupled by a conservative global (coarse-scale) problem. In most cases, the boundary conditions assigned for the local problems are satisfactory and the approximate conservative fluxes provided by the method are accurate. In numerically challenging cases, however, a more accurate localization is required to obtain a good approximation of the fine-scale solution. In this paper we develop a procedure to iteratively improve the boundary conditions of the local problems. The algorithm relies on the data structure of the MsFV method and employs a Krylov-subspace projection method to obtain an unconditionally stable scheme and accelerate convergence. Two variants are considered: in the first, only the MsFV operator is used; in the second, the MsFV operator is combined in a two-step method with an operator derived from the problem solved to construct the conservative flux field. The resulting iterative MsFV algorithms allow arbitrary reduction of the solution error without compromising the construction of a conservative flux field, which is guaranteed at any iteration. Since it converges to the exact solution, the method can be regarded as a linear solver. In this context, the schemes proposed here can be viewed as preconditioned versions of the Generalized Minimal Residual method (GMRES), with a very peculiar characteristic that the residual on the coarse grid is zero at any iteration (thus conservative fluxes can be obtained).

Modeling complex wells with the multi-scale finite-volume method

In this paper, an extension of the multi-scale finite-volume (MSFV) method is devised, which allows to Simulate flow and transport in reservoirs with complex well configurations. The new framework fits nicely into the data Structure of the original MSFV method,and has the important property that large patches covering the whole well are not required. For each well. an additional degree of freedom is introduced. While the treatment of pressure-constraint wells is trivial (the well-bore reference pressure is explicitly specified), additional equations have to be solved to obtain the unknown well-bore pressure of rate-constraint wells. Numerical Simulations of test cases with multiple complex wells demonstrate the ability of the new algorithm to capture the interference between the various wells and the reservoir accurately. (c) 2008 Elsevier Inc. All rights reserved.

Measurement of absolute cell volume, osmotic membrane water permeability, and refractive index of transmembrane water and solute flux by digital holographic microscopy.

ABSTRACT. A dual-wavelength digital holographic microscope to measure absolute volume of living cells is proposed. The optical setup allows us to reconstruct two quantitative phase contrast images at two different wavelengths from a single hologram acquisition. When adding the absorbing dye fast green FCF as a dispersive agent to the extracellular medium, cellular thickness can be univocally determined in the full field of view. In addition to the absolute cell volume, the method can be applied to derive important biophysical parameters of living cells including osmotic membrane water permeability coefficient and the integral intracellular refractive index (RI). Further, the RI of transmembrane flux can be determined giving an indication about the nature of transported solutes. The proposed method is applied to cultured human embryonic kidney cells, Chinese hamster ovary cells, human red blood cells, mouse cortical astrocytes, and neurons.

Accurate and efficient simulation of multiphase flow in a heterogeneous reservoir by using error estimate and control in the multiscale finite-volume framework

The multiscale finite-volume (MSFV) method is designed to reduce the computational cost of elliptic and parabolic problems with highly heterogeneous anisotropic coefficients. The reduction is achieved by splitting the original global problem into a set of local problems (with approximate local boundary conditions) coupled by a coarse global problem. It has been shown recently that the numerical errors in MSFV results can be reduced systematically with an iterative procedure that provides a conservative velocity field after any iteration step. The iterative MSFV (i-MSFV) method can be obtained with an improved (smoothed) multiscale solution to enhance the localization conditions, with a Krylov subspace method [e.g., the generalized-minimal-residual (GMRES) algorithm] preconditioned by the MSFV system, or with a combination of both. In a multiphase-flow system, a balance between accuracy and computational efficiency should be achieved by finding a minimum number of i-MSFV iterations (on pressure), which is necessary to achieve the desired accuracy in the saturation solution. In this work, we extend the i-MSFV method to sequential implicit simulation of time-dependent problems. To control the error of the coupled saturation/pressure system, we analyze the transport error caused by an approximate velocity field. We then propose an error-control strategy on the basis of the residual of the pressure equation. At the beginning of simulation, the pressure solution is iterated until a specified accuracy is achieved. To minimize the number of iterations in a multiphase-flow problem, the solution at the previous timestep is used to improve the localization assumption at the current timestep. Additional iterations are used only when the residual becomes larger than a specified threshold value. Numerical results show that only a few iterations on average are necessary to improve the MSFV results significantly, even for very challenging problems. Therefore, the proposed adaptive strategy yields efficient and accurate simulation of multiphase flow in heterogeneous porous media.

A multilevel multiscale finite volume method

The Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.