viernes, 15 de enero de 2010
Charge Transport Physics of Conjugated Polymer Field-Effect Transistors
Field-effect transistors based on conjugated polymers are being developed for large-area electronic applications on flexible substrates, but they also provide a very useful tool to probe the charge transport physics of these complex materials. In this review we discuss recent progress in polymer semiconductor materials, which have brought the performance and mobility of polymer devices to levels comparable to that of small-molecule organic semiconductors. These new materials have also enabled deeper insight into the charge transport physics of high mobility polymer semiconductors gained from experiments with high charge carrier concentration and better molecular-scale understanding of the electronic structure at the semiconductor/dielectric interface.
Finite volume schemes for locally constrained conservation laws
Abstract This paper is devoted to the numerical analysis of the road traffic model proposed by Colombo and Goatin (J. Differ. Equ.
234(2):654–675, 2007). The model involves a standard conservation law supplemented by a local unilateral constraint on the
flux at the point x = 0 (modelling a road light, a toll gate, etc.). We first show that the problem can be interpreted in terms of the theory
of conservation laws with discontinuous flux function, as developed by Adimurthi et al. (J. Hyperbolic Differ. Equ. 2(4):783–837,
2005) and Bürger et al. (SIAM J. Numer. Anal. 47(3):1684–1712, 2009). We reformulate accordingly the notion of entropy solution
introduced by Colombo and Goatin (J. Differ. Equ. 234(2):654–675, 2007), and extend the well-posedness results to the L
∞ framework. Then, starting from a general monotone finite volume scheme for the non-constrained conservation law, we produce
a simple scheme for the constrained problem and show its convergence. The proof uses a new notion of entropy process solution.
Numerical examples modelling a “green wave” are presented.
234(2):654–675, 2007). The model involves a standard conservation law supplemented by a local unilateral constraint on the
flux at the point x = 0 (modelling a road light, a toll gate, etc.). We first show that the problem can be interpreted in terms of the theory
of conservation laws with discontinuous flux function, as developed by Adimurthi et al. (J. Hyperbolic Differ. Equ. 2(4):783–837,
2005) and Bürger et al. (SIAM J. Numer. Anal. 47(3):1684–1712, 2009). We reformulate accordingly the notion of entropy solution
introduced by Colombo and Goatin (J. Differ. Equ. 234(2):654–675, 2007), and extend the well-posedness results to the L
∞ framework. Then, starting from a general monotone finite volume scheme for the non-constrained conservation law, we produce
a simple scheme for the constrained problem and show its convergence. The proof uses a new notion of entropy process solution.
Numerical examples modelling a “green wave” are presented.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0286-7
- Authors
- Boris Andreianov, Université de Franche-Comté Laboratoire de Mathématiques 16 route de Gray 25030 Besançon Cedex France
- Paola Goatin, ISITV, Université du Sud Toulon-Var Avenue Georges Pompidou BP 56 83162 La Valette du Var Cedex France
- Nicolas Seguin, Laboratoire J.-L. Lions, UPMC Univ Paris 06 BC 187 75252 Paris Cedex 05 France
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Numerical analysis of the Navier–Stokes/Darcy coupling
Abstract We consider a differential system based on the coupling of the Navier–Stokes and Darcy equations for modeling the interaction
between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear)
Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming
finite element approximation of the coupled problem.
between surface and porous-media flows. We formulate the problem as an interface equation, we analyze the associated (nonlinear)
Steklov–Poincaré operators, and we prove its well-posedness. We propose and analyze iterative methods to solve a conforming
finite element approximation of the coupled problem.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0279-6
- Authors
- Lori Badea, Institute of Mathematics of the Romanian Academy P.O. Box 1-764 014700 Bucharest Romania
- Marco Discacciati, Ecole Polytechnique Fédérale de Lausanne Department of Mathematics Station 8 1015 Lausanne Switzerland
- Alfio Quarteroni, Ecole Polytechnique Fédérale de Lausanne Department of Mathematics Station 8 1015 Lausanne Switzerland
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
A geometric approach for Hermite subdivision
Abstract We present a non-stationary, non-uniform scheme for two-point Hermite subdivision. The novelty of this approach relies on
a geometric interpretation of the subdivision steps—related to generalized Bernstein bases—which permits to overcome the usually
unavoidable analytical difficulties. The main advantages consist in extra smoothness conditions, which in turn produce highly
regular limit curves, and in an elegant structure of the subdivision—described by three de Casteljau type matrices. As a by-product,
the scheme is inherently shape preserving.
a geometric interpretation of the subdivision steps—related to generalized Bernstein bases—which permits to overcome the usually
unavoidable analytical difficulties. The main advantages consist in extra smoothness conditions, which in turn produce highly
regular limit curves, and in an elegant structure of the subdivision—described by three de Casteljau type matrices. As a by-product,
the scheme is inherently shape preserving.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0280-0
- Authors
- Paolo Costantini, Università di Siena Dipartimento di Scienze Matematiche ed Informatiche Siena Italy
- Carla Manni, Università di Roma “Tor Vergata” Dipartimento di Matematica Rome Italy
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Preserving stability implicit Euler method for nonlinear Volterra and neutral functional differential equations in Banach space
Abstract This paper is concerned with the contractivity and asymptotic stability properties of the implicit Euler method (IEM) for
nonlinear functional differential equations (FDEs). These properties are first analyzed for Volterra FDEs and then the analysis
is extended to the case of neutral FDEs (NFDEs). Such an extension is particularly important since NFDEs are more general
and have received little attention in the literature. The main result we establish is that the IEM with linear interpolation
can completely preserve these stability properties of the analytical solution to such FDEs.
nonlinear functional differential equations (FDEs). These properties are first analyzed for Volterra FDEs and then the analysis
is extended to the case of neutral FDEs (NFDEs). Such an extension is particularly important since NFDEs are more general
and have received little attention in the literature. The main result we establish is that the IEM with linear interpolation
can completely preserve these stability properties of the analytical solution to such FDEs.
- Content Type Journal Article
- DOI 10.1007/s00211-009-0281-z
- Authors
- Wansheng Wang, Huazhong University of Science and Technology School of Mathematics and Statistics 430074 Wuhan China
- Chengjian Zhang, Huazhong University of Science and Technology School of Mathematics and Statistics 430074 Wuhan China
- Journal Numerische Mathematik
- Online ISSN 0945-3245
- Print ISSN 0029-599X
Solutions of Jimbo-Miwa Equation and Konopelchenko-Dubrovsky Equations
Abstract The Jimbo-Miwa equation is the second equation in the well known KP hierarchy of integrable systems, which is used to describe
certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky
equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families
of explicit exact solutions with multiple parameter functions for these equations by using Xu’s stable-range method and our
logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related
practical models and boundary value problems.
certain interesting (3+1)-dimensional waves in physics but not pass any of the conventional integrability tests. The Konopelchenko-Dubrovsky
equations arose in physics in connection with the nonlinear weaves with a weak dispersion. In this paper, we obtain two families
of explicit exact solutions with multiple parameter functions for these equations by using Xu’s stable-range method and our
logarithmic generalization of the stable-range method. These parameter functions make our solutions more applicable to related
practical models and boundary value problems.
- Content Type Journal Article
- DOI 10.1007/s10440-009-9559-5
- Authors
- Bintao Cao, Chinese Academy of Sciences Institute of Mathematics, Academy of Mathematics and Systems Science Beijing 100190 P.R. China
- Journal Acta Applicandae Mathematicae
- Online ISSN 1572-9036
- Print ISSN 0167-8019
A practical method to estimate crack openings in concrete structures
Numerical modelling of concrete cracking requires robust models able to describe opening and propagation of cracks. Structural concrete codes provide practical relations to describe crack openings. However, these empirical methods were developed for specific structures and cannot be used for general applications. Here, a continuous modelling approach based on damage mechanics is used to compute crack openings in a tie-beam concrete structure. We propose a post-processing method to extract crack openings from a continuum damage finite element computation. This method can be applied to all continuum damage/plasticity models. The tie-beam concrete is characterized by a weak stress gradient; this aspect complicates predictions of crack positions and number. A stochastic method is used to take into account the spatial variability in concrete properties and create a spatially correlated random property field. Copyright © 2009 John Wiley & Sons, Ltd.
Constitutive approach for rate-sensitive anisotropic structured clays
This paper describes a constitutive approach to model the behavior of rate-dependent anisotropic structured clay. Rate-sensitivity is modeled using overstress viscoplasticity. Clay structure is treated as a viscous phenomenon whereby the viscosity of the undisturbed structured clay is initially very high and the viscosity degrades or decreases with plastic straining until the intrinsic or residual viscosity is reached. A microstructure tensor approach is used to make the structured viscosity anisotropic; whereas, the intrinsic viscosity is assumed to be isotropic. The behavior of the constitutive model is compared with the measured response of two clays (Gloucester and St. Vallier clay) from Eastern Canada during triaxial compression tests on specimens trimmed at different orientations to the vertical. The comparisons show that the constitutive framework is able to describe the anisotropic and rate-sensitive response of both clays. The response of the model is also examined for the more general case of anisotropic consolidated triaxial compression and extension. Copyright © 2010 John Wiley & Sons, Ltd.
A stabilized formulation for the advection-diffusion equation using the Generalized Finite Element Method
This paper presents a stable formulation for the advection-diffusion equation based on the Generalized (or eXtended) Finite Element Method, GFEM (or X-FEM). Using enrichment functions that represent the exponential character of the exact solution, smooth numerical solutions are obtained for problems with steep gradients and high Péclet numbers in one- and two-dimensions. In contrast with traditional stabilized methods that require the construction of stability parameters and stabilization terms, the present work avoids numerical instabilities by improving the classical Galerkin solution with enrichment functions (that need not be polynomials) using GFEM, which is an instance of the partition of unity framework.This work also presents a strategy for constructing enrichment functions for problems involving complex geometries by employing a global-local-type approach. Representative numerical results are presented to illustrate the performance of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.
A local domain-free discretization method for simulation of incompressible flows over moving bodies
This paper presents a local domain-free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier-Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of 'freshly cleared nodes/cells' encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite-element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual-time-stepping scheme based on artificial compressibility. In order to validate the present method for moving-boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in-line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving-pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data. Copyright © 2010 John Wiley & Sons, Ltd.
Numerical simulations of non-equilibrium turbulent boundary layer flowing over a bump
Large-eddy simulation (LES) and Reynolds-averaged Navier-Stokes simulation (RANS) with different turbulence models (including the standard k-[epsiv], the standard k-[omega], the shear stress transport k-[omega] (SST k-[omega]), and Spalart-Allmaras (S-A) turbulence models) have been employed to compute the turbulent flow of a two-dimensional turbulent boundary layer over an unswept bump. The predictions of the simulations were compared with available experimental measurements in the literature. The comparisons of the LES and the SST k-[omega] model including the mean flow and turbulence stresses are in satisfied agreements with the available measurements. Although the flow experiences a strong adverse pressure gradient along the rear surface, the boundary layer is unique in that intermittent detachment occurring near the wall. The numerical results indicate that the boundary layer is not followed by mean-flow separation or incipient separation as shown from the numerical results. The resolved turbulent shear stress is in a reasonable agreement with the experimental data, though the computational result of LES shows that its peak is overpredicted near the trailing edge of the bump, while the other used turbulence models, except the standard k-[epsiv], underpredicts it. Analysis of the numerical results from LES confirms the experimental data, in which the existence of internal layers over the bump surface upstream of the summit and along the downstream flat plate. It also demonstrates that the quasi-step increase in skin friction is due to perturbations in pressure gradient. The surface curvature enhances the near-wall shear production of turbulent stresses, and is responsible for the formation of the internal layers.The aim of the present work is to examine the response and prediction capability of LES with the dynamic eddy viscosity model as a sub-grid scale to the complex turbulence structure with the presence of streamline curvature generated by a bumpy surface. Aiming to reduce the computational costs with focus on the mean behavior of the non-equilibrium turbulent boundary layer of flow over the bump surface, the present investigation also explains the best capability of one of the used RANS turbulence models to capture the driving mechanism for the surprisingly rapid return to equilibrium over the trailing flat plate found in the measurements. Copyright © 2010 John Wiley & Sons, Ltd.
Asymptotic zero distribution of complex orthogonal polynomials associated with Gaussian quadrature. (arXiv:1001.2219v1 [math.CA])
In this paper we study the asymptotic behavior of a family of polynomials
which are orthogonal with respect to an exponential weight on certain contours
of the complex plane. The zeros of these polynomials are the nodes for complex
Gaussian quadrature of an oscillatory integral on the real axis with a high
order stationary point, and their limit distribution is also analyzed. We show
that the zeros accumulate along a contour in the complex plane that has the
S-property in an external field. In addition, the strong asymptotics of the
orthogonal polynomials is obtained by applying the nonlinear Deift--Zhou
steepest descent method to the corresponding Riemann--Hilbert problem.
Restoration of Poissonian Images Using Alternating Direction Optimization. (arXiv:1001.2244v2 [math.OC] UPDATED)
Much research has been devoted to the problem of restoring Poissonian images,
namely for medical and astronomical applications. However, the restoration of
these images using state-of-the-art regularizers (such as those based on
multiscale representations or total variation) is still an active research
area, since the associated optimization problems are quite challenging. In this
paper, we propose an approach to deconvolving Poissonian images, which is based
on an alternating direction optimization method. The standard regularization
(or maximum a posteriori) restoration criterion, which combines the Poisson
log-likelihood with a (non-smooth) convex regularizer (log-prior), leads to
hard optimization problems: the log-likelihood is non-quadratic and
non-separable, the regularizer is non-smooth, and there is a non-negativity
constraint. Using standard convex analysis tools, we present sufficient
conditions for existence and uniqueness of solutions of these optimization
problems, for several types of regularizers: total-variation, frame-based
analysis, and frame-based synthesis. We attack these problems with an instance
of the alternating direction method of multipliers (ADMM), which belongs to the
family of augmented Lagrangian algorithms. We study sufficient conditions for
convergence and show that these are satisfied, either under total-variation or
frame-based (analysis and synthesis) regularization. The resulting algorithms
are shown to outperform alternative state-of-the-art methods, both in terms of
speed and restoration accuracy.
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