Showing papers on "Boundary value problem published in 2011"
TL;DR: In this paper, the authors considered the initial value/boundary value problems for fractional diffusion-wave equation and established the unique existence of the weak solution and the asymptotic behavior as the time t goes to ∞ and the proofs are based on the eigenfunction expansions.
965 citations
TL;DR: In this article, potential-based models have been evaluated for mixed-mode cohesive fracture, and it is shown that these models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface.
Abstract: One of the fundamental aspects in cohesive zone modeling is the definition of the traction-separation relationship across fracture surfaces, which approximates the nonlinear fracture process. Cohesive traction-separation relationships may be classified as either nonpotential-based models or potential-based models. Potential-based models are of special interest in the present review article. Several potential-based models display limitations, especially for mixed-mode problems, because of the boundary conditions associated with cohesive fracture. In addition, this paper shows that most effective displacement-based models can be formulated under a single framework. These models lead to positive stiffness under certain separation paths, contrary to general cohesive fracture phenomena wherein the increase of separation generally results in the decrease of failure resistance across the fracture surface (i.e., negative stiffness). To this end, the constitutive relationship of mixed-mode cohesive fracture should be selected with great caution.
555 citations
TL;DR: In this article, a smoothed particle hydrodynamics model with numerical diffusive terms is used to analyze violent water flows and boundary conditions on solid surfaces of arbitrary shape are enforced with a new technique based on fixed ghost particles.
535 citations
TL;DR: The new holography, which may be called anti-de Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy, and can naturally derive a holographic g theorem.
Abstract: We propose a holographic dual of a conformal field theory defined on a manifold with boundaries, i.e., boundary conformal field theory (BCFT). Our new holography, which may be called anti-de Sitter BCFT, successfully calculates the boundary entropy or g function in two-dimensional BCFTs and it agrees with the finite part of the holographic entanglement entropy. Moreover, we can naturally derive a holographic g theorem. We also analyze the holographic dual of an interval at finite temperature and show that there is a first order phase transition.
468 citations
TL;DR: In this paper, the dynamic characteristics of functionally graded beam with material graduation in axially or transversally through the thickness based on the power law are presented. But the model is more effective for replacing the non-uniform geometrical beam with axially and transversely uniform geometrically graded beam.
458 citations
TL;DR: In this article, the stability problem of nano-sized beam based on the strain gradient elasticity and couple stress theories is addressed, and the size effect on the critical buckling load is investigated.
436 citations
TL;DR: In this paper, the authors established the skew-symmetric character of the couple-stress tensor in size-dependent continuum representations of matter by relying on the definition of admissible boundary conditions and some kinematical considerations.
407 citations
TL;DR: In this paper, the dynamic stability of microbeams made of functionally graded materials (FGMs) is investigated based on the modified couple stress theory and Timoshenko beam theory, and the boundary points on the unstable regions are determined by Bolotin's method.
329 citations
Book•
27 Aug 2011
TL;DR: A class of iterative methods is discussed in which these subproblems are solved by direct methods, while the interaction across the curves or surfaces which divide the region is handled by a conjugate gradient method.
Abstract: Finite element problems can often naturally be divided into subproblems which correspond to subregions into which the region has been partitioned or from which it was originally assembled. A class of iterative methods is discussed in which these subproblems are solved by direct methods, while the interaction across the curves or surfaces which divide the region is handled by a conjugate gradient method. A mathematical framework for this work is provided by regularity theory for elliptic finite element problems and by block Gaussian elimination. A full development of the theory, which shows that certain of these methods are optimal, is given for Lagrangian finite element approximations of second order linear elliptic problems in the plane. Results from numerical experiments are also reported.
328 citations
TL;DR: The ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice and the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency.
Abstract: We conduct a comparative study to evaluate several lattice Boltzmann (LB) models for solving the near incompressible Navier-Stokes equations, including the lattice Boltzmann equation with the multiple-relaxation-time (MRT), the two-relaxation-time (TRT), the single-relaxation-time (SRT) collision models, and the entropic lattice Boltzmann equation (ELBE). The lid-driven square cavity flow in two dimensions is used as a benchmark test. Our results demonstrate that the ELBE does not improve the numerical stability of the SRT or the lattice Bhatnagar-Gross-Krook (LBGK) model. Our results also show that the MRT and TRT LB models are superior to the ELBE and LBGK models in terms of accuracy, stability, and computational efficiency and that the ELBE scheme is the most inferior among the LB models tested in this study, thus is unfit for carrying out numerical simulations in practice. Our study suggests that, to optimize the accuracy, stability, and efficiency in the MRT model, it requires at least three independently adjustable relaxation rates: one for the shear viscosity ν (or the Reynolds number Re), one for the bulk viscosity ζ, and one to satisfy the criterion imposed by the Dirichlet boundary conditions which are realized by the bounce-back-type boundary conditions.
314 citations
TL;DR: In this paper, a Coupled Eulerian-Lagrangian (CEL) approach has been developed to overcome the difficulties with regard to finite element method and large deformation analyses.
TL;DR: In this article, the authors considered transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region and demonstrated the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys.
Abstract: Graphene subject to a spatially uniform, circularly polarized electric field supports a Floquet spectrum with properties akin to those of a topological insulator. The transport properties of this system, however, are complicated by the nonequilibrium occupations of the Floquet states. We address this by considering transport in a two-terminal ribbon geometry for which the leads have well-defined chemical potentials, with an irradiated central scattering region. We demonstrate the presence of edge states, which for infinite mass boundary conditions may be associated with only one of the two valleys. At low frequencies, the bulk dc conductivity near zero energy is shown to be dominated by a series of states with very narrow anticrossings, leading to superdiffusive behavior. For very long ribbons, a ballistic regime emerges in which edge state transport dominates.
Book•
08 Sep 2011
TL;DR: In this article, it was shown that monotone schemes, when convergent, always converge to the physically relevant solution of a single conservation law, and that this is not always the case with non-monotone scheme, such as the Lax-Wendroff scheme.
Abstract: Weak solutions of hyperbolic conservation laws are not uniquely determined by their initial values; an entropy condition is needed to pick out the physically relevant solution. The question arises whether finite-difference approximations converge to this particular solution. It is shown in this paper that, in the case of a single conservation law, monotone schemes, when convergent, always converge to the physically relevant solution. Numerical examples show that this is not always the case with nonmonotone schemes, such as the Lax--Wendroff scheme. 4 figures, 2 tables. (auth)
Book•
25 Jan 2011TL;DR: This book guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions.
Abstract: Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics provides a comprehensive tutorial of the most widely used method for solving Maxwell's equations -- the Finite Difference Time-Domain Method. This book is an essential guide for students, researchers, and professional engineers who want to gain a fundamental knowledge of the FDTD method. It can accompany an undergraduate or entry-level graduate course or be used for self-study. The book provides all the background required to either research or apply the FDTD method for the solution of Maxwell's equations to practical problems in engineering and science. Introduction to the Finite-Difference Time-Domain (FDTD) Method for Electromagnetics guides the reader through the foundational theory of the FDTD method starting with the one-dimensional transmission-line problem and then progressing to the solution of Maxwell's equations in three dimensions. It also provides step by step guides to modeling physical sources, lumped-circuit components, absorbing boundary conditions, perfectly matched layer absorbers, and sub-cell structures. Post processing methods such as network parameter extraction and far-field transformations are also detailed. Efficient implementations of the FDTD method in a high level language are also provided. Table of Contents: Introduction / 1D FDTD Modeling of the Transmission Line Equations / Yee Algorithm for Maxwell's Equations / Source Excitations / Absorbing Boundary Conditions / The Perfectly Matched Layer (PML) Absorbing Medium / Subcell Modeling / Post Processing
TL;DR: In this article, the authors considered the initial-boundary-value problems for the generalized multi-term time-fractional diffusion equation over an open bounded domain G × ( 0, T ), G ∈ R n.
TL;DR: In this article, the free vibration characteristics of microbeams made of functionally graded materials (FGMs) based on the strain gradient Timoshenko beam theory were investigated, where the material properties of the functionally graded beams were assumed to be graded in the thickness direction according to the Mori-Tanaka scheme.
TL;DR: An implicit high-order hybridizable discontinuous Galerkin method for the steady-state and time-dependent incompressible Navier-Stokes equations and displays superconvergence properties that allow it to use the above-mentioned optimal convergence properties to define an element-by-element postprocessing scheme to compute a new and better approximate velocity.
CERN1
TL;DR: In this article, the authors proposed to bypass the problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction, which can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum) are not affected.
Abstract: As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.
TL;DR: In this article, the inlet profiles and boundary conditions appropriate for modeling the flow using the standard k-e, RNG k−e, Wilcox k−ω and LRR QI turbulence models are provided.
TL;DR: In this paper, a variational approach based on Hamilton's principle is employed to obtain the governing equations of motion of micro-structures, and the effect of length scale parameter on the natural frequencies of the micro-plates is discussed.
Abstract: A microscale vibration analysis of micro-plates is developed based on a modified couple stress theory. The presence of the length scale parameter in this theory enables us to describe the size effect in micro-structures. A variational approach based on Hamilton’s principle is employed to obtain the governing equations of motion. To illustrate the new model, the free vibration analysis of a rectangular micro plate with two opposite edges simply supported and arbitrary boundary conditions along the other edges and a circular micro-plate are considered. The natural frequencies of micro-plates are presented for over a wide range of length scale parameters, different aspect ratios and various boundary conditions for both rectangular and circular micro-plates. The effect of length scale parameter on natural frequencies of micro-plates are discussed in details and the numerical results reveal that the intrinsic size dependence of material leads to increase the natural frequency.
01 Dec 2011
TL;DR: This work designs a full-state feedback law with actuation on only one end of the domain and proves exponential stability of the closed-loop system and constructs a collocated boundary observer which only needs measurements on the controlled end and proves convergence of observer estimates.
Abstract: We consider the problem of boundary stabilization and state estimation for a 2×2 system of first-order hyperbolic linear PDEs with spatially varying coefficients. First, we design a full-state feedback law with actuation on only one end of the domain and prove exponential stability of the closed-loop system. Then, we construct a collocated boundary observer which only needs measurements on the controlled end and prove convergence of observer estimates. Both results are combined to obtain a collocated output feedback law. The backstepping method is used to obtain both control and observer kernels. The kernels are the solution of a 4 × 4 system of first-order hyperbolic linear PDEs with spatially varying coefficients of Goursat type, whose well-posedness is shown.
TL;DR: This work presents M u M ax, a general-purpose micromagnetic simulation tool running on graphical processing units (GPUs), designed for high-performance computations and specifically targets large simulations.
TL;DR: In this paper, a higher order shear deformation theory for elastic composite/sandwich plates and shells is developed, which accounts for an approximately parabolic distribution of the transverse shear strains through the shell thickness and tangential stress-free boundary conditions on the shell boundary surface.
TL;DR: It is found that the influence of the residual surface stress and the surface piezoelectricity on the resonant frequencies and the critical electric potential for buckling is more prominent than the surface elasticity.
Abstract: In this work, the influence of surface effects, including residual surface stress, surface elasticity and surface piezoelectricity, on the vibrational and buckling behaviors of piezoelectric nanobeams is investigated by using the Euler-Bernoulli beam theory. The surface effects are incorporated by applying the surface piezoelectricity model and the generalized Young-Laplace equations. The results demonstrate that surface effects play a significant role in predicting these behaviors. It is found that the influence of the residual surface stress and the surface piezoelectricity on the resonant frequencies and the critical electric potential for buckling is more prominent than the surface elasticity. The nanobeam boundary conditions are also found to influence the surface effects on these parameters. This study also shows that the resonant frequencies can be tuned by adjusting the applied electrical load. The present study is envisaged to provide useful insights for the design and applications of piezoelectric-beam-based nanodevices.
TL;DR: In this article, the authors investigated the heat transfer of a viscous fluid flow over a stretching/shrinking sheet with a convective boundary condition, and the authors proposed the exact solutions of the momentum equations, which are valid for the whole Navier-Stokes equations.
TL;DR: In this paper, a holographic model with a pure gauge and a mixed gauge-gravitational Chern-Simons term in the action is analyzed and a charged asymptotically AdS black hole is proposed.
Abstract: We analyze a holographic model with a pure gauge and a mixed gauge-gravitational Chern-Simons term in the action. These are the holographic implementations of the usual chiral and the mixed gauge-gravitational anomalies in four dimensional field theories with chiral fermions. We discuss the holographic renormalization and show that the gauge-gravitational Chern-Simons term does not induce new divergences. In order to cancel contributions from the extrinsic curvature at a boundary at finite distance a new type of counterterm has to be added however. This counterterm can also serve to make the Dirichlet problem well defined in case the gauge field strength vanishes on the boundary. A charged asymptotically AdS black hole is a solution to the theory and as an application we compute the chiral magnetic and chiral vortical conductivities via Kubo formulas. We find that the characteristic term proportional to T2 is present also at strong coupling and that its numerical value is not renormalized compared to the weak coupling result.
TL;DR: In this paper, the buckling and vibration of nanoplates are studied using nonlocal elasticity theory, and the results show that nonlocality effects should be considered for nanoscale plates.
Abstract: In the present study, buckling and vibration of nanoplates are studied using nonlocal elasticity theory. Navier type solution is used for simply supported plates and Levy type method is used for plates with two opposite edge simply supported and remaining ones arbitrary. Results are given for different nonlocality parameter, different length of plates and different boundary conditions. The results show that nonlocality effects should be considered for nanoscale plates. Clamped boundary conditions are more sensitive to nonlocality effects. In the vibration problem nonlocality effects increase with increase in the mode number. Present result can be used for single layer graphene sheets.
TL;DR: A stability and convergence theory for a class of highly indefinite elliptic boundary value problems (bvps) by considering the Helmholtz equation at high wavenumber $k$ as the authors' model problem and it is shown that quasi optimality is obtained under the conditions that $kh/ p$ is sufficiently small and the polynomial degree $p$ is at least O(log $k) .
Abstract: We develop a stability and convergence theory for a class of highly indefinite elliptic boundary value problems (bvps) by considering the Helmholtz equation at high wavenumber $k$ as our model problem. The key element in this theory is a novel $k$-explicit regularity theory for Helmholtz bvps that is based on decomposing the solution into two parts: the first part has the Sobolev regularity properties expected of second order elliptic PDEs but features $k$-independent regularity constants; the second part is an analytic function for which $k$-explicit bounds for all derivatives are given. This decomposition is worked out in detail for several types of bvps, namely, the Helmholtz equation in bounded smooth domains or convex polygonal domains with Robin boundary conditions and in exterior domains with Dirichlet boundary conditions. We present an error analysis for the classical $hp$-version of the finite element method ($hp$-FEM) where the dependence on the mesh width $h$, the approximation order $p$, and the wavenumber $k$ is given explicitly. In particular, under the assumption that the solution operator for Helmholtz problems is polynomially bounded in $k$, it is shown that quasi optimality is obtained under the conditions that $kh/p$ is sufficiently small and the polynomial degree $p$ is at least O(log $k$).
Posted Content•
TL;DR: In this paper, the authors revisited the question at the level of bulk path integrals, showing that agreement in the presence of interactions requires careful treatment of the renormalization of bulk composite operators.
Abstract: Dual AdS/CFT correlators can be computed in two ways: differentiate the bulk partition function with respect to boundary conditions, or extrapolate bulk correlation functions to the boundary. These dictionaries were conjectured to be equivalent by Banks, Douglas, Horowitz, and Martinec. We revisit this question at the level of bulk path integrals, showing that agreement in the presence of interactions requires careful treatment of the renormalization of bulk composite operators. By contrast, we emphasize that proposed dS/CFT analogues of the two dictionaries are inequivalent. Next, we show quite generally that the wave function for Euclidean AdS analytically continues to the dS wave function with Euclidean initial conditions. Most of our arguments consider interacting fields on a fixed background, but in a final section we discuss the inclusion of bulk dynamical gravity.
TL;DR: In this article, a two-point boundary value problem for a finite fractional difference equation is introduced and sufficient conditions for the existence of positive solutions for a nonlinear finite fractionality difference equation are obtained.
Abstract: In this paper, we introduce a two-point boundary value problem for a finite fractional difference equation. We invert the problem and construct and analyse the corresponding Green's function. We then provide an application and obtain sufficient conditions for the existence of positive solutions for a two-point boundary value problem for a nonlinear finite fractional difference equation.