Showing papers on "Boundary value problem published in 2004"
TL;DR: The resulting equation overcomes the limitations of current approaches and shows remarkable agreement with exact theoretical predictions of the single-collector efficiency over a wide range of conditions commonly encountered in natural and engineered aquatic systems.
Abstract: A new equation for predicting the single-collector contact efficiency (eta0) in physicochemical particle filtration in saturated porous media is presented. The correlation equation is developed assuming that the overall single-collector efficiency can be calculated as the sum of the contributions of the individual transport mechanisms--Brownian diffusion, interception, and gravitational sedimentation. To obtain the correlation equation, the dimensionless parameters governing particle deposition are regressed against the theoretical value of the single-collector efficiency over a broad range of parameter values. Rigorous numerical solution of the convective-diffusion equation with hydrodynamic interactions and universal van der Waals attractive forces fully incorporated provided the theoretical single-collector efficiencies. The resulting equation overcomes the limitations of current approaches and shows remarkable agreement with exact theoretical predictions of the single-collector efficiency over a wide range of conditions commonly encountered in natural and engineered aquatic systems. Furthermore, experimental data are in much closer agreement with predictions based on the new correlation equation compared to other available expressions.
1,044 citations
TL;DR: Explicit numerical methods for spatial derivation, filtering, and time integration are proposed in this article with the aim of computing flow and noise with high accuracy and fidelity, and they are constructed in the same way by minimizing the dispersion and the dissipation errors in the wavenumber space up to kΔx = π/2 corresponding to four points per wavelength.
883 citations
TL;DR: In this paper, a new computational method, the immersed boundary-lattice Boltzmann method, is presented, which combines the most desirable features of the lattice Boltzman and immersed boundary methods and uses a regular Eulerian grid for the flow domain and a Lagrangian grid to follow particles contained in the flow field.
804 citations
TL;DR: Stochastic boundaries are compatible with H modes and may be attractive for ELM control in next-step fusion tokamaks, and the H mode transport barrier and core confinement are unaffected by the stochastic boundary.
Abstract: OAK-B135 A stochastic magnetic boundary, produced by an externally applied edge resonant magnetic perturbation, is used to suppress large edge localized modes (ELMs) in high confinement (H-mode) plasmas. The resulting H-mode displays rapid, small oscillations with a bursty character modulated by a coherent 130 Hz envelope. The H-mode transport barrier is unaffected by the stochastic boundary. The core confinement of these discharges is unaffected, despite a three-fold drop in the toroidal rotation in the plasma core. These results demonstrate that stochastic boundaries are compatible with H-modes and may be attractive for ELM control in next-step burning fusion tokamaks.
774 citations
Book•
01 Jan 2004
TL;DR: The Navier-Stokes equations under initial and boundary conditions were studied in this paper, where they were shown to be incompressible in the spatially periodic case and in the constant-coefficient case.
Abstract: Preface to the Classics Edition Introduction 1. The Navier-Stokes equations 2. Constant-coefficient Cauchy problems 3. Linear variable-coefficient Cauchy problems in 1D 4. A nonlinear example: Burgers' equations 5. Nonlinear systems in one space dimension 6. The Cauchy problem for systems in several dimensions 7. Initial-boundary value problems in one space dimension 8. Initial-boundary value problems in several space dimensions 9. The incompressible Navier-Stokes equations: the spatially periodic case 10. The incompressible Navier-Stokes equations under initial and boundary conditions Appendices References Author index Subject index.
764 citations
Book•
26 May 2004
TL;DR: In this article, a probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations based on the Probabilistic Approach was proposed. But this approach is not suitable for the nonlinear Dirichlet and Neumann problems.
Abstract: 1 Mean-square approximation for stochastic differential equations.- 2 Weak approximation for stochastic differential equations.- 3 Numerical methods for SDEs with small noise.- 4 Stochastic Hamiltonian systems and Langevin-type equations.- 5 Simulation of space and space-time bounded diffusions.- 6 Random walks for linear boundary value problems.- 7 Probabilistic approach to numerical solution of the Cauchy problem for nonlinear parabolic equations.- 8 Numerical solution of the nonlinear Dirichlet and Neumann problems based on the probabilistic approach.- 9 Application of stochastic numerics to models with stochastic resonance and to Brownian ratchets.- A Appendix: Practical guidance to implementation of the stochastic numerical methods.- A.1 Mean-square methods.- A.2 Weak methods and the Monte Carlo technique.- A.3 Algorithms for bounded diffusions.- A.4 Random walks for linear boundary value problems.- A.5 Nonlinear PDEs.- A.6 Miscellaneous.- References.
734 citations
TL;DR: In this paper, a three-dimensional exact solution for free and forced vibrations of simply supported functionally graded rectangular plates is presented, where suitable displacement functions that identically satisfy boundary conditions are used to reduce equations governing steady state vibrations of a plate to a set of coupled ordinary differential equations, which are then solved by employing the power series method.
544 citations
TL;DR: In this article, the authors developed a code for the reconstruction of nonlinear force-free and non-force-free coronal magnetic fields with the help of an optimization principle.
Abstract: We developed a code for the reconstruction of nonlinear force-free and non-force-free coronal magnetic fields. The 3D magnetic field is computed numerically with the help of an optimization principle. The force-free and non-force-free codes are compiled in one program. The force-free approach needs photospheric vector magnetograms as input. The non-force-free code additionally requires the line-of-sight integrated coronal density distribution in combination with a tomographic inversion code. Previously the optimization approach has been used to compute magnetic fields using all six boundaries of a computational box. Here we extend this method and show how the coronal magnetic field can be reconstructed only from the bottom boundary, where the boundary conditions are measured with vector magnetographs. The program is planed for use within the Stereo mission.
508 citations
TL;DR: These are the first solutions that deal with particulate flows with very flexible solids and the higher-ordered RKPM delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions.
496 citations
TL;DR: In this article, a conventional theory of mechanism-based strain gradient plasticity is established, and the difference between this theory and the higher-order MSG plasticity theory based on the same dislocation model is only significant within a thin boundary layer of the solid.
493 citations
TL;DR: In this article, the authors discuss the advantages of high-order non-reflecting boundary conditions (NRBCs) compared to low-order local NRBCs and discuss the different schemes which have been proposed in this context.
TL;DR: In this paper, a method to perform large-eddy simulations around complex boundaries on fixed Cartesian grids is presented, which is applicable to boundaries of arbitrary shape, does not involve special treatments, and allows the accurate imposition of the desired boundary conditions.
TL;DR: This paper presents a general overview on the existing techniques to enforce essential boundary conditions in Galerkin based mesh-free methods and special attention is paid to the mesh- free coupling with finite elements for the imposition of prescribed values and to methods based on a modification of theGalerkin weak form.
TL;DR: In this article, the authors review the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces, and present a summary of new improvements to the proximity force approximation and a synopsis of the current experimental situation.
Abstract: The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of δ-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measurements of the Casimir force between real materials is given, starting from a geometrical optics derivation of the Lifshitz formula, and including a rederivation of the Casimir–Polder forces. A great deal of attention is given to the recent controversy concerning temperature corrections to the Casimir force between real metal surfaces. A summary of new improvements to the proximity force approximation is given, followed by a synopsis of the current experimental situation. New results on Casimir self-stress are reported, again based on δ-function potentials. Progress in understanding divergences in the self-stress of dielectric bodies is described, in particular the status of a continuing calculation of the self-stress of a dielectric cylinder. Casimir effects for solitons, and the status of the so-called dynamical Casimir effect, are summarized. The possibilities of understanding dark energy, strongly constrained by both cosmological and terrestrial experiments, in terms of quantum fluctuations are discussed. Throughout, the centrality of quantum vacuum energy in fundamental physics is emphasized.
TL;DR: In this article, the Navier-Stokes equations for compressible barotropic fluids in a domain Ω⊂ R 3 were studied and the existence of the unique strong solution was proved.
TL;DR: In this paper, a general purpose hybrid Reynolds-averaged Navier-Stokes (RANS)/large-eddy simulation (LETS) framework is described, in which large-scale, statistically represented turbulence kinetic energy is converted automatically into resolved-scale velocity fluctuations wherever the local mesh resolution is sufficient to support them.
Abstract: Progress toward a general purpose hybrid Reynolds-averaged Navier-Stokes (RANS)/large-eddy simulation (LETS) framework is described, in which large-scale, statistically represented turbulence kinetic energy is converted automatically into resolved-scale velocity fluctuations wherever the local mesh resolution is sufficient to support them. Existing hybrid RANS/LES approaches alter the nature of the local partial differential equations according to the local mesh resolution, but they do not alter the nature of the data on which these equations operate. The implications of this are discussed. Subsequently, a simple mechanism is introduced to transfer statistical kinetic energy into resolved-scale fluctuations in a manner that preserves a given set of space/time correlations and set of second moments. This process, which can appropriately be termed Large-Eddy STimulation (LEST), generates the large-scale eddies needed to form the unsteady boundary conditions at RANS interfaces to LES regions, into which turbulence energy can be deposited either through mean convection or through turbulent transport
01 Jan 2004
TL;DR: A strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants that allows to guarantee the local convergence of the state towards a desired set point.
Abstract: We present a strict Lyapunov function for hyperbolic systems of conservation laws that can be diagonalized with Riemann invariants. The time derivative of this Lyapunov function can be made strictly negative definite by an appropriate choice of the boundary conditions. It is shown that the derived boundary control allows to guarantee the local convergence of the state towards a desired set point. Furthermore, the control can be implemented as a feedback of the state only measured at the boundaries. The control design method is illustrated with an hydraulic application, namely the level and flow regulation in an horizontal open channel
TL;DR: In this paper, a strain gradient-dependent crystal plasticity approach is presented to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation, and the resulting boundary value problem accommodates, in addition to the ordinary stress equilibrium condition, a condition which sets the additional nodal degrees of freedom, the edge and screw GND densities, proportional (in a weak sense) to the gradients of crystalline slip.
Abstract: A strain gradient-dependent crystal plasticity approach is presented to model the constitutive behaviour of polycrystal FCC metals under large plastic deformation. In order to be capable of predicting scale dependence, the heterogeneous deformation-induced evolution and distribution of geometrically necessary dislocations (GNDs) are incorporated into the phenomenological continuum theory of crystal plasticity. Consequently, the resulting boundary value problem accommodates, in addition to the ordinary stress equilibrium condition, a condition which sets the additional nodal degrees of freedom, the edge and screw GND densities, proportional (in a weak sense) to the gradients of crystalline slip. Next to this direct coupling between microstructural dislocation evolutions and macroscopic gradients of plastic slip, another characteristic of the presented crystal plasticity model is the incorporation of the GND-effect, which leads to an essentially different constitutive behaviour than the statistically stored dislocation (SSD) densities. The GNDs, by their geometrical nature of locally similar signs, are expected to influence the plastic flow through a non-local back-stress measure, counteracting the resolved shear stress on the slip systems in the undeformed situation and providing a kinematic hardening contribution. Furthermore, the interactions between both SSD and GND densities are subject to the formation of slip system obstacle densities and accompanying hardening, accountable for slip resistance. As an example problem and without loss of generality, the model is applied to predict the formation of boundary layers and the accompanying size effect of a constrained strip under simple shear deformation, for symmetric double-slip conditions.
TL;DR: In this article, the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit, are obtained using Haldane's harmonic-fluid approach (also known as 'bosonization'), and are valid for both bosons and fermions, in weakly and strongly interacting regimes.
Abstract: We present results for the long-distance asymptotics of correlation functions of mesoscopic one-dimensional systems with periodic and open (Dirichlet) boundary conditions, as well as at finite temperature in the thermodynamic limit. The results are obtained using Haldane's harmonic-fluid approach (also known as 'bosonization'), and are valid for both bosons and fermions, in weakly and strongly interacting regimes. The harmonic-fluid approach and the method of computing the correlation functions using conformal transformations are explained in great detail. As an application relevant to one-dimensional systems of cold atomic gases, we consider the model of bosons interacting with a zero-range potential. The Luttinger-liquid parameters are obtained from the exact solution by solving the Bethe-ansatz equations in finite-size systems. The range of applicability of the approach is discussed, and the prefactor of the one-body density matrix of bosons is fixed by finding an appropriate parametrization of the weak-coupling result. The formula thus obtained is shown to be accurate, when compared with recent diffusion Monte Carlo calculations, within less than 10%. The experimental implications of these results for Bragg scattering experiments at low and high momenta are also discussed.
TL;DR: In this article, the authors proposed a general methodology for calculating the self-diffusion tensor from molecular dynamics (MD) for a liquid with a liquid−gas or liquid−solid interface, based on imposing virtual boundary conditions on the molecular system and computing survival probabilities and specified time correlation functions in different layers of the fluid up to and including the interfacial layer.
Abstract: We propose a general methodology for calculating the self-diffusion tensor from molecular dynamics (MD) for a liquid with a liquid−gas or liquid−solid interface. The standard method used in bulk fluids, based on computing the mean square displacement as a function of time and extracting the asymptotic linear time dependence from this, is not valid for systems with interfaces or for confined fluids. The method proposed here is based on imposing virtual boundary conditions on the molecular system and computing survival probabilities and specified time correlation functions in different layers of the fluid up to and including the interfacial layer. By running dual simulations, one based on MD and the other based on Langevin dynamics, using the same boundary conditions, one can fit the Langevin survival probability at long time to the MD computed survival probability, thereby determining the diffusion coefficient as a function of distance of the layers from the interface. We compute the elements of the diffus...
TL;DR: In this paper, the authors compared differential quadrature (DQ) and harmonic DQ (HDQ) methods for buckling, bending, and free vibration analysis of thin isotropic plates and columns.
TL;DR: This work reviews artificial boundary conditions for simulation of inflow, outflow, and far-field (radiation) problems, with an emphasis on techniques suitable for compressible turbulent shear flows, and suggests directions for future modeling efforts.
Abstract: We review artificial boundary conditions (BCs) for simulation of inflow, outflow, and far-field (radiation) problems, with an emphasis on techniques suitable for compressible turbulent shear flows. BCs based on linearization near the boundary are usually appropriate for inflow and radiation problems. A variety of accurate techniques have been developed for this case, but some robustness and implementation issues remain. At an outflow boundary, the linearized BCs are usually not accurate enough. Various ad hoc models have been proposed for the nonlinear case, including absorbing layers and fringe methods. We discuss these techniques and suggest directions for future modeling efforts.
TL;DR: In this paper, a small viscosity in the constitutive equations for the cohesive interface is introduced to avoid the post-instability behavior of crack initiation by using boundary value problems.
Abstract: Numerical simulations of crack initiation which use a cohesive zone law to model a weak interface in the solid are often limited by the occurrence of an elastic snap-back instability. At the point of instability, quasi-static finite element computations are unable to converge to an equilibrium solution, which usually terminates the calculation and makes it impossible to follow the post-instability behaviour. In this paper, we show that such numerical difficulties can easily be avoided by introducing a small viscosity in the constitutive equations for the cohesive interface. Simple boundary value problems are used to develop guidelines for selecting appropriate values of viscosity in numerical simulations involving crack nucleation and growth. As a representative application, we model crack nucleation at the interface between an elastic thin film and an elastic–plastic substrate, which is subjected to contact loading.
TL;DR: This paper establishes a link between reachability, viability and invariance problems and viscosity solutions of a special form of the Hamilton-Jacobi equation to address optimal control problems where the cost function is the minimum of a function of the state over a specified horizon.
TL;DR: A gradient formula for the boundary beta function is proved, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature, which implies that s decreases under renormalization, except at critical points (where it stays constant).
Abstract: The boundary beta function generates the renormalization group acting on the universality classes of one-dimensional quantum systems with boundary which are critical in the bulk but not critical at the boundary. We prove a gradient formula for the boundary beta function, expressing it as the gradient of the boundary entropy s at fixed nonzero temperature. The gradient formula implies that s decreases under renormalization, except at critical points (where it stays constant). At a critical point, the number exp((s) is the "ground-state degeneracy," g, of Affleck and Ludwig, so we have proved their long-standing conjecture that g decreases under renormalization, from critical point to critical point. The gradient formula also implies that s decreases with temperature, except at critical points, where it is independent of temperature. It remains open whether the boundary entropy is always bounded below.
TL;DR: In this paper, the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model, was determined.
Abstract: We determine the stationary two-point correlation function of the one-dimensional KPZ equation through the scaling limit of a solvable microscopic model, the polynuclear growth model. The equivalence to a directed polymer problem with specific boundary conditions allows one to express the corresponding scaling function in terms of the solution to a Riemann–Hilbert problem related to the Painleve II equation. We solve these equations numerically with very high precision and compare our, up to numerical rounding exact, result with the prediction of Colaiori and Moore(1) obtained from the mode coupling approximation.
TL;DR: In this paper, the authors reduced the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations and showed that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbation.
Abstract: In recent years, there has been considerable interest in theories formulated in anti-de Sitter (AdS) spacetime. However, AdS spacetime fails to be globally hyperbolic, so a classical field satisfying a hyperbolic wave equation on AdS spacetime need not have a well-defined dynamics. Nevertheless, AdS spacetime is static, so the possible rules of dynamics for a field satisfying a linear wave equation are constrained by our previous general analysis—given in paper II—where it was shown that the possible choices of dynamics correspond to choices of positive, self-adjoint extensions of a certain differential operator, A. In the present paper, we reduce the analysis of electromagnetic and gravitational perturbations in AdS spacetime to scalar wave equations. We then apply our general results to analyse the possible dynamics of scalar, electromagnetic and gravitational perturbations in AdS spacetime. In AdS spacetime, the freedom (if any) in choosing self-adjoint extensions of A corresponds to the freedom (if any) in choosing suitable boundary conditions at infinity, so our analysis determines all the possible boundary conditions that can be imposed at infinity. In particular, we show that other boundary conditions besides the Dirichlet and Neumann conditions may be possible, depending on the value of the effective mass for scalar field perturbations, and depending on the number of spacetime dimensions and type of mode for electromagnetic and gravitational perturbations.
TL;DR: This work investigates the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids and shows that the contact line singularity is overcome by evaporation or condensation near the contact lines.
Abstract: We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one and two component, two phase fluids. In this, the first of two papers, we consider liquid-gas systems. Careful implementation of the thermodynamic boundary condition allows us to fix the static contact angle in the simulations. We then consider the behavior of a sheared interface. We show that the contact line singularity is overcome by evaporation or condensation near the contact line which is driven by the curvature of the diffuse interface. An analytic approximation is derived for the angular position of a sheared interface.
TL;DR: In this article, the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network were derived for regular lattices in one, two and three dimensions under various boundary conditions.
Abstract: The resistance between two arbitrary nodes in a resistor network is obtained in terms of the eigenvalues and eigenfunctions of the Laplacian matrix associated with the network. Explicit formulae for two-point resistances are deduced for regular lattices in one, two and three dimensions under various boundary conditions including that of a Mobius strip and a Klein bottle. The emphasis is on lattices of finite sizes. We also deduce summation and product identities which can be used to analyse large-size expansions in two and higher dimensions.
TL;DR: In this paper, a set of evolution equations for dislocation density was developed incorporating the combined evolution of statistically stored and geometrically necessary densities, and the statistical density evolves through Burgers vector-conserving reactions based in dislocation mechanics.
Abstract: A set of evolution equations for dislocation density is developed incorporating the combined evolution of statistically stored and geometrically necessary densities. The statistical density evolves through Burgers vector-conserving reactions based in dislocation mechanics. The geometric density evolves due to the divergence of dislocation fluxes associated with the inhomogeneous nature of plasticity in crystals. Integration of the density-based model requires additional dislocation density/density-flux boundary conditions to complement the standard traction/displacement boundary conditions. The dislocation density evolution equations and the coupling of the dislocation density flux to the slip deformation in a continuum crystal plasticity model are incorporated into a finite element model. Simulations of an idealized crystal with a simplified slip geometry are conducted to demonstrate the length scale-dependence of the mechanical behavior of the constitutive model. The model formulation and simulation results have direct implications on the ability to explicitly model the interaction of dislocation densities with grain boundaries and on the net effect of grain boundaries on the macroscopic mechanical response of polycrystals.