Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Is the Helmholtz equation really sign-indefinite?

The usual variational (or weak) formulations of the Helmholtz equation are sign-indefinite in the sense that the bilinear forms cannot be bounded below by a positive multiple of the appropriate norm squared. This is often for a good reason, since in bounded domains under certain boundary conditions the solution of the Helmholtz equation is not unique at wavenumbers that correspond to eigenvalues of the Laplacian, and thus the variational problem cannot be sign-definite. However, even in cases where the solution is unique for all wavenumbers, the standard variational formulations of the Helmholtz equation are still indefinite when the wavenumber is large. This indefiniteness has implications for both the analysis and the practical implementation of finite element methods. In this paper we introduce new sign-definite (also called coercive or elliptic) formulations of the Helmholtz equation posed in either the interior of a star-shaped domain with impedance boundary conditions, or the exterior of a star-shaped domain with Dirichlet boundary conditions. Like the standard variational formulations, these new formulations arise just by multiplying the Helmholtz equation by particular test functions and integrating by parts.

Implementation of an interior point source in the ultra weak variational formulation through source extraction

The Ultra Weak Variational Formulation (UWVF) is a powerful numerical method for the approximation of acoustic, elastic and electromagnetic waves in the time-harmonic regime. The use of Trefftz-type basis functions incorporates the known wave-like behaviour of the solution in the discrete space, allowing large reductions in the required number of degrees of freedom for a given accuracy, when compared to standard finite element methods. However, the UWVF is not well disposed to the accurate approximation of singular sources in the interior of the computational domain. We propose an adjustment to the UWVF for seismic imaging applications, which we call the Source Extraction UWVF. Differing fields are solved for in subdomains around the source, and matched on the inter-domain boundaries. Numerical results are presented for a domain of constant wavenumber and for a domain of varying sound speed in a model used for seismic imaging.

Intercomparison of general circulation models for hot extrasolar planets

We compare five general circulation models (GCMs) which have been recently used to study hot extrasolar planet atmospheres (BOB, CAM, IGCM, MITgcm, and PEQMOD), under three test cases useful for assessing model convergence and accuracy. Such a broad, detailed intercomparison has not been performed thus far for extrasolar planets study. The models considered all solve the traditional primitive equations, but employ di↵erent numerical algorithms or grids (e.g., pseudospectral and finite volume, with the latter separately in longitude-latitude and ‘cubed-sphere’ grids). The test cases are chosen to cleanly address specific aspects of the behaviors typically reported in hot extrasolar planet simulations: 1) steady-state, 2) nonlinearly evolving baroclinic wave, and 3) response to fast timescale thermal relaxation. When initialized with a steady jet, all models maintain the steadiness, as they should—except MITgcm in cubed-sphere grid. A very good agreement is obtained for a baroclinic wave evolving from an initial instability in pseudospectral models (only). However, exact numerical convergence is still not achieved across the pseudospectral models: amplitudes and phases are observably di↵erent. When subject to a typical ‘hot-Jupiter’-like forcing, all five models show quantitatively di↵erent behavior—although qualitatively similar, time-variable, quadrupole-dominated flows are produced. Hence, as have been advocated in several past studies, specific quantitative predictions (such as the location of large vortices and hot regions) by GCMs should be viewed with caution. Overall, in the tests considered here, pseudospectral models in pressure coordinate (PEBOB and PEQMOD) perform the best and MITgcm in cubed-sphere grid performs the worst.

Comparison of terrain following and cut cell grids using a non-hydrostatic model

Terrain following coordinates are widely used in operational models but the cut cell method has been proposed as an alternative that can more accurately represent atmospheric dynamics over steep orography. Because the type of grid is usually chosen during model implementation, it becomes necessary to use different models to compare the accuracy of different grids. In contrast, here a C-grid finite volume model enables a like-for-like comparison of terrain following and cut cell grids. A series of standard two-dimensional tests using idealised terrain are performed: tracer advection in a prescribed horizontal velocity field, a test starting from resting initial conditions, and orographically induced gravity waves described by nonhydrostatic dynamics. In addition, three new tests are formulated: a more challenging resting atmosphere case, and two new advection tests having a velocity field that is everywhere tangential to the terrain following coordinate surfaces. These new tests present a challenge on cut cell grids. The results of the advection tests demonstrate that accuracy depends primarily upon alignment of the flow with the grid rather than grid orthogonality. A resting atmosphere is well-maintained on all grids. In the gravity waves test, results on all grids are in good agreement with existing results from the literature, although terrain following velocity fields lead to errors on cut cell grids. Due to semi-implicit timestepping and an upwind-biased, explicit advection scheme, there are no timestep restrictions associated with small cut cells. We do not find the significant advantages of cut cells or smoothed coordinates that other authors find.

Mapping the cytoskeletal prestress

Park CY, Tambe D, Alencar AM, Trepat X, Zhou EH, Millet E, Butler JP, Fredberg JJ. Mapping the cytoskeletal prestress. Am J Physiol Cell Physiol 298: C1245-C1252, 2010. First published February 17, 2010; doi: 10.1152/ajpcell.00417.2009.-Cell mechanical properties on a whole cell basis have been widely studied, whereas local intracellular variations have been less well characterized and are poorly understood. To fill this gap, here we provide detailed intracellular maps of regional cytoskeleton (CSK) stiffness, loss tangent, and rate of structural rearrangements, as well as their relationships to the underlying regional F-actin density and the local cytoskeletal prestress. In the human airway smooth muscle cell, we used micropatterning to minimize geometric variation. We measured the local cell stiffness and loss tangent with optical magnetic twisting cytometry and the local rate of CSK remodeling with spontaneous displacements of a CSK-bound bead. We also measured traction distributions with traction microscopy and cell geometry with atomic force microscopy. On the basis of these experimental observations, we used finite element methods to map for the first time the regional distribution of intracellular prestress. Compared with the cell center or edges, cell corners were systematically stiffer and more fluidlike and supported higher traction forces, and at the same time had slower remodeling dynamics. Local remodeling dynamics had a close inverse relationship with local cell stiffness. The principal finding, however, is that systematic regional variations of CSK stiffness correlated only poorly with regional F-actin density but strongly and linearly with the regional prestress. Taken together, these findings in the intact cell comprise the most comprehensive characterization to date of regional variations of cytoskeletal mechanical properties and their determinants.

Extension And Testing Of A 2D Hydrodynamic Model For Direct Rainfall Runoff Simulation

While the simulation of flood risks originating from the overtopping of river banks is well covered within continuously evaluated programs to improve flood protection measures, flash flooding is not. Flash floods are triggered by short, local thunderstorm cells with high precipitation intensities. Small catchments have short response times and flow paths and convective thunder cells may result in potential flooding of endangered settlements. Assessing local flooding and pathways of flood requires a detailed hydraulic simulation of the surface runoff. Hydrological models usually do not incorporate surface runoff at this detailedness but rather empirical equations are applied for runoff detention. In return 2D hydrodynamic models usually do not allow distributed rainfall as input nor are any types of soil/surface interaction implemented as in hydrological models. Considering several cases of local flash flooding during the last years the issue emerged for practical reasons but as well as research topics to closing the model gap between distributed rainfall and distributed runoff formation. Therefore, a 2D hydrodynamic model, depth-averaged flow equations using the finite volume discretization, was extended to accept direct rainfall enabling to simulate the associated runoff formation. The model itself is used as numerical engine, rainfall is introduced via the modification of waterlevels at fixed time intervals. The paper not only deals with the general application of the software, but intends to test the numerical stability and reliability of simulation results. The performed tests are made using different artificial as well as measured rainfall series as input. Key parameters of the simulation such as losses, roughness or time intervals for water level manipulations are tested regarding their impact on the stability.

Avaliação de métodos numéricos para precificação de derivativos: aplicação ao mercado brasileiro

Os objetivos deste trabalho foram (i) rever métodos numéricos para precificação de derivativos; e (ii) comparar os métodos assumindo que os preços de mercado refletem àqueles obtidos pela fórmula de Black Scholes para precificação de opções do tipo européia. Aplicamos estes métodos para precificar opções de compra da ações Telebrás. Os critérios de acurácia e de custo computacional foram utilizados para comparar os seguintes modelos binomial, Monte Carlo, e diferenças finitas. Os resultados indicam que o modelo binomial possui boa acurácia e custo baixo, seguido pelo Monte Carlo e diferenças finitas. Entretanto, o método Monte Carlo poderia ser usado quando o derivativo depende de mais de dois ativos-objetos. É recomendável usar o método de diferenças finitas quando se obtém uma equação diferencial parcial cuja solução é o valor do derivativo.

Simulação da transferência de calor em amostras aquecidas por plasma

The processing of materials through plasma has been growing enough in the last times in several technological applications, more specifically in surfaces treatment. That growth is due, mainly, to the great applicability of plasmas as energy source, where it assumes behavior thermal, chemical and/or physical. On the other hand, the multiplicity of simultaneous physical effects (thermal, chemical and physical interactions) present in plasmas increases the complexity for understanding their interaction with solids. In that sense, as an initial step for the development of that subject, the present work treats of the computational simulation of the heating and cooling processes of steel and copper samples immersed in a plasma atmosphere, by considering two experimental geometric configurations: hollow and plane cathode. In order to reach such goal, three computational models were developed in Fortran 90 language: an one-dimensional transient model (1D, t), a two-dimensional transient model (2D, t) and a two-dimensional transient model (2D, t) which take into account the presence of a sample holder in the experimental assembly. The models were developed based on the finite volume method and, for the two-dimensional configurations, the effect of hollow cathode on the sample was considered as a lateral external heat source. The main results obtained with the three computational models, as temperature distribution and thermal gradients in the samples and in the holder, were compared with those developed by the Laboratory of Plasma, LabPlasma/UFRN, and with experiments available in the literature. The behavior showed indicates the validity of the developed codes and illustrate the need of the use of such computational tool in that process type, due to the great easiness of obtaining thermal information of interest

Modelagem dinâmica do escoamento de um sistema de elevação por plunger lift

A critical problem in mature gas wells is the liquid loading. As the reservoir pressure decreases, gas superficial velocities decreases and the drag exerted on the liquid phase may become insufficient to bring all the liquid to the surface. Liquid starts to drain downward, flooding the well and increasing the backpressure which decreases the gas superficial velocity and so on. A popular method to remedy this problem is the Plunger Lift. This method consists of dropping the "plunger"to the bottom of the tubing well with the main production valve closed. When the plunger reaches the well bottom the production valve is opened and the plunger carry the liquid to the surface. However, models presented in literature for predicting the behavior in plunger lift are simplistic, in many cases static (not considering the transient effects). Therefore work presents the development and validation of a numerical algorithm to solve one-dimensional compressible in gas wells using the Finite Volume Method and PRIME techniques for treating coupling of pressure and velocity fields. The code will be then used to develop a dynamic model for the plunger lift which includes the transient compressible flow within the well

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

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

Levenberg-Marquardt application to two-phase nonlinear parameter estimation for finned-tube coil evaporators

A procedure for calculation of refrigerant mass flow rate is implemented in the distributed numerical model to simulate the flow in finned-tube coil dry-expansion evaporators, usually found in refrigeration and air-conditioning systems. Two-phase refrigerant flow inside the tubes is assumed to be one-dimensional, unsteady, and homogeneous. In themodel the effects of refrigerant pressure drop and the moisture condensation from the air flowing over the external surface of the tubes are considered. The results obtained are the distributions of refrigerant velocity, temperature and void fraction, tube-wall temperature, air temperature, and absolute humidity. The finite volume method is used to discretize the governing equations. Additionally, given the operation conditions and the geometric parameters, the model allows the calculation of the refrigerant mass flow rate. The value of mass flow rate is computed using the process of parameter estimation with the minimization method of Levenberg-Marquardt minimization. In order to validate the developed model, the obtained results using HFC-134a as a refrigerant are compared with available data from the literature.

Avaliação da função renal do idoso em duas horas

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

Semiclassical scaling functions of sine-Gordon model

We present an analytic study of the finite size effects in sine-Gordon model, based on the semi-classical quantization of an appropriate kink background defined on a cylindrical geometry. The quasi-periodic kink is realized as an elliptic function with its real period related to the size of the system. The stability equation for the small quantum fluctuations around this classical background is of Lame type and the corresponding energy eigenvalues are selected inside the allowed bands by imposing periodic boundary conditions. We derive analytical expressions for the ground state and excited states scaling functions, which provide an explicit description of the flow between the IR and UV regimes of the model. Finally, the semiclassical form factors and two-point functions of the basic field and of the energy operator are obtained, completing the semiclassical quantization of the sine-Gordon model on the cylinder. (C) 2004 Elsevier B.V. All rights reserved.